From 10ad3706575653e03ac8c291be33c00cc059d1f3 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Thu, 15 Feb 2024 11:46:08 +0100 Subject: [PATCH 001/101] :arrow_up: Adding scaling section --- docs/_sidebar.md | 1 + .../img/scalability/ethereum-nodes.png | Bin 0 -> 790114 bytes .../protocol/img/scalability/trilemma.png | Bin 0 -> 179862 bytes docs/wiki/protocol/scalability.md | 77 ++++++++++++++++++ 4 files changed, 78 insertions(+) create mode 100644 docs/wiki/protocol/img/scalability/ethereum-nodes.png create mode 100644 docs/wiki/protocol/img/scalability/trilemma.png create mode 100644 docs/wiki/protocol/scalability.md diff --git a/docs/_sidebar.md b/docs/_sidebar.md index 73972309..c1d7f6d1 100644 --- a/docs/_sidebar.md +++ b/docs/_sidebar.md @@ -11,6 +11,7 @@ - [Overview](/wiki/protocol/overview.md) - [History](/wiki/protocol/history.md) - [Coordination](/wiki/protocol/pm.md) + - [Scalability](/wiki/protocol/scalability.md) - [CS Resources] - Execution Layer - [EL Clients](/wiki/EL/el-clients.md) diff --git a/docs/wiki/protocol/img/scalability/ethereum-nodes.png b/docs/wiki/protocol/img/scalability/ethereum-nodes.png new file mode 100644 index 0000000000000000000000000000000000000000..ca547f17f809c64724e4ae493cee4bcf0dd48398 GIT binary patch literal 790114 zcmV)VK(D`vP) z_r|tp%Hkr43rK(fdc8Me{)i4GLLPQ>|R8^{LVioC7H{H6t|*-3_4}?z&>?&sBN`b4_J`ss9Tf z4}rKE8=CV3Vr03OK-x4jh`_|m3}j+3B_;+ln20!o84PKKiHMmqb0T7p)M79*6EQOY zVh}OF%mfC3GZ@UIHooq74#GHwu95M50(3lt8Lh#F>eK1Q3<^H6bC_Bjc*llcS|6 zcag{mm`oCMk~5G124!#p7@0s^##GxaBH_Cd@1&4P3o}z9wr;=~M1Tnx*}tlH$|=?WX&dGt#ccs%;lvwd1`(Meu;`Tbr&A!EByeU*1VYdYB2MCaOhN!8 zK-AbxopO@xOqn(H3mKG%vT%nunTIPvVJ?wWh5=V$ZQWgr-9ThhWA<35mGl^9vh;j% zVKY-kAlC6nQzH0MQ`scyBqJs!kQn?LYYEB3(BX+|5;J0Ui?VQDCEpF8NsG|2?VB0qHCErWm4rNyVWcq zY*wWc;X@)-KoF3K!KMu=sg#fs0>)&Y9+^TDRVF4%?)8b1*jV9T1|?OH#Ex%ds+o{f zeJB$r!zhHL6G<$+>mZ5}a55{Mg4hUXrQ~9%L?luHmRrOgfQdjUk;yMv?_o+Pps&Wo zgk#4?@h<}BcQ3nFpQu?nb`MzVZdLER-Ay!h{?c=_X_x9c{nbcTxMeU^XzNT-G^}`` 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zm$|7FRf%x!zi~g=+Y|gyvwyJWDnXvCSYpf#kLeOb3POuwdgam4F=)LT3%+(5d(t_n zWNpe}ET-uVWr=x4sXiE+a_IkdZAQgN-gV2MD7K&Ll|`9+xm#9}2Z?L`ir38Kysw!| zgRD%>~%n_Q5;84H&5##XG;G!T4#e zo@U_vJ`qyfBR+EftigWwzE=$fp$QIib6KZ#?QdCo1tW9R$tmiHTCWqx?Q??K4eXbH zZb~&>F3XEhIgP!?!wl+{f8^@A0|~mIUj%6bJtHGH9ujY->6SXs`LsS_N*tLKma2Q^ zNp}FkX*^3eMBj@@*o;Vnx)cvExT*^TB>Ys;e8SyP`iO`&t(rNa_{EG!*6Y7*&!@C)Xa;&#_cJ9?YSUBZ z{8uqTmqvdBz?BUmcWq87|MQdi-@@5r-r$h{8JIo93MJ}Vz*?$SEQdX1W=uEmr@~3= zi(+j>xJALeCRt(4hjAu1zpzOg2T1l05NJ5xU%+o_nh4RGyE$e~A9Taa!zwM#>F3uE ziAR)cY_xhtdszd6QbmDmy==&YsF5r(ggbc|@yn^DTADIi#Wt%7subt11(uSNEC@sZ z%hUu_xJbQs7JZbp(5Sj|u4U$==2yo9mk}M}1<1EyLZ&{n2}vAsTtrDzne!Vzcnh)mG8v{^hS~9$m|56|)t$ z?Ga)TTjC?sZzYb=wU)qVLCA3#7{p+T#=bywi8PIn#VA2q#L|}upN)g7%v~_#@=}4r zy2ki7=UcE0*NoSIf?tQysXm?eQy%9G@dK{)oNLTYB1;5x&Wl@=zdBL2tor@l9|jwR zgkDsaE12L!d|f`ct|`|Opu{+6o{Nx3cT3o+WXW!6a|tc$Ob=k~lxMu#Bo@AVFY$37 zkE6W%@dRIw&HL1)cSu{(Ox~*5bm0)Bogvr59!d|IM-z=0)Dpbi<>G=`)C<4NUFby{ z)U1EG@vq=~;j1n`-_UX3Iu;fG3mU>aB6J@6MFuO(teosNR%g<}E zFTJTYcGOqPg{_K-&BcN%8aDU2Ok_sOJBdjp2CH-?>249(Vft^V7c1dUKeH8243ah; z;fo=%_(P)ZSn1}KiteV-%^(bwU6R+J7CukYO)etlY}&!8PQHV9v?x+@95Vl4$5BYQ z&-r!1Gx`l0#tS4tWu%MGT{E^nH6ej$$@kV=Y8b^PPe{Zi%0?zWz%OH_Yp2DJ-97z^ ztUbTw>Qa@igkuYE{`suZClb~8M1hXYU0L$UD~-9PJc?Pih>j{8hlq5w~ZEm*K_lS&!VqFrVtnw zlQ=p#iJ0G(xe@DuEku)Dx%Dx!$d7*^Kj# z`BKEbneVJ;WO&nW=XzhzS6(a;*Y&z@b4*m7eqUl@80M0%k-(=f^1ZhOqIU`Dd6AB| zUM;~^Ny&^$KcMfhR1L{o7>^B3Dor`P+Ez7>0ySg}(+%OCAR RI}z}os* **we can define the scalability of a specific blockchain as its capacity to perform well under an increase in user transaction demands or/and in the volume of users**. + +## Blockchain Scalability Limits +Consensus mechanics require most of validator nodes in the network to publicly agree on the next valid block. This directly affects the block latency, which is the time it takes for a new block to be created and validated. The block latency and block size directly determine the transactional throughput of the blockchain, which is measured by the **TPS** (transactions per second) metric. Block latency can be influenced by a variety of factors, such as the computational power of the network nodes, the complexity of the consensus mechanism, the network traffic and the block size. Hence, a network made up of a few high-performance nodes tightly connected to each other and using large block sizes can result in an exceptional blockchain with high TPS and remarkably low block latency. However, such a network would likely be highly centralized and require users to make significant trust assumptions. + +Note the tight relationship between the design and tuning of a blockchain (consensus mechanics, node requirements, state structure and size… ) and its capabilities of decentralization. High hardware or network bandwidth requirements to run a node result in harsh and expensive conditions that make it difficult to do so, directly impacting the number of nodes a blockchain will have. **To ensure decentralization, it is essential to make running a node affordable and feasible for everyone and incentivize users to do it.** Therefore, a game-theory sustainable incentive mechanism must be included by design. + +As part of the game-theory mechanism, to maintain the network sustainability, users must pay a fee to include their transactions. The price of fees is determined by market demand, and those who pay higher fees are prioritized. Due to limited TPS, including a transaction in a high decentralized blockchain has become a valuable service. An increase transaction demand for a limited and fixed TPS raises fees to the network usability threshold and requires sacrificing decentralization and/or security in order to scale. + +Another obstacle to decentralization is the size of the blockchain state. **The property of data being accessible when it is needed is known as data availability**. Availability of state data must be guaranteed, including availability of enough data to allow any new node in the network to reconstruct the latest version of the blockchain without any trust assumptions. Have to hold all the data to guarantee data availability can result in high storage requirements for nodes and a lengthy synchronization process for new ones, which can hinder decentralization. + + +> **Recalling the definition of scalability, classical blockchain systems are not scalable for mass adoption**. + +This problem is widely known as the **Blockchain Trilemma**, which states that blockchain networks must sacrifice either security, decentralization, or scalability, and maximizing all three at once is difficult. The holy grail of blockchain technology is to create a secure and decentralized transactional network that can achieve a high TPS rate. + + +Blockchain trilemma - Bankless.com + +## Blockchain Modularity +Modern blockchain designs propose a "divide et impera" approach dividing the system into different specific functional components to independently maximize each vertex of the trilemma. This approach encapsulates the complexity in each part of the system and reduces the systemic complexity through the definition of simpler interaction interfaces for system components. +Functional components of a blockchain: + +- Consensus: Agreement mechanics among nodes of block building and transaction ordering. +- Execution: Transaction execution mechanics that define the state evolution. +- Data availability: Data availability mechanics that ensures that the data is available to be queried when it is required. +- Settlement: Mechanics that guarantee the finality and immutability of transactions. + +Modular blockchain approach suggests the separation of a blockchain system into different logical layers which are designed to perform well as a few specific functional components. The result is a scalable blockchain architecture with simpler and more efficient modular components, rather than a large and complex monolithic blockchain that cannot scale effectively. + +## Scaling Ethereum +The core Ethereum protocol (Layer 1) is continuously developed by the community through EIPs, which open up the possibility of introducing changes to the base protocol to enhance network scalability. Furthermore, Ethereum's high level of programmability makes it possible to create scalable solutions on top of the platform (Layers 2). + +### Ethereum Layer 1 scaling +#### Split consensus from execution (The Merge). +On September 15, 2022, Ethereum implemented EIP-3675 (Upgrade consensus to Proof-of-Stake) through an event known as The Merge. The Merge has resulted in the deprecation of the Proof-of-Work consensus, which was previously implemented in the same logic layer as execution. Instead, it has been replaced by a much more complex and sophisticated Proof-of-Stake consensus that eliminates the need for energy-intensive mining. This new consensus mechanism enables the network to be secured through staking ETH. New Proof-of-Stake consensus named [Gasper](https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf) runs on its own tech stack and p2p network, this new abstraction layer is known as Beacon Chain. The Beacon Chain has been running and achieving consensus since December 1st, 2020. After a prolonged period of consistent performance without any failures, it was deemed ready to become Ethereum's consensus provider, The Merge gets its name from the union of the two networks. + +- Consensus Layer (Beacon Chain): Specifically designed to be really good to reaching consensus. In Ethereum, time is divided up into twelve second units called **slots**, the consensus is reached when a valid block has been proposed in a specific slot. However, occasionally validators might be offline when called to propose a block, meaning slots can sometimes go empty. + +- Execution Layer (State and Transactional Ledger): Driven by the consensus layer, it specializes in managing the transactions mempool, the Ethereum state, and Ethereum block construction and execution. + +As result, an Ethereum node requires running two different software components: an execution client (or execution engine) driven by a consensus client through an internal communication protocol (Engine API). Note, that no additional trust assumptions need to be made for the execution Layer to follow and execute consensus decisions since each execution client receives information from the consensus Layer through its corresponding twin consensus client, and both clients operate within the same node’s trust domain. + +Ethereum Nodes + +Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. + +Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. + +#### EIP-4844: Shard Blob Transactions (Proto-DankSharding) +TODO + +#### Full Data Sharding (Danksharding) +TODO + +### Ethereum Layer 2 scaling +## ZK Rollups +TODO + +## Optimistic Rollups +TODO + +Resources: + +[Vitalik The Limits to Blockchain Scalability](https://vitalik.eth.limo/general/2021/05/23/scaling.html), [archived](https://web.archive.org/web/20240205202358/https://vitalik.eth.limo/general/2021/05/23/scaling.html) + +[Ethereum Scaling](https://ethereum.org/en/developers/docs/scaling), [archived](https://web.archive.org/web/20240209083702/https://ethereum.org/en/developers/docs/scaling) + +[Gemini Cryptopedia The Blockchain Trilemma: Fast, Secure, and Scalable Networks](https://www.gemini.com/cryptopedia/blockchain-trilemma-decentralization-scalability-definition), [archived](https://web.archive.org/web/20240209073156/https://www.gemini.com/cryptopedia/blockchain-trilemma-decentralization-scalability-definition) + +[Combining GHOST and Casper](https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf), [archived](https://web.archive.org/web/20230907004049/https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf) + +[EIP-3675: Upgrade consensus to Proof-of-Stake](https://eips.ethereum.org/EIPS/eip-3675), [archived](https://web.archive.org/web/20240213102133/https://eips.ethereum.org/EIPS/eip-3675) + +[Ethereum Blocks](https://ethereum.org/developers/docs/blocks), [archived](https://web.archive.org/web/20240214052915/https://ethereum.org/developers/docs/blocks) \ No newline at end of file From f3fd397981574fd9355f72e865be641c8a62e6f6 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Fri, 16 Feb 2024 13:43:14 +0100 Subject: [PATCH 002/101] :car: Mooving scalability section to research --- docs/_sidebar.md | 3 +-- docs/wiki/{protocol/scalability.md => research/scaling.md} | 2 +- 2 files changed, 2 insertions(+), 3 deletions(-) rename docs/wiki/{protocol/scalability.md => research/scaling.md} (99%) diff --git a/docs/_sidebar.md b/docs/_sidebar.md index c1d7f6d1..987a70f7 100644 --- a/docs/_sidebar.md +++ b/docs/_sidebar.md @@ -11,7 +11,6 @@ - [Overview](/wiki/protocol/overview.md) - [History](/wiki/protocol/history.md) - [Coordination](/wiki/protocol/pm.md) - - [Scalability](/wiki/protocol/scalability.md) - [CS Resources] - Execution Layer - [EL Clients](/wiki/EL/el-clients.md) @@ -39,7 +38,7 @@ - Formal Verification - Research - [Roadmap overview](/wiki/research/roadmap.md) - - Scaling + - [Scaling](/wiki/research/scaling.md) - Blobs - Sharding - Statelessness diff --git a/docs/wiki/protocol/scalability.md b/docs/wiki/research/scaling.md similarity index 99% rename from docs/wiki/protocol/scalability.md rename to docs/wiki/research/scaling.md index a13c9b2c..2ec32a9c 100644 --- a/docs/wiki/protocol/scalability.md +++ b/docs/wiki/research/scaling.md @@ -1,4 +1,4 @@ -# Scalability +# Scaling In computer systems, scalability refers to the ability of a system to perform well under increased or expanding workloads. The primary purpose of blockchain is to handle users' transactions and manage network's ledger state. An increase in workload may result from either a higher demand for transactions by existing users or an increase in the volume of users. > **we can define the scalability of a specific blockchain as its capacity to perform well under an increase in user transaction demands or/and in the volume of users**. From 4cc7a94338502be48b08efccde445f82a9a7307a Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Fri, 16 Feb 2024 13:45:12 +0100 Subject: [PATCH 003/101] :recycle: Re-define blockchain scalability --- docs/wiki/research/scaling.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/wiki/research/scaling.md b/docs/wiki/research/scaling.md index 2ec32a9c..99446926 100644 --- a/docs/wiki/research/scaling.md +++ b/docs/wiki/research/scaling.md @@ -1,6 +1,6 @@ # Scaling In computer systems, scalability refers to the ability of a system to perform well under increased or expanding workloads. The primary purpose of blockchain is to handle users' transactions and manage network's ledger state. An increase in workload may result from either a higher demand for transactions by existing users or an increase in the volume of users. -> **we can define the scalability of a specific blockchain as its capacity to perform well under an increase in user transaction demands or/and in the volume of users**. +> **Scalability of a blockchain system can be defined as its capacity to process increasing volumes operations, i.e. more transactions from users without raising demands on network operators**. ## Blockchain Scalability Limits Consensus mechanics require most of validator nodes in the network to publicly agree on the next valid block. This directly affects the block latency, which is the time it takes for a new block to be created and validated. The block latency and block size directly determine the transactional throughput of the blockchain, which is measured by the **TPS** (transactions per second) metric. Block latency can be influenced by a variety of factors, such as the computational power of the network nodes, the complexity of the consensus mechanism, the network traffic and the block size. Hence, a network made up of a few high-performance nodes tightly connected to each other and using large block sizes can result in an exceptional blockchain with high TPS and remarkably low block latency. However, such a network would likely be highly centralized and require users to make significant trust assumptions. From 5955e11a47d7cbed008f2b4627e60fdd93d3b462 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Fri, 16 Feb 2024 14:00:49 +0100 Subject: [PATCH 004/101] :hammer: Fix images --- .../img/scaling/blockchain-trilemma.png} | Bin .../img/scaling}/ethereum-nodes.png | Bin docs/wiki/research/scaling.md | 6 +++--- 3 files changed, 3 insertions(+), 3 deletions(-) rename docs/wiki/{protocol/img/scalability/trilemma.png => research/img/scaling/blockchain-trilemma.png} (100%) rename docs/wiki/{protocol/img/scalability => research/img/scaling}/ethereum-nodes.png (100%) diff --git a/docs/wiki/protocol/img/scalability/trilemma.png b/docs/wiki/research/img/scaling/blockchain-trilemma.png similarity index 100% rename from docs/wiki/protocol/img/scalability/trilemma.png rename to docs/wiki/research/img/scaling/blockchain-trilemma.png diff --git a/docs/wiki/protocol/img/scalability/ethereum-nodes.png b/docs/wiki/research/img/scaling/ethereum-nodes.png similarity index 100% rename from docs/wiki/protocol/img/scalability/ethereum-nodes.png rename to docs/wiki/research/img/scaling/ethereum-nodes.png diff --git a/docs/wiki/research/scaling.md b/docs/wiki/research/scaling.md index 99446926..a3f023d0 100644 --- a/docs/wiki/research/scaling.md +++ b/docs/wiki/research/scaling.md @@ -2,7 +2,7 @@ In computer systems, scalability refers to the ability of a system to perform well under increased or expanding workloads. The primary purpose of blockchain is to handle users' transactions and manage network's ledger state. An increase in workload may result from either a higher demand for transactions by existing users or an increase in the volume of users. > **Scalability of a blockchain system can be defined as its capacity to process increasing volumes operations, i.e. more transactions from users without raising demands on network operators**. -## Blockchain Scalability Limits +## Scalability Limits Consensus mechanics require most of validator nodes in the network to publicly agree on the next valid block. This directly affects the block latency, which is the time it takes for a new block to be created and validated. The block latency and block size directly determine the transactional throughput of the blockchain, which is measured by the **TPS** (transactions per second) metric. Block latency can be influenced by a variety of factors, such as the computational power of the network nodes, the complexity of the consensus mechanism, the network traffic and the block size. Hence, a network made up of a few high-performance nodes tightly connected to each other and using large block sizes can result in an exceptional blockchain with high TPS and remarkably low block latency. However, such a network would likely be highly centralized and require users to make significant trust assumptions. Note the tight relationship between the design and tuning of a blockchain (consensus mechanics, node requirements, state structure and size… ) and its capabilities of decentralization. High hardware or network bandwidth requirements to run a node result in harsh and expensive conditions that make it difficult to do so, directly impacting the number of nodes a blockchain will have. **To ensure decentralization, it is essential to make running a node affordable and feasible for everyone and incentivize users to do it.** Therefore, a game-theory sustainable incentive mechanism must be included by design. @@ -17,7 +17,7 @@ Another obstacle to decentralization is the size of the blockchain state. **The This problem is widely known as the **Blockchain Trilemma**, which states that blockchain networks must sacrifice either security, decentralization, or scalability, and maximizing all three at once is difficult. The holy grail of blockchain technology is to create a secure and decentralized transactional network that can achieve a high TPS rate. -Blockchain trilemma - Bankless.com +!["Blockchain trilemma - Bankless.com"](./img/scaling/blockchain-trilemma.png "Blockchain trilemma - Bankless.com") ## Blockchain Modularity Modern blockchain designs propose a "divide et impera" approach dividing the system into different specific functional components to independently maximize each vertex of the trilemma. This approach encapsulates the complexity in each part of the system and reduces the systemic complexity through the definition of simpler interaction interfaces for system components. @@ -43,7 +43,7 @@ On September 15, 2022, Ethereum implemented EIP-3675 (Upgrade consensus to Proof As result, an Ethereum node requires running two different software components: an execution client (or execution engine) driven by a consensus client through an internal communication protocol (Engine API). Note, that no additional trust assumptions need to be made for the execution Layer to follow and execute consensus decisions since each execution client receives information from the consensus Layer through its corresponding twin consensus client, and both clients operate within the same node’s trust domain. -Ethereum Nodes +!["Ethereum Nodes"](./img/scaling/ethereum-nodes.png "Ethereum Nodes") Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. From 03283c320cbd2996ea7f3e8b2c42952185c0fb31 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Sun, 18 Feb 2024 21:18:56 +0100 Subject: [PATCH 005/101] :pencil2: Re-write scalability limits section --- docs/wiki/research/scaling.md | 24 ++++++++++++++++++------ 1 file changed, 18 insertions(+), 6 deletions(-) diff --git a/docs/wiki/research/scaling.md b/docs/wiki/research/scaling.md index a3f023d0..e7b05cda 100644 --- a/docs/wiki/research/scaling.md +++ b/docs/wiki/research/scaling.md @@ -1,18 +1,22 @@ # Scaling In computer systems, scalability refers to the ability of a system to perform well under increased or expanding workloads. The primary purpose of blockchain is to handle users' transactions and manage network's ledger state. An increase in workload may result from either a higher demand for transactions by existing users or an increase in the volume of users. -> **Scalability of a blockchain system can be defined as its capacity to process increasing volumes operations, i.e. more transactions from users without raising demands on network operators**. +> **Scalability of a blockchain system can be defined as its capacity to process increasing volumes operations, i.e. more transactions without raising demands on network node operators**. ## Scalability Limits -Consensus mechanics require most of validator nodes in the network to publicly agree on the next valid block. This directly affects the block latency, which is the time it takes for a new block to be created and validated. The block latency and block size directly determine the transactional throughput of the blockchain, which is measured by the **TPS** (transactions per second) metric. Block latency can be influenced by a variety of factors, such as the computational power of the network nodes, the complexity of the consensus mechanism, the network traffic and the block size. Hence, a network made up of a few high-performance nodes tightly connected to each other and using large block sizes can result in an exceptional blockchain with high TPS and remarkably low block latency. However, such a network would likely be highly centralized and require users to make significant trust assumptions. +For each block included in the chain, a general agreement on its validity must be reached among a certain percentage of validator nodes, the consensus mechanism is the methodology to achieve this agreement. The **block latency** is the time that takes to a valid block to be included in the chain. +Ethereum uses a proof-of-stake (PoS) based consensus protocol known as [Gasper](https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf) with an ideal block latency fixed in the specification by the constant `SECONDS_PER_SLOT` (12 seconds), however real block latency could be slightly different since blocks could be missed by a specific validator and not to be included in a specific slot. + + Another fundamental blockchain design parameter is the **block size** that is the limit on the amount of data that can be stored in a single block. Ethereum has a config parameter called `gas_limit` to cap the computational effort needed to process a block, which effectively also limits the size of a block. Each operation that takes place within Ethereum, requires a certain amount of "gas" to complete. The total amount of gas for all operations within a block can't exceed Ethereum's `gas_limit`. This approach ensures the network's processing capacity isn't overextended. [EIP-1559](https://eips.ethereum.org/EIPS/eip-1559) defines Ethereum gas pricing mechanism that allows to dynamically adjust the block size to deal with transient network congestions (without never exceed the limit of 30M gas units) and incentivize the network to target a gas amount defined by `gas_target` (15M). A gas limitation restricts the number of transactions (and their computational complexity) that can be included in an Ethereum block. -Note the tight relationship between the design and tuning of a blockchain (consensus mechanics, node requirements, state structure and size… ) and its capabilities of decentralization. High hardware or network bandwidth requirements to run a node result in harsh and expensive conditions that make it difficult to do so, directly impacting the number of nodes a blockchain will have. **To ensure decentralization, it is essential to make running a node affordable and feasible for everyone and incentivize users to do it.** Therefore, a game-theory sustainable incentive mechanism must be included by design. +The block latency and block size directly determine the transactional throughput of the blockchain, which is measured by the **TPS** (transactions per second) metric. Block latency can be influenced by a variety of factors, such as the computational power of the network nodes, the complexity of the consensus mechanism, the network traffic congestion and the block size. Hence, a network made up of a few high-performance nodes tightly connected to each other and using large block sizes can result in an exceptional blockchain with high TPS and remarkably low block latency. However, such a network would likely be highly centralized and require users to make significant trust assumptions. -As part of the game-theory mechanism, to maintain the network sustainability, users must pay a fee to include their transactions. The price of fees is determined by market demand, and those who pay higher fees are prioritized. Due to limited TPS, including a transaction in a high decentralized blockchain has become a valuable service. An increase transaction demand for a limited and fixed TPS raises fees to the network usability threshold and requires sacrificing decentralization and/or security in order to scale. +Another obstacle to decentralization is the size of the blockchain state. **The property of data being accessible when it is needed is known as data availability**. Availability of state data must be guaranteed, including availability of enough data to allow any new node in the network to reconstruct the latest version of the blockchain without any trust assumptions. Have to hold all the data to guarantee data availability can result in high storage requirements for nodes and a lengthy synchronization process for new ones, which can hinder decentralization. Handling a large amount of data is also problematic in terms of network congestion and will require demanding high connection bandwidth from node operators. Ethereum discourages the indiscriminate state growth by making operations that read or write state very expensive. -Another obstacle to decentralization is the size of the blockchain state. **The property of data being accessible when it is needed is known as data availability**. Availability of state data must be guaranteed, including availability of enough data to allow any new node in the network to reconstruct the latest version of the blockchain without any trust assumptions. Have to hold all the data to guarantee data availability can result in high storage requirements for nodes and a lengthy synchronization process for new ones, which can hinder decentralization. +Note the tight relationship between the design and tuning of a blockchain (consensus mechanics, node requirements, state structure and size… ) and its capabilities of decentralization. High hardware or network bandwidth requirements to run a node result in harsh and expensive conditions that make it difficult to do so, directly impacting the number of nodes a blockchain will have. **To ensure decentralization, it is essential to make running a node affordable and feasible for everyone and incentivize users to do it**. +As part of the game-theory mechanism, to maintain the network sustainability, users must pay a fee to include their transactions. In Ethereum the price of fees is determined by the base fee of the protocol, the amount of gas consumed by a specific transaction and a priority market, those who pay higher priority fees are prioritized. Due to limited TPS, including a transaction in a high decentralized blockchain like Ethereum has become a valuable service. An increase transaction demand for a limited and fixed TPS raises fees to the network usability threshold and requires sacrificing decentralization and/or security in order to scale. -> **Recalling the definition of scalability, classical blockchain systems are not scalable for mass adoption**. +> **Recalling the definition of scalability, classical blockchain systems are not scalable for mass adoption without sacrificing certain levels of decentralization.** This problem is widely known as the **Blockchain Trilemma**, which states that blockchain networks must sacrifice either security, decentralization, or scalability, and maximizing all three at once is difficult. The holy grail of blockchain technology is to create a secure and decentralized transactional network that can achieve a high TPS rate. @@ -64,6 +68,14 @@ TODO Resources: +[Ethereum Consensus Mechanism](https://ethereum.org/developers/docs/consensus-mechanisms), [archived](https://web.archive.org/web/20240214225609/https://ethereum.org/developers/docs/consensus-mechanisms) + +[Gasper](https://ethereum.org/developers/docs/consensus-mechanisms/pos/gasper), [archived](https://web.archive.org/web/20240214225630/https://ethereum.org/developers/docs/consensus-mechanisms/pos/gasper) + +[Ethereum Proof-of-Stake Consensus Specifications](https://github.com/ethereum/consensus-specs/tree/dev?tab=readme-ov-file#ethereum-proof-of-stake-consensus-specifications), [archived](https://web.archive.org/web/20240208050731/https://github.com/ethereum/consensus-specs/tree/dev) + +[Ethereum Proof-of-Stake Consensus Specifications](https://ethereum.github.io/consensus-specs/), [archived](https://web.archive.org/web/20240217155014/https://ethereum.github.io/consensus-specs/) + [Vitalik The Limits to Blockchain Scalability](https://vitalik.eth.limo/general/2021/05/23/scaling.html), [archived](https://web.archive.org/web/20240205202358/https://vitalik.eth.limo/general/2021/05/23/scaling.html) [Ethereum Scaling](https://ethereum.org/en/developers/docs/scaling), [archived](https://web.archive.org/web/20240209083702/https://ethereum.org/en/developers/docs/scaling) From 966b600103e5b06e58accf6e9cb524f3a92f6b18 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Sun, 18 Feb 2024 21:36:19 +0100 Subject: [PATCH 006/101] :pencil2: Re-write modularity section --- docs/wiki/research/scaling.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/wiki/research/scaling.md b/docs/wiki/research/scaling.md index e7b05cda..a5b26489 100644 --- a/docs/wiki/research/scaling.md +++ b/docs/wiki/research/scaling.md @@ -32,7 +32,7 @@ Functional components of a blockchain: - Data availability: Data availability mechanics that ensures that the data is available to be queried when it is required. - Settlement: Mechanics that guarantee the finality and immutability of transactions. -Modular blockchain approach suggests the separation of a blockchain system into different logical layers which are designed to perform well as a few specific functional components. The result is a scalable blockchain architecture with simpler and more efficient modular components, rather than a large and complex monolithic blockchain that cannot scale effectively. +Modular blockchain approach suggests dividing a blockchain system into different logical layers. This results in a design with reduced systemic complexity, and simpler components that can be more easily optimized and re-enginered to introduce new scaling solutions. ## Scaling Ethereum The core Ethereum protocol (Layer 1) is continuously developed by the community through EIPs, which open up the possibility of introducing changes to the base protocol to enhance network scalability. Furthermore, Ethereum's high level of programmability makes it possible to create scalable solutions on top of the platform (Layers 2). From cfadbf7fe0310e510f7cd3b40dc96b951793ce45 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Sun, 18 Feb 2024 21:43:19 +0100 Subject: [PATCH 007/101] :pencil2: Re-write Scaling Ethereum section --- docs/wiki/research/scaling.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/wiki/research/scaling.md b/docs/wiki/research/scaling.md index a5b26489..f63309eb 100644 --- a/docs/wiki/research/scaling.md +++ b/docs/wiki/research/scaling.md @@ -39,7 +39,7 @@ The core Ethereum protocol (Layer 1) is continuously developed by the community ### Ethereum Layer 1 scaling #### Split consensus from execution (The Merge). -On September 15, 2022, Ethereum implemented EIP-3675 (Upgrade consensus to Proof-of-Stake) through an event known as The Merge. The Merge has resulted in the deprecation of the Proof-of-Work consensus, which was previously implemented in the same logic layer as execution. Instead, it has been replaced by a much more complex and sophisticated Proof-of-Stake consensus that eliminates the need for energy-intensive mining. This new consensus mechanism enables the network to be secured through staking ETH. New Proof-of-Stake consensus named [Gasper](https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf) runs on its own tech stack and p2p network, this new abstraction layer is known as Beacon Chain. The Beacon Chain has been running and achieving consensus since December 1st, 2020. After a prolonged period of consistent performance without any failures, it was deemed ready to become Ethereum's consensus provider, The Merge gets its name from the union of the two networks. +On September 15, 2022, Ethereum implemented [EIP-3675](https://eips.ethereum.org/EIPS/eip-3675) (Upgrade consensus to Proof-of-Stake) through an event known as The Merge. The Merge has resulted in the deprecation of the Proof-of-Work consensus, which was previously implemented in the same logic layer as execution. Instead, it has been replaced by a much more complex and sophisticated Proof-of-Stake consensus that eliminates the need for energy-intensive mining. New Proof-of-Stake consensus Gasper runs on its own tech stack and p2p network, this new abstraction layer is known as Beacon Chain. The Beacon Chain has been running and achieving consensus since December 1st, 2020. After a prolonged period of consistent performance without any failures, it was deemed ready to become Ethereum's consensus provider, The Merge gets its name from the union of the two networks. - Consensus Layer (Beacon Chain): Specifically designed to be really good to reaching consensus. In Ethereum, time is divided up into twelve second units called **slots**, the consensus is reached when a valid block has been proposed in a specific slot. However, occasionally validators might be offline when called to propose a block, meaning slots can sometimes go empty. From 3263354a63181011154a1af41a28658533e09392 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Sun, 18 Feb 2024 21:43:51 +0100 Subject: [PATCH 008/101] :pencil2: Move EIPs to core development section --- docs/wiki/dev/core-development.md | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/wiki/dev/core-development.md b/docs/wiki/dev/core-development.md index f4b853a9..97ae43b3 100644 --- a/docs/wiki/dev/core-development.md +++ b/docs/wiki/dev/core-development.md @@ -1,4 +1,5 @@ # Core development +The core Ethereum protocol (Layer 1) is continuously developed by the community through EIPs, which open up the possibility of introducing changes to the base protocol. Resources for aspiring core developers. What is it like to work on the core protocol? From 94a2eeb1e2261a8b101b1e9151bf456dca495aa0 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Mon, 19 Feb 2024 20:09:02 +0100 Subject: [PATCH 009/101] :pencil2: Re-write Ethereum scalability section --- docs/wiki/research/scaling.md | 21 +++++++++++++++++++-- 1 file changed, 19 insertions(+), 2 deletions(-) diff --git a/docs/wiki/research/scaling.md b/docs/wiki/research/scaling.md index f63309eb..7e91b150 100644 --- a/docs/wiki/research/scaling.md +++ b/docs/wiki/research/scaling.md @@ -35,9 +35,24 @@ Functional components of a blockchain: Modular blockchain approach suggests dividing a blockchain system into different logical layers. This results in a design with reduced systemic complexity, and simpler components that can be more easily optimized and re-enginered to introduce new scaling solutions. ## Scaling Ethereum -The core Ethereum protocol (Layer 1) is continuously developed by the community through EIPs, which open up the possibility of introducing changes to the base protocol to enhance network scalability. Furthermore, Ethereum's high level of programmability makes it possible to create scalable solutions on top of the platform (Layers 2). +The primary objective of Ethereum's scalability efforts is to increase TPS metric without compromising decentralization or security. + +Layer 1 scaling is the set of all those techniques that increases the TPS of the underlying blockchain protocol itself. blockchains with "bigger blocks" have a major TPS but are more difficult to verify and likely to become more centralized. For this reason, an increase in the capacity of each block must be accompanied by various modifications to the protocol that allow decentralization to be maintained. Examples of layer 1 scaling solutions include Sharding, Proof-Of-Stake consensus mechanisms, and protocol upgrades aimed at optimizing block processing efficiency. + +!["Layer 1 Scaling"](./img/scaling/layer-1-scaling.png "Layer 1 Scaling") + +> In Ethereum, an increase of gas limits will effectively expand the amount of computation and data that Ethereum can hold but will also raise the demands on network node operators. + +Layer 2 scaling is the set of solutions built on top of Layer 1 blockchain protocols that can achieve a higher TPS without requiring an increase in Layer 1 resource consumption, while still relying on its security model. These solutions typically process transactions off-chain or by using alternative consensus mechanisms that are faster and more scalable than the main blockchain. Examples of Layer 2 scaling solutions include, State Channels, Plasma Chains, or Rollups. + +!["Layer 2 Scaling"](./img/scaling/layer-2-scaling.png "Layer 2 Scaling") + + The solution predominantly adopted by the Ethereum community to solve the scalability problem is a multi-rollup-centric approach. Here, Ethereum acts as fundamental secure layer of Settlement, and Data Availability, while the majority of Execution tasks are delegated to upper layers referred to as Rollups.R ollups bundle multiple Layer 2 transactions into a single Layer 1 transaction. These transactions are stored in Layer 1, but the their execution is delegated to off-chain mechanisms. This allows for significant scalability improvements without sacrificing security. Ethereum's high level of programmability makes possible to create scalable solutions on top of the platform through Ethereum smart contracts. As previously mentioned, to maintain a high level of decentralization, Ethereum imposes limitations on the computational and storage resources that can use the transactions included in the blocks through gas limitations. + +> **Rollups can be seen as a way to compress transaction execution, reducing the computational burden on the Layer 1 blockchain, thereby providing the possibility to increase the TPS while still maintaining the security level of Layer 1 for the Layer2 transactions.** + + -### Ethereum Layer 1 scaling #### Split consensus from execution (The Merge). On September 15, 2022, Ethereum implemented [EIP-3675](https://eips.ethereum.org/EIPS/eip-3675) (Upgrade consensus to Proof-of-Stake) through an event known as The Merge. The Merge has resulted in the deprecation of the Proof-of-Work consensus, which was previously implemented in the same logic layer as execution. Instead, it has been replaced by a much more complex and sophisticated Proof-of-Stake consensus that eliminates the need for energy-intensive mining. New Proof-of-Stake consensus Gasper runs on its own tech stack and p2p network, this new abstraction layer is known as Beacon Chain. The Beacon Chain has been running and achieving consensus since December 1st, 2020. After a prolonged period of consistent performance without any failures, it was deemed ready to become Ethereum's consensus provider, The Merge gets its name from the union of the two networks. @@ -80,6 +95,8 @@ Resources: [Ethereum Scaling](https://ethereum.org/en/developers/docs/scaling), [archived](https://web.archive.org/web/20240209083702/https://ethereum.org/en/developers/docs/scaling) +[An Incomplete Guide to Rollups](https://vitalik.eth.limo/general/2021/01/05/rollup.html), [archived](https://web.archive.org/web/20240212014637/https://vitalik.eth.limo/general/2021/01/05/rollup.html) + [Gemini Cryptopedia The Blockchain Trilemma: Fast, Secure, and Scalable Networks](https://www.gemini.com/cryptopedia/blockchain-trilemma-decentralization-scalability-definition), [archived](https://web.archive.org/web/20240209073156/https://www.gemini.com/cryptopedia/blockchain-trilemma-decentralization-scalability-definition) [Combining GHOST and Casper](https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf), [archived](https://web.archive.org/web/20230907004049/https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf) From 43d3a5000c95a64f062a49915755ce19587f92cd Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Mon, 19 Feb 2024 20:09:33 +0100 Subject: [PATCH 010/101] :mount_fuji: Adding images and .excalidraw files --- .../img/scaling/ethereum-nodes.excalidraw | 1692 +++++++++++++++++ .../research/img/scaling/ethereum-nodes.png | Bin 790114 -> 143272 bytes .../img/scaling/layer-1-scaling.excalidraw | 964 ++++++++++ .../research/img/scaling/layer-1-scaling.png | Bin 0 -> 101754 bytes .../img/scaling/layer-2-scaling.excalidraw | 665 +++++++ .../research/img/scaling/layer-2-scaling.png | Bin 0 -> 87546 bytes 6 files changed, 3321 insertions(+) create mode 100644 docs/wiki/research/img/scaling/ethereum-nodes.excalidraw create mode 100644 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z8qDb#Bsj`;f!*f^z|)d4`Fp?ZH5P6Cfi47Y%oz@2QNy$SDfHuv5*({{e^&Rz<-dgczd*RZ#QICD|7S$< ze>={a9$szg;d$V|c4+d~P4^GBucEdgv=Jz{7TSeeFC5q3YAAB|IU~Eo!QA4jMefLy zqVJdwLhvACC!gBABDsTf#LCp7rutG1@(rYrU|dn)H8d1JYCo%r(n>DMocCUxR*rCW z_}y^g^3scg^45rDqo$s9&pWEFajAy8)jv|t=-E!E2=uM@}2(DyE3{!AzLHj;mJkIeWgO01I~eZPpuij(V6lG z5c#H2g-JR6Pe<~7g1)G|?P#W*JK4JjsPL@Fj=h@(rRov=N~h||CAAe)2mYGrA)iam zXO!z^cxqfHS1do z?A+%bKZ$F!Lnp`f&&mZKaTZW01YZK6f3kBWBXi#9T4Hm<htT z>jxfD<|mqJm0qsw#TtJ(LM^||)c|G({q&u|2HLp|v7K?PchCjiJ?KR=dZ!w6%(*NO z=AoA67kyI1@YjeQC8j}ba(0RfH~1iN(t`&P#>mB;keY*TLJq98oyeJD4H!Iv`CO8uLL%B7AiPdR z^8f<4T}#vA4z4KgS08turwsdcj5*{lREuT2!5*y;Ho9AtBRyTK6+bzTe36){Ic@TVa_9i>f@Qf_VT1msZR&m1J2wubK}+7I z_;gnWdd$9iN%35qvo4Cs!1ut9^g-Z7kxcG#^B}oGrECqW(K1FU4yLGqz6&c-shdw0*xx%^_Kry%F<>~CZqI+6#VRdxOQf;Nm(O;GWREO;;53J}{|6@}z z9xFTpPC2R4V4SnE^jrG=RYN^_ppzc6>6r|~RJ{%q{gxTuR9IZReDMoJiYfhH)q0%^ zqzprmN;xIsA6frw#zNb0u+Vc6RFbr>Xa=cRW1rJl~+=b!!KQjLAt~ zaUWQ0vStvvHw1k2!B@1MC$cTXtl-pQ$vC zeL%kYmeDC2)c+sM25Ml-v8BP{|C9G_GJ%yHai?zb*<9`a)q4nSpq;APv#5UM|LXBg o3jbZC4F>qTNdKRZq+iIRrLjL1c8*zY1OJ>oWvH8d()!;20enX^R{#J2 literal 0 HcmV?d00001 From 2243f5e7c541362882eda766d0048c7d927341f0 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 9 Apr 2024 06:01:37 +0800 Subject: [PATCH 083/101] Fix typos --- docs/wiki/research/Preconfirmations/Preconfirmations.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/wiki/research/Preconfirmations/Preconfirmations.md b/docs/wiki/research/Preconfirmations/Preconfirmations.md index 5bd0c76c..d482433e 100644 --- a/docs/wiki/research/Preconfirmations/Preconfirmations.md +++ b/docs/wiki/research/Preconfirmations/Preconfirmations.md @@ -8,11 +8,11 @@ Based preconfirmations (preconfs) represent a significant advancement in Ethereu ## [Construction of Preconf Promises](#construction-of-preconf-promises) -Preconfirmation promises, or "preconfs," reply on two foundational on-chain infrastructure components: +Preconfirmation promises, or "preconfs," rely on two foundational on-chain infrastructure components: - **Proposer Slashing:** Proposers can opt into additional slashing conditions to ensure reliability and accountability. This approach draws inspiration from EigenLayer's model, which employs restaking as a means of enforcing these slashing mechanisms. -- **Proposer Forced Inclusions:** To ensure the seamless execution of transactions, proposers have the authority to mandate the inclusion of specific transactions on-chain. This capability is necessary in situations where the separation between proposers and builders (PBS) renders self-building impractical. The implementation of this mechanism typically involves the use of inclusion lists. +- **Proposer Forced Inclusions:** To ensure the seamless execution of transactions, proposers have the authority to mandate the inclusion of specific transactions on-chain. This power is crucial in situations where the separation between proposers and builders (PBS) renders self-building uneconomical. The implementation of this mechanism typically involves the use of inclusion lists. When a L1 proposer decides to become a "preconfer," they are essentially agreeing to adhere to two distinct slashing conditions related to preconf promises. In return for their service, preconfers issue signed promises to users and are compensated with tips for successfully fulfilling these promises. The hierarchy among preconfers is determined based on their position in the slot order, with precedence given to those with earlier slot assignments. @@ -121,7 +121,7 @@ The promise acquisition process in the context of Ethereum's sequencing and pre- - **Promise Generation:** If the preconfer decides to accept the request, they generate a signed preconf promise. This promise includes the preconfer's commitment to ensuring the transaction's inclusion and execution within their upcoming slot, adhering to the agreed conditions. -- **Communication of Promise:** The preconf promise is then communicated back to the user, providing them with a guarantee of transaction execution. The communication method used is similar to that of the initial request, ensuring secure and verifiable delivery. +- **Communication of Promise:** The preconf promise is then communicated back to the user, providing them with a guarantee of transaction execution. The communication method used is like that of the initial request, ensuring secure and verifiable delivery. **5. Payment of Preconf Tip** From af3e4eb34453710c23232b867e638c86c519630a Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 9 Apr 2024 08:24:32 +0800 Subject: [PATCH 084/101] Added a proposer lookahead diagram --- docs/wiki/research/Preconfirmations/Preconfirmations.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/docs/wiki/research/Preconfirmations/Preconfirmations.md b/docs/wiki/research/Preconfirmations/Preconfirmations.md index d482433e..22067537 100644 --- a/docs/wiki/research/Preconfirmations/Preconfirmations.md +++ b/docs/wiki/research/Preconfirmations/Preconfirmations.md @@ -64,7 +64,12 @@ Each of these elements plays a crucial role in the functionality and efficiency ## [Preconfs Acquisition Process Flow](#preconfs-acquisition-process-flow) -*Figure: Preconfs Acquisition Process Flow* +![Promise acquisition flow](https://ethresear.ch/uploads/default/original/2X/9/9667dc80c8d911fa3cd86108c3375d0de06e4252.png) + +*Figure: Preconf Promise acquisition process flow. Source: Justin Drake* + + +*Here is a sequence diagram explaining the interactions in a typical Preconfs Acquisition Process Flow* ```mermaid sequenceDiagram From f4eebc300c90889819f0d2f95e239ea562c8f2aa Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 9 Apr 2024 08:25:38 +0800 Subject: [PATCH 085/101] Fixed typos --- docs/wiki/research/Preconfirmations/Preconfirmations.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/wiki/research/Preconfirmations/Preconfirmations.md b/docs/wiki/research/Preconfirmations/Preconfirmations.md index 22067537..6a71527f 100644 --- a/docs/wiki/research/Preconfirmations/Preconfirmations.md +++ b/docs/wiki/research/Preconfirmations/Preconfirmations.md @@ -69,7 +69,7 @@ Each of these elements plays a crucial role in the functionality and efficiency *Figure: Preconf Promise acquisition process flow. Source: Justin Drake* -*Here is a sequence diagram explaining the interactions in a typical Preconfs Acquisition Process Flow* +*Here is a sequence diagram explaining the interactions in a typical Preconfs Acquisition Process Flow.* ```mermaid sequenceDiagram From 7a6ac2a15eecff69cc33d5c1d4e081ed74937e0c Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 10 Apr 2024 12:08:12 +0800 Subject: [PATCH 086/101] Fixed spelling erors --- docs/_sidebar.md | 2 +- docs/wiki/research/scaling/scaling.md | 2 +- wordlist.txt | 437 ++++++++++++++++++++++++++ 3 files changed, 439 insertions(+), 2 deletions(-) create mode 100644 wordlist.txt diff --git a/docs/_sidebar.md b/docs/_sidebar.md index ed396446..cc9cb9cf 100644 --- a/docs/_sidebar.md +++ b/docs/_sidebar.md @@ -65,7 +65,7 @@ - BLS - [Commitments] - Polynomials - - Commitment schemes + - [KZG Commitment scheme](/wiki/Cryptography/KZG.md) - ZK - [Protocol Fellowship](/wiki/epf.md) diff --git a/docs/wiki/research/scaling/scaling.md b/docs/wiki/research/scaling/scaling.md index 9c8a6872..60fc475d 100644 --- a/docs/wiki/research/scaling/scaling.md +++ b/docs/wiki/research/scaling/scaling.md @@ -35,7 +35,7 @@ Functional components of a blockchain: - Data availability: Data availability mechanics that ensures that the data is available to be queried when it is required. - Settlement: Mechanics that guarantee the finality and immutability of transactions. -Modular blockchain approach suggests dividing a blockchain system into different logical layers. This results in a design with reduced systemic complexity, and simpler components that can be more easily optimized and re-enginered to introduce new scaling solutions. +Modular blockchain approach suggests dividing a blockchain system into different logical layers. This results in a design with reduced systemic complexity, and simpler components that can be more easily optimized and re-engineered to introduce new scaling solutions. ## Scaling Ethereum diff --git a/wordlist.txt b/wordlist.txt new file mode 100644 index 00000000..818ec2b6 --- /dev/null +++ b/wordlist.txt @@ -0,0 +1,437 @@ +personal_ws-1.1 en 10000 utf-8 +aantop +ABI +accelerometer +ACD +allowfullscreen +Andreas +Antonopoulos +API +APIs +ary +ASE +Assche +Assertoor +assignees +autoplay +Bankless +Barnabe +backfill +Beiko +Bertoni +BFT +bitrate +bitwise +BLOBHASH +blockchain +blockchain's +blockchains +blockquotes +blocksize +BLS +Boneh +bool +borderless +broadcasted +Buterin +Buterin's +bytecode +calldata +Casper +cdots +centric +chainId +cli +CoC +codebase +codebases +CODECOPY +config +congestions +Corbellini +cmd +Crypto +cryptocurrencies +cryptocurrency +cryptoeconomic +cryptoeconomically +cryptographic +cryptographically +Cryptopedia +cybersecurity +Cypherpunks +D'Amato +Daemen +Dankrad +danksharding +Dany +dapp +dapps +DAS +dataset +Degatchi +delegator +delegators +deliverables +Dencun +deployer +Desmos +dev +Devcon +Devops +devp +Devs +Diffie +discv +distro +docsify +Domothy +Dragan +Driscoll +DSA +DVT +EB +ECADD +ECC +ECDSA +ECMUL +ECPAIRING +ECRECOVER +Edgington +Edgington's +efd +eg +EIP +EIPs +eK +EL +Elmore +ELs +Encodings +env +EOF +EOY +eP +ePBS +EPF +EPFsg +Ephemery +EPS +epubs +ERC +ERCs +Erigon +estimateGas +eth +Ethereum +Ethereum's +ethers +ethresearch +EVM +EVM's +evmlab +EVMONE +excalidraw +exchangeTransitionConfigurationV +Explainer +Feist +Femboy +finalise +Forkchoice +forkchoiceUpdatedV +FOSS +frameborder +Francesco +frontend +fullscreen +Fullstack +func +fuzzer +FuzzyVM +GasLimit +Gasper +gasPrice +gasUsed +Georgios +geth +getPayloadBodiesByHashV +getPayloadV +getters +Gilles +Goron +gpg +Grafana +Guillaume +hoc +Holesky +Hsiao +ics +iframe +ify +impera +implementers +incentivize +inevitableeth +infrastracture +Infura +init +InsertCoin +interop +IPC +ISA +Jitsi +js +JSON +JUMPDEST +JVM +Karapetsas +Katex +keccak +Keccak's +keecak +Kleppmann +Koblitz +KZG +KZGCommitment +KZGProof +Lamport +Lefteris +libp +lifecycle +Lightclient +Lightclient's +liveness +LLM +LLMs +LMD +Longrightarrow +LST +Lua +LuaVM +mainnet +Mário +mathbb +mem +MDS +Mempool +Menezes +Merkle +Merkleization +Merkleize +MEV +Michaël +mload +MMPTs +MODEXP +modularity +Monnot +MPT +MSIZE +mstore +MUL +MVE +n't +namespace +namespaces +Nand +natively +newPayloadV +NFT +NIST +NOXX +Occhipinti +offsites +onchain +Oorschot +OpenRPC +OpenZeppelin +OSI +OSI's +Parametrizing +params +Pari +Paritosh +Pectra +PeerDAS +Peeters +permissionless +Pilipovic +Playdate +pmod +POC +POS +pre +preconfirmations +precompile +precompiled +precompiles +privateKey +probabilistically +programmability +proto +PRs +Prysm +PUSHX +py +Pyspec +pytest +radix +Rareskills +README +referrerpolicy +repo +responder +retesteth +Reth +revm +RIPEMD +Ritchie +rK +RLP +roadmap +rollup +rollups +rollup's +RPC +RPCs +runtime +scalability +scalable +schemas +Schocken +SECG +secp +SELFDESTRUCT +sexualized +SHA +Shafu +sharding +ShareAlike +Shead +Shimon +Silverman +Sipser +SLOAD +smlXL +SNARKify +socio +solvm +SSF +SSLE +SSTORE +sstorge +SSZ +stakers +Stallman +StateDB +stateRoot +stf +StreamEth +systemd +Takenobu +Tani +Teku +testnet +Tetris +textnormal +TODO +TPS +tradeoff +transactional +trapdoored +trie +trilemma +trustless +trustlessly +TrustLook +TSTORE +txpool +txs +Unbundling +underbrace +Unformatted +upstreamed +utils +validator +validators +Vanstone +VDFs +Verkle +verkled +Victorio +Vitalik +VM +Vyper +walkthrough +webkit +WebRTC +Whitepaper +WIP +WSS +XORed +xy +Yellowpaper +zk +Extractable +Consensys +api's +tldr +cartelization +bypassability +suboptimal +amidst +mvepbs +permissionlessness +tbhl +timeframe +neuder +attesters +bidpool +ptc +attestors +pepc +trustlessness +pepc's +tradeoffs +atomicity +eigenlayer +restaking +lmd +ghost +addons +Baranabé's +Barnabé +Flashbot's +Flashbots +orderflows +DeFi +Flashboys +Flashloans +PGA +BDN +OFAC +Carb +RANDAO +bloXroute +bloXroute's +centralisation +ethresear +mevboost +DEX +EigenLayer's +Preconf +Preconfer +Preconfers +Preconfirmation +Preconfs +incentivizes +intermediation +lookahead +preconf +preconfed +preconfer +preconfer's +preconfers +preconfirmation +preconfirmed +preconfs From 3e17f1a99de7b21869f94034130e71fa97b91575 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Fri, 12 Apr 2024 21:09:11 +0800 Subject: [PATCH 087/101] Edited per review and suggestions --- docs/_sidebar.md | 1 + .../Preconfirmations/Preconfirmations.md | 15 +++++++++------ .../Promise-acquisition-flow-JustinDrake.png | Bin 0 -> 143884 bytes 3 files changed, 10 insertions(+), 6 deletions(-) create mode 100644 docs/wiki/research/img/preconfs/Promise-acquisition-flow-JustinDrake.png diff --git a/docs/_sidebar.md b/docs/_sidebar.md index cc9cb9cf..21cb2a5d 100644 --- a/docs/_sidebar.md +++ b/docs/_sidebar.md @@ -60,6 +60,7 @@ - ASE - EOF - Portal Network + - Preconfirmations - [Cryptography](/wiki/Cryptography/intro.md) - [ECDSA](/wiki/Cryptography/ecdsa.md) - BLS diff --git a/docs/wiki/research/Preconfirmations/Preconfirmations.md b/docs/wiki/research/Preconfirmations/Preconfirmations.md index 6a71527f..2e3cd1bd 100644 --- a/docs/wiki/research/Preconfirmations/Preconfirmations.md +++ b/docs/wiki/research/Preconfirmations/Preconfirmations.md @@ -8,16 +8,16 @@ Based preconfirmations (preconfs) represent a significant advancement in Ethereu ## [Construction of Preconf Promises](#construction-of-preconf-promises) -Preconfirmation promises, or "preconfs," rely on two foundational on-chain infrastructure components: +Preconfirmation promises, or "preconfs," rely on two foundational on-chain infrastructure components[^2][^3]: - **Proposer Slashing:** Proposers can opt into additional slashing conditions to ensure reliability and accountability. This approach draws inspiration from EigenLayer's model, which employs restaking as a means of enforcing these slashing mechanisms. - **Proposer Forced Inclusions:** To ensure the seamless execution of transactions, proposers have the authority to mandate the inclusion of specific transactions on-chain. This power is crucial in situations where the separation between proposers and builders (PBS) renders self-building uneconomical. The implementation of this mechanism typically involves the use of inclusion lists. -When a L1 proposer decides to become a "preconfer," they are essentially agreeing to adhere to two distinct slashing conditions related to preconf promises. In return for their service, preconfers issue signed promises to users and are compensated with tips for successfully fulfilling these promises. The hierarchy among preconfers is determined based on their position in the slot order, with precedence given to those with earlier slot assignments. +When a Beacon Chain validator decides to become a "preconfer," they are essentially agreeing to adhere to two distinct slashing conditions related to preconf promises. In return for their service, preconfers issue signed promises to users and are compensated with tips for successfully fulfilling these promises. The hierarchy among preconfers is determined based on their position in the slot order within an epoch, with precedence given to those with earlier slot assignments. -A transaction that secures a preconf promise gains the eligibility for immediate inclusion and execution on-chain by any proposer positioned before the issuer of the promise (preconfer). The primary obligation of the preconfer is to honor all such promises during their designated slot, utilizing the inclusion list to facilitate this process. +A transaction that secures a preconf promise gains the eligibility for immediate inclusion and execution on-chain by any proposer positioned before the issuer of the promise (preconfer). The primary obligation of the preconfer is to honor all such promises during their designated slot, utilizing the inclusion list to facilitate this process[^3]. There are two main types of promise-related faults, each carrying the potential for slashing: @@ -33,7 +33,7 @@ Preconfers are not limited to a single type of preconfirmation promise. They can ## [Key Elements of Preconfs](#key-elements-of-preconfs) -The process towards securing a preconfirmation promise for transactions within the Ethereum network is initiated by establishing a connection with the next available preconfer. This process entails a series of critical steps and factors, including: +The process towards securing a preconfirmation promise for transactions within the Ethereum network is initiated by establishing a connection with the next available preconfer. This process entails a series of critical steps and factors, including[^1]: - **Endpoints:** Preconfers may offer direct API endpoints or utilize decentralized peer-to-peer (p2p) networks for the exchange of promises, striking a balance between quick response times and widespread availability. @@ -64,7 +64,8 @@ Each of these elements plays a crucial role in the functionality and efficiency ## [Preconfs Acquisition Process Flow](#preconfs-acquisition-process-flow) -![Promise acquisition flow](https://ethresear.ch/uploads/default/original/2X/9/9667dc80c8d911fa3cd86108c3375d0de06e4252.png) +![Promise acquisition flow](/docs/wiki/research/img/preconfs/Promise-acquisition-flow-JustinDrake.png) + *Figure: Preconf Promise acquisition process flow. Source: Justin Drake* @@ -102,7 +103,7 @@ sequenceDiagram ``` -The promise acquisition process in the context of Ethereum's sequencing and pre-confirmation mechanism is a critical aspect, ensuring transactions receive a preconfirmation or "promise" from a proposer or sequencer. This process involves several steps, each integral to securing a promise that a transaction will be included and executed on-chain within a specified time frame. The above figure shows the preconf promise acquisition flow through a sequence of interactions. Below is a detailed explanation of the acquisition process flow: +The promise acquisition process in the context of Ethereum's sequencing and pre-confirmation mechanism is a critical aspect, ensuring transactions receive a preconfirmation or "promise" from a proposer or sequencer. This process involves several steps, each integral to securing a promise that a transaction will be included and executed on-chain within a specified time frame. The above figure shows the preconf promise acquisition flow through a sequence of interactions[^2]. Below is a detailed explanation of the acquisition process flow: **1. User Identifies Next Preconfer** @@ -150,3 +151,5 @@ The promise acquisition process in the context of Ethereum's sequencing and pre- ## References [^1]: https://ethresear.ch/t/based-preconfirmations/17353 +[^2]: https://www.youtube.com/watch?v=2IK136vz-PM +[^3]: https://notes.ethereum.org/@JustinDrake/rJ2eXRcKa diff --git a/docs/wiki/research/img/preconfs/Promise-acquisition-flow-JustinDrake.png b/docs/wiki/research/img/preconfs/Promise-acquisition-flow-JustinDrake.png new file mode 100644 index 0000000000000000000000000000000000000000..dc8ea3e606c5f384cdb9d0bf332671078526de1e GIT binary patch literal 143884 zcmeEvWmHt%8!sXXf)Y|n4TvZWN=gi)h#*KvNS8>rbdG>HC@s=b3JOYhBdxS_rzkx% zL*G3n`ttgIxoh3~;m=w)hdKM~{p@Ey`}gENK9-XaKZQ$yi-Cc0>ZZhXc?=93Cr zJkD|O4Fw$q9r!q6BQJgpBfW)c8vGHauX58sS{j2HT;pJ19ihNDhHe6Wp+_ixUf(#v zh;j7m_m~(M2xAPa?`>qjC;BG{{Gy-v_KEfM5e7E+>ooX%7=PsZli+?l=8q?Fpz%k4 zTw}$9b{JO`L~q^%p9*^S_4O@mj4W-n;_tlxU!1U#P_@CpAY(xP9=R!hei4k-YpkeZ zt0H|%K+n>gUH6{lU43>(b1QT|7($K$;L=>*R+rY%+|0s8z)|?z*A@cc8vQlLIohvH zY)ysFsYuJwidx>+r{!hmWam5w#igaC6}o@VKtTTbjqi_xzl6^j+1gqOaBw&{IIuf# zv0L6Z*`O(jHeH*>|##Xk*mKL<=es%9! z+Sv-9JBJ?V=g&7f^&O3Wjbvf-eOh3G9Oye7m)JQue)bI>6+(Y2AZP5TZ>DjVF|^=rrjkE;B7^zx-koChC0aO=-Um2C9yi&~n4L2aSG7VP`O2XB6V zP>2IP_XE86#^|r#0!~A5g*bk$8Wi`4Km<8hNGjv&vWnmnh#dL{Qx5#Y`0W#Yjg*z( zGt0-ofMMLcepS)&$lMV2^Yi*KBBLWs3v*^cj5vip53oqDUcY@ECN?Q|DL#Vqw2x*9#9S+|?7%Pgb4Wk$-FUwTB2Y zLRTyL|LXAwW)Uf&>-+gOWB$L4`|TDjYLw2nD_6dE_u#>(m&;$-_qE~svR@jn6lH;MTl0v?8$|3kok z)jI!E!G|gB|Eb_ZVE3C0{m%wG%%J&yZUcV0F*=vi8bE1Tnq}a!(PtRv*!hx1Dd+j$ zZSYUpz_i}iOUA}>zA+l17x0*r}*dREte0Ks9Xb7jy zf~(lGCe#c+Z~pT_t^gR`LyEYkX*oxLiMt|3kxD(c`Mfk!-E;LSJIig z@Xt2G zt8~ICd+?wIM0c0|=g|MWXe$KGCk$F>VLGv37N1WH>;KK$u+0R`u?YfR5z%IrKNzjv zqJa_}hD$%VMM#GlWv7MF@_~sKon=1tw~2BZf<`ts=C5JlGyzXaH{Y}6Z;nNq8)!bn z_saQtyeaS-itUZ;{QeaTU=Ls&pt*F%m0%2yBH(XEm|FMzl`os1d5p*nHHioBj)F^z zV}BJ;NkD<5nCk^tydJm`us7oV8!hijPvAhCD9iAOY1@(kLtox)_?t^Mg_eK?h@SBI zHXcBVCf758Yd;wL&lQEm>w`vYFBOT7V9tY?8Wm)2{cTA<$%3r~*Lziq;&R)6BPLf1bh-A*UQ;F?g4TuLA9#nY1A9P&gj)7%>1z7F( zndSIf^M24}p8qpiSiC5DgWsd&_WGNEVS_$x+jNX@k6?0vftuzf82{G0773y2RPF5^ zL(D7axW@E5W8S|t=LNoOE|GE<7EUgDnet*y{wltw0PRDZPqtw3;(&JNd+~N5f1@2O z;-_?&Bp@skaGB^_FkRGQ=%cMGKWzej}73&*{aPh5~c;N zmIdzjOQW}bC?K6VrC0ng81SeAEh+eH0RL9N_?)tf>{94<=4fW(y_Gy{x>HvH>u9KK zH7^7ydl1VCUD{hjh;*9mQ4TLYa-30!Q~RNyb)ca0&k7@XhxT#-^kP9F?MC+lmfrgV z_E|iV6g{-L6=;qRp>6&-^C=nh3Q{STo%_+j0p+5zfF62ykn~qy4@bSC4`aa*%rx|5 z{a>nmlN^r=SPQCLq%VnyDA}fc#qgq&;~SV9GGd?XmFKOk>u0QFNlS~RHf-@lmRXeM za*(aIinA=+HQ%%A*;UB0yRwa`J1$OmpcQeh&L zUb5mLLlWvHX;7rs9o}bAFd|4QQh1Mb&)$XCzOQg7`~KxR$W&cbYF{+#tgmKR26e$j z%L-cFhPrI(futVk8vP#GdmF8agAqgFDQp`A8S@*D`U=g}I96#?J<(xrr#Ib{@XjY_ouF%v zicX^{877wEM5vic22Epm2`ycn*Jro;)^~mD$88J)>l`Ny-*pg7iEKvI>f0#}WHIBB zx$?bTNgWBOcOwu=Ouv)w2*;%grCe53v`f-OZ!({=3mNB-RxS=sk9oM&KEdrf(J z`q;C*)^i&-#s^v7-!4vi&~R0CJ9;R+Oz(bi*_Rz_SIxGBJDPYo&ue|-xCt``4CD24 zI1}Hskh@=@2-i@Ue3jas%+0=^x&NYfjVSLZ;fUHLvbffT?K@`E!@G-(GyD4zEa@ru zha%Fat3cTkyiD}}Dz)*|$KD)+Xl3=lcHGuScV8O%*Yx#?E=1;Yb6qW~L_qc|grM6i z!FF6XniMUQ^rq>y-sZ^F>2C8va3$7WMdCttc7x6CJY4Q0W7aIN)mCd6)5fQH9(#54 zSeyp2aktNS+JGkk@!5_OB9xCI`V$52vc4|DE8E<&)h@AoXJiLb?5E<@q?vSK5?h{9u zas-FjIwG%nSr0}|av9hvEYf)k?5&m1pK48)Gp23#J1eelfIZibN+pIDnO_drLiPo! zCukn+L%B@_)h>N9+YFS99u;LE-9A)PwW*xqM6Nm0cND69H1g(cb71ob?9r^&g@Ka3?%uGTg*@igOK>IiF~S$R>}3lHC_ zCYaW8-Bw1Jvim=s8D6DxyA(BKv(ZIlc5@5?hfj_>y7HRdoW6jPV;<)^)EZIa07jp) z0?%nQFnh!jCzH7*9}fSc9#SJwAv_tK?Hq#Gy2%nF=FRxMkU1;2>E1x`;3gyt)1 zM`@lDb{w{D+;cQqZ*yjrI-U5SN;_v{QRE_?l!l|-I!Q^xdT=;LK$$%w+(hbp33+LFntUvG&lUCzC6VE_eM=pi|4=(vp^s(}8O>n?H}y7Rv;&n+-4eQIt?jyr48JuZ z6*|K{9PY`0Y^Y)mACcRHN^CSW=GZ4rvgE&CXyhgq??-D7zCoU|BJbfgQ$J=CI# zS4Nv>`iX1b%(L9v@v)<#YOy-V7_u7QSbjp;_n5f;tQ^*=WMq!A`Ki~F5H*cCstm(% zyPx-4)SGu;{NAU~d-P07P>ckf-ztW%utY{)%;rEA|Cr%RQeU=)3lJ1ym;5W1h~pn>3b+-Hwm1ZL>wCJXs46 z-Y)DSMNT6jMcllMxJ{`JPYM3elV7(2A*~#6BIIt|#r`I2ZOO2-QBhnH*QuaN#~ogt zSXSjiE4B3TMUGRo%`AjTsy1pa&sM53fS}xVX_b{Ass4>y`RrbbBa-jYTc|{<%OV|{d9Z=Y znGDVkRSDbpH3{47Z_W}j_3lo!FQGaES+L1vgv>sy&Ykhj4%HgjPa7+o;+Q<;G;WVK z{xU;_3eTXWIrZ)Gx>;X9fq|P^Xfqaob5)3p%XWM5_Ia?0rVigkQN+MFX=zsd#u8ZY zyIYkA5@%Fv4_ixEcJj)H`?t%c=gC{n`gd?J@0;%{B9%u<@748TO1_EOLxrx~n8?Lz zoEc7CB>XvRA-G^t8> z&b%+;SAX?siZxT-czcjCyhf()DfOC}C&3ycljvclm&Z@9>FZq+oF)=i6darNiC0b% zB&x6d))53%#f1e*_Wk)S`Z&Qe*ur$`>MttIjcl3m1&tZo&G3>2;H4(kbHU9RKoBdY z;cID=1j~>jRk-WYB7 zko(WL(9{Y!+&cqruR^aXJKh+`Lsw(fwNfmo34I6Q{Hp;X!e@`?FHV^(w@B zHZn`(Ct3Cci0Yqf6~!5!MX0Igsb11r>-6B?i45IVc-vyT(~I=4DN+syCr!I(d%wN! z<MYV=uLyl+rH4^MwtForX z+A+<#=+;-bIh=2AB1jq-YdzybE}T_<-g{IuCARg@X&cD^*X0VI;rBp~7-p9zL963j z6)K!uS=%!{`N$<2#1{6$;;|R^jUf#~|%~I2l_RJl6GPNj6-mG4r|zwi$KY7w!D66Uur^N!nqE zJ6bEb9*z?oEZEE!vTq9DH-!~Puv*F_>fFR_Z>qn5;)Kkk-#kPVVSH#yd?I;<_$#`cbjWAnhoKEIgz-G`s~v$F

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link to preconf --- docs/_sidebar.md | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/_sidebar.md b/docs/_sidebar.md index 21cb2a5d..bcb4a44f 100644 --- a/docs/_sidebar.md +++ b/docs/_sidebar.md @@ -61,6 +61,7 @@ - EOF - Portal Network - Preconfirmations + - [Preconfirmations](/wiki/research/Preconfirmations/Preconfirmations.md) - [Cryptography](/wiki/Cryptography/intro.md) - [ECDSA](/wiki/Cryptography/ecdsa.md) - BLS From 65b09b606259a24bfb78b80b0a625fe229b8f6e8 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Fri, 12 Apr 2024 21:53:18 +0800 Subject: [PATCH 089/101] Based Sequencing with Preconfs - new wiki article --- docs/_sidebar.md | 1 + .../Preconfirmations/BasedSequencingPreconfs.md | 16 ++++++++++++++++ 2 files changed, 17 insertions(+) create mode 100644 docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md diff --git a/docs/_sidebar.md b/docs/_sidebar.md index bcb4a44f..753e94e3 100644 --- a/docs/_sidebar.md +++ b/docs/_sidebar.md @@ -62,6 +62,7 @@ - Portal Network - Preconfirmations - [Preconfirmations](/wiki/research/Preconfirmations/Preconfirmations.md) + - [Based Sequencing with Preconfs](/wiki/research/Preconfirmations/BasedSequencingPreconfs.md) - [Cryptography](/wiki/Cryptography/intro.md) - [ECDSA](/wiki/Cryptography/ecdsa.md) - BLS diff --git a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md new file mode 100644 index 00000000..c1b02562 --- /dev/null +++ b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md @@ -0,0 +1,16 @@ +# Ethereum Based Sequencing with Preconfirmations + +## [Overview](#overview) + +Ethereum's evolving ecosystem is set to introduce new paradigms for rollups and chain interactions, emphasizing seamless transitions and enhanced user experiences. This section introduces a framework for Ethereum sequencing and pre-onfirmations, originally proposed by Justin Drake[^1][^4], a step toward realizing this vision, offering a unified platform for all Ethereum chains and rollups. + + +## [Motivation](Motivation) + + + +## References +[^1]: https://docs.google.com/presentation/d/1v429N4jdikMIWWkcVwfjMlV2LlOXSawFCMKoBnZVDNU/edit#slide=id.g1f1d94ef56e_0_655 +[^2]: https://ethresear.ch/t/based-preconfirmations/17353 +[^3]: https://thogiti.github.io/2024/04/07/Based-Preconfirmations.html +[^4]: https://youtu.be/2IK136vz-PM From 06000e5478b0cdb9feb2b7d235121384ee6ff971 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Fri, 19 Apr 2024 09:50:13 +0800 Subject: [PATCH 090/101] Motivation section is added --- .../BasedSequencingPreconfs.md | 16 +++++++++++++++- .../img/preconfs/united-chains-of-ethereum.jpg | Bin 0 -> 429726 bytes 2 files changed, 15 insertions(+), 1 deletion(-) create mode 100644 docs/wiki/research/img/preconfs/united-chains-of-ethereum.jpg diff --git a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md index c1b02562..bcd8b1cc 100644 --- a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md +++ b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md @@ -2,11 +2,25 @@ ## [Overview](#overview) -Ethereum's evolving ecosystem is set to introduce new paradigms for rollups and chain interactions, emphasizing seamless transitions and enhanced user experiences. This section introduces a framework for Ethereum sequencing and pre-onfirmations, originally proposed by Justin Drake[^1][^4], a step toward realizing this vision, offering a unified platform for all Ethereum chains and rollups. +Ethereum's evolving ecosystem is set to introduce new paradigms for rollups and chain interactions, emphasizing seamless transitions and enhanced user experiences. This wiki article introduces a framework for Ethereum sequencing and pre-onfirmations, originally proposed by Justin Drake[^1][^4], a step toward realizing this vision, offering a unified platform for all Ethereum chains and rollups. ## [Motivation](Motivation) +### [United Chains of Ethereum](#united-chains-of-ethereum) + +The vision for Ethereum is not just a network of isolated chains but a cohesive ecosystem where all rollups and chains coexist without friction, termed the "United Chains of Ethereum." This concept envisions a scenario where users can move between different states (rollups) with ease, akin to crossing state lines without the need for passports or the imposition of tariffs. Such an environment would not only enhance user experience but also foster a more integrated and efficient blockchain ecosystem. + + +![United Chains of Ethereum](/docs/wiki/research/img/preconfs/united-chains-of-ethereum.jpg) + +_Figure: United Chains of Ethereum, Credit Justin Drake_ + +### [Ethereum's Services for Rollups](#ethereums-services-for-rollups) + +- **Current Services:** Ethereum currently provides two critical services to rollups: settlement and data availability. These services lay the foundation for rollups to operate effectively on Ethereum's decentralized platform. + +- **Introduction of Ethereum Sequencing:** Ethereum sequencing, is proposed to complement the existing ones, offering a new resource that rollups can leverage to further optimize their operations. Although sequencing has always been inherent to Ethereum, its potential as a dedicated service for rollups represents an innovative application, akin to the adaptive use of core data for new functionalities. ## References diff --git a/docs/wiki/research/img/preconfs/united-chains-of-ethereum.jpg b/docs/wiki/research/img/preconfs/united-chains-of-ethereum.jpg new file mode 100644 index 0000000000000000000000000000000000000000..e4c41b96637a2a9a02014fa78071bef5ec5356b9 GIT binary patch literal 429726 zcmbTdcU)6J(?5FXNEHP^1R|nT0TGZ+M1>#-NJpv^>Agz}h!kl70Z~9fI?{XZB@_|q zT}tRu1B8+geg~iDeSi1Qd++ig+2qWb-I+5p`<=A%}00A>V@~;m7Is~`=w{J|q{a+eF03f{nf9b<)0OJ4BgFG)Afzsv6|GtyO z0stBK4e^7A4~60g{?jKQBm&a^=X;?C57G(#FUNGk|KUjfJ)P)(`XoJBr2nM>nf<3- zY!U>>X{c%a`(#*g0|4f^0U%Hs08nZGz-NPx{K5`Zn01hCF00V*p=fIrP70BtV`&@)T|7|xOalB*;D215dPQjr22 zw@3lEd!ztHfE4f&Ck3XTk^-hLNr919qyV!ODX`!|3SwhHrf5<}z%0oy@Ohim}DGvdm*QKy@#3bxOq}Sxs z$xL0Y-+35BPX8qCds*8R4q=Tw1~bIJYXi4Kh4>lff~2 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create mode 100644 docs/wiki/research/img/preconfs/based-sequencing-problems-space.png diff --git a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md index bcd8b1cc..cc2d4206 100644 --- a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md +++ b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md @@ -11,7 +11,6 @@ Ethereum's evolving ecosystem is set to introduce new paradigms for rollups and The vision for Ethereum is not just a network of isolated chains but a cohesive ecosystem where all rollups and chains coexist without friction, termed the "United Chains of Ethereum." This concept envisions a scenario where users can move between different states (rollups) with ease, akin to crossing state lines without the need for passports or the imposition of tariffs. Such an environment would not only enhance user experience but also foster a more integrated and efficient blockchain ecosystem. - ![United Chains of Ethereum](/docs/wiki/research/img/preconfs/united-chains-of-ethereum.jpg) _Figure: United Chains of Ethereum, Credit Justin Drake_ @@ -22,9 +21,66 @@ _Figure: United Chains of Ethereum, Credit Justin Drake_ - **Introduction of Ethereum Sequencing:** Ethereum sequencing, is proposed to complement the existing ones, offering a new resource that rollups can leverage to further optimize their operations. Although sequencing has always been inherent to Ethereum, its potential as a dedicated service for rollups represents an innovative application, akin to the adaptive use of core data for new functionalities. +### [Current Sequencing Options](#current-sequencing-options) + +![Sequencing Types](/docs/wiki/research/img/preconfs/based-sequencing-problems-space.png) + +_Figure: Different Sequencing Options and their Problem Space, Credit Justin Drake_ + + +#### [Decentralized Sequencing](#decentralized-sequencing) + +**Overview:** Decentralized sequencing distributes the responsibility of transaction ordering among multiple nodes rather than a single central authority. This method enhances security and resistance to censorship, as no single node can dictate the transaction order by itself. + +**Problems and Challenges:** +- **Complexity in Coordination:** Since multiple nodes are involved in transaction ordering, achieving consensus can be challenging and complex, particularly when the nodes have varying incentives. +- **Network Integrity Maintenance:** Ensuring that all participating nodes follow the protocol without any malicious behavior can be difficult to enforce. +- **Front-Running and MEV:** Miners or validators might exploit their ability to order transactions to extract maximal extractable value (MEV), which can lead to unfair transaction processing and a negative user experience. +- **Resilience to Censorship:** Although decentralized sequencing makes censorship more difficult, it doesn't eliminate the possibility, especially if a collusion of nodes occurs. + +#### [Shared Sequencing](#shared-sequencing) + +**Concept:** Shared sequencing is a form of decentralized sequencing where the task of ordering transactions is shared among several entities, typically across different layers or platforms. This approach is designed to further decentralize the process and reduce the influence any single participant might have over the sequence of transactions. + +**Application:** In Ethereum, shared sequencing could involve various rollups solutions that coordinate to manage transaction order. This coordination can help ensure that transactions are processed efficiently and fairly, reducing the potential for bottlenecks or biased sequencing practices. + +**Benefits:** Shared sequencing aims to promote scalability by distributing the load of transaction processing and enhancing the network’s throughput. It also strives for neutrality and fairness in transaction handling, critical for maintaining trust in a decentralized ecosystem. + +**Problems and Challenges:** +- **MEV Sharing:** Coordinating MEV sharing, like the approach Espresso is investigating, requires sophisticated mechanisms to fairly distribute MEV across participating rollups and chains[^5]. +- **Deposits Sharing:** Solutions like zkSync's deposit sharing are innovative but require widespread adoption and trust among different rollups to function effectively, potentially leading to centralization of trust[^6]. +- **Execution Sharing:** Implementation of execution sharing strategies, such as Polygon's aggregation layer, requires standardization and integration across different rollups to ensure compatibility and trustless atomicity[^7]. + +**Based Sequencing:** + +**Concept:** A specialized form of decentralized sequencing that uses the base layer of a Ethereum, Beacon chain, to manage transaction ordering. This method leverages the security and consensus mechanisms of the Beacon chain to ensure that transactions are sequenced in a trustless manner. + +**Focus:** Based sequencing aims to integrate the robust security features of the Beacon chain into transaction sequencing, reducing dependency on external sequencers or centralized systems. It aligns with Ethereum's decentralized principles by using the existing Ethereum infrastructure to secure transaction order. + +**Integration with Shared Sequencing:** Based sequencing can be a pivotal part of a larger shared sequencing strategy, providing a reliable, secure foundation that other layers or rollups can build upon. It ensures that at least one layer of the transaction ordering process is closely tied to the highly secure, well-tested consensus mechanisms of the Ethereum blockchain. + +**Problems and Challenges:** +- **Proposer Responsibility:** Proposers must opt into based sequencing by posting collateral, adding financial risk and responsibility to their role. +- **Inclusion List Management:** The concept of inclusion lists must be maintained and managed carefully to ensure fair transaction inclusion. +- **Consensus Mechanism Dependence:** Based sequencing is inherently tied to the underlying consensus mechanism, which means any issues with the consensus could directly affect transaction sequencing. +- **Preconfirm Complexity:** Implementing preconfirm mechanisms, where users get assurance of transaction execution from proposers, adds complexity to transaction processing and requires a new level of trust and interaction between users and proposers. + + +## Resources +- [Ethereum Sequencing](https://docs.google.com/presentation/d/1v429N4jdikMIWWkcVwfjMlV2LlOXSawFCMKoBnZVDNU/) +- [Based preconfirmations](https://ethresear.ch/t/based-preconfirmations/17353) +- [Preconfirmations](/docs/wiki/research/Preconfirmations/Preconfirmations.md) +- [Ethereum Sequencing and Preconfirmations Call #1](https://youtu.be/2IK136vz-PM) +- [Espresso Shared Sequencing](https://hackmd.io/@EspressoSystems/SharedSequencing) +- [Zksync Deposit Sharing](https://docs.zksync.io/zk-stack/components/shared-bridges.html) +- [Polygon Aggregate Layer](https://polygon.technology/blog/aggregated-blockchains-a-new-thesis) + ## References [^1]: https://docs.google.com/presentation/d/1v429N4jdikMIWWkcVwfjMlV2LlOXSawFCMKoBnZVDNU/edit#slide=id.g1f1d94ef56e_0_655 [^2]: https://ethresear.ch/t/based-preconfirmations/17353 [^3]: https://thogiti.github.io/2024/04/07/Based-Preconfirmations.html [^4]: https://youtu.be/2IK136vz-PM +[^5]: https://hackmd.io/@EspressoSystems/SharedSequencing +[^6]: 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a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md index cc2d4206..ad5f608e 100644 --- a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md +++ b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md @@ -19,7 +19,7 @@ _Figure: United Chains of Ethereum, Credit Justin Drake_ - **Current Services:** Ethereum currently provides two critical services to rollups: settlement and data availability. These services lay the foundation for rollups to operate effectively on Ethereum's decentralized platform. -- **Introduction of Ethereum Sequencing:** Ethereum sequencing, is proposed to complement the existing ones, offering a new resource that rollups can leverage to further optimize their operations. Although sequencing has always been inherent to Ethereum, its potential as a dedicated service for rollups represents an innovative application, akin to the adaptive use of core data for new functionalities. +- **Introduction of Ethereum Sequencing:** Ethereum sequencing[^2][^3], is proposed to complement the existing ones, offering a new resource that rollups can leverage to further optimize their operations. Although sequencing has always been inherent to Ethereum, its potential as a dedicated service for rollups represents an innovative application, akin to the adaptive use of core data for new functionalities. ### [Current Sequencing Options](#current-sequencing-options) @@ -77,9 +77,9 @@ _Figure: Different Sequencing Options and their Problem Space, Credit Justin Dra ## References -[^1]: https://docs.google.com/presentation/d/1v429N4jdikMIWWkcVwfjMlV2LlOXSawFCMKoBnZVDNU/edit#slide=id.g1f1d94ef56e_0_655 -[^2]: https://ethresear.ch/t/based-preconfirmations/17353 -[^3]: https://thogiti.github.io/2024/04/07/Based-Preconfirmations.html +[^1]: https://docs.google.com/presentation/d/1v429N4jdikMIWWkcVwfjMlV2LlOXSawFCMKoBnZVDNU/ +[^2]: https://ethresear.ch/t/based-preconfirmations/17353 +[^3]: /docs/wiki/research/Preconfirmations/Preconfirmations.md [^4]: https://youtu.be/2IK136vz-PM [^5]: https://hackmd.io/@EspressoSystems/SharedSequencing [^6]: https://docs.zksync.io/zk-stack/components/shared-bridges.html From 4768e5f60ffe1fd3cb608cae7e42b2528f3268df Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 20 Apr 2024 11:30:49 +0800 Subject: [PATCH 093/101] Look ahead preconf construction section is added --- docs/wiki/Cryptography/KZG.md | 28 ++++++------- .../BasedSequencingPreconfs.md | 37 ++++++++++++++++- .../img/preconfs/lookahead-preconfs.png | Bin 0 -> 178687 bytes wordlist.txt | 39 ++++++++++++++++++ 4 files changed, 88 insertions(+), 16 deletions(-) create mode 100644 docs/wiki/research/img/preconfs/lookahead-preconfs.png diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 2587aafe..ab61b6b6 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -59,7 +59,7 @@ The "order" of this set is the number of elements it contains, and for a finite When we do modular arithmetic operations in the finite field $\mathbb F_p$, we have a nice "wrap around" property i.e. the field behaves as if it "wraps around" after reaching $(p - 1)$. -In genral, when we define a finite field, we define, the order $p$ of the field and an arithemetic operation like addition or multiplication. If it is addition, we denote the field by $(\mathbb F_p, +)$. If it is multiplication, we denote it by $(\mathbb F^*_p, +)$. The `*` is telling us to exclude the zero element from our field so that we can satisfy all the required properties of the finite field i.e. mainly we can divide the numbers and find inverse of all elements. If we include the zero element, we can't find the inverse of zero element. +In general, when we define a finite field, we define, the order $p$ of the field and an arithmetic operation like addition or multiplication. If it is addition, we denote the field by $(\mathbb F_p, +)$. If it is multiplication, we denote it by $(\mathbb F^*_p, +)$. The `*` is telling us to exclude the zero element from our field so that we can satisfy all the required properties of the finite field i.e. mainly we can divide the numbers and find inverse of all elements. If we include the zero element, we can't find the inverse of zero element. In the next section, we will learn how generators of a Group enable the KZG commitment scheme to function as an efficient, secure, and verifiable method of committing to polynomials, making it a powerful tool for cryptographic protocols, particularly in blockchain technologies where these properties are very important. @@ -166,7 +166,7 @@ In simpler terms, the Discrete Logarithm problem tells us that even though it's **Strong Diffie-Hellman** -Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a, b$ are any elements in the finite field $\mathbb F^*_p$ and $g^a$, $g^b$ are some elements in the group $\mathbb G^\*_p$. The Strong Diffie-Hellman assumption says that $g^a$ and $g^b$ are indistinguishable from $g^{ab}$. This means we can't extract any extra information aboout $g^{ab}$ given $g^a$ and $g^b$. +Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a, b$ are any elements in the finite field $\mathbb F^*_p$ and $g^a$, $g^b$ are some elements in the group $\mathbb G^\*_p$. The Strong Diffie-Hellman assumption says that $g^a$ and $g^b$ are indistinguishable from $g^{ab}$. This means we can't extract any extra information about $g^{ab}$ given $g^a$ and $g^b$. **Developing an intuition for Strong Diffie-Hellman** @@ -196,7 +196,7 @@ Bilinear property: $e(g^a, g^b) = e(g, g^{ab}) = e(g^{ab}, g) = e(g,g)^{ab}$ Non-degenerate property: $e(g,g) \neq 1$, means the output is not an identity element. -When $\mathbb G_1$ and $\mathbb G_2$ are the same Group, we call this symmetric pairing function. Otherwise, it is an assymetric pairing function. +When $\mathbb G_1$ and $\mathbb G_2$ are the same Group, we call this symmetric pairing function. Otherwise, it is an asymmetric pairing function. Here are some great resources to learn more about pairing functions from a practical POV[^3][^8][^9]. @@ -207,7 +207,7 @@ Imagine two separate islands, each inhabited by a unique species of magical crea Here's how to think about this pairing function without getting bogged down by technicalities: - **Two Groups:** Think of the Unicorns and Dragons as belonging to two different groups (in mathematical terms, these are usually called groups $\mathbb G_1$ and $\mathbb G_2$). -- **Pairing Function:** The magical bridge acts as the pairing function. When a Unicorn and a Dragon meet on this bridge, the pairing function combines them into a Dracorn. This Dracorn has a special glow that uniquely corresponds to the combination of that specific Unicorn and Dragon (reversable). +- **Pairing Function:** The magical bridge acts as the pairing function. When a Unicorn and a Dragon meet on this bridge, the pairing function combines them into a Dracorn. This Dracorn has a special glow that uniquely corresponds to the combination of that specific Unicorn and Dragon (reversible). - **Unique Outcome:** Just like every Unicorn and Dragon pair produces a Dracorn with a unique glow, in mathematics, a pairing function takes one element from each group and produces a unique output in a third group (often denoted as $\mathbb G_T$). **Why is this magical?** Because even though there are countless possible combinations of Unicorns and Dragons, each combination (pairing) produces a unique Dracorn. This is powerful in cryptography because it allows for complex operations that underpin many security protocols, ensuring that each combination is distinct and traceable to its original pair. @@ -274,7 +274,7 @@ sequenceDiagram ``` ### [Trusted Setup](#trusted-setup) -A trusted third party picks a random element $a \in \mathbb{F}_p$. They compute the public parameter (PP) or common reference string (CRS), as < $g, {a^1}.g, {a^2}.g, \ldots, {a^t}.g$ >. Then, they **delete** $a$. This step of deleteing $a$ is extremely important to secure the system. +A trusted third party picks a random element $a \in \mathbb{F}_p$. They compute the public parameter (PP) or common reference string (CRS), as < $g, {a^1}.g, {a^2}.g, \ldots, {a^t}.g$ >. Then, they **delete** $a$. This step of deleting $a$ is extremely important to secure the system. Then, the trusted party sends the CRS to the Prover and the Verifier. @@ -293,7 +293,7 @@ We often denote this as $f(x) \in \mathbb{F}_p[x]$. $\mathbb{G}_p$ is an Elliptic Curve group of order $p$ with a generator $g$. -Often, the prime order $p$ is choosen such that $p \gt 2^k$, for some security parameter k. The prime number $p$ is very large in practice. +Often, the prime order $p$ is chosen such that $p \gt 2^k$, for some security parameter k. The prime number $p$ is very large in practice. Prover also picks a pairing function that satisfies both bilinear and non-degenerate properties. The pairing is denoted as below: @@ -305,7 +305,7 @@ To simplify this step, Prover picks a polynomial $f(x) \in \mathbb{F}_p[x]$, the ### [Commitment of the Polynomial](#commitment-of-the-polynomial) Say, the commitment of the polynomial $f(x)$ is denoted as $C_f$. The commitment is like hash function. -So $C_f = {f(a)} \cdot g = {(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)} \cdot g$. Here $f(a)$ is the polynomial evaluted at $x=a$. +So $C_f = {f(a)} \cdot g = {(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)} \cdot g$. Here $f(a)$ is the polynomial evaluated at $x=a$. Though, the Prover doesn't know $a$, he or she can still compute the commitment of the polynomial at $x=a$. @@ -428,7 +428,7 @@ Though the Verifier doesn’t know $a$, he or she knows $a \cdot g$ from the Com - This partial revelation is known as the Evaluation Proof. ## [KZG by Hands](#kzg-by-hands) -Now, let us practically dervie the steps in KZG protocol using a small finite field. We can compute all finite field operations and pairing operations by hand and get a feel for the KZG protocol flow and verifying polynomial commitments. +Now, let us practically derive the steps in KZG protocol using a small finite field. We can compute all finite field operations and pairing operations by hand and get a feel for the KZG protocol flow and verifying polynomial commitments. ### [KZG by Hands - Initial Configuration](#kzg-by-hands---initial-configuration) - We will work with the finite field $(\mathbb F_{11}, + )$. So, the prime order $p = 11$. This means all finite field operations are done modulo 11. @@ -440,7 +440,7 @@ Now, let us practically dervie the steps in KZG protocol using a small finite fi - The pairing function $e(x, y) = xy$ over $(\mathbb G_{11}, +)$. ### [KZG by Hands - Trusted Setup](#kzg-by-hands---trusted-setup) -- The Trusted Party choses a secret number randomly. Say, $a = 3$ is the secret number. +- The Trusted Party chooses a secret number randomly. Say, $a = 3$ is the secret number. - They generate the public parameter or the common reference string (CRS) < $g, {a^1}.g, {a^2}.g, \ldots, {a^t}.g$ >. - This is equal to < $2, 3 \cdot 2, {3^2} \cdot 2$ > which is equal to < $2, 6, 7$ > after applying modulo 11. - The Trusted Party **deletes** the secret number $a$. @@ -480,11 +480,11 @@ Now, let us practically dervie the steps in KZG protocol using a small finite fi - Imagine the Prover somehow finds out the secret number $a$ or the Trusted Party leaks $a$ to a malicious Prover. - The Prover computes $f_1(x) = 3x^2 + 5x + 7$ at $x=3$. So we get, $f_1(2) = 3.3^2 + 5.3 + 7 = 49 = 5 mod(11)$ - The Prover computes $f_2(x) = 2x^2 + 7x + 10$ at $x=3$. So we get, $f_2(2) = 2.3^2 + 7.3 + 10 = 49 = 5 mod(11)$ -- This breaks the binding property of the commitment scheme leading to fradulent proofs by the malicious Prover. +- This breaks the binding property of the commitment scheme leading to fraudulent proofs by the malicious Prover. - Hence, it is extremely important to **delete** the secret number $a$ by the Trusted Party after generating the CRS. -## [Assymetic Pairing Fuctions](#assymetic-pairing-fuctions) -An assymetric pairing function is denoted as: +## [Asymmetric Pairing Functions](#asymmetric-pairing-functions) +An asymmetric pairing function is denoted as: $e:$ $\mathbb G_1 X \mathbb G_2 \rightarrow \mathbb G_T$. @@ -498,7 +498,7 @@ $(a−b) \cdot Q(a) \cdot g_1 = f(a) \cdot g_1 − d \cdot g_1$ $(a−b) \cdot C_Q = C_f − d \cdot g_1$ -Applying the assymetric pairing function on both sides, we get +Applying the asymmetric pairing function on both sides, we get $e((a−b) \cdot C_Q, g_2) = e(C_f − d \cdot g_1, g_2)$ @@ -516,7 +516,7 @@ The KZG Polynomial Commitment Scheme ensures that both commitments and evaluatio One key benefit of the KZG Polynomial Commitment Scheme is its efficient use of space. No matter the length or complexity of the polynomial we're working with, the commitment to that polynomial—essentially its cryptographic "footprint"—is always a single, fixed-size element within a mathematical group, $\mathbb G$. This means that as the polynomial grows in degree, the size of the commitment does not increase. The same principle applies to the evaluation proof, which is the evidence we provide to show that our commitment is accurate. Whether we're verifying just one value or many at once (in batch mode), the proof will always be of a consistent size. This consistency in size translates to predictable and efficient storage requirements, an important feature for practical applications in cryptography. ## [KZG Batch Mode](#kzg-batch-mode) -KZG commitments can also be opened and verified at multiple points or using multiple polynmials or any combination of them. This is called batch mode in practice. +KZG commitments can also be opened and verified at multiple points or using multiple polynomials or any combination of them. This is called batch mode in practice. ### [Single Polynomial, Multiple Points](#single-polynomial-multiple-points) In batch mode, the Verifier requests the Prover to validate a set of points $B =$ { $b_1, b_2, b_3, \ldots, b_n$ } with $n < t$, where $t$ is the degree of the polynomial $f(x)$. For these points, the Prover computes the values $f(b_1) = d_1, f(b_2) = d_2, \ldots, f(b_n) = d_n$ and forms the set $D =$ { $d_1, d_2, d_3, \ldots, d_n$ }. diff --git a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md index ad5f608e..30a43922 100644 --- a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md +++ b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md @@ -2,7 +2,7 @@ ## [Overview](#overview) -Ethereum's evolving ecosystem is set to introduce new paradigms for rollups and chain interactions, emphasizing seamless transitions and enhanced user experiences. This wiki article introduces a framework for Ethereum sequencing and pre-onfirmations, originally proposed by Justin Drake[^1][^4], a step toward realizing this vision, offering a unified platform for all Ethereum chains and rollups. +Ethereum's evolving ecosystem is set to introduce new paradigms for rollups and chain interactions, emphasizing seamless transitions and enhanced user experiences. This wiki article introduces a framework for Ethereum sequencing and preconfirmations, originally proposed by Justin Drake[^1][^4], a step toward realizing this vision, offering a unified platform for all Ethereum chains and rollups. ## [Motivation](Motivation) @@ -65,6 +65,39 @@ _Figure: Different Sequencing Options and their Problem Space, Credit Justin Dra - **Consensus Mechanism Dependence:** Based sequencing is inherently tied to the underlying consensus mechanism, which means any issues with the consensus could directly affect transaction sequencing. - **Preconfirm Complexity:** Implementing preconfirm mechanisms, where users get assurance of transaction execution from proposers, adds complexity to transaction processing and requires a new level of trust and interaction between users and proposers. +## [Technical Construction](#technical-construction) + +### [Based Sequencing](#based-sequencing) + +- **Mechanism:** The proposal for based sequencing involves utilizing the beacon chain's look-ahead period to invite proposers to opt into providing sequencing services by posting collateral. This approach leverages Ethereum's existing structure to introduce a new layer of functionality for rollups. + +- **Look-Ahead Period:** By capitalizing on the beacon chain's ability to predict the next set of proposers, the system can prepare and designate specific proposers to take on the additional role of sequencers, ensuring that rollups have predictable and reliable sequencing services. + + +### [Preconfirm Mechanism](#preconfirm-mechanism) + +In the [Preconfirmations](/docs/wiki/research/Preconfirmations/Preconfirmations.md) article, I explained the details on how Preconfirmations work and the promise acquisition process flow[^2][^3]. + +- **User Interaction with Proposers:** Users can identify which proposers within the look-ahead period have opted for based sequencing and request preconfirmations from them. These preconfirmations are akin to promises that the user's transaction will be included and executed in the future, with penalties applied for non-fulfillment. + +- **Slashing for Non-Fulfillment:** The system imposes penalties, or slashing, for proposers who fail to fulfill their preconfirmations. This adds a layer of accountability, ensuring that proposers are incentivized to honor their commitments. + +### [Look-Ahead Preconf Construction](#look-ahead-preconf-construction) + +![Look-ahead preconf construction](/docs/wiki/research/img/preconfs/lookahead-preconfs.png) + +_Figure: Look-ahead mechanism for Preconfirmations, Credit Justin Drake_ + + +- **Lookahead Period:** On the Ethereum Beacon chain, there is a lookahead period where upcoming proposers for block slots are known ahead of time. This period can typically include a set number of the next 32 slots. +- **Preconfirmation Request:** A user who wants to make a transaction sends a preconfirmation request to a proposer who is scheduled to create a block in the near future (within the lookahead period). The request includes the transaction details and possibly a fee offer. +- **Promise Issuance:** Upon receiving the preconfirmation request, the chosen proposer – referred to as a preconfer – assesses the transaction and decides whether or not to make a promise. If the proposer agrees, they issue a promise to the user, committing to include and execute the transaction in a future block when their turn to propose comes up. This promise is backed by collateral that the proposer has posted, which can be slashed if they fail to honor their promise. +- **Inclusion of the Preconfirmed Transaction:** When the proposer's slot (n+1 in the above figure) arrives, they must include and execute the preconfirmed transaction as they promised. If the proposer fails to do so without a valid reason, they risk being slashed. +- **Sharing of the Preconfirmation:** The promise made by the proposer may need to be communicated to others in the network, especially if there are multiple proposers who might include the transaction before the proposer’s slot arrives. This communication can be facilitated through various means, including MEV boost relays, to ensure that the transaction is settled and included appropriately. +- **Execution of the Transaction:** Once the proposer’s turn comes, and if they have not been preempted by an earlier proposer, they include the preconfirmed transaction in the block they are proposing. This ensures that the transaction is executed on-chain as was promised to the user. + + + ## Resources - [Ethereum Sequencing](https://docs.google.com/presentation/d/1v429N4jdikMIWWkcVwfjMlV2LlOXSawFCMKoBnZVDNU/) @@ -79,7 +112,7 @@ _Figure: Different Sequencing Options and their Problem Space, Credit Justin Dra ## References [^1]: https://docs.google.com/presentation/d/1v429N4jdikMIWWkcVwfjMlV2LlOXSawFCMKoBnZVDNU/ [^2]: https://ethresear.ch/t/based-preconfirmations/17353 -[^3]: /docs/wiki/research/Preconfirmations/Preconfirmations.md +[^3]: https://epf.wiki/#/wiki/research/Preconfirmations/Preconfirmations [^4]: https://youtu.be/2IK136vz-PM [^5]: https://hackmd.io/@EspressoSystems/SharedSequencing [^6]: https://docs.zksync.io/zk-stack/components/shared-bridges.html diff --git a/docs/wiki/research/img/preconfs/lookahead-preconfs.png b/docs/wiki/research/img/preconfs/lookahead-preconfs.png new file mode 100644 index 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      - + \ No newline at end of file diff --git a/docs/wiki/protocol/data-structures.md b/docs/wiki/EL/data-structures.md similarity index 100% rename from docs/wiki/protocol/data-structures.md rename to docs/wiki/EL/data-structures.md diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index 86ce4bd4..becf5374 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -252,3 +252,4 @@ Please note that the aforementioned EIPs, [EIP-4488](https://eips.ethereum.org/E - [https://www.eip4844.com/](https://www.eip4844.com/) - [https://domothy.com/blobspace/](https://domothy.com/blobspace/) +- [EIP-4844 Explained](https://www.youtube.com/watch?v=HT9PHWloIiU) diff --git a/wordlist.txt b/wordlist.txt index a55e957d..0f3e4164 100644 --- a/wordlist.txt +++ b/wordlist.txt @@ -3,23 +3,38 @@ aantop ABI accelerometer ACD +addons allowfullscreen +amidst Andreas Antonopoulos API +api's APIs +Aritra ary ASE Assche Assertoor assignees +atomicity +Attacknet +attesters +attestors autoplay +backfill Bankless +Baranabé's Barnabe -backfill +Barnabé +BDN Beiko Bertoni +Besu +Besu BFT +bidpool +BIP bitrate bitwise BLOBHASH @@ -28,6 +43,8 @@ blockchain's blockchains blockquotes blocksize +bloXroute +bloXroute's BLS Boneh bool @@ -35,40 +52,51 @@ borderless broadcasted Buterin Buterin's +bypassability bytecode calldata +Carb +cartelization Casper cdots +centralisation centric chainId +Challanges cli +cmd CoC codebase codebases CODECOPY config congestions +Consensys +Consensys Corbellini -cmd Crypto cryptocurrencies cryptocurrency cryptoeconomic cryptoeconomically +cryptoeconomics cryptographic cryptographically Cryptopedia +cryptosystem cybersecurity Cypherpunks -D'Amato Daemen +D'Amato Dankrad danksharding +Danno Dany dapp dapps DAS dataset +DeFi Degatchi delegator delegators @@ -78,10 +106,13 @@ deployer Desmos dev Devcon +devnet +devnets Devops devp Devs Diffie +DILITHIUM discv distro docsify @@ -94,13 +125,16 @@ EB ECADD ECC ECDSA +ECDSA's ECMUL ECPAIRING ECRECOVER Edgington Edgington's +EF efd eg +eigenlayer EIP EIPs eK @@ -109,6 +143,8 @@ Elmore ELs Encodings env +EOA +EOAs EOF EOY eP @@ -126,19 +162,27 @@ eth Ethereum Ethereum's ethers +ethresear ethresearch EVM -EVM's evmlab EVMONE +EVM's excalidraw exchangeTransitionConfigurationV Explainer +Extractable Feist Femboy +Ferrin finalise +Flashbot's +Flashbots +Flashboys +Flashloans Forkchoice forkchoiceUpdatedV +Forky FOSS frameborder Francesco @@ -157,14 +201,20 @@ geth getPayloadBodiesByHashV getPayloadV getters +ghost Gilles +Goomy Goron +Gorondan gpg Grafana Guillaume hoc Holesky Hsiao +HSP +Hulsing +Hyperledger ics iframe ify @@ -189,12 +239,17 @@ Katex keccak Keccak's keecak +KEM +Kira Kleppmann Koblitz +Kurtosis +KYBER KZG KZGCommitment KZGProof Lamport +Lamport's Lefteris libp lifecycle @@ -203,84 +258,112 @@ Lightclient's liveness LLM LLMs +lmd LMD Longrightarrow LST Lua LuaVM +Lyubashevsky mainnet Mário mathbb -mem MDS +meldsun +mem Mempool Menezes Merkle Merkleization Merkleize MEV +mevboost Michaël mload MMPTs MODEXP modularity Monnot +mortem MPT MSIZE mstore MUL MVE -n't +mvepbs +Nagu namespace namespaces Nand natively +neuder newPayloadV NFT NIST +NIST's NOXX +n't Occhipinti +OFAC offsites +onboarding onchain Oorschot OpenRPC OpenZeppelin +OQS +orderflows OSI OSI's Parametrizing params Pari -Paritosh +Parithosh Pectra PeerDAS Peeters +pepc +pepc's permissionless +permissionlessness +PGA Pilipovic Playdate pmod POC POS +Potuz's +PQ +PQC +PQCA pre -preconfirmations precompile precompiled precompiles +preconfirmations +preimage +Prest privateKey probabilistically programmability proto PRs Prysm +ptc PUSHX py Pyspec pytest +qubits radix +rahul +RANDAO Rareskills README referrerpolicy repo responder +restaking retesteth Reth revm @@ -290,25 +373,32 @@ rK RLP roadmap rollup -rollups rollup's +rollups RPC RPCs +RSA +RSA's runtime scalability scalable schemas Schocken +Schwabe SECG secp SELFDESTRUCT sexualized SHA +shadowfork Shafu sharding ShareAlike Shead Shimon +Shor +Shor's +Siddharth Silverman Sipser SLOAD @@ -316,6 +406,7 @@ smlXL SNARKify socio solvm +SPHINCS SSF SSLE SSTORE @@ -324,25 +415,33 @@ SSZ stakers Stallman StateDB +stateful stateRoot stf StreamEth +suboptimal systemd Takenobu Tani +tbhl Teku testnet Tetris textnormal +timeframe +tldr TODO TPS +tracoor tradeoff +tradeoffs transactional trapdoored trie trilemma trustless trustlessly +trustlessness TrustLook TSTORE txpool @@ -352,6 +451,7 @@ underbrace Unformatted upstreamed utils +Vadim validator validators Vanstone @@ -368,112 +468,9 @@ WebRTC Whitepaper WIP WSS +Xatu +XMSS XORed xy Yellowpaper -zk -Extractable -Consensys -api's -tldr -cartelization -bypassability -suboptimal -amidst -mvepbs -permissionlessness -tbhl -timeframe -neuder -attesters -bidpool -ptc -attestors -pepc -trustlessness -pepc's -tradeoffs -atomicity -eigenlayer -restaking -lmd -ghost -addons -Baranabé's -Barnabé -Flashbot's -Flashbots -orderflows -DeFi -Flashboys -Flashloans -PGA -BDN -OFAC -Carb -RANDAO -bloXroute -bloXroute's -centralisation -ethresear -mevboost -DEX -EigenLayer's -Preconf -Preconfer -Preconfers -Preconfirmation -Preconfs -incentivizes -intermediation -lookahead -preconf -preconfed -preconfer -preconfer's -preconfers -preconfirmation -preconfirmed -preconfs -Bezout’s -Bilinear -Bilinearity -CPUs -CRS -Dracorn -Goldwasser -Hyperplonk -IOP -MPC -POV -PSE -PSE's -Prover -Prover's -Provers -Solvenecy -Summa -Verifier -ZKSNARK -ZKSNARKs -Zaverucha -bilinear -bilinearity -cdot -dx -frac -homomorphic -ldots -moduli -neq -prover -rightarrow -unguessable -verifier -verifiers -Preconfirm -Zksync -incentivized -EPSsg -licence -Preconfirms \ No newline at end of file +zk \ No newline at end of file From 27cea87a043e2e6d75739dd85f968bcd29268085 Mon Sep 17 00:00:00 2001 From: taxmeifyoucan Date: Mon, 22 Apr 2024 13:58:07 +0200 Subject: [PATCH 100/101] add resources --- docs/eps/week10-research.md | 27 +++++++++++++++++++++++++++ docs/eps/week3.md | 1 + docs/eps/week7-research.md | 2 +- docs/eps/week9-research.md | 2 +- docs/wiki/EL/evm.md | 2 +- 5 files changed, 31 insertions(+), 3 deletions(-) create mode 100644 docs/eps/week10-research.md diff --git a/docs/eps/week10-research.md b/docs/eps/week10-research.md new file mode 100644 index 00000000..6f774743 --- /dev/null +++ b/docs/eps/week10-research.md @@ -0,0 +1,27 @@ +# Study Group Week 10 | Consensus upgrades + +Week 10 research talk will cover variety of Beacon Chain upgrades currently researched, analyzed and considered for inclusion. + +Join the presentation by [](https://twitter.com/), on [Wednesday, April 24, 4PM UTC](https://savvytime.com/converter/utc-to-germany-berlin-united-kingdom-london-china-shanghai-ny-new-york-city-japan-tokyo-australia-sydney-india-delhi-argentina-buenos-aires/apr-24-2024/4pm). + +The talk will be streamed live on [StreamEth](https://streameth.org/65cf97e702e803dbd57d823f/epf_study_group) and [Youtube](https://www.youtube.com/@ethprotocolfellows/streams), links will be provided before the call in the [Discord server](https://discord.gg/addwpQbhpq). Discord also serves for the discussion and questions during the stream. + +## Pre-reading + +Before starting with the week 10 development content, make yourself familiar with resources in previous weeks, especially week 3 and week 5. You should have understanding of Beacon Chain and current consensus research topics. + +Additionally, you can get ready by studying the following resources: +- [A simple single slot finality](https://ethresear.ch/t/a-simple-single-slot-finality-protocol/14920) + +## Outline + +- Single Slot Finality +- MaxEB +- Inclusion lists +- PeerDAS +- SSLE + +## Additional reading and exercises + +- [Paths toward single-slot finality, 2022](https://notes.ethereum.org/@vbuterin/single_slot_finality) +- [Notes on SSF, Lincoln Murr](https://publish.obsidian.md/single-slot-finality/Welcome+to+My+Research!) \ No newline at end of file diff --git a/docs/eps/week3.md b/docs/eps/week3.md index 439307e8..de1d859c 100644 --- a/docs/eps/week3.md +++ b/docs/eps/week3.md @@ -40,5 +40,6 @@ Additionally, you can read and get ready by studying the following resources: - [Slashing scenario explanation by Dankrad Feist](https://dankradfeist.de/ethereum/2022/03/24/run-the-majority-client-at-your-own-peril.html) - [Beacon Chain design mistakes by Justin Drake](https://www.youtube.com/watch?v=10Ym34y3Eoo) - [Casper and Consensus from Devcon 3](https://archive.devcon.org/archive/watch/3/casper-and-consensus/?tab=YouTube) +- [Anatomy of a slot](https://www.youtube.com/watch?v=EswDO0kL_O0) After learning about both EL and CL, run a client pair. Spin a pair of one execution and consensus client, read their logs to learn how they operate. diff --git a/docs/eps/week7-research.md b/docs/eps/week7-research.md index 6f16c78c..55c1d8e2 100644 --- a/docs/eps/week7-research.md +++ b/docs/eps/week7-research.md @@ -12,7 +12,7 @@ Before starting with the week 7 development content, make yourself familiar with Additionally, you can read and get ready by studying the following resources: -- [Data structures in Ethereum](/wiki/protocol/data-structures.md) +- [Data structures in Ethereum](/wiki/EL/data-structures.md) - [Guillaume Ballet - The Verge](https://www.youtube.com/watch?v=F1Ne19Vew6w) ## Outline diff --git a/docs/eps/week9-research.md b/docs/eps/week9-research.md index 6034b52d..0858d515 100644 --- a/docs/eps/week9-research.md +++ b/docs/eps/week9-research.md @@ -13,7 +13,7 @@ Before starting with the week 9 research content, make yourself familiar with re Additionally, you can get ready by studying the following resources: - [Statelessness and history expiry, Ethereum.org](https://ethereum.org/en/roadmap/statelessness/) - [Portal Network web](https://www.ethportal.net/) -- [EL Data structure](https://epf.wiki/#/wiki/protocol/data-structures) +- [EL Data structure](https://epf.wiki/#/wiki/EL/data-structures) ## Outline diff --git a/docs/wiki/EL/evm.md b/docs/wiki/EL/evm.md index 31f6119d..e49b3c89 100644 --- a/docs/wiki/EL/evm.md +++ b/docs/wiki/EL/evm.md @@ -70,7 +70,7 @@ Ethereum has two kinds of accounts: - **External account:** An account [controlled by an associated private key](/wiki/Cryptography/ecdsa.md) and empty EVM code. - **Contract account:** An account controlled by an associated non-empty EVM code. The EVM code as part of such an account is colloquially known as a _smart contract._ -Refer [Ethereum data structures](wiki/protocol/data-structures.md) for details on how the world state is implemented. +Refer [Ethereum data structures](wiki/EL/data-structures.md) for details on how the world state is implemented. ## Virtual machine paradigm From 55869150a797b55b694a3ff8940f19b102f415c2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?M=C3=A1rio=20Havel?= <61149543+taxmeifyoucan@users.noreply.github.com> Date: Mon, 22 Apr 2024 16:53:02 +0200 Subject: [PATCH 101/101] Week 10 update --- docs/eps/week10-dev.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/eps/week10-dev.md b/docs/eps/week10-dev.md index 23183c2c..35375d65 100644 --- a/docs/eps/week10-dev.md +++ b/docs/eps/week10-dev.md @@ -1,6 +1,6 @@ # Study Group Week 10 | Precompiles -Week 10 dev talk is focused on history expiry and dives into Portal Network, an overlay network for light clients enabling alternative access to current and historical data. +Week 10 dev talk is diving into EVM precompiles and their integration in execution clients. Join the presentation by [Danno Ferrin](https://twitter.com/shemnon), on [Monday, April 22, 4PM UTC](https://savvytime.com/converter/utc-to-germany-berlin-united-kingdom-london-china-shanghai-ny-new-york-city-japan-tokyo-australia-sydney-india-delhi-argentina-buenos-aires/apr-22-2024/4pm). @@ -28,4 +28,4 @@ Additionally, you can get ready by studying the following resources: - [EVM Precompiled and System Contract Catalog](https://github.com/shemnon/precompiles/) - [RollCall breakout on precompiles](https://www.youtube.com/watch?v=tg01COfxi_M) -- [Custom RPCs and Precompiles for Hyperledger Besu](https://www.youtube.com/watch?v=djL5nczlYFw) \ No newline at end of file +- [Custom RPCs and Precompiles for Hyperledger Besu](https://www.youtube.com/watch?v=djL5nczlYFw)

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+ZKSNARK +ZKSNARKs +Zaverucha +bilinear +bilinearity +cdot +dx +frac +homomorphic +ldots +moduli +neq +prover +rightarrow +unguessable +verifier +verifiers +Preconfirm +Zksync +incentivized From 6cf1d3242c0c4149e8d58e1b8f08510a2c1f15fc Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 20 Apr 2024 11:42:01 +0800 Subject: [PATCH 094/101] typos and spelling errors fixed --- docs/contributing.md | 2 +- docs/eps/week2.md | 2 +- docs/readme.md | 4 ++-- docs/topics.md | 2 +- docs/wiki/Cryptography/keccak256.md | 2 +- docs/wiki/protocol/data-structures.md | 8 ++++---- docs/wiki/research/scaling/core-changes/eip-4844.md | 10 +++++----- wordlist.txt | 2 ++ 8 files changed, 17 insertions(+), 15 deletions(-) diff --git a/docs/contributing.md b/docs/contributing.md index a004bd26..7e727420 100644 --- a/docs/contributing.md +++ b/docs/contributing.md @@ -6,7 +6,7 @@ The Protocol Wiki is an open and collaborative project. Whether you are part of When creating contributions, consider whether it doesn't exist in another form elsewhere. Use it and reference it in your text but do not copy its content. Focus on adding it into a big picture, connecting it with related topics. -Write contributions based on what you learned about the protocol along the way, what experience you gathered and missing pieces that slowed you down. Consider it as explaining to your peers, reflect on your own journey as a core developer/reseacher. +Write contributions based on what you learned about the protocol along the way, what experience you gathered and missing pieces that slowed you down. Consider it as explaining to your peers, reflect on your own journey as a core developer/researcher. ## Contributing diff --git a/docs/eps/week2.md b/docs/eps/week2.md index 451fa24c..4f6ef77e 100644 --- a/docs/eps/week2.md +++ b/docs/eps/week2.md @@ -18,7 +18,7 @@ Before starting with week 2 content, make yourself familiar with resources in [w Additionally, you should read through the following documents to prepare for the presentation: * [Nodes and clients](https://ethereum.org/developers/docs/nodes-and-clients) -* [Ethereum: mechanics](https://cs251.stanford.edu/lectures/lecture7.pdf) (a lecture based on these slides is also available on YouTube: [An Overview of the Ethereum Excecution Layer - Dan Boneh](https://www.youtube.com/watch?v=7sxBjSfmROc)) +* [Ethereum: mechanics](https://cs251.stanford.edu/lectures/lecture7.pdf) (a lecture based on these slides is also available on YouTube: [An Overview of the Ethereum Execution Layer - Dan Boneh](https://www.youtube.com/watch?v=7sxBjSfmROc)) ## Outline diff --git a/docs/readme.md b/docs/readme.md index b1ea3b68..2d26da4b 100644 --- a/docs/readme.md +++ b/docs/readme.md @@ -1,8 +1,8 @@ # Welcome to the protocol -The protocol wiki is a collection of technical resources about the Ethereum protocol. This includes information about the core protocol theory, client development and ongoing research. It's not intented for smart contract or other high level development. +The protocol wiki is a collection of technical resources about the Ethereum protocol. This includes information about the core protocol theory, client development and ongoing research. It's not intended for smart contract or other high level development. -> :warning: Protocol Wiki is under contruction, [join us](/eps/intro.md) and [contribute](contributing.md). +> :warning: Protocol Wiki is under construction, [join us](/eps/intro.md) and [contribute](contributing.md). ![](https://raw.githubusercontent.com/eth-protocol-fellows/protocol-studies/wiki-pages/docs/images/epfsg_hero.jpg) diff --git a/docs/topics.md b/docs/topics.md index e0ee40eb..58219a75 100644 --- a/docs/topics.md +++ b/docs/topics.md @@ -61,7 +61,7 @@ [Roadmap] ### S -[Statlessness] +[Statelessness] [SSF] [SSZ] diff --git a/docs/wiki/Cryptography/keccak256.md b/docs/wiki/Cryptography/keccak256.md index 1830e02b..471ee73b 100644 --- a/docs/wiki/Cryptography/keccak256.md +++ b/docs/wiki/Cryptography/keccak256.md @@ -26,7 +26,7 @@ The sponge function, central to Keccak's design, operates in two distinct phases For a deeper understanding of Keccak's internal workings, the [Keccak reference](https://keccak.team/files/CSF-0.1.pdf) provides detailed insights into its algorithms and security features. ## EVM Implementation -The EVM (Ethereum Virtual Machine) processes the excution of transactions for the Ethereum blockchain with a stack based architecture. EVM opcodes are predefined instructions that the EVM interprets and subsequently executes to fulfill transaction and run the smart contracts. There are arthmetic, environmental, control flow, and stack operations Opcodes. Now there is no keccak256 opcode, but there is a SHA3 opcode. The SHA3 opcode is used to encrypt input data from the stack and outputs a Keccak256 hash. +The EVM (Ethereum Virtual Machine) processes the execution of transactions for the Ethereum blockchain with a stack based architecture. EVM opcodes are predefined instructions that the EVM interprets and subsequently executes to fulfill transaction and run the smart contracts. There are arithmetic, environmental, control flow, and stack operations Opcodes. Now there is no keccak256 opcode, but there is a SHA3 opcode. The SHA3 opcode is used to encrypt input data from the stack and outputs a Keccak256 hash. The [Ethereum Yellow Paper](https://ethereum.github.io/yellowpaper/paper.pdf), outlines other implementations of Keccak256 in the Ethereum blockchain: diff --git a/docs/wiki/protocol/data-structures.md b/docs/wiki/protocol/data-structures.md index cbc3cd34..727bed5a 100644 --- a/docs/wiki/protocol/data-structures.md +++ b/docs/wiki/protocol/data-structures.md @@ -2,17 +2,17 @@ ## Primer on Merkle Tree -Merkle tree is a hash-based data structure which is very effecient at data integrity and verification. It is a tree based structure where the leaf nodes hold the data values and each non-leaf node is a hash of its child nodes. +Merkle tree is a hash-based data structure which is very efficient at data integrity and verification. It is a tree based structure where the leaf nodes hold the data values and each non-leaf node is a hash of its child nodes. A Merkle tree stores all the transactions in a block by producing a digital fingerprint of the entire set of transactions. It allows the user to verify whether a transaction is included in a block or not. Merkle trees are created by repeatedly calculating hashing pairs of nodes until there is only one hash left. This hash is called the **Merkle Root**, or the Root Hash. The Merkle Trees are constructed in a bottom-up approach. It is important to note that Merkle trees are in a **binary tree**, so it requires an even number of leaf nodes. If there is an odd number of transactions, the last hash will be duplicated once to create an even number of leaf nodes. Merkle Trees provide a tamper-proof structure to store transaction data. Hash functions have an Avalanche Effect i.e. a small change in the data will result in a huge change in the resulting hash. Hence, if the data in the leaf nodes are ever modified, the Root Hash will not match the expected value. -You can try out [SHA-256](https://emn178.github.io/online-tools/sha256.html) hashing function youself as well. +You can try out [SHA-256](https://emn178.github.io/online-tools/sha256.html) hashing function yourself as well. To learn more about Hashing, you may refer to [this](https://github.com/ethereumbook/ethereumbook/blob/develop/04keys-addresses.asciidoc) -Merkle Root is stored in the **Block Header**. Read more about the strucutre of a Block inside Ethereum (_will be linked this to relevant doc once its ready_) +Merkle Root is stored in the **Block Header**. Read more about the structure of a Block inside Ethereum (_will be linked this to relevant doc once its ready_) The main parent node is called Root, hence the hash inside is Root Hash. There is infinitesimally small chance(1 in 1.16x10^77 for a single SHA-256 hash) to create two different states with the same root hash, and any attempt to modify state with different values will result in a different state root hash. @@ -31,7 +31,7 @@ More on [Merkle Trees in Ethereum](https://blog.ethereum.org/2015/11/15/merkling ## Primer on Patricia Tree -Patricia Tries(also called Radix tree) are n-ary trees which unlike Merkel Trees,is used for storage of data instead of verification. +Patricia Tries(also called Radix tree) are n-ary trees which unlike Merkle Trees,is used for storage of data instead of verification. Simply put, Patricia Tries is a tree data structure where all the data is store in the leaf nodes, and each non-leaf nodes is a character of a unique string identifying the data. Using the unique string we navigate through the character nodes and finally reach the data. Hence, it is very efficient at data retrieval. diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index b5b91b22..86ce4bd4 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -45,11 +45,11 @@ Is important to note that Blobs will not be added to the block to which they bel KZG commitments are a type of cryptographic commitment particularly useful for their efficiency in creating and verifying proofs of data availability and correctness. -KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correcteness. +KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correctness. Check the following links to learn more: -- [KZG Cerymony](https://github.com/ethereum/kzg-ceremony) +- [KZG Ceremony](https://github.com/ethereum/kzg-ceremony) - [Arithmetic hash based alternatives to KZG for proto-danksharding (EIP-4844)](https://ethresear.ch/t/arithmetic-hash-based-alternatives-to-kzg-for-proto-danksharding-eip-4844/13863) - [Sharding multi-party computation ceremony](https://ethresear.ch/t/sharding-multi-party-computation-ceremony/11779) @@ -66,7 +66,7 @@ The node receiving the sidecar should verify that blob sidecar is well-formatted This "sidecars" design provides forward compatibility for further data increases by black-boxing [is_data_available](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/fork-choice.md#is_data_available), which means that in future upgrades `is_data_available()` implementation may change, for example to include data-availability-sampling (DAS), and the system interacting with this function is not required to understand the inner implementation of the function (in programming terms, `is_data_available()` can be considered as an interface method where the implementation may change over time). -#### 3. Inclusion of KZG Committment versioned hashes +#### 3. Inclusion of KZG Commitment versioned hashes The Consensus Layer (CL, also called Beacon chain) calls the [`process_execution_payload`](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) function when a new block payload is submitted to the chain. This function is responsible to perform some validity checks on the block's payload and then invoke the Execution Layer (EL) via the `verify_and_notify_new_payload` function. @@ -78,7 +78,7 @@ Once invoked, the EL will: With EIP-4844, the `process_execution_payload` adds the parameter `versioned_hashes` to be passed to the `verify_and_notify_new_payload` function. -`versioned_hashes` is an array of [hashes](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) for each blob of KZG Committment. +`versioned_hashes` is an array of [hashes](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) for each blob of KZG Commitment. #### 4. Execution Payload and Execution Payload Header @@ -132,7 +132,7 @@ blob_gas_used += get_total_blob_gas(tx) #### 2. New Transaction Data Structure (BLOB_TX_TYPE) -Before EIP-4844, the Transaction data structure was the following ([ethereum exeuction-specs repository](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49C1-L108C2)): +Before EIP-4844, the Transaction data structure was the following ([ethereum execution-specs repository](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49C1-L108C2)): ```python @slotted_freezable diff --git a/wordlist.txt b/wordlist.txt index 6298f0b3..a52b7728 100644 --- a/wordlist.txt +++ b/wordlist.txt @@ -474,3 +474,5 @@ verifiers Preconfirm Zksync incentivized +EPSsg +licence From 09b3c60da9bfa5e7726324d8cd13d3df62f3f132 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 20 Apr 2024 12:23:22 +0800 Subject: [PATCH 095/101] Preconfs flow through MEV boost section is added --- .../BasedSequencingPreconfs.md | 55 +++++++++++++++++++ 1 file changed, 55 insertions(+) diff --git a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md index 30a43922..7646cad4 100644 --- a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md +++ b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md @@ -96,7 +96,62 @@ _Figure: Look-ahead mechanism for Preconfirmations, Credit Justin Drake_ - **Sharing of the Preconfirmation:** The promise made by the proposer may need to be communicated to others in the network, especially if there are multiple proposers who might include the transaction before the proposer’s slot arrives. This communication can be facilitated through various means, including MEV boost relays, to ensure that the transaction is settled and included appropriately. - **Execution of the Transaction:** Once the proposer’s turn comes, and if they have not been preempted by an earlier proposer, they include the preconfirmed transaction in the block they are proposing. This ensures that the transaction is executed on-chain as was promised to the user. +### [Communication through MEV Boost](#communication-through-mev-boost) +The integration of preconfirmations with MEV Boost represents a critical aspect of the technical construction, facilitating the efficient flow of information between users, proposers, builders, and the Ethereum network. By routing preconfirmation details through MEV Boost, the system ensures that builders are aware of preconfirmed transactions and can construct blocks accordingly. This process not only optimizes the inclusion of transactions but also maintains the integrity and value of the constructed blocks, aligning with the overarching goals of the Ethereum sequencing and pre-confirmation framework. + +## [Preconfirmations Flow through MEV Boost](#preconfirmations-flow-through-mev-boost) + + +```mermaid +sequenceDiagram + participant U as User + participant P as Proposer + participant R as MEV Boost/Relays + participant B as Builders + participant BC as Beacon Chain + + U->>+P: Request Preconfirmation + P-->>-U: Promise Preconfirmation + P->>+R: Send Preconfirmation Promise + R->>+B: Relay Promise to Builders + B-->>-R: Build Block with Preconfirmed Tx + R->>+P: Send Block to Proposer + P->>+BC: Propose Block on Beacon Chain + BC-->>-U: Execute and Finalize Tx +``` + +*Figure: Preconfirmations Flow through MEV Boost* + + +The process of how preconfirmations would flow through MEV Boost within the context of Ethereum's base layer sequencing and preconfirmations involves several key steps and entities and it is valuable to discuss in details. This mechanism aims to ensure that transactions preconfirmed by proposers (who have opted into providing sequencing services) are communicated effectively to builders through Relays in MEV Boost and ultimately included in the constructed blocks. Here's a detailed step-by-step explanation of the process: + +- **User Requests Preconfirmation:** + - A user identifies proposers within the beacon chain's look-ahead period who have opted into providing based sequencing by posting collateral. + - The user then sends a preconfirmation request to one of these proposers, seeking assurance that their transaction will be included and executed in a future slot. + +- **Proposer Provides Preconfirmation:** + - The selected proposer evaluates the request and, if accepted, provides the user with a preconfirmation. This preconfirmation is essentially a promise to include and execute the user's transaction in a specified future slot, subject to certain conditions and penalties for non-fulfillment. + +- **Proposer to MEV Boost Communication:** + - Once a proposer issues a preconfirmation, they communicate this information to MEV Boost. MEV Boost acts as an intermediary that facilitates the communication between proposers (now acting as sequencers for their respective slots), builders, and ultimately, the Ethereum network. + +- **MEV Boost Relays Preconfirmations to Builders:** + - MEV Boost relays the preconfirmation details to builders, who are responsible for constructing the blocks. Builders receive information about all preconfirmed transactions, which they must consider while building their blocks. + +- **Builders Construct Blocks Considering Preconfirmations:** + - With the preconfirmation details at hand, builders construct blocks that honor these preconfirmations. This involves including the preconfirmed transactions in the block for the specified slot and ensuring that the execution conditions promised in the preconfirmations are met. + +- **Blocks Are Proposed to the Network:** + - Once builders construct a block that respects all preconfirmations and optimizes for other factors (like MEV), the block is proposed to the Ethereum network. The proposer for the relevant slot, who initially issued the preconfirmation, is responsible for ensuring that this block gets submitted. + +- **Execution and Settlement:** + - If the block is successfully included in the blockchain, the preconfirmed transactions are executed as promised, fulfilling the proposer's commitment to the user. If a proposer fails to fulfill the preconfirmation, penalties (slashing) may be applied depending on the nature of the fault (e.g., liveness fault, safety fault). + +**Additional Considerations:** + +- **Slashing Mechanism:** The process incorporates a slashing mechanism to penalize proposers if they fail to honor their preconfirmations. This ensures a level of accountability and trust in the system. +- **Dynamic Communication:** The flow of information through MEV Boost allows for dynamic adjustments based on real-time conditions, such as changes in transaction priority or network congestion. ## Resources From 5716f63bc41eb80dfb1550e47e7003fc10e20589 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 20 Apr 2024 13:21:08 +0800 Subject: [PATCH 096/101] future areas of research section is added --- .../BasedSequencingPreconfs.md | 19 +++++++++++++++++++ wordlist.txt | 1 + 2 files changed, 20 insertions(+) diff --git a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md index 7646cad4..c3ae3251 100644 --- a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md +++ b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md @@ -153,6 +153,25 @@ The process of how preconfirmations would flow through MEV Boost within the cont - **Slashing Mechanism:** The process incorporates a slashing mechanism to penalize proposers if they fail to honor their preconfirmations. This ensures a level of accountability and trust in the system. - **Dynamic Communication:** The flow of information through MEV Boost allows for dynamic adjustments based on real-time conditions, such as changes in transaction priority or network congestion. +## [Future Areas of Research](#future-areas-of-research) + +Previous discussions on Ethereum Based Sequencing with Preconfirmations[^4] revealed that the design space of this framework involves many complex topics and left with several open questions and concerns raised by community. Below are the some of the areas of research and complexities involved: + +- **Suboptimal Block Value**: Preconfirmations could lead to less valuable blocks for validators, as constraints imposed by preconfirmed transactions could limit MEV opportunities. +- **Complexity with Multiple Preconfirms**: Managing and coordinating multiple preconfirms can complicate the execution state and challenge the uniformity of transaction sequencing. +- **Pricing and Economic Incentives**: Determining the right price for preconfirmation tips is complex, as preconfirms could affect the expected MEV and thus the economic incentives for proposers and users. +- **Execution Guarantees**: Variability in the execution guarantees of preconfirms might require different levels of sophistication from proposers, with more complex preconfirms potentially necessitating higher capabilities. +- **Centralization Risks**: Some expressed concerns that the preconfirmation system could lead to centralization, with a few entities controlling the sequence of transactions. +- **Liveness and Safety Faults**: Understanding and implementing the proper response to liveness and safety faults within the system, including the correct attribution of faults and management of associated slashing, is complex. +- **Infrastructure Requirements**: The need for validators to run full nodes, manage bandwidth, and provide Denial-of-Service protection adds to the operational complexity. +- **Collateral Posting**: Managing the posting and efficiency of collateral for preconfirms is a significant consideration, particularly concerning the scaling of collateral relative to the value of transactions. +- **User Experience**: How users experience the process, including the speed and reliability of preconfirmations, and the transparency of the system. +- **Relay Trust**: Trust in relays and their role in the preconfirmation process, considering that relays must balance the interests of various network participants and manage the associated risks. +- **Communication Channels**: Establishing secure and efficient channels for communication between users, proposers, relays, and builders. +- **Lookahead and Selection Mechanisms**: The lookahead mechanism's impact on preconfer selection and whether an alternative selection mechanism would be more advantageous. +- **Layer 1 and Layer 2 Coordination**: Coordinating between Beacon Chain proposers and Layer 2 sequencers, particularly with rollups designating their own sequencers, can be challenging. +- **Legal and Regulatory Considerations**: Potential legal and regulatory implications of the preconfirmation process, especially regarding financial transactions. +- **Technological Adaptability**: The need for the system to adapt to new technologies, like the eventual integration of execution tickets, which could alter the preconfirmation landscape. ## Resources - [Ethereum Sequencing](https://docs.google.com/presentation/d/1v429N4jdikMIWWkcVwfjMlV2LlOXSawFCMKoBnZVDNU/) diff --git a/wordlist.txt b/wordlist.txt index a52b7728..a55e957d 100644 --- a/wordlist.txt +++ b/wordlist.txt @@ -476,3 +476,4 @@ Zksync incentivized EPSsg licence +Preconfirms \ No newline at end of file From b3cb69808f70629391f03fdf2f97d047403c501d Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 20 Apr 2024 13:22:23 +0800 Subject: [PATCH 097/101] typos fixed --- docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md index c3ae3251..e1612fb5 100644 --- a/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md +++ b/docs/wiki/research/Preconfirmations/BasedSequencingPreconfs.md @@ -98,7 +98,7 @@ _Figure: Look-ahead mechanism for Preconfirmations, Credit Justin Drake_ ### [Communication through MEV Boost](#communication-through-mev-boost) -The integration of preconfirmations with MEV Boost represents a critical aspect of the technical construction, facilitating the efficient flow of information between users, proposers, builders, and the Ethereum network. By routing preconfirmation details through MEV Boost, the system ensures that builders are aware of preconfirmed transactions and can construct blocks accordingly. This process not only optimizes the inclusion of transactions but also maintains the integrity and value of the constructed blocks, aligning with the overarching goals of the Ethereum sequencing and pre-confirmation framework. +The integration of preconfirmations with MEV Boost represents a critical aspect of the technical construction, facilitating the efficient flow of information between users, proposers, builders, and the Ethereum network. By routing preconfirmation details through MEV Boost, the system ensures that builders are aware of preconfirmed transactions and can construct blocks accordingly. This process not only optimizes the inclusion of transactions but also maintains the integrity and value of the constructed blocks, aligning with the overarching goals of the Ethereum sequencing and preconfirmation framework. ## [Preconfirmations Flow through MEV Boost](#preconfirmations-flow-through-mev-boost) From 40398edf0d958ee024a936667027a8972d4ed8a2 Mon Sep 17 00:00:00 2001 From: Bruce Xu Date: Sun, 21 Apr 2024 23:55:52 +1200 Subject: [PATCH 098/101] Fix incorrect week number --- docs/eps/week3.md | 2 +- docs/eps/week4.md | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/eps/week3.md b/docs/eps/week3.md index be567662..439307e8 100644 --- a/docs/eps/week3.md +++ b/docs/eps/week3.md @@ -6,7 +6,7 @@ Watch the presentation on overview of the CL with Alex Stokes on [StreamEth](htt [recording](https://streameth.org/embed/?playbackId=66a30awapcuiok0z&vod=true&streamId=&playerName=Consensus+Layer+Overview+%7C+Alex+Stokes+%7C+Week+3 ':include :type=iframe width=100% height=520 frameborder="0" allow="fullscreen" allowfullscreen') -For written summary of week 2 presentation, check the [notes](https://github.com/eth-protocol-fellows/protocol-studies/files/14850973/Week.3.EPFsg.Consensus.Layer.Overview.pdf) +For written summary of week 3 presentation, check the [notes](https://github.com/eth-protocol-fellows/protocol-studies/files/14850973/Week.3.EPFsg.Consensus.Layer.Overview.pdf) For archive of the discussion during the talk, check [this thread](https://discord.com/channels/1205546645496795137/1214219045205835776/1214219052969492541) in our Discord server. diff --git a/docs/eps/week4.md b/docs/eps/week4.md index 99b9c3ed..1ec8004c 100644 --- a/docs/eps/week4.md +++ b/docs/eps/week4.md @@ -9,7 +9,7 @@ Watch the presentation on Ethereum core testing infrastracture on [Youtube](http [recording](https://www.youtube.com/embed/PQVW5dJ8J0c?si=fv5ww4_6zInGXpjO ':include :type=iframe width=100% height=560 frameborder="0" allow="fullscreen" allowfullscreen encrypted-media gyroscope picture-in-picture web-share') -For written summary of week 2 presentation, check the [notes](https://github.com/eth-protocol-fellows/protocol-studies/files/14850974/Week.4.EPFsg.Test.Security.Overview.pdf) +For written summary of week 4 presentation, check the [notes](https://github.com/eth-protocol-fellows/protocol-studies/files/14850974/Week.4.EPFsg.Test.Security.Overview.pdf) For archive of the discussion during the talk, check [this thread](https://discord.com/channels/1205546645496795137/1216771776810455160/1216771782040621118) in our Discord server. From 9a236105a48ad6c612523f05529ff114ed6f9a77 Mon Sep 17 00:00:00 2001 From: taxmeifyoucan Date: Mon, 22 Apr 2024 12:58:54 +0200 Subject: [PATCH 099/101] resolve conficts --- docs/_sidebar.md | 41 ++-- docs/wiki/{protocol => EL}/data-structures.md | 0 .../research/scaling/core-changes/eip-4844.md | 1 + wordlist.txt | 227 +++++++++--------- 4 files changed, 139 insertions(+), 130 deletions(-) rename docs/wiki/{protocol => EL}/data-structures.md (100%) diff --git a/docs/_sidebar.md b/docs/_sidebar.md index 753e94e3..b4cd0e4b 100644 --- a/docs/_sidebar.md +++ b/docs/_sidebar.md @@ -6,33 +6,44 @@ - [Week 1](/eps/week1.md) - [Week 2](/eps/week2.md) - [Week 3](/eps/week3.md) + - [Week 4](/eps/week4.md) + - [Week 5](/eps/week5.md) + - [Node Workshop](/eps/nodes_workshop.md) + - [Week 6 | Dev](/eps/week6-dev.md) + - [Week 6 | Research](/eps/week6-research.md) + - [Week 7 | Dev](/eps/week7-dev.md) + - [Week 7 | Research](/eps/week7-research.md) + - [Week 8 | Dev](/eps/week8-dev.md) + - [Week 8 | Research](/eps/week8-research.md) + - [Week 9 | Dev](/eps/week9-dev.md) + - [Week 9 | Research](/eps/week9-research.md) + - [Week 10 | Dev](/eps/week10-dev.md) - [Contributing](contributing.md) - **Protocol Wiki** - The Protocol - [Overview](/wiki/protocol/overview.md) - [History](/wiki/protocol/history.md) - - [Coordination](/wiki/protocol/pm.md) - - [Data Structures](/wiki/protocol/data-structures.md) - - [CS Resources] - Execution Layer - [EL Clients](/wiki/EL/el-clients.md) - [EL Specs](/wiki/EL/el-specs.md) - Client architecture - - [EVM] - - [Transaction] + - [EVM](/wiki/EL/evm.md) + - [Transaction anatomy](/wiki/EL/transaction.md) + - [JSON-RPC](/wiki/EL/JSON-RPC.md) + - [Data Structures](/wiki/EL/data-structures.md) - [DevP2P] - - [MPT] - - [JSON-RPC] -- Consensus Layer + - [Precompiled Contracts](/wiki/EL/precompiled-contracts.md) +- [Consensus Layer](/wiki/CL/overview.md) - [CL Clients](/wiki/CL/cl-clients.md) - [CL Specs](/wiki/CL/cl-specs.md) + - Client architecture - [Proof-of-Stake] - [Beacon API] - [Networking](/wiki/CL/cl-networking.md) - - Client architecture - Development - [Core development](/wiki/dev/core-development.md) - - [Network upgrades](/wiki/dev/upgrades.md) + - [Coordination](/wiki/protocol/pm.md) + - [CS Resources] - Testing and security - [Testing overview](/wiki/testing/overview.md) - [Incidents](/wiki/testing/incidents.md) @@ -43,8 +54,6 @@ - [Scaling](/wiki/research/scaling/scaling.md) - [Core Changes](/wiki/research/scaling/core-changes/core-changes.md) - [EIP-4844](/wiki/research/scaling/core-changes/eip-4844.md) - - Blobs - - Sharding - Statelessness - Purge - MEV @@ -64,12 +73,14 @@ - [Preconfirmations](/wiki/research/Preconfirmations/Preconfirmations.md) - [Based Sequencing with Preconfs](/wiki/research/Preconfirmations/BasedSequencingPreconfs.md) - [Cryptography](/wiki/Cryptography/intro.md) - - [ECDSA](/wiki/Cryptography/ecdsa.md) + - [ECDSA](/wiki/Cryptography/ecdsa.md) + - [Keccak256](/wiki/Cryptography/keccak256.md) - BLS - [Commitments] - Polynomials - - [KZG Commitment scheme](/wiki/Cryptography/KZG.md) + - Commitment schemes - ZK + - [Post-Quantum Cryptography](/wiki/Cryptography/post-quantum-cryptography.md) - [Protocol Fellowship](/wiki/epf.md) - **Wiki Info** @@ -77,4 +88,4 @@

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zlsS+x_h7WcgQ>?$eCAvgfug&E5tHsZTAXpg6a;gqMWg`?Cl;vnqMEmGA6$N`He#Zj z@j%wZx_VcNncQgS9xeJEjr=>Hz0q!o619}HzBOaq=h1gpqMvFpKETGtS~@U3|KkKP zNePRyQ{BUKLgk-g_z#|a!?8r#KaHl-YyZP$KjOVhRr?~4N?d_I zve9&YgC8yidU zZhg-{o#1Y3_CCAMit{}g;N1e2uh!o#wNPT|0byj}2LasnMoL7%ISc9$Qrko<$6_{VA8%t9#le=HI6A9~sLcNyCA;Pv9e%ep%+4v6 zr;p6+V95!|a=5C;a{jzrrZ=~-md9-0{Kt!xI2eoe-6Sl_Gw`sUKValR6$vKR;5zhs8rcl*ABbl7j=npKB5JP(kz|9sR_m z>PbbjBSJ;Et>PELe5oHG6b-ndAnHx6>Hcs0@J|c(l>W0=SCpX5rH%v@{emtPR5y+4 zI{$ywcok}Ay`A~s@k^DKirSm~4Lla0s(JM?g71u?!o{8*3d>!>KyOsjXnqMMmcZbt U&WTzV&tR!^|AJ}~)gQn8AL{i%P5=M^ diff --git a/docs/wiki/research/scaling.md b/docs/wiki/research/scaling.md index 243c205b..6d2a5b9e 100644 --- a/docs/wiki/research/scaling.md +++ b/docs/wiki/research/scaling.md @@ -86,6 +86,4 @@ Resources: [Combining GHOST and Casper](https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf), [archived](https://web.archive.org/web/20230907004049/https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf) -[EIP-3675: Upgrade consensus to Proof-of-Stake](https://eips.ethereum.org/EIPS/eip-3675), [archived](https://web.archive.org/web/20240213102133/https://eips.ethereum.org/EIPS/eip-3675) - [Ethereum Blocks](https://ethereum.org/developers/docs/blocks), [archived](https://web.archive.org/web/20240214052915/https://ethereum.org/developers/docs/blocks) \ No newline at end of file From e6816d426290cc95d46b5c8b7c25f7d6aa198db0 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Mon, 26 Feb 2024 17:30:19 +0100 Subject: [PATCH 014/101] Create history.md --- docs/wiki/protocol/history.md | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 docs/wiki/protocol/history.md diff --git a/docs/wiki/protocol/history.md b/docs/wiki/protocol/history.md new file mode 100644 index 00000000..e69de29b From 244932f1eab02ff76a86978da954f5207eaf72c8 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Mon, 26 Feb 2024 17:34:54 +0100 Subject: [PATCH 015/101] Update scaling.md --- docs/wiki/research/scaling.md | 2 -- 1 file changed, 2 deletions(-) diff --git a/docs/wiki/research/scaling.md b/docs/wiki/research/scaling.md index 6d2a5b9e..f38b27ac 100644 --- a/docs/wiki/research/scaling.md +++ b/docs/wiki/research/scaling.md @@ -70,8 +70,6 @@ Resources: [Ethereum Consensus Mechanism](https://ethereum.org/developers/docs/consensus-mechanisms), [archived](https://web.archive.org/web/20240214225609/https://ethereum.org/developers/docs/consensus-mechanisms) -[Gasper](https://ethereum.org/developers/docs/consensus-mechanisms/pos/gasper), [archived](https://web.archive.org/web/20240214225630/https://ethereum.org/developers/docs/consensus-mechanisms/pos/gasper) - [Ethereum Proof-of-Stake Consensus Specifications](https://github.com/ethereum/consensus-specs/tree/dev?tab=readme-ov-file#ethereum-proof-of-stake-consensus-specifications), [archived](https://web.archive.org/web/20240208050731/https://github.com/ethereum/consensus-specs/tree/dev) [Ethereum Proof-of-Stake Consensus Specifications](https://ethereum.github.io/consensus-specs/), [archived](https://web.archive.org/web/20240217155014/https://ethereum.github.io/consensus-specs/) From fee880ec25be29c16ce6d1d86d59112cdeb0ade3 Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Tue, 27 Feb 2024 12:25:17 +0100 Subject: [PATCH 016/101] added core changes section and updated directory structure --- docs/_sidebar.md | 3 +- docs/wiki/research/scaling/core-changes.md | 140 ++++++++++++++++++++ docs/wiki/research/{ => scaling}/scaling.md | 0 3 files changed, 142 insertions(+), 1 deletion(-) create mode 100644 docs/wiki/research/scaling/core-changes.md rename docs/wiki/research/{ => scaling}/scaling.md (100%) diff --git a/docs/_sidebar.md b/docs/_sidebar.md index 82376132..ed1c87f8 100644 --- a/docs/_sidebar.md +++ b/docs/_sidebar.md @@ -38,7 +38,8 @@ - Formal Verification - Research - [Roadmap overview](/wiki/research/roadmap.md) - - [Scaling](/wiki/research/scaling.md) + - [Scaling](/wiki/research/scaling/scaling.md) + - [Core Changes](/wiki/research/scaling/core-changes.md) - Blobs - Sharding - Statelessness diff --git a/docs/wiki/research/scaling/core-changes.md b/docs/wiki/research/scaling/core-changes.md new file mode 100644 index 00000000..02c0c78f --- /dev/null +++ b/docs/wiki/research/scaling/core-changes.md @@ -0,0 +1,140 @@ +# Changes to Ethereum core to accomplish scalability + +## Introduction + +L2 Rollups need to enable the permissionless reconstruction of the L2 state. To achieve this, they must ensure Data Availability, which refers to the global ordering of inputs for transactions that have altered the state. +Until EIP-4844 goes live on the Mainnet (expected in March 2023), Rollups have been storing Data Availability within a section of the transaction known as "calldata". Currently, this "calldata" represents the primary bottleneck for scaling Ethereum, as storing data in calldata is expensive. + +To accomplish scalability, the idea was initially to decrease transaction calldata gas cost with EIP-4488. However, this EIP is now irrelevant because EIP-4844 has been implemented instead, which as we will see in the following section, introduces a new data section inside the transactions called Blob. + +But before talking about the changes introduced by the EIP-4844, let's first understand the structure of an Ethereum transaction. + +## EIP-2718 + +[EIP-2718](https://github.com/ethereum/EIPs/blob/master/EIPS/eip-2718.md) introduced an envelope transaction type. The envelope makes possible to incapsulate transaction in a common header structure, allowing to change the transaction fields without breaking backwards compatibility. + +The envelope transaction type is defined as follows: + +`TransactionType || TransactionPayload` + +Where `TransactionType` is a 1 byte field identyfing the format of the transaction, and `TransactionPayload` is a variable length field which contains the actual transaction content. + +Same concept apply to receipts: + +`TransactionType || ReceiptPayload` + +Please note that the `||` is the byte/byte-array concatenation operator. + +This way, when defining new standards for a new type of transaction, the only concern is to ensure there are not duplicated `TransactionType` numbers. + +## Transaction data structure before EIP-4844 + +The following is the current transaction data structure of Ethereum as for the London upgrade (which included the latest update to the transaction format in EIP-1559). +The following python code can be found in the [ethereum exeuction-specs repository](https://github.com/ethereum/execution-specs). + +```python +@slotted_freezable +@dataclass +class LegacyTransaction: + nonce: U256 + gas_price: Uint + gas: Uint + to: Union[Bytes0, Address] + value: U256 + data: Bytes + v: U256 + r: U256 + s: U256 + +@slotted_freezable +@dataclass +class AccessListTransaction: + chain_id: U64 + nonce: U256 + gas_price: Uint + gas: Uint + to: Union[Bytes0, Address] + value: U256 + data: Bytes + access_list: Tuple[Tuple[Address, Tuple[Bytes32, ...]], ...] + y_parity: U256 + r: U256 + s: U256 + +@slotted_freezable +@dataclass +class FeeMarketTransaction: + chain_id: U64 + nonce: U256 + max_priority_fee_per_gas: Uint + max_fee_per_gas: Uint + gas: Uint + to: Union[Bytes0, Address] + value: U256 + data: Bytes + access_list: Tuple[Tuple[Address, Tuple[Bytes32, ...]], ...] + y_parity: U256 + r: U256 + s: U256 + +Transaction = Union[ + LegacyTransaction, AccessListTransaction, FeeMarketTransaction +] +``` + +The "calldata" is encoded inside the `data` field of the Transaction class. The "calldata" is accessible by the EVM, and the format to encode and decode it is specified in the [Contract ABI](https://docs.soliditylang.org/en/latest/abi-spec.html). + +## EIP-4844 + +[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces Blobs, a new space to store data that will be much cheaper than calldata because they will have a new type of gas that is independent of normal gas and follows its own targeting rule. +With the EIP-4844, the new Transaction data structure will be the following. + +```python +@slotted_freezable +@dataclass +class BlobTransaction: # the class name may change + chain_id: U64 + nonce: U256 + max_priority_fee_per_gas: Uint + max_fee_per_gas: Uint + gas: Uint + to: Union[Bytes0, Address] + value: U256 + data: Bytes + access_list: Tuple[Tuple[Address, Tuple[Bytes32, ...]], ...] + max_fee_per_blob_gas: U256 + blob_versioned_hashes: VersionedHash + y_parity: U256 + r: U256 + s: U256 +``` + +EIP-4844 will introduce two more fields in the Transaction class, which are `max_fee_per_blob_gas` and `blob_versioned_hashes`. +EIP-4844 introduced a new transaction type where `TransactionType == BLOB_TX_TYPE` and the `TransactionPayload` is the rlp encoding of the above class. + +### Changes on the Execution Specs + +TODO + +### Changes on the Consensus Specs + +TODO + +## EIP-4488 + +Initally [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488) was proposed to decrease the gas cost of calldata, and to add a limit of how much total transaction calldata can be in a block. The goal was to make Rollups transactions cheaper. +Currently, the cost for a non zero byte of calldata costs 16 units of gas. With this EIP, the cost for a byte of calldata (regardless if is 0 or a non zero byte) would be 3 bytes. + +This would have introduced the following parameters: + +| Parameter | Value | +| --------------------------- | --------- | +| NEW_CALLDATA_GAS_COST | 3 | +| BASE_MAX_CALLDATA_PER_BLOCK | 1,048,576 | +| CALLDATA_PER_TX_STIPEND | 300 | + +However, this EIP is now irrelevant because EIP-4844 has been implemented instead. Contrary to the original idea, the approach will be the exact opposite with EIP-7623. + +## EIP-7623 + +[EIP-7623](https://eips.ethereum.org/EIPS/eip-7623) is a very recent EIP created in February 2024, with the purpose of increasing calldata cost to decrease the maximum block size. diff --git a/docs/wiki/research/scaling.md b/docs/wiki/research/scaling/scaling.md similarity index 100% rename from docs/wiki/research/scaling.md rename to docs/wiki/research/scaling/scaling.md From 58e076c3ce45922ba921daf47353bfab8f6bbd42 Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Tue, 27 Feb 2024 12:59:55 +0100 Subject: [PATCH 017/101] Add "Inclusion of KZG Committment versioned hashes" as the first change in the consensus-specs introduced by the eip-4844 --- docs/wiki/research/scaling/core-changes.md | 20 ++++++++++++++++++-- 1 file changed, 18 insertions(+), 2 deletions(-) diff --git a/docs/wiki/research/scaling/core-changes.md b/docs/wiki/research/scaling/core-changes.md index 02c0c78f..b4c12e9a 100644 --- a/docs/wiki/research/scaling/core-changes.md +++ b/docs/wiki/research/scaling/core-changes.md @@ -3,7 +3,7 @@ ## Introduction L2 Rollups need to enable the permissionless reconstruction of the L2 state. To achieve this, they must ensure Data Availability, which refers to the global ordering of inputs for transactions that have altered the state. -Until EIP-4844 goes live on the Mainnet (expected in March 2023), Rollups have been storing Data Availability within a section of the transaction known as "calldata". Currently, this "calldata" represents the primary bottleneck for scaling Ethereum, as storing data in calldata is expensive. +Until EIP-4844 goes live on the Mainnet (expected in March 2024), Rollups have been storing Data Availability within a section of the transaction known as "calldata". Currently, this "calldata" represents the primary bottleneck for scaling Ethereum, as storing data in calldata is expensive. To accomplish scalability, the idea was initially to decrease transaction calldata gas cost with EIP-4488. However, this EIP is now irrelevant because EIP-4844 has been implemented instead, which as we will see in the following section, introduces a new data section inside the transactions called Blob. @@ -118,7 +118,23 @@ TODO ### Changes on the Consensus Specs -TODO +#### 1. Inclusion of KZG Committment versioned hashes + +The Consensus Layer (CL, also called Beacon chain) calls the [`process_execution_payload`](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) function when a new block payload is submitted to the chain. This function is responsible to perform some validity checks on the block's payload and then invoke the Execution Layer (EL) via the `verify_and_notify_new_payload` function. + +Once invoked, the EL will: + +- validate the block payload +- execute transactions inside the block payload +- update the state, which is the result of executing transactions +- build the new block +- return the new block to the CL + +With EIP-4844, the `process_execution_payload` adds the parameter `versioned_hashes` to be passed to the `verify_and_notify_new_payload` function. + +`versioned_hashes` is an array of [hashes](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) for each blob of KZG Committment, which are a type of cryptographic commitment particularly useful for their efficiency in creating and verifying proofs of data availability and correctness. + +KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correcteness. ## EIP-4488 From a62a6f6bbc833baca0b217fa120c002b9d6473e4 Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Tue, 27 Feb 2024 23:20:08 +0100 Subject: [PATCH 018/101] this commits add the changes required by the EL to support EIP-4844 and new custom types defined in the CL for EIP-4844 --- docs/wiki/research/scaling/core-changes.md | 30 +++++++++++++++++++++- 1 file changed, 29 insertions(+), 1 deletion(-) diff --git a/docs/wiki/research/scaling/core-changes.md b/docs/wiki/research/scaling/core-changes.md index b4c12e9a..1bb7397f 100644 --- a/docs/wiki/research/scaling/core-changes.md +++ b/docs/wiki/research/scaling/core-changes.md @@ -114,10 +114,33 @@ EIP-4844 introduced a new transaction type where `TransactionType == BLOB_TX_TYP ### Changes on the Execution Specs -TODO +The upgrade which will introduce EIP-4844 into the Execution Layer has been labeled **Cancun**. + +#### 1. Add checks inside the State Transition Function + +The EL now must check that the blob specific fields are valid for each transaction that is going to be executed in the State Transition Function (STF). + +The checks include: + +- check that the signer has enough balance to cover the cost of both transaction gas fee and blob gas fees +- check that the blob transaction contains at least 1 valid `blob_versioned_hash` (see CL changes) and that they are formatted correctly +- check that the user is willing to pay at least the current blob base fee + +Finally, the EL STF must keep track of the gas being gas used for blob transactions (same as it already happens for EIP1559 transactions). + +For the specs code, see [here](https://eips.ethereum.org/EIPS/eip-4844#execution-layer-validation) ### Changes on the Consensus Specs +The upgrade which will introduce EIP-4844 into the Consensus Layer has been labeled **Deneb**. + +#### Custom types + +| Name | SSZ equivalent | Description | +| --------------- | -------------- | ------------------------ | +| `VersionedHash` | `Bytes32` | _[New in Deneb:EIP4844]_ | +| `BlobIndex` | `uint64` | _[New in Deneb:EIP4844]_ | + #### 1. Inclusion of KZG Committment versioned hashes The Consensus Layer (CL, also called Beacon chain) calls the [`process_execution_payload`](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) function when a new block payload is submitted to the chain. This function is responsible to perform some validity checks on the block's payload and then invoke the Execution Layer (EL) via the `verify_and_notify_new_payload` function. @@ -136,6 +159,11 @@ With EIP-4844, the `process_execution_payload` adds the parameter `versioned_has KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correcteness. +#### 2. New Block Header checks + +TODO +see go-ethereum file consensus.go also mentioned in [week2](https://youtu.be/pniTkWo70OY?t=2773) + ## EIP-4488 Initally [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488) was proposed to decrease the gas cost of calldata, and to add a limit of how much total transaction calldata can be in a block. The goal was to make Rollups transactions cheaper. From 49091f574afc5709708b130925e71e1c223c0c8f Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Tue, 27 Feb 2024 23:21:58 +0100 Subject: [PATCH 019/101] change ordering in CL changes for EIP-4844 --- docs/wiki/research/scaling/core-changes.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/wiki/research/scaling/core-changes.md b/docs/wiki/research/scaling/core-changes.md index 1bb7397f..f226d263 100644 --- a/docs/wiki/research/scaling/core-changes.md +++ b/docs/wiki/research/scaling/core-changes.md @@ -134,14 +134,14 @@ For the specs code, see [here](https://eips.ethereum.org/EIPS/eip-4844#execution The upgrade which will introduce EIP-4844 into the Consensus Layer has been labeled **Deneb**. -#### Custom types +#### 1. Custom types | Name | SSZ equivalent | Description | | --------------- | -------------- | ------------------------ | | `VersionedHash` | `Bytes32` | _[New in Deneb:EIP4844]_ | | `BlobIndex` | `uint64` | _[New in Deneb:EIP4844]_ | -#### 1. Inclusion of KZG Committment versioned hashes +#### 2. Inclusion of KZG Committment versioned hashes The Consensus Layer (CL, also called Beacon chain) calls the [`process_execution_payload`](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) function when a new block payload is submitted to the chain. This function is responsible to perform some validity checks on the block's payload and then invoke the Execution Layer (EL) via the `verify_and_notify_new_payload` function. @@ -159,7 +159,7 @@ With EIP-4844, the `process_execution_payload` adds the parameter `versioned_has KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correcteness. -#### 2. New Block Header checks +#### 3. New Block Header checks TODO see go-ethereum file consensus.go also mentioned in [week2](https://youtu.be/pniTkWo70OY?t=2773) From 6247c60564cfc1e0c4ad155da0b165e5e4ca7bd2 Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Fri, 1 Mar 2024 09:08:50 +0100 Subject: [PATCH 020/101] add code examples for checks in the State Transition Function --- docs/wiki/research/scaling/core-changes.md | 24 ++++++++++++++++++++-- 1 file changed, 22 insertions(+), 2 deletions(-) diff --git a/docs/wiki/research/scaling/core-changes.md b/docs/wiki/research/scaling/core-changes.md index f226d263..60ffc552 100644 --- a/docs/wiki/research/scaling/core-changes.md +++ b/docs/wiki/research/scaling/core-changes.md @@ -120,15 +120,35 @@ The upgrade which will introduce EIP-4844 into the Execution Layer has been labe The EL now must check that the blob specific fields are valid for each transaction that is going to be executed in the State Transition Function (STF). -The checks include: +The checks include (For the specs code, see [here](https://eips.ethereum.org/EIPS/eip-4844#execution-layer-validation)): - check that the signer has enough balance to cover the cost of both transaction gas fee and blob gas fees + +```python +# modify the check for sufficient balance +max_total_fee = tx.gas * tx.max_fee_per_gas +if get_tx_type(tx) == BLOB_TX_TYPE: + max_total_fee += get_total_blob_gas(tx) * tx.max_fee_per_blob_gas +assert signer(tx).balance >= max_total_fee +``` + - check that the blob transaction contains at least 1 valid `blob_versioned_hash` (see CL changes) and that they are formatted correctly + +```python +assert len(tx.blob_versioned_hashes) > 0 +``` + - check that the user is willing to pay at least the current blob base fee +```python +assert tx.max_fee_per_blob_gas >= get_blob_base_fee(block.header) +``` + Finally, the EL STF must keep track of the gas being gas used for blob transactions (same as it already happens for EIP1559 transactions). -For the specs code, see [here](https://eips.ethereum.org/EIPS/eip-4844#execution-layer-validation) +```python +blob_gas_used += get_total_blob_gas(tx) +``` ### Changes on the Consensus Specs From 894b84021b5701cd77be4b1a1ff376946502e629 Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Fri, 1 Mar 2024 09:50:23 +0100 Subject: [PATCH 021/101] move eip-4844 in a separate file --- docs/wiki/research/scaling/core-changes.md | 157 ------------------- docs/wiki/research/scaling/eip-4844.md | 166 +++++++++++++++++++++ 2 files changed, 166 insertions(+), 157 deletions(-) create mode 100644 docs/wiki/research/scaling/eip-4844.md diff --git a/docs/wiki/research/scaling/core-changes.md b/docs/wiki/research/scaling/core-changes.md index 60ffc552..89dd9f49 100644 --- a/docs/wiki/research/scaling/core-changes.md +++ b/docs/wiki/research/scaling/core-changes.md @@ -27,163 +27,6 @@ Please note that the `||` is the byte/byte-array concatenation operator. This way, when defining new standards for a new type of transaction, the only concern is to ensure there are not duplicated `TransactionType` numbers. -## Transaction data structure before EIP-4844 - -The following is the current transaction data structure of Ethereum as for the London upgrade (which included the latest update to the transaction format in EIP-1559). -The following python code can be found in the [ethereum exeuction-specs repository](https://github.com/ethereum/execution-specs). - -```python -@slotted_freezable -@dataclass -class LegacyTransaction: - nonce: U256 - gas_price: Uint - gas: Uint - to: Union[Bytes0, Address] - value: U256 - data: Bytes - v: U256 - r: U256 - s: U256 - -@slotted_freezable -@dataclass -class AccessListTransaction: - chain_id: U64 - nonce: U256 - gas_price: Uint - gas: Uint - to: Union[Bytes0, Address] - value: U256 - data: Bytes - access_list: Tuple[Tuple[Address, Tuple[Bytes32, ...]], ...] - y_parity: U256 - r: U256 - s: U256 - -@slotted_freezable -@dataclass -class FeeMarketTransaction: - chain_id: U64 - nonce: U256 - max_priority_fee_per_gas: Uint - max_fee_per_gas: Uint - gas: Uint - to: Union[Bytes0, Address] - value: U256 - data: Bytes - access_list: Tuple[Tuple[Address, Tuple[Bytes32, ...]], ...] - y_parity: U256 - r: U256 - s: U256 - -Transaction = Union[ - LegacyTransaction, AccessListTransaction, FeeMarketTransaction -] -``` - -The "calldata" is encoded inside the `data` field of the Transaction class. The "calldata" is accessible by the EVM, and the format to encode and decode it is specified in the [Contract ABI](https://docs.soliditylang.org/en/latest/abi-spec.html). - -## EIP-4844 - -[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces Blobs, a new space to store data that will be much cheaper than calldata because they will have a new type of gas that is independent of normal gas and follows its own targeting rule. -With the EIP-4844, the new Transaction data structure will be the following. - -```python -@slotted_freezable -@dataclass -class BlobTransaction: # the class name may change - chain_id: U64 - nonce: U256 - max_priority_fee_per_gas: Uint - max_fee_per_gas: Uint - gas: Uint - to: Union[Bytes0, Address] - value: U256 - data: Bytes - access_list: Tuple[Tuple[Address, Tuple[Bytes32, ...]], ...] - max_fee_per_blob_gas: U256 - blob_versioned_hashes: VersionedHash - y_parity: U256 - r: U256 - s: U256 -``` - -EIP-4844 will introduce two more fields in the Transaction class, which are `max_fee_per_blob_gas` and `blob_versioned_hashes`. -EIP-4844 introduced a new transaction type where `TransactionType == BLOB_TX_TYPE` and the `TransactionPayload` is the rlp encoding of the above class. - -### Changes on the Execution Specs - -The upgrade which will introduce EIP-4844 into the Execution Layer has been labeled **Cancun**. - -#### 1. Add checks inside the State Transition Function - -The EL now must check that the blob specific fields are valid for each transaction that is going to be executed in the State Transition Function (STF). - -The checks include (For the specs code, see [here](https://eips.ethereum.org/EIPS/eip-4844#execution-layer-validation)): - -- check that the signer has enough balance to cover the cost of both transaction gas fee and blob gas fees - -```python -# modify the check for sufficient balance -max_total_fee = tx.gas * tx.max_fee_per_gas -if get_tx_type(tx) == BLOB_TX_TYPE: - max_total_fee += get_total_blob_gas(tx) * tx.max_fee_per_blob_gas -assert signer(tx).balance >= max_total_fee -``` - -- check that the blob transaction contains at least 1 valid `blob_versioned_hash` (see CL changes) and that they are formatted correctly - -```python -assert len(tx.blob_versioned_hashes) > 0 -``` - -- check that the user is willing to pay at least the current blob base fee - -```python -assert tx.max_fee_per_blob_gas >= get_blob_base_fee(block.header) -``` - -Finally, the EL STF must keep track of the gas being gas used for blob transactions (same as it already happens for EIP1559 transactions). - -```python -blob_gas_used += get_total_blob_gas(tx) -``` - -### Changes on the Consensus Specs - -The upgrade which will introduce EIP-4844 into the Consensus Layer has been labeled **Deneb**. - -#### 1. Custom types - -| Name | SSZ equivalent | Description | -| --------------- | -------------- | ------------------------ | -| `VersionedHash` | `Bytes32` | _[New in Deneb:EIP4844]_ | -| `BlobIndex` | `uint64` | _[New in Deneb:EIP4844]_ | - -#### 2. Inclusion of KZG Committment versioned hashes - -The Consensus Layer (CL, also called Beacon chain) calls the [`process_execution_payload`](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) function when a new block payload is submitted to the chain. This function is responsible to perform some validity checks on the block's payload and then invoke the Execution Layer (EL) via the `verify_and_notify_new_payload` function. - -Once invoked, the EL will: - -- validate the block payload -- execute transactions inside the block payload -- update the state, which is the result of executing transactions -- build the new block -- return the new block to the CL - -With EIP-4844, the `process_execution_payload` adds the parameter `versioned_hashes` to be passed to the `verify_and_notify_new_payload` function. - -`versioned_hashes` is an array of [hashes](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) for each blob of KZG Committment, which are a type of cryptographic commitment particularly useful for their efficiency in creating and verifying proofs of data availability and correctness. - -KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correcteness. - -#### 3. New Block Header checks - -TODO -see go-ethereum file consensus.go also mentioned in [week2](https://youtu.be/pniTkWo70OY?t=2773) - ## EIP-4488 Initally [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488) was proposed to decrease the gas cost of calldata, and to add a limit of how much total transaction calldata can be in a block. The goal was to make Rollups transactions cheaper. diff --git a/docs/wiki/research/scaling/eip-4844.md b/docs/wiki/research/scaling/eip-4844.md new file mode 100644 index 00000000..5fb554c7 --- /dev/null +++ b/docs/wiki/research/scaling/eip-4844.md @@ -0,0 +1,166 @@ +# EIP-4844 + +[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces Blobs, a new space to store data inside a transaction that will be much cheaper than `calldata` because they will have a new type of gas that is independent of normal gas and follows its own targeting rule. + +Before EIP-4844, the Transaction data structure was the following ([ethereum exeuction-specs repository](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49)): + +```python +@slotted_freezable +@dataclass +class LegacyTransaction: + nonce: U256 + gas_price: Uint + gas: Uint + to: Union[Bytes0, Address] + value: U256 + data: Bytes + v: U256 + r: U256 + s: U256 + +@slotted_freezable +@dataclass +class AccessListTransaction: + chain_id: U64 + nonce: U256 + gas_price: Uint + gas: Uint + to: Union[Bytes0, Address] + value: U256 + data: Bytes + access_list: Tuple[Tuple[Address, Tuple[Bytes32, ...]], ...] + y_parity: U256 + r: U256 + s: U256 + +@slotted_freezable +@dataclass +class FeeMarketTransaction: + chain_id: U64 + nonce: U256 + max_priority_fee_per_gas: Uint + max_fee_per_gas: Uint + gas: Uint + to: Union[Bytes0, Address] + value: U256 + data: Bytes + access_list: Tuple[Tuple[Address, Tuple[Bytes32, ...]], ...] + y_parity: U256 + r: U256 + s: U256 + +Transaction = Union[ + LegacyTransaction, AccessListTransaction, FeeMarketTransaction +] +``` + +The `calldata` is encoded inside the `data` field of the Transaction class. The `calldata` is accessible by the EVM, and the format to encode and decode it is specified in the [Contract ABI](https://docs.soliditylang.org/en/latest/abi-spec.html). + +With the EIP-4844, the new Transaction data structure will be the following: + +```python +@slotted_freezable +@dataclass +class BlobTransaction: # the class name may change + chain_id: U64 + nonce: U256 + max_priority_fee_per_gas: Uint + max_fee_per_gas: Uint + gas: Uint + to: Union[Bytes0, Address] + value: U256 + data: Bytes + access_list: Tuple[Tuple[Address, Tuple[Bytes32, ...]], ...] + max_fee_per_blob_gas: U256 + blob_versioned_hashes: VersionedHash + y_parity: U256 + r: U256 + s: U256 +``` + +EIP-4844 will introduce two more fields in the Transaction class, which are `max_fee_per_blob_gas` and `blob_versioned_hashes`. +EIP-4844 introduced a new transaction type where `TransactionType == BLOB_TX_TYPE` and the `TransactionPayload` is the rlp encoding of the above class. + +## Changes on the Execution Specs + +The upgrade which will introduce EIP-4844 into the Execution Layer has been labeled **Cancun**. + +### 1. Add checks inside the State Transition Function + +The EL now must check that the blob specific fields are valid for each transaction that is going to be executed in the State Transition Function (STF). + +The checks include (For the specs code, see [here](https://eips.ethereum.org/EIPS/eip-4844#execution-layer-validation)): + +- check that the signer has enough balance to cover the cost of both transaction gas fee and blob gas fees + +```python +# modify the check for sufficient balance +max_total_fee = tx.gas * tx.max_fee_per_gas +if get_tx_type(tx) == BLOB_TX_TYPE: + max_total_fee += get_total_blob_gas(tx) * tx.max_fee_per_blob_gas +assert signer(tx).balance >= max_total_fee +``` + +- check that the blob transaction contains at least 1 valid `blob_versioned_hash` (see CL changes) and that they are formatted correctly + +```python +assert len(tx.blob_versioned_hashes) > 0 +``` + +- check that the user is willing to pay at least the current blob base fee + +```python +assert tx.max_fee_per_blob_gas >= get_blob_base_fee(block.header) +``` + +Finally, the EL STF must keep track of the gas being gas used for blob transactions (same as it already happens for EIP1559 transactions). + +```python +blob_gas_used += get_total_blob_gas(tx) +``` + +## Changes on the Consensus Specs + +The upgrade which will introduce EIP-4844 into the Consensus Layer has been labeled **Deneb**. + +### 1. Consensus Layer Validation + +As stated in the [EIP-4844](https://eips.ethereum.org/EIPS/eip-4844#consensus-layer-validation) blobs are referenced but not fully encoded inside the beacon block body. Instead of embedding the full contents in the body, the blobs are propagated separately, as "sidecars". + +This "sidecars" design provides forward compatibility for further data increases by black-boxing `is_data_available()`, which means that in future upgrades `is_data_available()` implementation may change, for example to include data-availability-sampling (DAS), and the system interacting with this function is not required to understand the inner implementation of the function (in programming terms, `is_data_available()` can be considered as an interface method where the implementation may change over time). + +To learn more about the changes, see the consensus-specs: + +- [is_data_available](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/fork-choice.md#is_data_available) +- [BeaconBlockBody](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#beaconblockbody) +- [p2p network](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/p2p-interface.md#why-are-blobs-relayed-as-a-sidecar-separate-from-beacon-blocks) + +### 2. Custom types + +| Name | SSZ equivalent | Description | +| --------------- | -------------- | ------------------------ | +| `VersionedHash` | `Bytes32` | _[New in Deneb:EIP4844]_ | +| `BlobIndex` | `uint64` | _[New in Deneb:EIP4844]_ | + +### 3. Inclusion of KZG Committment versioned hashes + +The Consensus Layer (CL, also called Beacon chain) calls the [`process_execution_payload`](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) function when a new block payload is submitted to the chain. This function is responsible to perform some validity checks on the block's payload and then invoke the Execution Layer (EL) via the `verify_and_notify_new_payload` function. + +Once invoked, the EL will: + +- validate the block payload +- execute transactions inside the block payload +- update the state, which is the result of executing transactions +- build the new block +- return the new block to the CL + +With EIP-4844, the `process_execution_payload` adds the parameter `versioned_hashes` to be passed to the `verify_and_notify_new_payload` function. + +`versioned_hashes` is an array of [hashes](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) for each blob of KZG Committment, which are a type of cryptographic commitment particularly useful for their efficiency in creating and verifying proofs of data availability and correctness. + +KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correcteness. + +### 4. New Block Header checks + +TODO +see go-ethereum file consensus.go also mentioned in [week2](https://youtu.be/pniTkWo70OY?t=2773) From a08058afbf9e07745fd30e1b1114dd6882a389d2 Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Fri, 1 Mar 2024 10:53:05 +0100 Subject: [PATCH 022/101] eip-4844 - included references to code --- docs/wiki/research/scaling/eip-4844.md | 133 ++++++++++++++++--------- 1 file changed, 84 insertions(+), 49 deletions(-) diff --git a/docs/wiki/research/scaling/eip-4844.md b/docs/wiki/research/scaling/eip-4844.md index 5fb554c7..d859d6dd 100644 --- a/docs/wiki/research/scaling/eip-4844.md +++ b/docs/wiki/research/scaling/eip-4844.md @@ -2,6 +2,37 @@ [EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces Blobs, a new space to store data inside a transaction that will be much cheaper than `calldata` because they will have a new type of gas that is independent of normal gas and follows its own targeting rule. +The page outlines the EIP, providing code references to understand the changes brought by this hard fork. It targets aspiring Ethereum core developers interested in comprehending Ethereum's code post-update. + +## Specification + +_PLEASE NOTE that some specification links may be broken/missing due to the currently active development of EIP-4844._ + +### Parameters + +- [BLOB_TX_TYPE](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/tests/core/pyspec/eth2spec/test/helpers/sharding.py#L24) +- [BYTES_PER_FIELD_ELEMENT](https://github.com/ethereum/consensus-specs/blob/dev/pysetup/spec_builders/deneb.py) +- [FIELD_ELEMENTS_PER_BLOB](https://github.com/ethereum/consensus-specs/blob/dev/pysetup/spec_builders/deneb.py) +- [BLS_MODULUS](https://github.com/ethereum/consensus-specs/blob/dev/specs/_features/whisk/beacon-chain.md#bls) +- [VERSIONED_HASH_VERSION_KZG](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md) +- [MAX_BLOB_GAS_PER_BLOCK](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md) +- [GAS_PER_BLOB](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md) +- [MIN_EPOCHS_FOR_BLOB_SIDECARS_REQUESTS](https://github.com/ethereum/consensus-specs/blob/dev/configs/mainnet.yaml) + +### Type Aliases + +- [Blob](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md) +- [VersionedHash](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md) +- [KZGCommitment](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md) +- [KZGProof](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md) + +### Cryptographic Helpers + +- [verify_kzg_proof()](https://github.com/ethereum/consensus-specs/blob/86fb82b221474cc89387fa6436806507b3849d88/specs/deneb/polynomial-commitments.md#verify_kzg_proof) +- [verify_blob_kzg_proof_batch()](https://github.com/ethereum/consensus-specs/blob/86fb82b221474cc89387fa6436806507b3849d88/specs/deneb/polynomial-commitments.md#verify_blob_kzg_proof_batch) + +### New Transaction Data Structure (BLOB_TX_TYPE) + Before EIP-4844, the Transaction data structure was the following ([ethereum exeuction-specs repository](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49)): ```python @@ -56,6 +87,9 @@ Transaction = Union[ The `calldata` is encoded inside the `data` field of the Transaction class. The `calldata` is accessible by the EVM, and the format to encode and decode it is specified in the [Contract ABI](https://docs.soliditylang.org/en/latest/abi-spec.html). +EIP-4844 will introduce two more fields in the Transaction class, which are `max_fee_per_blob_gas` and `blob_versioned_hashes`. +EIP-4844 introduced a new transaction type where `TransactionType == BLOB_TX_TYPE` and the `TransactionPayload` is the rlp encoding of the above class. + With the EIP-4844, the new Transaction data structure will be the following: ```python @@ -78,52 +112,21 @@ class BlobTransaction: # the class name may change s: U256 ``` -EIP-4844 will introduce two more fields in the Transaction class, which are `max_fee_per_blob_gas` and `blob_versioned_hashes`. -EIP-4844 introduced a new transaction type where `TransactionType == BLOB_TX_TYPE` and the `TransactionPayload` is the rlp encoding of the above class. - -## Changes on the Execution Specs +### Header Extension -The upgrade which will introduce EIP-4844 into the Execution Layer has been labeled **Cancun**. - -### 1. Add checks inside the State Transition Function - -The EL now must check that the blob specific fields are valid for each transaction that is going to be executed in the State Transition Function (STF). - -The checks include (For the specs code, see [here](https://eips.ethereum.org/EIPS/eip-4844#execution-layer-validation)): +The current header encoding is extended with two new 64-bit unsigned integer fields, `blob_gas_used` and `excess_blob_gas`. Blob transactions have their own gas targeting rules (similar to EIP-1559) and nodes must take into account gas spent to store data in blobs in addition to the normal gas fees spent to execute transaction (see below in **Changes on the Execution Specs**). -- check that the signer has enough balance to cover the cost of both transaction gas fee and blob gas fees - -```python -# modify the check for sufficient balance -max_total_fee = tx.gas * tx.max_fee_per_gas -if get_tx_type(tx) == BLOB_TX_TYPE: - max_total_fee += get_total_blob_gas(tx) * tx.max_fee_per_blob_gas -assert signer(tx).balance >= max_total_fee -``` - -- check that the blob transaction contains at least 1 valid `blob_versioned_hash` (see CL changes) and that they are formatted correctly - -```python -assert len(tx.blob_versioned_hashes) > 0 -``` - -- check that the user is willing to pay at least the current blob base fee - -```python -assert tx.max_fee_per_blob_gas >= get_blob_base_fee(block.header) -``` +- [ExecutionPayloadHeader](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/specs/deneb/beacon-chain.md?plain=1#L149) -Finally, the EL STF must keep track of the gas being gas used for blob transactions (same as it already happens for EIP1559 transactions). +### Opcode to get versioned hashes -```python -blob_gas_used += get_total_blob_gas(tx) -``` +- [BLOBHASH](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/lists/evm/proposed-opcodes.md?plain=1#L60) -## Changes on the Consensus Specs +### Changes on the Consensus Specs The upgrade which will introduce EIP-4844 into the Consensus Layer has been labeled **Deneb**. -### 1. Consensus Layer Validation +#### 1. Consensus Layer Validation As stated in the [EIP-4844](https://eips.ethereum.org/EIPS/eip-4844#consensus-layer-validation) blobs are referenced but not fully encoded inside the beacon block body. Instead of embedding the full contents in the body, the blobs are propagated separately, as "sidecars". @@ -135,14 +138,7 @@ To learn more about the changes, see the consensus-specs: - [BeaconBlockBody](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#beaconblockbody) - [p2p network](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/p2p-interface.md#why-are-blobs-relayed-as-a-sidecar-separate-from-beacon-blocks) -### 2. Custom types - -| Name | SSZ equivalent | Description | -| --------------- | -------------- | ------------------------ | -| `VersionedHash` | `Bytes32` | _[New in Deneb:EIP4844]_ | -| `BlobIndex` | `uint64` | _[New in Deneb:EIP4844]_ | - -### 3. Inclusion of KZG Committment versioned hashes +#### 2. Inclusion of KZG Committment versioned hashes The Consensus Layer (CL, also called Beacon chain) calls the [`process_execution_payload`](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) function when a new block payload is submitted to the chain. This function is responsible to perform some validity checks on the block's payload and then invoke the Execution Layer (EL) via the `verify_and_notify_new_payload` function. @@ -160,7 +156,46 @@ With EIP-4844, the `process_execution_payload` adds the parameter `versioned_has KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correcteness. -### 4. New Block Header checks +#### 3. New Block Header checks + +see go-ethereum file consensus.go for checks added to the block header: + +- [link](https://github.com/ethereum/go-ethereum/blob/0a2f33946b95989e8ce36e72a88138adceab6a23/consensus/beacon/consensus.go#L274) + +### Changes on the Execution Specs + +The upgrade which will introduce EIP-4844 into the Execution Layer has been labeled **Cancun**. + +#### 1. Add checks inside the State Transition Function + +The EL now must check that the blob specific fields are valid for each transaction that is going to be executed in the State Transition Function (STF). + +The checks include (For the specs code, see [here](https://eips.ethereum.org/EIPS/eip-4844#execution-layer-validation)): -TODO -see go-ethereum file consensus.go also mentioned in [week2](https://youtu.be/pniTkWo70OY?t=2773) +- check that the signer has enough balance to cover the cost of both transaction gas fee and blob gas fees + +```python +# modify the check for sufficient balance +max_total_fee = tx.gas * tx.max_fee_per_gas +if get_tx_type(tx) == BLOB_TX_TYPE: + max_total_fee += get_total_blob_gas(tx) * tx.max_fee_per_blob_gas +assert signer(tx).balance >= max_total_fee +``` + +- check that the blob transaction contains at least 1 valid `blob_versioned_hash` (see CL changes) and that they are formatted correctly + +```python +assert len(tx.blob_versioned_hashes) > 0 +``` + +- check that the user is willing to pay at least the current blob base fee + +```python +assert tx.max_fee_per_blob_gas >= get_blob_base_fee(block.header) +``` + +Finally, the EL STF must keep track of the gas being gas used for blob transactions (same as it already happens for EIP1559 transactions). + +```python +blob_gas_used += get_total_blob_gas(tx) +``` From d599f8780efa8dee21e70d83adafe1bf8d11206a Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Fri, 1 Mar 2024 10:55:44 +0100 Subject: [PATCH 023/101] eip-4844 - add section to discuss previous research for scalability with eip-4488 --- docs/wiki/research/scaling/eip-4844.md | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) diff --git a/docs/wiki/research/scaling/eip-4844.md b/docs/wiki/research/scaling/eip-4844.md index d859d6dd..ec284b65 100644 --- a/docs/wiki/research/scaling/eip-4844.md +++ b/docs/wiki/research/scaling/eip-4844.md @@ -199,3 +199,26 @@ Finally, the EL STF must keep track of the gas being gas used for blob transacti ```python blob_gas_used += get_total_blob_gas(tx) ``` + +### A note about previous attempts/research to improve scalability for rollups + +To accomplish scalability, the idea was initially to decrease transaction `calldata` gas cost with [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488). However, this EIP is now irrelevant because EIP-4844 has been implemented instead. Here is a brief introduction for the EIP-4488. + +## EIP-4488 + +Initally [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488) was proposed to decrease the gas cost of `calldata`, and to add a limit of how much total transaction `calldata` can be in a block. The goal was to make Rollups transactions cheaper. +Currently, the cost for a non zero byte of `calldata` costs 16 units of gas. With this EIP, the cost for a byte of `calldata` (regardless if is 0 or a non zero byte) would be 3 bytes. + +This would have introduced the following parameters: + +| Parameter | Value | +| --------------------------- | --------- | +| NEW_CALLDATA_GAS_COST | 3 | +| BASE_MAX_CALLDATA_PER_BLOCK | 1,048,576 | +| CALLDATA_PER_TX_STIPEND | 300 | + +However, this EIP is now irrelevant because EIP-4844 has been implemented instead. Contrary to the original idea, the approach will be the exact opposite with EIP-7623. + +## EIP-7623 + +[EIP-7623](https://eips.ethereum.org/EIPS/eip-7623) is a very recent EIP created in February 2024, with the purpose of increasing `calldata` cost to decrease the maximum block size. From eebf63d343c3707dfe14c8d4e1c497c8097416aa Mon Sep 17 00:00:00 2001 From: Luca Di Domenico <56132403+lucadidomenico@users.noreply.github.com> Date: Fri, 1 Mar 2024 11:08:00 +0100 Subject: [PATCH 024/101] Update eip-4844.md --- docs/wiki/research/scaling/eip-4844.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/wiki/research/scaling/eip-4844.md b/docs/wiki/research/scaling/eip-4844.md index ec284b65..f256cb73 100644 --- a/docs/wiki/research/scaling/eip-4844.md +++ b/docs/wiki/research/scaling/eip-4844.md @@ -88,7 +88,7 @@ Transaction = Union[ The `calldata` is encoded inside the `data` field of the Transaction class. The `calldata` is accessible by the EVM, and the format to encode and decode it is specified in the [Contract ABI](https://docs.soliditylang.org/en/latest/abi-spec.html). EIP-4844 will introduce two more fields in the Transaction class, which are `max_fee_per_blob_gas` and `blob_versioned_hashes`. -EIP-4844 introduced a new transaction type where `TransactionType == BLOB_TX_TYPE` and the `TransactionPayload` is the rlp encoding of the above class. +EIP-4844 introduced a new transaction type where `TransactionType == BLOB_TX_TYPE` and the `TransactionPayload` is the rlp encoding of the class below. With the EIP-4844, the new Transaction data structure will be the following: From c95feadcb8d59846db955ae85232ef2a5cdd5489 Mon Sep 17 00:00:00 2001 From: Luca Di Domenico <56132403+lucadidomenico@users.noreply.github.com> Date: Fri, 1 Mar 2024 11:10:32 +0100 Subject: [PATCH 025/101] Update eip-4844.md --- docs/wiki/research/scaling/eip-4844.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/wiki/research/scaling/eip-4844.md b/docs/wiki/research/scaling/eip-4844.md index f256cb73..9a04d056 100644 --- a/docs/wiki/research/scaling/eip-4844.md +++ b/docs/wiki/research/scaling/eip-4844.md @@ -158,7 +158,7 @@ KZG commitments provide the ability to prove that specific pieces of data are in #### 3. New Block Header checks -see go-ethereum file consensus.go for checks added to the block header: +See go-ethereum file "consensus.go" for checks added to the block header: - [link](https://github.com/ethereum/go-ethereum/blob/0a2f33946b95989e8ce36e72a88138adceab6a23/consensus/beacon/consensus.go#L274) From 5b1e4567defb007fb1add00cfeebea679bf6f171 Mon Sep 17 00:00:00 2001 From: Luca Di Domenico <56132403+lucadidomenico@users.noreply.github.com> Date: Fri, 1 Mar 2024 11:12:50 +0100 Subject: [PATCH 026/101] Update eip-4844.md --- docs/wiki/research/scaling/eip-4844.md | 6 +----- 1 file changed, 1 insertion(+), 5 deletions(-) diff --git a/docs/wiki/research/scaling/eip-4844.md b/docs/wiki/research/scaling/eip-4844.md index 9a04d056..5acc8898 100644 --- a/docs/wiki/research/scaling/eip-4844.md +++ b/docs/wiki/research/scaling/eip-4844.md @@ -217,8 +217,4 @@ This would have introduced the following parameters: | BASE_MAX_CALLDATA_PER_BLOCK | 1,048,576 | | CALLDATA_PER_TX_STIPEND | 300 | -However, this EIP is now irrelevant because EIP-4844 has been implemented instead. Contrary to the original idea, the approach will be the exact opposite with EIP-7623. - -## EIP-7623 - -[EIP-7623](https://eips.ethereum.org/EIPS/eip-7623) is a very recent EIP created in February 2024, with the purpose of increasing `calldata` cost to decrease the maximum block size. +However, this EIP is now irrelevant because EIP-4844 has been implemented instead. Contrary to the original idea, the approach will be the exact opposite with [EIP-7623](https://eips.ethereum.org/EIPS/eip-7623), to increase `calldata` cost to decrease the maximum block size. From 04182e6c47748c1225f5a8579887cbc06b608b66 Mon Sep 17 00:00:00 2001 From: Luca Di Domenico <56132403+lucadidomenico@users.noreply.github.com> Date: Fri, 1 Mar 2024 11:13:30 +0100 Subject: [PATCH 027/101] Update eip-4844.md --- docs/wiki/research/scaling/eip-4844.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/wiki/research/scaling/eip-4844.md b/docs/wiki/research/scaling/eip-4844.md index 5acc8898..cb70f2e7 100644 --- a/docs/wiki/research/scaling/eip-4844.md +++ b/docs/wiki/research/scaling/eip-4844.md @@ -200,11 +200,11 @@ Finally, the EL STF must keep track of the gas being gas used for blob transacti blob_gas_used += get_total_blob_gas(tx) ``` -### A note about previous attempts/research to improve scalability for rollups +## A note about previous attempts/research to improve scalability for rollups To accomplish scalability, the idea was initially to decrease transaction `calldata` gas cost with [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488). However, this EIP is now irrelevant because EIP-4844 has been implemented instead. Here is a brief introduction for the EIP-4488. -## EIP-4488 +### EIP-4488 Initally [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488) was proposed to decrease the gas cost of `calldata`, and to add a limit of how much total transaction `calldata` can be in a block. The goal was to make Rollups transactions cheaper. Currently, the cost for a non zero byte of `calldata` costs 16 units of gas. With this EIP, the cost for a byte of `calldata` (regardless if is 0 or a non zero byte) would be 3 bytes. From 25bf896d8112d109061b6284a5f8e5dee51dce29 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Mon, 4 Mar 2024 08:34:02 +0100 Subject: [PATCH 028/101] :link: Adding gas limits resource --- docs/wiki/research/scaling/scaling.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/docs/wiki/research/scaling/scaling.md b/docs/wiki/research/scaling/scaling.md index f38b27ac..292b7963 100644 --- a/docs/wiki/research/scaling/scaling.md +++ b/docs/wiki/research/scaling/scaling.md @@ -84,4 +84,6 @@ Resources: [Combining GHOST and Casper](https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf), [archived](https://web.archive.org/web/20230907004049/https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf) -[Ethereum Blocks](https://ethereum.org/developers/docs/blocks), [archived](https://web.archive.org/web/20240214052915/https://ethereum.org/developers/docs/blocks) \ No newline at end of file +[Ethereum Blocks](https://ethereum.org/developers/docs/blocks), [archived](https://web.archive.org/web/20240214052915/https://ethereum.org/developers/docs/blocks) + +[On Block Sizes, Gas Limits and Scalability](https://ethresear.ch/t/on-block-sizes-gas-limits-and-scalability/18444), [archived](https://web.archive.org/web/20240220230246/https://ethresear.ch/t/on-block-sizes-gas-limits-and-scalability/18444) \ No newline at end of file From 2a83134c4be61692307551082d0917c545d473b3 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Mon, 4 Mar 2024 09:43:05 +0100 Subject: [PATCH 029/101] :mount_fuji: Fix images --- docs/wiki/research/scaling/scaling.md | 15 +++++++++------ 1 file changed, 9 insertions(+), 6 deletions(-) diff --git a/docs/wiki/research/scaling/scaling.md b/docs/wiki/research/scaling/scaling.md index 292b7963..1b829020 100644 --- a/docs/wiki/research/scaling/scaling.md +++ b/docs/wiki/research/scaling/scaling.md @@ -21,7 +21,7 @@ As part of the game-theory mechanism, to maintain the network sustainability, us This problem is widely known as the **Blockchain Trilemma**, which states that blockchain networks must sacrifice either security, decentralization, or scalability, and maximizing all three at once is difficult. The holy grail of blockchain technology is to create a secure and decentralized transactional network that can achieve a high TPS rate. -!["Blockchain trilemma - Bankless.com"](./img/scaling/blockchain-trilemma.png "Blockchain trilemma - Bankless.com") +!["Blockchain trilemma - Bankless.com"](../img/scaling/blockchain-trilemma.png "Blockchain trilemma - Bankless.com") ## Blockchain Modularity Modern blockchain designs propose a "divide et impera" approach dividing the system into different specific functional components to independently maximize each vertex of the trilemma. This approach encapsulates the complexity in each part of the system and reduces the systemic complexity through the definition of simpler interaction interfaces for system components. @@ -39,17 +39,20 @@ The primary objective of Ethereum's scalability efforts is to increase TPS metri Layer 1 scaling is the set of all those techniques that increases the TPS of the underlying blockchain protocol itself. blockchains with "bigger blocks" have a major TPS but are more difficult to verify and likely to become more centralized. For this reason, an increase in the capacity of each block must be accompanied by various modifications to the protocol that allow decentralization to be maintained. Examples of layer 1 scaling solutions include Sharding, Proof-Of-Stake consensus mechanisms, and protocol upgrades aimed at optimizing block processing efficiency. -!["Layer 1 Scaling"](./img/scaling/layer-1-scaling.png "Layer 1 Scaling") +!["Layer 1 Scaling"](../img/scaling/layer-1-scaling.png "Layer 1 Scaling") -> In Ethereum, an increase of gas limits will effectively expand the amount of computation and data that Ethereum can hold but will also raise the demands on network node operators. +> **An increase of gas limits will effectively expand the amount of computation and data that Ethereum can hold but will also raise the demands on network node operators. Another design choice that will directly affect the block size is the gas pricing of operations. Cheaper operations will allow the inclusion of a greater number of and more complex transactions within the same gas limits boundary.** Layer 2 scaling is the set of solutions built on top of Layer 1 blockchain protocols that can achieve a higher TPS without requiring an increase in Layer 1 resource consumption, while still relying on its security model. These solutions typically process transactions off-chain or by using alternative consensus mechanisms that are faster and more scalable than the main blockchain. Examples of Layer 2 scaling solutions include, State Channels, Plasma Chains, or Rollups. -!["Layer 2 Scaling"](./img/scaling/layer-2-scaling.png "Layer 2 Scaling") +!["Layer 2 Scaling"](../img/scaling/layer-2-scaling.png "Layer 2 Scaling") - The solution predominantly adopted by the Ethereum community to solve the scalability problem is a multi-rollup-centric approach. Here, Ethereum acts as fundamental secure layer of Settlement, and Data Availability, while the majority of Execution tasks are delegated to upper layers referred to as Rollups.Rollups bundle multiple Layer 2 transactions into a single Layer 1 transaction. These transactions are stored in Layer 1, but the their execution is delegated to off-chain mechanisms. This allows for significant scalability improvements without sacrificing security. Ethereum's high level of programmability makes possible to create scalable solutions on top of the platform through Ethereum smart contracts. As previously mentioned, to maintain a high level of decentralization, Ethereum imposes limitations on the computational and storage resources that transactions included in the blocks can use, through gas limitations. Therefore, the data stored in L1 is minimized, and only raw transactions are stored along with a hash root of the L2 state tree. + The solution predominantly adopted by the Ethereum community to solve the scalability problem is a multi-rollup-centric approach. Here, Ethereum acts as fundamental secure layer of Settlement, and Data Availability, while the majority of Execution tasks are delegated to upper layers referred to as Rollups. Rollups bundle multiple Layer 2 transactions into a single Layer 1 transaction. These transactions are stored in Layer 1, but their execution is delegated to off-chain mechanisms. This allows for significant scalability improvements without sacrificing security. Ethereum's high level of programmability makes possible to create scalable solutions on top of the platform through Ethereum smart contracts. As previously mentioned, to maintain a high level of decentralization, Ethereum imposes limitations on the computational and storage resources that transactions included in the blocks can use, through gas limitations. Therefore, the data stored in Layer 1 is minimized, with only raw transactions being stored along with a hash commitment of the Layer 2 state resulting from the execution of those transactions. + +> **Rollups can be seen as a way to compress transaction execution, thereby reducing the computational burden on the Layer 1 blockchain. This provides the possibility to increase the TPS while still maintaining the security level of Layer 1 for the Layer 2 transactions, as their data and Layer 2 state transition commitments are stored in Layer 1.** + +## Ethereum Core Changes Towards a Rollup-Centric Roadmap -> **Rollups can be seen as a way to compress transaction execution, reducing the computational burden on the Layer 1 blockchain, thereby providing the possibility to increase the TPS while still maintaining the security level of Layer 1 for the Layer2 transactions.** From b215fc0e7e989635b4f174b3380a04c91f2a9a91 Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Wed, 6 Mar 2024 12:19:54 +0100 Subject: [PATCH 030/101] Addressing feedback at [comment](https://github.com/eth-protocol-fellows/protocol-studies/pull/51#discussion_r1508794587): adding L1 scalability to the intro section --- docs/_sidebar.md | 3 +- docs/wiki/research/scaling/core-changes.md | 47 ------------------- .../scaling/core-changes/core-changes.md | 19 ++++++++ .../scaling/{ => core-changes}/eip-4844.md | 7 ++- 4 files changed, 27 insertions(+), 49 deletions(-) delete mode 100644 docs/wiki/research/scaling/core-changes.md create mode 100644 docs/wiki/research/scaling/core-changes/core-changes.md rename docs/wiki/research/scaling/{ => core-changes}/eip-4844.md (92%) diff --git a/docs/_sidebar.md b/docs/_sidebar.md index 4d106bcc..ed396446 100644 --- a/docs/_sidebar.md +++ b/docs/_sidebar.md @@ -41,7 +41,8 @@ - Research - [Roadmap overview](/wiki/research/roadmap.md) - [Scaling](/wiki/research/scaling/scaling.md) - - [Core Changes](/wiki/research/scaling/core-changes.md) + - [Core Changes](/wiki/research/scaling/core-changes/core-changes.md) + - [EIP-4844](/wiki/research/scaling/core-changes/eip-4844.md) - Blobs - Sharding - Statelessness diff --git a/docs/wiki/research/scaling/core-changes.md b/docs/wiki/research/scaling/core-changes.md deleted file mode 100644 index 89dd9f49..00000000 --- a/docs/wiki/research/scaling/core-changes.md +++ /dev/null @@ -1,47 +0,0 @@ -# Changes to Ethereum core to accomplish scalability - -## Introduction - -L2 Rollups need to enable the permissionless reconstruction of the L2 state. To achieve this, they must ensure Data Availability, which refers to the global ordering of inputs for transactions that have altered the state. -Until EIP-4844 goes live on the Mainnet (expected in March 2024), Rollups have been storing Data Availability within a section of the transaction known as "calldata". Currently, this "calldata" represents the primary bottleneck for scaling Ethereum, as storing data in calldata is expensive. - -To accomplish scalability, the idea was initially to decrease transaction calldata gas cost with EIP-4488. However, this EIP is now irrelevant because EIP-4844 has been implemented instead, which as we will see in the following section, introduces a new data section inside the transactions called Blob. - -But before talking about the changes introduced by the EIP-4844, let's first understand the structure of an Ethereum transaction. - -## EIP-2718 - -[EIP-2718](https://github.com/ethereum/EIPs/blob/master/EIPS/eip-2718.md) introduced an envelope transaction type. The envelope makes possible to incapsulate transaction in a common header structure, allowing to change the transaction fields without breaking backwards compatibility. - -The envelope transaction type is defined as follows: - -`TransactionType || TransactionPayload` - -Where `TransactionType` is a 1 byte field identyfing the format of the transaction, and `TransactionPayload` is a variable length field which contains the actual transaction content. - -Same concept apply to receipts: - -`TransactionType || ReceiptPayload` - -Please note that the `||` is the byte/byte-array concatenation operator. - -This way, when defining new standards for a new type of transaction, the only concern is to ensure there are not duplicated `TransactionType` numbers. - -## EIP-4488 - -Initally [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488) was proposed to decrease the gas cost of calldata, and to add a limit of how much total transaction calldata can be in a block. The goal was to make Rollups transactions cheaper. -Currently, the cost for a non zero byte of calldata costs 16 units of gas. With this EIP, the cost for a byte of calldata (regardless if is 0 or a non zero byte) would be 3 bytes. - -This would have introduced the following parameters: - -| Parameter | Value | -| --------------------------- | --------- | -| NEW_CALLDATA_GAS_COST | 3 | -| BASE_MAX_CALLDATA_PER_BLOCK | 1,048,576 | -| CALLDATA_PER_TX_STIPEND | 300 | - -However, this EIP is now irrelevant because EIP-4844 has been implemented instead. Contrary to the original idea, the approach will be the exact opposite with EIP-7623. - -## EIP-7623 - -[EIP-7623](https://eips.ethereum.org/EIPS/eip-7623) is a very recent EIP created in February 2024, with the purpose of increasing calldata cost to decrease the maximum block size. diff --git a/docs/wiki/research/scaling/core-changes/core-changes.md b/docs/wiki/research/scaling/core-changes/core-changes.md new file mode 100644 index 00000000..fddb9fb7 --- /dev/null +++ b/docs/wiki/research/scaling/core-changes/core-changes.md @@ -0,0 +1,19 @@ +# Changes to Ethereum Core to Achieve Scalability + +With the [Rollup-Centric Roadmap](https://ethereum-magicians.org/t/a-rollup-centric-ethereum-roadmap/4698) published by Vitalik Buterin in 2020, Ethereum has embarked on a path toward achieving scalability. The ultimate goals of Ethereum scalability can be summarized as follows: + +- Transition the execution layer (dApps) entirely to Layer 2 (L2) rollups. +- Optimize Ethereum, the Layer 1 (L1), to serve primarily as the settlement and data availability layer. + +Following the [Merge](https://github.com/ethereum/consensus-specs/tree/dev/specs/bellatrix), (see the [consensus spec](https://github.com/ethereum/consensus-specs), [annotated spec](https://github.com/ethereum/annotated-spec/blob/master/merge/beacon-chain.md), and [execution spec](https://github.com/ethereum/execution-specs/blob/master/network-upgrades/mainnet-upgrades/paris.md)), the Ethereum chain has been divided into two distinct chains: the [consensus layer (CL)](https://github.com/ethereum/consensus-specs) and the [execution layer (EL)](https://github.com/ethereum/execution-specs). The consensus layer is responsible for the security, decentralization, and censorship-resistant properties of Ethereum, while the execution layer is responsible for executing transactions within each new block proposed by the consensus layer. These transactions update the global state of the chain, which is securely stored on the CL. + +While the EL can be used for direct L1 dApp transactions, the goal, as mentioned earlier, is for dApp transactions to move entirely to L2 rollups. The EL will primarily be used by rollups to update the L2 state or as a backup if for some reasons the L2 is [stopping working](https://docs.arbitrum.io/sequencer#unhappyuncommon-case-sequencer-isnt-doing-its-job). + +The CL will be used by rollups for Data Availability (DA) and to store proofs of validity, especially for ZK rollups. To achieve scalability and reduce gas costs, storing data on the CL blocks must be affordable in the long term. To accomplish this ambitious roadmap, the development of the CL can be outlined in the following phases: + +- Proto-danksharding ([EIP-4844](https://eips.ethereum.org/EIPS/eip-4844)), the upgrade introducing blobs (live on March 14, 2024). +- Increasing [blob count & gas modifications](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567) (planned for EOY 2024). +- Addition of [PeerDAS](https://ethresear.ch/t/peerdas-a-simpler-das-approach-using-battle-tested-p2p-components/16541). +- Full implementation of [Danksharding](https://ethresear.ch/t/from-4844-to-danksharding-a-path-to-scaling-ethereum-da/18046). + +In the following section, we discuss how EIP-4844 will impact the EL and CL. diff --git a/docs/wiki/research/scaling/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md similarity index 92% rename from docs/wiki/research/scaling/eip-4844.md rename to docs/wiki/research/scaling/core-changes/eip-4844.md index cb70f2e7..b0cdfcfe 100644 --- a/docs/wiki/research/scaling/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -1,6 +1,11 @@ # EIP-4844 -[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces Blobs, a new space to store data inside a transaction that will be much cheaper than `calldata` because they will have a new type of gas that is independent of normal gas and follows its own targeting rule. +## Overview + +L2 Rollups must allow the permissionless reconstruction of the L2 state. To achieve this, they must ensure Data Availability, which refers to the global ordering of inputs for transactions that have altered the state. +Before 4844 was live on mainnet, rollups have been storing data only via a section of the transaction known as `calldata`. + +This `calldata` represented the primary bottleneck for scaling Ethereum, as storing data in calldata is expensive and the plan is to make it [even more expensive](https://eips.ethereum.org/EIPS/eip-7623). [EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces Blobs, a new space to store data inside a transaction that will be much cheaper than `calldata` because they will have a new type of gas that is independent of normal gas and follows its own targeting rule. The page outlines the EIP, providing code references to understand the changes brought by this hard fork. It targets aspiring Ethereum core developers interested in comprehending Ethereum's code post-update. From 41f21a0c1f1ee6e389ba52752a943842119fd11c Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Wed, 6 Mar 2024 15:07:45 +0100 Subject: [PATCH 031/101] Addressing feedback at [comment](https://github.com/eth-protocol-fellows/protocol-studies/pull/51#discussion_r1508807677): describe the discussion around gas handling with the introduction of eip-4844 --- .../research/scaling/core-changes/eip-4844.md | 16 ++++++++++++++-- 1 file changed, 14 insertions(+), 2 deletions(-) diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index b0cdfcfe..380a6959 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -5,9 +5,21 @@ L2 Rollups must allow the permissionless reconstruction of the L2 state. To achieve this, they must ensure Data Availability, which refers to the global ordering of inputs for transactions that have altered the state. Before 4844 was live on mainnet, rollups have been storing data only via a section of the transaction known as `calldata`. -This `calldata` represented the primary bottleneck for scaling Ethereum, as storing data in calldata is expensive and the plan is to make it [even more expensive](https://eips.ethereum.org/EIPS/eip-7623). [EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces Blobs, a new space to store data inside a transaction that will be much cheaper than `calldata` because they will have a new type of gas that is independent of normal gas and follows its own targeting rule. +This page outlines the EIP, providing code references to understand the changes brought by this hard fork. It targets aspiring Ethereum core developers interested in comprehending Ethereum's code post-update. -The page outlines the EIP, providing code references to understand the changes brought by this hard fork. It targets aspiring Ethereum core developers interested in comprehending Ethereum's code post-update. +## New Gas Handling + +`calldata` has represented a primary bottleneck for scaling Ethereum, as storing data in `calldata` is costly, with plans to make it [even more so](https://eips.ethereum.org/EIPS/eip-7623). + +[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs," a new way to store data within a transaction that will be significantly cheaper than using `calldata`. This is because Blobs will utilize a new type of gas, independent from the conventional gas, and follow their own pricing rules. + +EIP-4844 marks the initial step towards [achieving more efficient gas usage](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). + +The aim of these EIPs is to achieve a smaller and less variable block size. This goal is beneficial for two main reasons: it offers protection for solo stakers and creates additional capacity for future Blob storage. + +But how can we achieve a smaller and less variable block size? One method is by increasing the cost of non-zero `calldata` bytes as proposed in [EIP-7623](https://eips.ethereum.org/EIPS/eip-7623). Raising the `calldata` cost reduces the maximum possible block size (assuming the `gas limit` remains at 30,000,000 and the gas cost for each `calldata` byte increases, resulting in fewer bytes fitting inside a block). Moreover, the increased `calldata` costs further encourage the use of Blobs for data availability. + +The exploration of new, efficient ways to manage gas and the block gas limit remains [a subject of active discussion](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). ## Specification From ad9422b9a3aa6bb510f0fd76f2719bba0358bfdb Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Wed, 6 Mar 2024 15:33:43 +0100 Subject: [PATCH 032/101] Addressing feedback at [comment](https://github.com/eth-protocol-fellows/protocol-studies/pull/51#discussion_r1508812872): mentioning both EIP-4490 and EIP-4488 as previous attempts to improve scalability of Ethereum. --- .../research/scaling/core-changes/eip-4844.md | 18 +++++++----------- 1 file changed, 7 insertions(+), 11 deletions(-) diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index 380a6959..6e6774db 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -219,19 +219,15 @@ blob_gas_used += get_total_blob_gas(tx) ## A note about previous attempts/research to improve scalability for rollups -To accomplish scalability, the idea was initially to decrease transaction `calldata` gas cost with [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488). However, this EIP is now irrelevant because EIP-4844 has been implemented instead. Here is a brief introduction for the EIP-4488. +To enhance scalability, two Ethereum Improvement Proposals (EIPs) were proposed: [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488) and [EIP-4490](https://github.com/ethereum/EIPs/pull/4490). -### EIP-4488 +At their core, both EIPs aim to reduce the gas cost associated with transaction `calldata`. EIP-4490 suggests lowering the `calldata` cost from 16 to 6 gas per byte. This change, while straightforward to implement, could potentially increase the maximum block size to 5MB. Conversely, EIP-4488 proposes a more significant reduction, from 16 to 3 gas per byte, but introduces a cap on the amount of `CALLDATA` permitted in each block to limit block size effectively. -Initally [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488) was proposed to decrease the gas cost of `calldata`, and to add a limit of how much total transaction `calldata` can be in a block. The goal was to make Rollups transactions cheaper. -Currently, the cost for a non zero byte of `calldata` costs 16 units of gas. With this EIP, the cost for a byte of `calldata` (regardless if is 0 or a non zero byte) would be 3 bytes. +For a more detailed discussion on these two proposals, consider checking [this tweet](https://twitter.com/TimBeiko/status/1464268807854190594) by Tim Beiko. -This would have introduced the following parameters: +Please note that the aforementioned EIPs, [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488) and [EIP-4490](https://github.com/ethereum/EIPs/pull/4490), are now deprecated in favor of the introduction of Blobs. -| Parameter | Value | -| --------------------------- | --------- | -| NEW_CALLDATA_GAS_COST | 3 | -| BASE_MAX_CALLDATA_PER_BLOCK | 1,048,576 | -| CALLDATA_PER_TX_STIPEND | 300 | +## Further Reading -However, this EIP is now irrelevant because EIP-4844 has been implemented instead. Contrary to the original idea, the approach will be the exact opposite with [EIP-7623](https://eips.ethereum.org/EIPS/eip-7623), to increase `calldata` cost to decrease the maximum block size. +- [https://www.eip4844.com/](https://www.eip4844.com/) +- [https://domothy.com/blobspace/](https://domothy.com/blobspace/) From 64281d6032c8fc145719e9fd372a1b9a96a561fb Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Wed, 6 Mar 2024 17:20:16 +0100 Subject: [PATCH 033/101] Add a quote from the protodanksharding faq in the overview section of eip-4844 --- docs/wiki/research/scaling/core-changes/eip-4844.md | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index 6e6774db..a30e2b00 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -5,13 +5,19 @@ L2 Rollups must allow the permissionless reconstruction of the L2 state. To achieve this, they must ensure Data Availability, which refers to the global ordering of inputs for transactions that have altered the state. Before 4844 was live on mainnet, rollups have been storing data only via a section of the transaction known as `calldata`. +[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs", which modifies the current transaction structure defined in the [exeuction-specs](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49) by introducing a new transaction type, the blob-carrying transaction. + +Quoted from [proto-danksharding-faq(aka EIP-4844)](https://notes.ethereum.org/@vbuterin/proto_danksharding_faq#What-is-proto-danksharding-aka-EIP-4844): + +> The main feature introduced by proto-danksharding is new transaction type, which we call a blob-carrying transaction. A blob-carrying transaction is like a regular transaction, except it also carries an extra piece of data called a blob. Blobs are extremely large (~125 kB), and can be much cheaper than similar amounts of calldata. However, blob data is not accessible to EVM execution; the EVM can only view a commitment to the blob. + This page outlines the EIP, providing code references to understand the changes brought by this hard fork. It targets aspiring Ethereum core developers interested in comprehending Ethereum's code post-update. ## New Gas Handling `calldata` has represented a primary bottleneck for scaling Ethereum, as storing data in `calldata` is costly, with plans to make it [even more so](https://eips.ethereum.org/EIPS/eip-7623). -[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs," a new way to store data within a transaction that will be significantly cheaper than using `calldata`. This is because Blobs will utilize a new type of gas, independent from the conventional gas, and follow their own pricing rules. +[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs" a new way to store data within a transaction that will be significantly cheaper than using `calldata`. This is because Blobs will utilize a new type of gas, independent from the conventional gas, and follow their own pricing rules. EIP-4844 marks the initial step towards [achieving more efficient gas usage](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). From b00c671f4aad6930bd3fb0eab5121e257a1b9968 Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Wed, 6 Mar 2024 17:24:11 +0100 Subject: [PATCH 034/101] Addressing [comment](https://github.com/eth-protocol-fellows/protocol-studies/pull/51#discussion_r1508810204): add more resources for KZG commitments --- docs/wiki/research/scaling/core-changes/eip-4844.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index a30e2b00..97e23ad0 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -179,6 +179,12 @@ With EIP-4844, the `process_execution_payload` adds the parameter `versioned_has KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correcteness. +Check the following links to learn more: + +- [KZG Cerymony](https://github.com/ethereum/kzg-ceremony) +- [Arithmetic hash based alternatives to KZG for proto-danksharding (EIP-4844)](https://ethresear.ch/t/arithmetic-hash-based-alternatives-to-kzg-for-proto-danksharding-eip-4844/13863) +- [Sharding multi-party computation ceremony](https://ethresear.ch/t/sharding-multi-party-computation-ceremony/11779) + #### 3. New Block Header checks See go-ethereum file "consensus.go" for checks added to the block header: From 23ab42d34100f92d3ab897c3c64b1e6ce5fa8bfb Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Sun, 10 Mar 2024 10:25:50 +0100 Subject: [PATCH 035/101] fix typo --- docs/wiki/research/scaling/core-changes/core-changes.md | 2 +- docs/wiki/research/scaling/core-changes/eip-4844.md | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/wiki/research/scaling/core-changes/core-changes.md b/docs/wiki/research/scaling/core-changes/core-changes.md index fddb9fb7..16900115 100644 --- a/docs/wiki/research/scaling/core-changes/core-changes.md +++ b/docs/wiki/research/scaling/core-changes/core-changes.md @@ -11,7 +11,7 @@ While the EL can be used for direct L1 dApp transactions, the goal, as mentioned The CL will be used by rollups for Data Availability (DA) and to store proofs of validity, especially for ZK rollups. To achieve scalability and reduce gas costs, storing data on the CL blocks must be affordable in the long term. To accomplish this ambitious roadmap, the development of the CL can be outlined in the following phases: -- Proto-danksharding ([EIP-4844](https://eips.ethereum.org/EIPS/eip-4844)), the upgrade introducing blobs (live on March 14, 2024). +- Proto-danksharding ([EIP-4844](https://eips.ethereum.org/EIPS/eip-4844)), the upgrade introducing blobs (live on March 14th, 2024). - Increasing [blob count & gas modifications](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567) (planned for EOY 2024). - Addition of [PeerDAS](https://ethresear.ch/t/peerdas-a-simpler-das-approach-using-battle-tested-p2p-components/16541). - Full implementation of [Danksharding](https://ethresear.ch/t/from-4844-to-danksharding-a-path-to-scaling-ethereum-da/18046). diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index 97e23ad0..f967b721 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -5,7 +5,7 @@ L2 Rollups must allow the permissionless reconstruction of the L2 state. To achieve this, they must ensure Data Availability, which refers to the global ordering of inputs for transactions that have altered the state. Before 4844 was live on mainnet, rollups have been storing data only via a section of the transaction known as `calldata`. -[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs", which modifies the current transaction structure defined in the [exeuction-specs](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49) by introducing a new transaction type, the blob-carrying transaction. +[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs", which modifies the current transaction structure defined in the [execution-specs](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49) by introducing a new transaction type, the blob-carrying transaction. Quoted from [proto-danksharding-faq(aka EIP-4844)](https://notes.ethereum.org/@vbuterin/proto_danksharding_faq#What-is-proto-danksharding-aka-EIP-4844): From e81f281b4f06a2b616fd29a3ffc3b91d28d6948f Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Sun, 10 Mar 2024 10:36:53 +0100 Subject: [PATCH 036/101] fix links --- .../research/scaling/core-changes/eip-4844.md | 20 +++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index f967b721..8373c29b 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -34,20 +34,20 @@ _PLEASE NOTE that some specification links may be broken/missing due to the curr ### Parameters - [BLOB_TX_TYPE](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/tests/core/pyspec/eth2spec/test/helpers/sharding.py#L24) -- [BYTES_PER_FIELD_ELEMENT](https://github.com/ethereum/consensus-specs/blob/dev/pysetup/spec_builders/deneb.py) -- [FIELD_ELEMENTS_PER_BLOB](https://github.com/ethereum/consensus-specs/blob/dev/pysetup/spec_builders/deneb.py) +- [BYTES_PER_FIELD_ELEMENT](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/pysetup/spec_builders/deneb.py#L70) +- [FIELD_ELEMENTS_PER_BLOB](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/pysetup/spec_builders/deneb.py#L71) - [BLS_MODULUS](https://github.com/ethereum/consensus-specs/blob/dev/specs/_features/whisk/beacon-chain.md#bls) -- [VERSIONED_HASH_VERSION_KZG](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md) -- [MAX_BLOB_GAS_PER_BLOCK](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md) -- [GAS_PER_BLOB](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md) -- [MIN_EPOCHS_FOR_BLOB_SIDECARS_REQUESTS](https://github.com/ethereum/consensus-specs/blob/dev/configs/mainnet.yaml) +- [VERSIONED_HASH_VERSION_KZG](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#blob) +- [MAX_BLOB_GAS_PER_BLOCK](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#execution) +- [GAS_PER_BLOB](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#execution) +- [MIN_EPOCHS_FOR_BLOB_SIDECARS_REQUESTS](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/configs/mainnet.yaml#L148) ### Type Aliases -- [Blob](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md) -- [VersionedHash](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md) -- [KZGCommitment](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md) -- [KZGProof](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md) +- [Blob](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md#blob) +- [VersionedHash](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#custom-types) +- [KZGCommitment](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md#custom-types) +- [KZGProof](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md#custom-types) ### Cryptographic Helpers From 14967618465d30e43d2684ddfdc02fb6459bedaf Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Sun, 10 Mar 2024 10:40:31 +0100 Subject: [PATCH 037/101] fix link --- .../research/scaling/core-changes/eip-4844.md | 30 +++++++++---------- 1 file changed, 15 insertions(+), 15 deletions(-) diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index 8373c29b..1ee4c984 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -13,20 +13,6 @@ Quoted from [proto-danksharding-faq(aka EIP-4844)](https://notes.ethereum.org/@v This page outlines the EIP, providing code references to understand the changes brought by this hard fork. It targets aspiring Ethereum core developers interested in comprehending Ethereum's code post-update. -## New Gas Handling - -`calldata` has represented a primary bottleneck for scaling Ethereum, as storing data in `calldata` is costly, with plans to make it [even more so](https://eips.ethereum.org/EIPS/eip-7623). - -[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs" a new way to store data within a transaction that will be significantly cheaper than using `calldata`. This is because Blobs will utilize a new type of gas, independent from the conventional gas, and follow their own pricing rules. - -EIP-4844 marks the initial step towards [achieving more efficient gas usage](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). - -The aim of these EIPs is to achieve a smaller and less variable block size. This goal is beneficial for two main reasons: it offers protection for solo stakers and creates additional capacity for future Blob storage. - -But how can we achieve a smaller and less variable block size? One method is by increasing the cost of non-zero `calldata` bytes as proposed in [EIP-7623](https://eips.ethereum.org/EIPS/eip-7623). Raising the `calldata` cost reduces the maximum possible block size (assuming the `gas limit` remains at 30,000,000 and the gas cost for each `calldata` byte increases, resulting in fewer bytes fitting inside a block). Moreover, the increased `calldata` costs further encourage the use of Blobs for data availability. - -The exploration of new, efficient ways to manage gas and the block gas limit remains [a subject of active discussion](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). - ## Specification _PLEASE NOTE that some specification links may be broken/missing due to the currently active development of EIP-4844._ @@ -135,6 +121,20 @@ class BlobTransaction: # the class name may change s: U256 ``` +### New Gas Handling + +`calldata` has represented a primary bottleneck for scaling Ethereum, as storing data in `calldata` is costly, with plans to make it [even more so](https://eips.ethereum.org/EIPS/eip-7623). + +[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs" a new way to store data within a transaction that will be significantly cheaper than using `calldata`. This is because Blobs will utilize a new type of gas, independent from the conventional gas, and follow their own pricing rules. + +EIP-4844 marks the initial step towards [achieving more efficient gas usage](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). + +The aim of these EIPs is to achieve a smaller and less variable block size. This goal is beneficial for two main reasons: it offers protection for solo stakers and creates additional capacity for future Blob storage. + +But how can we achieve a smaller and less variable block size? One method is by increasing the cost of non-zero `calldata` bytes as proposed in [EIP-7623](https://eips.ethereum.org/EIPS/eip-7623). Raising the `calldata` cost reduces the maximum possible block size (assuming the `gas limit` remains at 30,000,000 and the gas cost for each `calldata` byte increases, resulting in fewer bytes fitting inside a block). Moreover, the increased `calldata` costs further encourage the use of Blobs for data availability. + +The exploration of new, efficient ways to manage gas and the block gas limit remains [a subject of active discussion](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). + ### Header Extension The current header encoding is extended with two new 64-bit unsigned integer fields, `blob_gas_used` and `excess_blob_gas`. Blob transactions have their own gas targeting rules (similar to EIP-1559) and nodes must take into account gas spent to store data in blobs in addition to the normal gas fees spent to execute transaction (see below in **Changes on the Execution Specs**). @@ -189,7 +189,7 @@ Check the following links to learn more: See go-ethereum file "consensus.go" for checks added to the block header: -- [link](https://github.com/ethereum/go-ethereum/blob/0a2f33946b95989e8ce36e72a88138adceab6a23/consensus/beacon/consensus.go#L274) +- [link](https://github.com/ethereum/go-ethereum/blob/0a2f33946b95989e8ce36e72a88138adceab6a23/consensus/beacon/consensus.go#L274C1-L284C3) ### Changes on the Execution Specs From c33fde7656f182c4a595d6eea14b80510d97d2de Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Sun, 10 Mar 2024 11:04:34 +0100 Subject: [PATCH 038/101] fix link --- docs/wiki/research/scaling/core-changes/eip-4844.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index 1ee4c984..80c8caa4 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -42,7 +42,7 @@ _PLEASE NOTE that some specification links may be broken/missing due to the curr ### New Transaction Data Structure (BLOB_TX_TYPE) -Before EIP-4844, the Transaction data structure was the following ([ethereum exeuction-specs repository](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49)): +Before EIP-4844, the Transaction data structure was the following ([ethereum exeuction-specs repository](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49C1-L108C2)): ```python @slotted_freezable From 94d706d36ff85319e18c4928a21872c6a5e1c4d1 Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Sun, 10 Mar 2024 12:47:11 +0100 Subject: [PATCH 039/101] improve eip-4844 doc structure and include sidecar design explanation --- .../research/scaling/core-changes/eip-4844.md | 249 +++++++++--------- 1 file changed, 129 insertions(+), 120 deletions(-) diff --git a/docs/wiki/research/scaling/core-changes/eip-4844.md b/docs/wiki/research/scaling/core-changes/eip-4844.md index 80c8caa4..b5b91b22 100644 --- a/docs/wiki/research/scaling/core-changes/eip-4844.md +++ b/docs/wiki/research/scaling/core-changes/eip-4844.md @@ -5,7 +5,9 @@ L2 Rollups must allow the permissionless reconstruction of the L2 state. To achieve this, they must ensure Data Availability, which refers to the global ordering of inputs for transactions that have altered the state. Before 4844 was live on mainnet, rollups have been storing data only via a section of the transaction known as `calldata`. -[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs", which modifies the current transaction structure defined in the [execution-specs](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49) by introducing a new transaction type, the blob-carrying transaction. +[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs", which modifies the current transaction and block structure defined in the [execution-specs](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49) and [consensus-specs](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/specs/deneb/beacon-chain.md#beaconblockbody) respectively. + +EIP-4844 introduces a new transaction type, the blob-carrying transaction. Quoted from [proto-danksharding-faq(aka EIP-4844)](https://notes.ethereum.org/@vbuterin/proto_danksharding_faq#What-is-proto-danksharding-aka-EIP-4844): @@ -13,34 +15,122 @@ Quoted from [proto-danksharding-faq(aka EIP-4844)](https://notes.ethereum.org/@v This page outlines the EIP, providing code references to understand the changes brought by this hard fork. It targets aspiring Ethereum core developers interested in comprehending Ethereum's code post-update. -## Specification +## Core changes -_PLEASE NOTE that some specification links may be broken/missing due to the currently active development of EIP-4844._ +### New Gas Handling -### Parameters +`calldata` has represented a primary bottleneck for scaling Ethereum, as storing data in `calldata` is costly, with plans to make it [even more so](https://eips.ethereum.org/EIPS/eip-7623). -- [BLOB_TX_TYPE](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/tests/core/pyspec/eth2spec/test/helpers/sharding.py#L24) -- [BYTES_PER_FIELD_ELEMENT](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/pysetup/spec_builders/deneb.py#L70) -- [FIELD_ELEMENTS_PER_BLOB](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/pysetup/spec_builders/deneb.py#L71) -- [BLS_MODULUS](https://github.com/ethereum/consensus-specs/blob/dev/specs/_features/whisk/beacon-chain.md#bls) -- [VERSIONED_HASH_VERSION_KZG](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#blob) -- [MAX_BLOB_GAS_PER_BLOCK](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#execution) -- [GAS_PER_BLOB](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#execution) -- [MIN_EPOCHS_FOR_BLOB_SIDECARS_REQUESTS](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/configs/mainnet.yaml#L148) +[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs" a new way to store data within a transaction that will be significantly cheaper than using `calldata`. This is because Blobs will utilize a new type of gas, independent from the conventional gas, and follow their own pricing rules. -### Type Aliases +EIP-4844 marks the initial step towards [achieving more efficient gas usage](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). -- [Blob](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md#blob) -- [VersionedHash](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#custom-types) -- [KZGCommitment](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md#custom-types) -- [KZGProof](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md#custom-types) +The aim of these EIPs is to achieve a smaller and less variable block size. This goal is beneficial for two main reasons: it offers protection for solo stakers and creates additional capacity for future Blob storage. + +But how can we achieve a smaller and less variable block size? One method is by increasing the cost of non-zero `calldata` bytes as proposed in [EIP-7623](https://eips.ethereum.org/EIPS/eip-7623). Raising the `calldata` cost reduces the maximum possible block size (assuming the `gas limit` remains at 30,000,000 and the gas cost for each `calldata` byte increases, resulting in fewer bytes fitting inside a block). Moreover, the increased `calldata` costs further encourage the use of Blobs for data availability. -### Cryptographic Helpers +The exploration of new, efficient ways to manage gas and the block gas limit remains [a subject of active discussion](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). -- [verify_kzg_proof()](https://github.com/ethereum/consensus-specs/blob/86fb82b221474cc89387fa6436806507b3849d88/specs/deneb/polynomial-commitments.md#verify_kzg_proof) -- [verify_blob_kzg_proof_batch()](https://github.com/ethereum/consensus-specs/blob/86fb82b221474cc89387fa6436806507b3849d88/specs/deneb/polynomial-commitments.md#verify_blob_kzg_proof_batch) +### Changes on the Consensus Specs + +The upgrade which will introduce EIP-4844 into the Consensus Layer has been labeled **Deneb**. + +#### 1. Beacon Block Data Structure changes + +The `BeaconBlockBody` (the data structure representing a block of transactions in the Consensus Layer) is updated to include 2 new more fields: `blob_kzg_commitments` and an updated version of the `execution_payload` field. + +See [here](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#beaconblockbody). + +Is important to note that Blobs will not be added to the block to which they belong to. They will instead referenced in the block by using the `blob_kzg_commitments`. Blobs are propagated separately to the network via "sidecars". + +KZG commitments are a type of cryptographic commitment particularly useful for their efficiency in creating and verifying proofs of data availability and correctness. + +KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correcteness. + +Check the following links to learn more: + +- [KZG Cerymony](https://github.com/ethereum/kzg-ceremony) +- [Arithmetic hash based alternatives to KZG for proto-danksharding (EIP-4844)](https://ethresear.ch/t/arithmetic-hash-based-alternatives-to-kzg-for-proto-danksharding-eip-4844/13863) +- [Sharding multi-party computation ceremony](https://ethresear.ch/t/sharding-multi-party-computation-ceremony/11779) + +#### 2. Blob Sidecars + +As stated in the [EIP-4844](https://eips.ethereum.org/EIPS/eip-4844#consensus-layer-validation) blobs are referenced but not fully encoded inside the [beacon block body](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#beaconblockbody). Instead of embedding the full contents in the body, the blobs are propagated separately, as "sidecars". + +For the sidecar data structure, see [here](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/p2p-interface.md#blobsidecar) + +Before propagating the blob sidecars to the p2p network, nodes must verify the Blobs are valid (see [here](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/p2p-interface.md#blob-subnets)). + +When a node requests a blob to the network the network responds with a `BlobSidecar` data structure. +The node receiving the sidecar should verify that blob sidecar is well-formatted, has valid inclusion proof, and is correct w.r.t. the expected KZG commitments before reading the data in a blob. + +This "sidecars" design provides forward compatibility for further data increases by black-boxing [is_data_available](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/fork-choice.md#is_data_available), which means that in future upgrades `is_data_available()` implementation may change, for example to include data-availability-sampling (DAS), and the system interacting with this function is not required to understand the inner implementation of the function (in programming terms, `is_data_available()` can be considered as an interface method where the implementation may change over time). + +#### 3. Inclusion of KZG Committment versioned hashes + +The Consensus Layer (CL, also called Beacon chain) calls the [`process_execution_payload`](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) function when a new block payload is submitted to the chain. This function is responsible to perform some validity checks on the block's payload and then invoke the Execution Layer (EL) via the `verify_and_notify_new_payload` function. + +Once invoked, the EL will: + +- validate the block payload +- execute transactions inside the block payload +- update the state, which is the result of executing transactions + +With EIP-4844, the `process_execution_payload` adds the parameter `versioned_hashes` to be passed to the `verify_and_notify_new_payload` function. + +`versioned_hashes` is an array of [hashes](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) for each blob of KZG Committment. + +#### 4. Execution Payload and Execution Payload Header + +The Execution Payload [which is the payload sent from the Consensus Layer to the State Transition Function on the Execution Layer](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/specs/deneb/beacon-chain.md#execution-payload) is extended with two new 64-bit unsigned integer fields, `blob_gas_used` and `excess_blob_gas`. Blob transactions have their own gas targeting rules (as described in the above section) and nodes must take into account gas spent to store data in blobs in addition to the normal gas fees spent to execute transaction (see below in **Changes on the Execution Specs**). + +- See [1](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/specs/deneb/beacon-chain.md#executionpayload) and [2](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/specs/deneb/beacon-chain.md?plain=1#L149) + +#### 5. New Block Header checks + +See go-ethereum file "consensus.go" for checks added to the block header: + +- [link](https://github.com/ethereum/go-ethereum/blob/0a2f33946b95989e8ce36e72a88138adceab6a23/consensus/beacon/consensus.go#L274C1-L284C3) + +### Changes on the Execution Specs + +The upgrade which will introduce EIP-4844 into the Execution Layer has been labeled **Cancun**. + +#### 1. Add checks inside the State Transition Function + +The EL now must check that the blob specific fields are valid for each transaction that is going to be executed in the State Transition Function (STF). + +The checks include (For the specs code, see [here](https://eips.ethereum.org/EIPS/eip-4844#execution-layer-validation)): + +- check that the signer has enough balance to cover the cost of both transaction gas fee and blob gas fees + +```python +# modify the check for sufficient balance +max_total_fee = tx.gas * tx.max_fee_per_gas +if get_tx_type(tx) == BLOB_TX_TYPE: + max_total_fee += get_total_blob_gas(tx) * tx.max_fee_per_blob_gas +assert signer(tx).balance >= max_total_fee +``` + +- check that the blob transaction contains at least 1 valid `blob_versioned_hash` (see CL changes) and that they are formatted correctly + +```python +assert len(tx.blob_versioned_hashes) > 0 +``` + +- check that the user is willing to pay at least the current blob base fee + +```python +assert tx.max_fee_per_blob_gas >= get_blob_base_fee(block.header) +``` + +Finally, the EL STF must keep track of the gas being gas used for blob transactions (same as it already happens for EIP1559 transactions). + +```python +blob_gas_used += get_total_blob_gas(tx) +``` -### New Transaction Data Structure (BLOB_TX_TYPE) +#### 2. New Transaction Data Structure (BLOB_TX_TYPE) Before EIP-4844, the Transaction data structure was the following ([ethereum exeuction-specs repository](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/src/ethereum/london/fork_types.py#L49C1-L108C2)): @@ -121,114 +211,33 @@ class BlobTransaction: # the class name may change s: U256 ``` -### New Gas Handling +### New Parameters -`calldata` has represented a primary bottleneck for scaling Ethereum, as storing data in `calldata` is costly, with plans to make it [even more so](https://eips.ethereum.org/EIPS/eip-7623). - -[EIP-4844](https://eips.ethereum.org/EIPS/eip-4844) introduces "Blobs" a new way to store data within a transaction that will be significantly cheaper than using `calldata`. This is because Blobs will utilize a new type of gas, independent from the conventional gas, and follow their own pricing rules. - -EIP-4844 marks the initial step towards [achieving more efficient gas usage](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). - -The aim of these EIPs is to achieve a smaller and less variable block size. This goal is beneficial for two main reasons: it offers protection for solo stakers and creates additional capacity for future Blob storage. - -But how can we achieve a smaller and less variable block size? One method is by increasing the cost of non-zero `calldata` bytes as proposed in [EIP-7623](https://eips.ethereum.org/EIPS/eip-7623). Raising the `calldata` cost reduces the maximum possible block size (assuming the `gas limit` remains at 30,000,000 and the gas cost for each `calldata` byte increases, resulting in fewer bytes fitting inside a block). Moreover, the increased `calldata` costs further encourage the use of Blobs for data availability. +- [BLOB_TX_TYPE](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/tests/core/pyspec/eth2spec/test/helpers/sharding.py#L24) +- [BYTES_PER_FIELD_ELEMENT](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/pysetup/spec_builders/deneb.py#L70) +- [FIELD_ELEMENTS_PER_BLOB](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/pysetup/spec_builders/deneb.py#L71) +- [BLS_MODULUS](https://github.com/ethereum/consensus-specs/blob/dev/specs/_features/whisk/beacon-chain.md#bls) +- [VERSIONED_HASH_VERSION_KZG](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#blob) +- [MAX_BLOB_GAS_PER_BLOCK](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#execution) +- [GAS_PER_BLOB](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#execution) +- [MIN_EPOCHS_FOR_BLOB_SIDECARS_REQUESTS](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/configs/mainnet.yaml#L148) -The exploration of new, efficient ways to manage gas and the block gas limit remains [a subject of active discussion](https://ethresear.ch/t/on-increasing-the-block-gas-limit/18567). +### New Type Aliases -### Header Extension +- [Blob](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md#blob) +- [VersionedHash](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#custom-types) +- [KZGCommitment](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md#custom-types) +- [KZGProof](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/polynomial-commitments.md#custom-types) -The current header encoding is extended with two new 64-bit unsigned integer fields, `blob_gas_used` and `excess_blob_gas`. Blob transactions have their own gas targeting rules (similar to EIP-1559) and nodes must take into account gas spent to store data in blobs in addition to the normal gas fees spent to execute transaction (see below in **Changes on the Execution Specs**). +### New Cryptographic Helpers -- [ExecutionPayloadHeader](https://github.com/ethereum/consensus-specs/blob/1a33bf8a00bb593d61a9128c929b8dcacef0b437/specs/deneb/beacon-chain.md?plain=1#L149) +- [verify_kzg_proof()](https://github.com/ethereum/consensus-specs/blob/86fb82b221474cc89387fa6436806507b3849d88/specs/deneb/polynomial-commitments.md#verify_kzg_proof) +- [verify_blob_kzg_proof_batch()](https://github.com/ethereum/consensus-specs/blob/86fb82b221474cc89387fa6436806507b3849d88/specs/deneb/polynomial-commitments.md#verify_blob_kzg_proof_batch) -### Opcode to get versioned hashes +### New Opcodes - [BLOBHASH](https://github.com/ethereum/execution-specs/blob/0f9e4345b60d36c23fffaa69f70cf9cdb975f4ba/lists/evm/proposed-opcodes.md?plain=1#L60) -### Changes on the Consensus Specs - -The upgrade which will introduce EIP-4844 into the Consensus Layer has been labeled **Deneb**. - -#### 1. Consensus Layer Validation - -As stated in the [EIP-4844](https://eips.ethereum.org/EIPS/eip-4844#consensus-layer-validation) blobs are referenced but not fully encoded inside the beacon block body. Instead of embedding the full contents in the body, the blobs are propagated separately, as "sidecars". - -This "sidecars" design provides forward compatibility for further data increases by black-boxing `is_data_available()`, which means that in future upgrades `is_data_available()` implementation may change, for example to include data-availability-sampling (DAS), and the system interacting with this function is not required to understand the inner implementation of the function (in programming terms, `is_data_available()` can be considered as an interface method where the implementation may change over time). - -To learn more about the changes, see the consensus-specs: - -- [is_data_available](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/fork-choice.md#is_data_available) -- [BeaconBlockBody](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#beaconblockbody) -- [p2p network](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/p2p-interface.md#why-are-blobs-relayed-as-a-sidecar-separate-from-beacon-blocks) - -#### 2. Inclusion of KZG Committment versioned hashes - -The Consensus Layer (CL, also called Beacon chain) calls the [`process_execution_payload`](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) function when a new block payload is submitted to the chain. This function is responsible to perform some validity checks on the block's payload and then invoke the Execution Layer (EL) via the `verify_and_notify_new_payload` function. - -Once invoked, the EL will: - -- validate the block payload -- execute transactions inside the block payload -- update the state, which is the result of executing transactions -- build the new block -- return the new block to the CL - -With EIP-4844, the `process_execution_payload` adds the parameter `versioned_hashes` to be passed to the `verify_and_notify_new_payload` function. - -`versioned_hashes` is an array of [hashes](https://github.com/ethereum/consensus-specs/blob/dev/specs/deneb/beacon-chain.md#modified-process_execution_payload) for each blob of KZG Committment, which are a type of cryptographic commitment particularly useful for their efficiency in creating and verifying proofs of data availability and correctness. - -KZG commitments provide the ability to prove that specific pieces of data are included in the set without revealing the entire dataset. This is particularly useful for scalability solutions because it does not require for every node to store the whole blockchain to prove transactions correcteness. - -Check the following links to learn more: - -- [KZG Cerymony](https://github.com/ethereum/kzg-ceremony) -- [Arithmetic hash based alternatives to KZG for proto-danksharding (EIP-4844)](https://ethresear.ch/t/arithmetic-hash-based-alternatives-to-kzg-for-proto-danksharding-eip-4844/13863) -- [Sharding multi-party computation ceremony](https://ethresear.ch/t/sharding-multi-party-computation-ceremony/11779) - -#### 3. New Block Header checks - -See go-ethereum file "consensus.go" for checks added to the block header: - -- [link](https://github.com/ethereum/go-ethereum/blob/0a2f33946b95989e8ce36e72a88138adceab6a23/consensus/beacon/consensus.go#L274C1-L284C3) - -### Changes on the Execution Specs - -The upgrade which will introduce EIP-4844 into the Execution Layer has been labeled **Cancun**. - -#### 1. Add checks inside the State Transition Function - -The EL now must check that the blob specific fields are valid for each transaction that is going to be executed in the State Transition Function (STF). - -The checks include (For the specs code, see [here](https://eips.ethereum.org/EIPS/eip-4844#execution-layer-validation)): - -- check that the signer has enough balance to cover the cost of both transaction gas fee and blob gas fees - -```python -# modify the check for sufficient balance -max_total_fee = tx.gas * tx.max_fee_per_gas -if get_tx_type(tx) == BLOB_TX_TYPE: - max_total_fee += get_total_blob_gas(tx) * tx.max_fee_per_blob_gas -assert signer(tx).balance >= max_total_fee -``` - -- check that the blob transaction contains at least 1 valid `blob_versioned_hash` (see CL changes) and that they are formatted correctly - -```python -assert len(tx.blob_versioned_hashes) > 0 -``` - -- check that the user is willing to pay at least the current blob base fee - -```python -assert tx.max_fee_per_blob_gas >= get_blob_base_fee(block.header) -``` - -Finally, the EL STF must keep track of the gas being gas used for blob transactions (same as it already happens for EIP1559 transactions). - -```python -blob_gas_used += get_total_blob_gas(tx) -``` - ## A note about previous attempts/research to improve scalability for rollups To enhance scalability, two Ethereum Improvement Proposals (EIPs) were proposed: [EIP-4488](https://eips.ethereum.org/EIPS/eip-4488) and [EIP-4490](https://github.com/ethereum/EIPs/pull/4490). From 46ca873fcc5f8750101a70acbd3c140e92098572 Mon Sep 17 00:00:00 2001 From: lucadidomenico Date: Mon, 11 Mar 2024 12:55:40 +0100 Subject: [PATCH 040/101] remove "Proto-DankSharding" and "Full Data Sharding" sections from the scalability page as them are already covered in "core-changes.md". --- docs/wiki/research/scaling/scaling.md | 40 +++++++++++++-------------- 1 file changed, 20 insertions(+), 20 deletions(-) diff --git a/docs/wiki/research/scaling/scaling.md b/docs/wiki/research/scaling/scaling.md index 1b829020..9c8a6872 100644 --- a/docs/wiki/research/scaling/scaling.md +++ b/docs/wiki/research/scaling/scaling.md @@ -1,14 +1,17 @@ # Scaling + In computer systems, scalability refers to the ability of a system to perform well under increased or expanding workloads. The primary purpose of blockchain is to handle users' transactions and manage network's ledger state. An increase in workload may result from either a higher demand for transactions by existing users or an increase in the volume of users. + > **Scalability of a blockchain system can be defined as its capacity to process increasing volumes operations, i.e. more transactions without raising demands on network node operators**. ## Scalability Limits -For each block included in the chain, a general agreement on its validity must be reached among a certain percentage of validator nodes, the consensus mechanism is the methodology to achieve this agreement. The **block latency** is the time that takes to a valid block to be included in the chain. -Ethereum uses a proof-of-stake (PoS) based consensus protocol known as [Gasper](https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf) with an ideal block latency fixed in the specification by the constant `SECONDS_PER_SLOT` (12 seconds), however real block latency could be slightly different since blocks could be missed by a specific validator and not to be included in a specific slot. - - Another fundamental blockchain design parameter is the **block size** that is the limit on the amount of data that can be stored in a single block. Ethereum has a config parameter called `gas_limit` to cap the computational effort needed to process a block, which effectively also limits the size of a block. Each operation that takes place within Ethereum, requires a certain amount of "gas" to complete. The total amount of gas for all operations within a block can't exceed Ethereum's `gas_limit`. This approach ensures the network's processing capacity isn't overextended. [EIP-1559](https://eips.ethereum.org/EIPS/eip-1559) defines Ethereum gas pricing mechanism that allows to dynamically adjust the block size to deal with transient network congestions (without never exceed the limit of 30M gas units) and incentivize the network to target a gas amount defined by `gas_target` (15M). A gas limitation restricts the number of transactions (and their computational complexity) that can be included in an Ethereum block. -The block latency and block size directly determine the transactional throughput of the blockchain, which is measured by the **TPS** (transactions per second) metric. Block latency can be influenced by a variety of factors, such as the computational power of the network nodes, the complexity of the consensus mechanism, the network traffic congestion and the block size. Hence, a network made up of a few high-performance nodes tightly connected to each other and using large block sizes can result in an exceptional blockchain with high TPS and remarkably low block latency. However, such a network would likely be highly centralized and require users to make significant trust assumptions. +For each block included in the chain, a general agreement on its validity must be reached among a certain percentage of validator nodes, the consensus mechanism is the methodology to achieve this agreement. The **block latency** is the time that takes to a valid block to be included in the chain. +Ethereum uses a proof-of-stake (PoS) based consensus protocol known as [Gasper](https://eips.ethereum.org/assets/eip-2982/arxiv-2003.03052-Combining-GHOST-and-Casper.pdf) with an ideal block latency fixed in the specification by the constant `SECONDS_PER_SLOT` (12 seconds), however real block latency could be slightly different since blocks could be missed by a specific validator and not to be included in a specific slot. + +Another fundamental blockchain design parameter is the **block size** that is the limit on the amount of data that can be stored in a single block. Ethereum has a config parameter called `gas_limit` to cap the computational effort needed to process a block, which effectively also limits the size of a block. Each operation that takes place within Ethereum, requires a certain amount of "gas" to complete. The total amount of gas for all operations within a block can't exceed Ethereum's `gas_limit`. This approach ensures the network's processing capacity isn't overextended. [EIP-1559](https://eips.ethereum.org/EIPS/eip-1559) defines Ethereum gas pricing mechanism that allows to dynamically adjust the block size to deal with transient network congestions (without never exceed the limit of 30M gas units) and incentivize the network to target a gas amount defined by `gas_target` (15M). A gas limitation restricts the number of transactions (and their computational complexity) that can be included in an Ethereum block. + +The block latency and block size directly determine the transactional throughput of the blockchain, which is measured by the **TPS** (transactions per second) metric. Block latency can be influenced by a variety of factors, such as the computational power of the network nodes, the complexity of the consensus mechanism, the network traffic congestion and the block size. Hence, a network made up of a few high-performance nodes tightly connected to each other and using large block sizes can result in an exceptional blockchain with high TPS and remarkably low block latency. However, such a network would likely be highly centralized and require users to make significant trust assumptions. Another obstacle to decentralization is the size of the blockchain state. **The property of data being accessible when it is needed is known as data availability**. Availability of state data must be guaranteed, including availability of enough data to allow any new node in the network to reconstruct the latest version of the blockchain without any trust assumptions. Have to hold all the data to guarantee data availability can result in high storage requirements for nodes and a lengthy synchronization process for new ones, which can hinder decentralization. Handling a large amount of data is also problematic in terms of network congestion and will require demanding high connection bandwidth from node operators. Ethereum discourages the indiscriminate state growth by making operations that read or write state very expensive. @@ -16,15 +19,15 @@ Note the tight relationship between the design and tuning of a blockchain (conse As part of the game-theory mechanism, to maintain the network sustainability, users must pay a fee to include their transactions. In Ethereum the price of fees is determined by the base fee of the protocol, the amount of gas consumed by a specific transaction and a priority market, those who pay higher priority fees are prioritized. Due to limited TPS, including a transaction in a high decentralized blockchain like Ethereum has become a valuable service. An increase transaction demand for a limited and fixed TPS raises fees to the network usability threshold and requires sacrificing decentralization and/or security in order to scale. -> **Recalling the definition of scalability, classical blockchain systems are not scalable for mass adoption without sacrificing certain levels of decentralization.** +> **Recalling the definition of scalability, classical blockchain systems are not scalable for mass adoption without sacrificing certain levels of decentralization.** This problem is widely known as the **Blockchain Trilemma**, which states that blockchain networks must sacrifice either security, decentralization, or scalability, and maximizing all three at once is difficult. The holy grail of blockchain technology is to create a secure and decentralized transactional network that can achieve a high TPS rate. - !["Blockchain trilemma - Bankless.com"](../img/scaling/blockchain-trilemma.png "Blockchain trilemma - Bankless.com") -## Blockchain Modularity -Modern blockchain designs propose a "divide et impera" approach dividing the system into different specific functional components to independently maximize each vertex of the trilemma. This approach encapsulates the complexity in each part of the system and reduces the systemic complexity through the definition of simpler interaction interfaces for system components. +## Blockchain Modularity + +Modern blockchain designs propose a "divide et impera" approach dividing the system into different specific functional components to independently maximize each vertex of the trilemma. This approach encapsulates the complexity in each part of the system and reduces the systemic complexity through the definition of simpler interaction interfaces for system components. Functional components of a blockchain: - Consensus: Agreement mechanics among nodes of block building and transaction ordering. @@ -35,7 +38,8 @@ Functional components of a blockchain: Modular blockchain approach suggests dividing a blockchain system into different logical layers. This results in a design with reduced systemic complexity, and simpler components that can be more easily optimized and re-enginered to introduce new scaling solutions. ## Scaling Ethereum -The primary objective of Ethereum's scalability efforts is to increase TPS metric without compromising decentralization or security. + +The primary objective of Ethereum's scalability efforts is to increase TPS metric without compromising decentralization or security. Layer 1 scaling is the set of all those techniques that increases the TPS of the underlying blockchain protocol itself. blockchains with "bigger blocks" have a major TPS but are more difficult to verify and likely to become more centralized. For this reason, an increase in the capacity of each block must be accompanied by various modifications to the protocol that allow decentralization to be maintained. Examples of layer 1 scaling solutions include Sharding, Proof-Of-Stake consensus mechanisms, and protocol upgrades aimed at optimizing block processing efficiency. @@ -47,26 +51,22 @@ Layer 2 scaling is the set of solutions built on top of Layer 1 blockchain proto !["Layer 2 Scaling"](../img/scaling/layer-2-scaling.png "Layer 2 Scaling") - The solution predominantly adopted by the Ethereum community to solve the scalability problem is a multi-rollup-centric approach. Here, Ethereum acts as fundamental secure layer of Settlement, and Data Availability, while the majority of Execution tasks are delegated to upper layers referred to as Rollups. Rollups bundle multiple Layer 2 transactions into a single Layer 1 transaction. These transactions are stored in Layer 1, but their execution is delegated to off-chain mechanisms. This allows for significant scalability improvements without sacrificing security. Ethereum's high level of programmability makes possible to create scalable solutions on top of the platform through Ethereum smart contracts. As previously mentioned, to maintain a high level of decentralization, Ethereum imposes limitations on the computational and storage resources that transactions included in the blocks can use, through gas limitations. Therefore, the data stored in Layer 1 is minimized, with only raw transactions being stored along with a hash commitment of the Layer 2 state resulting from the execution of those transactions. +The solution predominantly adopted by the Ethereum community to solve the scalability problem is a multi-rollup-centric approach. Here, Ethereum acts as fundamental secure layer of Settlement, and Data Availability, while the majority of Execution tasks are delegated to upper layers referred to as Rollups. Rollups bundle multiple Layer 2 transactions into a single Layer 1 transaction. These transactions are stored in Layer 1, but their execution is delegated to off-chain mechanisms. This allows for significant scalability improvements without sacrificing security. Ethereum's high level of programmability makes possible to create scalable solutions on top of the platform through Ethereum smart contracts. As previously mentioned, to maintain a high level of decentralization, Ethereum imposes limitations on the computational and storage resources that transactions included in the blocks can use, through gas limitations. Therefore, the data stored in Layer 1 is minimized, with only raw transactions being stored along with a hash commitment of the Layer 2 state resulting from the execution of those transactions. > **Rollups can be seen as a way to compress transaction execution, thereby reducing the computational burden on the Layer 1 blockchain. This provides the possibility to increase the TPS while still maintaining the security level of Layer 1 for the Layer 2 transactions, as their data and Layer 2 state transition commitments are stored in Layer 1.** ## Ethereum Core Changes Towards a Rollup-Centric Roadmap - - - -#### EIP-4844: Shard Blob Transactions (Proto-DankSharding) -TODO - -#### Full Data Sharding (Danksharding) -TODO +See the [Next Section](/wiki/research/scaling/core-changes/core-changes.md). ### Ethereum Layer 2 scaling + ## ZK Rollups + TODO ## Optimistic Rollups + TODO Resources: @@ -89,4 +89,4 @@ Resources: [Ethereum Blocks](https://ethereum.org/developers/docs/blocks), [archived](https://web.archive.org/web/20240214052915/https://ethereum.org/developers/docs/blocks) -[On Block Sizes, Gas Limits and Scalability](https://ethresear.ch/t/on-block-sizes-gas-limits-and-scalability/18444), [archived](https://web.archive.org/web/20240220230246/https://ethresear.ch/t/on-block-sizes-gas-limits-and-scalability/18444) \ No newline at end of file +[On Block Sizes, Gas Limits and Scalability](https://ethresear.ch/t/on-block-sizes-gas-limits-and-scalability/18444), [archived](https://web.archive.org/web/20240220230246/https://ethresear.ch/t/on-block-sizes-gas-limits-and-scalability/18444) From 9d1255e94c63e8ec471e2a2ea2ffe92db25549e8 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 11:02:14 +0800 Subject: [PATCH 041/101] KZG - 01 First commit added structure and intro. --- docs/wiki/Cryptography/KZG.md | 128 ++++++++++++++++++++++++++++++++++ 1 file changed, 128 insertions(+) create mode 100644 docs/wiki/Cryptography/KZG.md diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md new file mode 100644 index 00000000..6375cba1 --- /dev/null +++ b/docs/wiki/Cryptography/KZG.md @@ -0,0 +1,128 @@ +# KZG Commitments Unveiled: A Beginner's Guide + +## [TLDR] +The KZG commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. + +## [Motivation] + +### [ZKSNARKs] +Learning about Polynomial Commitment Schemes (PCS) is important because they play a key role in creating Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (ZKSNARKs). ZKSNARKs are special cryptographic methods that allow someone (the prover) to show to someone else (the verifier) that they know a specific piece of information (like a number) without revealing that information. This is done by using PCS and Interactive Oracle Proofs (IOP) together. + +*Modern ZKSNARK = Functional Commitment Scheme + Compatible Interactive Oracle Proof (IOP)* + +PCS is a way to prove that you know a secret function (represented by a polynomial) without showing the function itself. It's like promising to show a secret recipe to someone, but you only show them the final dish without revealing the recipe. This is crucial for ZKSNARKs because it allows the prover to prove they know a secret function without revealing it. + +IOP is another method that helps in proving that you know a secret value without revealing it. It's used along with PCS to make a ZKSNARK. The IOP helps in proving the knowledge, while PCS makes the proof short and easy to check. This combination allows for creating efficient ZKSNARKs that can be used in many areas, like blockchain and privacy-preserving computations. + +To make ZKSNARKs, you need to choose a PCS and IOP that work well together. The PCS is used to commit to a polynomial and prove the evaluation of the polynomial at a certain point without revealing the polynomial. The IOP is used to create a proof of knowledge, which is then turned into a non-interactive proof using a method called the Fiat-Shamir heuristic. This makes it possible to generate and verify the proof without needing to communicate in real-time, making ZKSNARKs useful for blockchain and distributed systems. + +### [Ethereum Danksharding] +KZG commitment scheme has emerged as a pivotal technology in the Ethereum ecosystem, particularly in the context of Proto-Danksharding and its anticipated evolution into Danksharding. This commitment scheme is a cornerstone of many Zero-Knowledge (ZK) related applications within Ethereum, enabling efficient and secure verification of data without revealing the underlying information. + +The adoption of KZG commitments in Proto-Danksharding and its future application in Danksharding represents a significant step towards Ethereum's full sharding implementation. Sharding is a long-term scaling solution for Ethereum, aiming to improve the network's scalability and capacity by dividing the network into smaller, more manageable pieces. The KZG commitment scheme plays a vital role in this process by facilitating the efficient verification of data across shards, thereby enhancing the overall security and performance of the Ethereum network. + +Moreover, the KZG commitment scheme is not only limited to Ethereum but has broader applications in the blockchain and cryptographic communities. Its ability to commit to a polynomial and verify evaluations of the polynomial without revealing the polynomial itself makes it a versatile tool for various cryptographic protocols and applications. + + +## [Goal] +Now that we are motivated to learn PCS, let us get started with defining what is our goal i.e. what is the exact problem we want to solve with KZG scheme. + +Say we have a function or polynomial $f(x)$ defined as $f(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^t$. + +Our main goal with KZG scheme is that we want to prove to someone that we know this polynomial without revealing the polynomial. What do we mean by without revealing by polynomial? We meant that without revealing the coefficients of the polynomial. + +In practice what we exactly do is that we prove that we know a specific evaluation of this polynomial at a point $x=a$. + +We write this, $f(a)$, for some $x=a$. + +## [What we need to know before we discuss KZG] + +There are some important concepts we need to know before we can move further to understand KZG scheme. Fortunately, we can get an Engineering level understanding of the KZG scheme from just enough high school mathematics. We will try to gain some intuition on advanced concepts and their important properties without knowing them intimately. This can help us see the KZG protocol flow without bogged down by the advanced mathematics. + +We need to know: + +### [Modular Arithmetic] +- Can you read a clock? Can you add/subtract two time values? In general can you do clock arithmetic? This is called Modular arithmetic. We know only need to know how to add, subtract, multiply or divide numbers and apply modulus operation (the clock scale). +- We usually write this mod $p$ to mean modulo $p$, where $p$ is some number. + +### [Finite Field of order prime $p$, $\mathbb F_p$] + +A finite field of order prime $p$, we denote it by $\mathbb F_p$, is a special set of numbers where you can do all the usual math operations (addition, subtraction, multiplication, and division, except by zero) and still follow the rules of arithmetic. + +The "order" of this set is the number of elements it contains, and for a finite field of order prime $p$, this number is a prime number. The most common way to create a $\mathbb F_p$ is by taking the set of all integers greathan or equal to $0$ and dividing them by $p$, keeping only the remainders. This gives us a set of numbers from $0$ to $p-1$ that can be used for arithmetic operations. For example, if $p = 5$, the set would be {0, 1, 2, 3, 4}, and you can add, subtract, multiply, and divide these numbers in a way that follows the rules of arithmetic. This set is a finite field of order 5, we denote this by $\mathbb F_5$, because it has exactly 5 elements, and it's a prime number. + +When we do modular arithmetic operations in the finite field $\mathbb F_p$, we have a nice "wrap around" property i.e. the field behaves as if it "wraps around" after reaching $(p - 1)$. + +In genral, when we define a finite field, we define, the order $p$ of the field and an arithemetic operation like addition or multiplication. If it is addition, we denote the field by $(\mathbb F_p, +)$. If it is multiplication, we denote it by $(\mathbb F^*_p, +)$. The `*` is telling us to exclude the zero element from our field so that we can satisfy all the required properties of the finite field i.e. mainly we can divide the numbers and find inverse of all elements. If we include the zero element, we can't find the inverse of zero element. + +### [Multiplicative Group ($\mathbb G^*, .)$] +The group is a similar to finite field with some small changes. In a Group, we only have arithmetic operation on the set, usually addition or multiplication as opposed to in a finite field we have addition and multiplication both. We denote a Group by ($\mathbb G, +)$ for a Group with addition as the group operation, ($\mathbb G^*, .)$ for Group with multiplication operation; the `*` is telling to exclude zero element to avoid division by zero. + +### [Generator of a Group] + + +### [Why choosing a prime number for modulo operations in finite fields] + +### [Cryptographic Assumptions needed for KZG Scheme] + +**Discrete Logarithm** + +**String Diffie-Hellman** + +### [Pairing Function] + +## [Important properties of Commitments] + +Let $F(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^d$ + +$F(a) = f_0 + f_1a + f_2a^2 + \ldots + f_da^d$ + +So $C_F = F(a) \cdot G = (f_0 + f_1a + f_2a^2 + \ldots + f_da^d) \cdot G$ + +$C_F = f_0 \cdot G + f_1a \cdot G + f_2a^2 \cdot G + \ldots + f_da^d \cdot G$ + +### [Binding Property] + +### [Hiding Property] + + +## [KZG Protocol Flow] + +### [Initial Configuration] + +### [Trusted Setup] + +### [Commitment of the polynomial] + +### [Opening] + +### [Verification] + +## [KZG by Hands] + +### KZG by Hands - [Initial Configuration] + +### [KZG by Hands - Trusted Setup] + +### [KZG by Hands - Commitment of the polynomial] + +### [KZG by Hands - Opening] + +### [KZG by Hands - Verification] + +## [Security of KZG - Deleting the toxic waste] + +## [Implementing KZG in Sagemath] + +## [KZG using Assymetic Pairing Fuctions] + +## [KZG Batch Mode Single Polynomial, multiple points] + +## [KZG Batch Mode Multiple Polynomials, same point] + +## [KZG Batch Mode Multiple Polynomials, multiple points] + + + + + From 333c134e74b02829b6466431278ac1339b60309b Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 11:04:25 +0800 Subject: [PATCH 042/101] KZG - 02 DRAFT MODE - WIP label at the top. --- docs/wiki/Cryptography/KZG.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 6375cba1..50c0d0a2 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -1,5 +1,7 @@ # KZG Commitments Unveiled: A Beginner's Guide +## [DRAFT MODE - WORK IN PROGRESS] + ## [TLDR] The KZG commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. From 627777ee1ed0472d694ae763f31a7f0fdb286044 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 11:12:56 +0800 Subject: [PATCH 043/101] KZG - 03 Table of contents added, fixed the headers. --- docs/wiki/Cryptography/KZG.md | 109 +++++++++++++++++++++++----------- 1 file changed, 74 insertions(+), 35 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 50c0d0a2..fcf95701 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -2,12 +2,51 @@ ## [DRAFT MODE - WORK IN PROGRESS] -## [TLDR] +## [TLDR](#tldr) The KZG commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. -## [Motivation] - -### [ZKSNARKs] +**Table of Contents** +- [KZG Commitments Unveiled: A Beginner's Guide](#kzg-commitments-unveiled-a-beginners-guide) + - [\[DRAFT MODE - WORK IN PROGRESS\]](#draft-mode---work-in-progress) + - [TLDR](#tldr) + - [Motivation](#motivation) + - [ZKSNARKs](#zksnarks) + - [Ethereum Danksharding](#ethereum-danksharding) + - [Goal](#goal) + - [What we need to know before we discuss KZG](#what-we-need-to-know-before-we-discuss-kzg) + - [Modular Arithmetic](#modular-arithmetic) + - [Finite Field of order prime $p$, $\\mathbb F\_p$](#finite-field-of-order-prime-p-mathbb-f_p) + - [Multiplicative Group ($\\mathbb G^\*, .)$](#multiplicative-group-mathbb-g-) + - [Generator of a Group](#generator-of-a-group) + - [Why choosing a prime number for modulo operations in finite fields](#why-choosing-a-prime-number-for-modulo-operations-in-finite-fields) + - [Cryptographic Assumptions needed for KZG Scheme](#cryptographic-assumptions-needed-for-kzg-scheme) + - [Pairing Function](#pairing-function) + - [Important Properties of Commitments](#important-properties-of-commitments) + - [Binding Property](#binding-property) + - [Hiding Property](#hiding-property) + - [KZG Protocol Flow](#kzg-protocol-flow) + - [Initial Configuration](#initial-configuration) + - [Trusted Setup](#trusted-setup) + - [Commitment of the polynomial](#commitment-of-the-polynomial) + - [Opening](#opening) + - [Verification](#verification) + - [KZG by Hands](#kzg-by-hands) + - [KZG by Hands - Initial Configuration](#kzg-by-hands---initial-configuration) + - [KZG by Hands - Trusted Setup](#kzg-by-hands---trusted-setup) + - [KZG by Hands - Commitment of the polynomial](#kzg-by-hands---commitment-of-the-polynomial) + - [KZG by Hands - Opening](#kzg-by-hands---opening) + - [KZG by Hands - Verification](#kzg-by-hands---verification) + - [Security of KZG - Deleting the toxic waste](#security-of-kzg---deleting-the-toxic-waste) + - [Implementing KZG in Sagemath](#implementing-kzg-in-sagemath) + - [KZG using Assymetic Pairing Fuctions](#kzg-using-assymetic-pairing-fuctions) + - [KZG Batch Mode Single Polynomial, multiple points](#kzg-batch-mode-single-polynomial-multiple-points) + - [KZG Batch Mode Multiple Polynomials, same point](#kzg-batch-mode-multiple-polynomials-same-point) + - [KZG Batch Mode Multiple Polynomials, multiple points](#kzg-batch-mode-multiple-polynomials-multiple-points) + + +## [Motivation](#motivation) + +### [ZKSNARKs](#zksnarks) Learning about Polynomial Commitment Schemes (PCS) is important because they play a key role in creating Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (ZKSNARKs). ZKSNARKs are special cryptographic methods that allow someone (the prover) to show to someone else (the verifier) that they know a specific piece of information (like a number) without revealing that information. This is done by using PCS and Interactive Oracle Proofs (IOP) together. *Modern ZKSNARK = Functional Commitment Scheme + Compatible Interactive Oracle Proof (IOP)* @@ -18,7 +57,7 @@ IOP is another method that helps in proving that you know a secret value without To make ZKSNARKs, you need to choose a PCS and IOP that work well together. The PCS is used to commit to a polynomial and prove the evaluation of the polynomial at a certain point without revealing the polynomial. The IOP is used to create a proof of knowledge, which is then turned into a non-interactive proof using a method called the Fiat-Shamir heuristic. This makes it possible to generate and verify the proof without needing to communicate in real-time, making ZKSNARKs useful for blockchain and distributed systems. -### [Ethereum Danksharding] +### [Ethereum Danksharding](#ethereum-danksharding) KZG commitment scheme has emerged as a pivotal technology in the Ethereum ecosystem, particularly in the context of Proto-Danksharding and its anticipated evolution into Danksharding. This commitment scheme is a cornerstone of many Zero-Knowledge (ZK) related applications within Ethereum, enabling efficient and secure verification of data without revealing the underlying information. The adoption of KZG commitments in Proto-Danksharding and its future application in Danksharding represents a significant step towards Ethereum's full sharding implementation. Sharding is a long-term scaling solution for Ethereum, aiming to improve the network's scalability and capacity by dividing the network into smaller, more manageable pieces. The KZG commitment scheme plays a vital role in this process by facilitating the efficient verification of data across shards, thereby enhancing the overall security and performance of the Ethereum network. @@ -26,7 +65,7 @@ The adoption of KZG commitments in Proto-Danksharding and its future application Moreover, the KZG commitment scheme is not only limited to Ethereum but has broader applications in the blockchain and cryptographic communities. Its ability to commit to a polynomial and verify evaluations of the polynomial without revealing the polynomial itself makes it a versatile tool for various cryptographic protocols and applications. -## [Goal] +## [Goal](#goal) Now that we are motivated to learn PCS, let us get started with defining what is our goal i.e. what is the exact problem we want to solve with KZG scheme. Say we have a function or polynomial $f(x)$ defined as $f(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^t$. @@ -37,17 +76,17 @@ In practice what we exactly do is that we prove that we know a specific evaluati We write this, $f(a)$, for some $x=a$. -## [What we need to know before we discuss KZG] +## [What we need to know before we discuss KZG](#what-we-need-to-know-before-we-discuss-kzg) There are some important concepts we need to know before we can move further to understand KZG scheme. Fortunately, we can get an Engineering level understanding of the KZG scheme from just enough high school mathematics. We will try to gain some intuition on advanced concepts and their important properties without knowing them intimately. This can help us see the KZG protocol flow without bogged down by the advanced mathematics. We need to know: -### [Modular Arithmetic] +### [Modular Arithmetic](#modular-arithmetic) - Can you read a clock? Can you add/subtract two time values? In general can you do clock arithmetic? This is called Modular arithmetic. We know only need to know how to add, subtract, multiply or divide numbers and apply modulus operation (the clock scale). - We usually write this mod $p$ to mean modulo $p$, where $p$ is some number. -### [Finite Field of order prime $p$, $\mathbb F_p$] +### [Finite Field of order prime $p$, $\mathbb F_p$](#finite-field-of-order-prime) A finite field of order prime $p$, we denote it by $\mathbb F_p$, is a special set of numbers where you can do all the usual math operations (addition, subtraction, multiplication, and division, except by zero) and still follow the rules of arithmetic. @@ -57,23 +96,23 @@ When we do modular arithmetic operations in the finite field $\mathbb F_p$, we h In genral, when we define a finite field, we define, the order $p$ of the field and an arithemetic operation like addition or multiplication. If it is addition, we denote the field by $(\mathbb F_p, +)$. If it is multiplication, we denote it by $(\mathbb F^*_p, +)$. The `*` is telling us to exclude the zero element from our field so that we can satisfy all the required properties of the finite field i.e. mainly we can divide the numbers and find inverse of all elements. If we include the zero element, we can't find the inverse of zero element. -### [Multiplicative Group ($\mathbb G^*, .)$] +### [Multiplicative Group ($\mathbb G^*, .)$](#multiplicative-group) The group is a similar to finite field with some small changes. In a Group, we only have arithmetic operation on the set, usually addition or multiplication as opposed to in a finite field we have addition and multiplication both. We denote a Group by ($\mathbb G, +)$ for a Group with addition as the group operation, ($\mathbb G^*, .)$ for Group with multiplication operation; the `*` is telling to exclude zero element to avoid division by zero. -### [Generator of a Group] +### [Generator of a Group](#generator-of-a-group) -### [Why choosing a prime number for modulo operations in finite fields] +### [Why choosing a prime number for modulo operations in finite fields](#why-choosing-a-prime-number-for-modulo-operations-in-finite-fields) -### [Cryptographic Assumptions needed for KZG Scheme] +### [Cryptographic Assumptions needed for KZG Scheme](#cryptographic-assumptions-needed-for-kzg-scheme) **Discrete Logarithm** **String Diffie-Hellman** -### [Pairing Function] +### [Pairing Function](#pairing-function) -## [Important properties of Commitments] +## [Important Properties of Commitments](#important-properties-of-commitments) Let $F(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^d$ @@ -83,46 +122,46 @@ So $C_F = F(a) \cdot G = (f_0 + f_1a + f_2a^2 + \ldots + f_da^d) \cdot G$ $C_F = f_0 \cdot G + f_1a \cdot G + f_2a^2 \cdot G + \ldots + f_da^d \cdot G$ -### [Binding Property] +### [Binding Property](#binding-property) -### [Hiding Property] +### [Hiding Property](#hiding-property) -## [KZG Protocol Flow] +## [KZG Protocol Flow](#kzg-protocol-flow) -### [Initial Configuration] +### [Initial Configuration](#initial-configuration) -### [Trusted Setup] +### [Trusted Setup](#trusted-setup) -### [Commitment of the polynomial] +### [Commitment of the polynomial](#commitment-of-the-polynomial) -### [Opening] +### [Opening](#opening) -### [Verification] +### [Verification](#verification) -## [KZG by Hands] +## [KZG by Hands](#kzg-by-hands) -### KZG by Hands - [Initial Configuration] +### [KZG by Hands - Initial Configuration](#kzg-by-hands---initial-configuration) -### [KZG by Hands - Trusted Setup] +### [KZG by Hands - Trusted Setup](#kzg-by-hands---trusted-setup) -### [KZG by Hands - Commitment of the polynomial] +### [KZG by Hands - Commitment of the polynomial](#kzg-by-hands---commitment-of-the-polynomial) -### [KZG by Hands - Opening] +### [KZG by Hands - Opening](#kzg-by-hands---opening) -### [KZG by Hands - Verification] +### [KZG by Hands - Verification](#kzg-by-hands---verification) -## [Security of KZG - Deleting the toxic waste] +## [Security of KZG - Deleting the toxic waste](#security-of-kzg---deleting-the-toxic-waste) -## [Implementing KZG in Sagemath] +## [Implementing KZG in Sagemath](#implementing-kzg-in-sagemath) -## [KZG using Assymetic Pairing Fuctions] +## [KZG using Assymetic Pairing Fuctions](#kzg-using-assymetic-pairing-fuctions) -## [KZG Batch Mode Single Polynomial, multiple points] +## [KZG Batch Mode Single Polynomial, multiple points](#kzg-batch-mode-single-polynomial-multiple-points) -## [KZG Batch Mode Multiple Polynomials, same point] +## [KZG Batch Mode Multiple Polynomials, same point](#kzg-batch-mode-multiple-polynomials-same-point) -## [KZG Batch Mode Multiple Polynomials, multiple points] +## [KZG Batch Mode Multiple Polynomials, multiple points](#kzg-batch-mode-multiple-polynomials-multiple-points) From 56d26cc44e0168dc395d8fcaf22c7b1c9244f219 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 15:49:25 +0800 Subject: [PATCH 044/101] KZG - 04 Additive and multiplicative generators section added. --- docs/wiki/Cryptography/KZG.md | 62 +++++++++++++++++++++++++++++++++++ 1 file changed, 62 insertions(+) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index fcf95701..25491878 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -100,6 +100,68 @@ In genral, when we define a finite field, we define, the order $p$ of the field The group is a similar to finite field with some small changes. In a Group, we only have arithmetic operation on the set, usually addition or multiplication as opposed to in a finite field we have addition and multiplication both. We denote a Group by ($\mathbb G, +)$ for a Group with addition as the group operation, ($\mathbb G^*, .)$ for Group with multiplication operation; the `*` is telling to exclude zero element to avoid division by zero. ### [Generator of a Group](#generator-of-a-group) +A generator is an element within a group that, when combined with itself repeatedly through the group's operation, can eventually produce every other element within the group. + +In mathematical sense, if you have a group $(G, .)$ and an element $g$ in $G$, we say that $g$ is a generator of $G$ if the set of all powers of $g$, $(g, g^2, g^3, ...)$, is equal to $G$ for a finite group, or covers all elements of $G$ through this repeated operation in the case of an infinite group. + +*Remember, a group only has one operation* + +This concept is best explained with an example. + +We will work with $(G_7, +) and $(G_7, .)$, the group of elements ${1,2,3,4,5,6}$ with modulo operation of addition and multiplication. + +**Generator of Additive Group $(G_7, +)** + +This is a Group because it satisfies the definition of a Group. + +**Closure:** When you add any two numbers in the set and take the remainder when divided by $7$, you end up with a result that's still in the set. +**Associativity:** For any numbers $a, b$ and $c$ in the set, $(a+b)+c$ is always the same as $a+(b+c)$, even with modulo $7$. +**Identity element:** The number $0$ acts as an identity element because when you add $0$ to any number in the set, you get the same number back. +**Inverse elements:** Every number in the set has an inverse such that when you add them together, you end up back at the identity element $0$. For example, the inverse of $3$ is $4$ because $3 + 4 = 7$, which is $0$ modulo $7$. + +Now, for the generator. Since our group has a prime order $7$, any element except for the identity element $0$ is a generator. Let's pick the element $1$ as our generator i.e $g = 1$. Since we are working with an additive group, our group elements with generator g will be $\{0, g, 2g, 3g, 4g, 5g, 6g\}$. + + +Starting with $1$ and adding it to itself modulo $7$, we get: +- $1 + 1 = 2$ (which is $2*1$ modulo 7) +- $1 + 1 + 1 = 3$ (which is $3*1$ modulo 7) +- $1 + 1 + 1 + 1 = 4$ (which is $4*1$ modulo 7) +- $1 + 1 + 1 + 1 + 1 = 5$ (which is $5*1$ modulo 7) +- $1 + 1 + 1 + 1 + 1 + 1 = 6$ (which is $6*1$ modulo 7) +- $1 + 1 + 1 + 1 + 1 + 1 + 1 = 7$, which is $0$ modulo 7 (which is $7*1$ modulo 7) + +As you can see, by repeatedly adding $1$ modulo $7$, we can generate every other element in the group. Hence, $1$ is a generator of the group $G_7$. Similarly, we could pick $2, 3, 4, 5, or 6$ as our generator, and by performing repeated addition modulo $7$, we would still generate the entire group. This is a special property of groups with a prime number of elements. + + +**Generator of Multiplicative Group $(G_7, .)** +For the multiplicative group of integers modulo a prime $p$, the group $G$ consists of the integers ${1, 2, 3, \ldots, p-1}$, where the operation is multiplication modulo $p$. We'll choose a small prime to make it simple, say $p = 7$. So, our group $(G^*_7, .)$ under multiplication modulo 7 consists of the elements ${1, 2, 3, 4, 5, 6}$. Remember, division by zero element is not excluded, that's why we have $G^*_7 as notation. + +Here's the group structure: + +- **Closure:** The product of any two elements, when reduced modulo $7$, is still an element of the set. +- **Associativity:** For any numbers $a, b, c$ in the set, $(a \cdot b) \cdot c$ is always the same as $a \cdot (b \cdot c)$, even when considering modulo $7$. +- **Identity element:** The number $1$ acts as an identity element because when you multiply any number in the set by $1$, you get the same number back. +- **Inverse elements:** Every number in the set has a multiplicative inverse in the set such that when you multiply them together, you get the identity element $1$. For example, the multiplicative inverse of $3$ is $5$ because $3 \cdot 5 = 15$, which is $1$ modulo $7$. + +Let's verify that each element is indeed a generator by multiplying it repeatedly modulo $7$: + +- Starting with $2$, we multiply by $2$ each time and take the result modulo $7$: + - $2^1 = 2$ + - $2^2 = 4$ + - $2^3 = 8 \equiv 1 \mod 7$ + - $2^4 = 16 \equiv 2 \mod 7$ (and here we cycle back to the beginning, showing that $2$ is not a generator) + +- Let's try $3$: + - $3^1 = 3$ + - $3^2 = 9 \equiv 2 \mod 7$ + - $3^3 = 27 \equiv 6 \mod 7$ + - $3^4 = 81 \equiv 4 \mod 7$ + - $3^5 = 243 \equiv 5 \mod 7$ + - $3^6 = 729 \equiv 1 \mod 7$ (and since we've reached the identity after hitting all elements, $3$ is a generator) + +You can verify that $5$ is also a generator for our multiplicative group $G^*_7$ modulo $7$. + +In the next section, you will learn how generators enable the KZG commitment scheme to function as an efficient, secure, and verifiable method of committing to polynomials, making it a powerful tool for cryptographic protocols, particularly in blockchain technologies where these qualities are very important. ### [Why choosing a prime number for modulo operations in finite fields](#why-choosing-a-prime-number-for-modulo-operations-in-finite-fields) From 3e10e185c28bc4ad94ad3a2cccafb597c7b12d68 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 15:54:56 +0800 Subject: [PATCH 045/101] KZG - 05 fixed the header errors. --- docs/wiki/Cryptography/KZG.md | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 25491878..b1f8cfdd 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -15,8 +15,8 @@ The KZG commitment scheme is like a cryptographic vault for securely locking awa - [Goal](#goal) - [What we need to know before we discuss KZG](#what-we-need-to-know-before-we-discuss-kzg) - [Modular Arithmetic](#modular-arithmetic) - - [Finite Field of order prime $p$, $\\mathbb F\_p$](#finite-field-of-order-prime-p-mathbb-f_p) - - [Multiplicative Group ($\\mathbb G^\*, .)$](#multiplicative-group-mathbb-g-) + - [Finite Field of order prime p](#finite-field-of-order-prime-p) + - [Group](#group) - [Generator of a Group](#generator-of-a-group) - [Why choosing a prime number for modulo operations in finite fields](#why-choosing-a-prime-number-for-modulo-operations-in-finite-fields) - [Cryptographic Assumptions needed for KZG Scheme](#cryptographic-assumptions-needed-for-kzg-scheme) @@ -86,7 +86,7 @@ We need to know: - Can you read a clock? Can you add/subtract two time values? In general can you do clock arithmetic? This is called Modular arithmetic. We know only need to know how to add, subtract, multiply or divide numbers and apply modulus operation (the clock scale). - We usually write this mod $p$ to mean modulo $p$, where $p$ is some number. -### [Finite Field of order prime $p$, $\mathbb F_p$](#finite-field-of-order-prime) +### [Finite Field of order prime p](#finite-field-of-order-prime) A finite field of order prime $p$, we denote it by $\mathbb F_p$, is a special set of numbers where you can do all the usual math operations (addition, subtraction, multiplication, and division, except by zero) and still follow the rules of arithmetic. @@ -96,9 +96,11 @@ When we do modular arithmetic operations in the finite field $\mathbb F_p$, we h In genral, when we define a finite field, we define, the order $p$ of the field and an arithemetic operation like addition or multiplication. If it is addition, we denote the field by $(\mathbb F_p, +)$. If it is multiplication, we denote it by $(\mathbb F^*_p, +)$. The `*` is telling us to exclude the zero element from our field so that we can satisfy all the required properties of the finite field i.e. mainly we can divide the numbers and find inverse of all elements. If we include the zero element, we can't find the inverse of zero element. -### [Multiplicative Group ($\mathbb G^*, .)$](#multiplicative-group) +### [Group](#group) The group is a similar to finite field with some small changes. In a Group, we only have arithmetic operation on the set, usually addition or multiplication as opposed to in a finite field we have addition and multiplication both. We denote a Group by ($\mathbb G, +)$ for a Group with addition as the group operation, ($\mathbb G^*, .)$ for Group with multiplication operation; the `*` is telling to exclude zero element to avoid division by zero. +In the next section we use an example to define a Group. This will help develop an intuition on when we call a set of numbers a Group. + ### [Generator of a Group](#generator-of-a-group) A generator is an element within a group that, when combined with itself repeatedly through the group's operation, can eventually produce every other element within the group. @@ -110,7 +112,7 @@ This concept is best explained with an example. We will work with $(G_7, +) and $(G_7, .)$, the group of elements ${1,2,3,4,5,6}$ with modulo operation of addition and multiplication. -**Generator of Additive Group $(G_7, +)** +**Generator of Additive Group** This is a Group because it satisfies the definition of a Group. @@ -133,7 +135,7 @@ Starting with $1$ and adding it to itself modulo $7$, we get: As you can see, by repeatedly adding $1$ modulo $7$, we can generate every other element in the group. Hence, $1$ is a generator of the group $G_7$. Similarly, we could pick $2, 3, 4, 5, or 6$ as our generator, and by performing repeated addition modulo $7$, we would still generate the entire group. This is a special property of groups with a prime number of elements. -**Generator of Multiplicative Group $(G_7, .)** +**Generator of Multiplicative Group** For the multiplicative group of integers modulo a prime $p$, the group $G$ consists of the integers ${1, 2, 3, \ldots, p-1}$, where the operation is multiplication modulo $p$. We'll choose a small prime to make it simple, say $p = 7$. So, our group $(G^*_7, .)$ under multiplication modulo 7 consists of the elements ${1, 2, 3, 4, 5, 6}$. Remember, division by zero element is not excluded, that's why we have $G^*_7 as notation. Here's the group structure: From 01645ba846620c6845fbae87464f4990ccd04108 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 16:15:40 +0800 Subject: [PATCH 046/101] KZG - 07 fixed the format errors. --- docs/wiki/Cryptography/KZG.md | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index b1f8cfdd..815f074c 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -83,12 +83,12 @@ There are some important concepts we need to know before we can move further to We need to know: ### [Modular Arithmetic](#modular-arithmetic) -- Can you read a clock? Can you add/subtract two time values? In general can you do clock arithmetic? This is called Modular arithmetic. We know only need to know how to add, subtract, multiply or divide numbers and apply modulus operation (the clock scale). +- Can you read a clock? Can you add/subtract two time values? In general can you do clock arithmetic? This is called Modular arithmetic. We only need to know how to add, subtract, multiply or divide numbers and apply modulus operation (the clock scale). - We usually write this mod $p$ to mean modulo $p$, where $p$ is some number. ### [Finite Field of order prime p](#finite-field-of-order-prime) -A finite field of order prime $p$, we denote it by $\mathbb F_p$, is a special set of numbers where you can do all the usual math operations (addition, subtraction, multiplication, and division, except by zero) and still follow the rules of arithmetic. +A finite field of order prime $p$, we denote it by $\mathbb F_p$, is a special set of numbers, $\{1, 2, 3, \ldots, p-1\}$, where you can do all the usual math operations (addition, subtraction, multiplication, and division, except by zero) and still follow the rules of arithmetic. The "order" of this set is the number of elements it contains, and for a finite field of order prime $p$, this number is a prime number. The most common way to create a $\mathbb F_p$ is by taking the set of all integers greathan or equal to $0$ and dividing them by $p$, keeping only the remainders. This gives us a set of numbers from $0$ to $p-1$ that can be used for arithmetic operations. For example, if $p = 5$, the set would be {0, 1, 2, 3, 4}, and you can add, subtract, multiply, and divide these numbers in a way that follows the rules of arithmetic. This set is a finite field of order 5, we denote this by $\mathbb F_5$, because it has exactly 5 elements, and it's a prime number. @@ -97,24 +97,24 @@ When we do modular arithmetic operations in the finite field $\mathbb F_p$, we h In genral, when we define a finite field, we define, the order $p$ of the field and an arithemetic operation like addition or multiplication. If it is addition, we denote the field by $(\mathbb F_p, +)$. If it is multiplication, we denote it by $(\mathbb F^*_p, +)$. The `*` is telling us to exclude the zero element from our field so that we can satisfy all the required properties of the finite field i.e. mainly we can divide the numbers and find inverse of all elements. If we include the zero element, we can't find the inverse of zero element. ### [Group](#group) -The group is a similar to finite field with some small changes. In a Group, we only have arithmetic operation on the set, usually addition or multiplication as opposed to in a finite field we have addition and multiplication both. We denote a Group by ($\mathbb G, +)$ for a Group with addition as the group operation, ($\mathbb G^*, .)$ for Group with multiplication operation; the `*` is telling to exclude zero element to avoid division by zero. +The group is a similar concept as finite field with some small changes. In a Group, we only have one arithmetic operation on the set, usually addition or multiplication as opposed to in a finite field we have addition and multiplication both and this group must satisfy few properties which we will below with an example. We denote a Group by ($\mathbb G, +)$ for a Group with addition as the group operation, ($\mathbb G^*, .)$ for Group with multiplication operation; the `*` is telling to exclude zero element to avoid division by zero. In the next section we use an example to define a Group. This will help develop an intuition on when we call a set of numbers a Group. ### [Generator of a Group](#generator-of-a-group) A generator is an element within a group that, when combined with itself repeatedly through the group's operation, can eventually produce every other element within the group. -In mathematical sense, if you have a group $(G, .)$ and an element $g$ in $G$, we say that $g$ is a generator of $G$ if the set of all powers of $g$, $(g, g^2, g^3, ...)$, is equal to $G$ for a finite group, or covers all elements of $G$ through this repeated operation in the case of an infinite group. +In mathematical sense, if you have a group ($\mathbb G, .)$ and an element $g$ in $\mathbb G$ we say that $g$ is a generator of $\mathbb G$ if the set of all powers of $g$, $(g, g^2, g^3, ...)$, is equal to $\mathbb G$ for a finite group, or covers all elements of $\mathbb G$ through this repeated operation in the case of an infinite group. *Remember, a group only has one operation* This concept is best explained with an example. -We will work with $(G_7, +) and $(G_7, .)$, the group of elements ${1,2,3,4,5,6}$ with modulo operation of addition and multiplication. +We will work with ($\mathbb G_7, +)$ and ($\mathbb G^*_7, .)$, the group of elements ${0,1,2,3,4,5,6}$ and ${1,2,3,4,5,6}$ respectively. **Generator of Additive Group** -This is a Group because it satisfies the definition of a Group. +Our set ($\mathbb G_7, +)$ with elements ${0,1,2,3,4,5,6}$ is a Group because it satisfies the definition of a Group. **Closure:** When you add any two numbers in the set and take the remainder when divided by $7$, you end up with a result that's still in the set. **Associativity:** For any numbers $a, b$ and $c$ in the set, $(a+b)+c$ is always the same as $a+(b+c)$, even with modulo $7$. @@ -132,11 +132,11 @@ Starting with $1$ and adding it to itself modulo $7$, we get: - $1 + 1 + 1 + 1 + 1 + 1 = 6$ (which is $6*1$ modulo 7) - $1 + 1 + 1 + 1 + 1 + 1 + 1 = 7$, which is $0$ modulo 7 (which is $7*1$ modulo 7) -As you can see, by repeatedly adding $1$ modulo $7$, we can generate every other element in the group. Hence, $1$ is a generator of the group $G_7$. Similarly, we could pick $2, 3, 4, 5, or 6$ as our generator, and by performing repeated addition modulo $7$, we would still generate the entire group. This is a special property of groups with a prime number of elements. +As you can see, by repeatedly adding $1$ modulo $7$, we can generate every other element in the group. Hence, $1$ is a generator of the group ($\mathbb G_7, +)$. Similarly, we could pick $2, 3, 4, 5, or 6$ as our generator, and by performing repeated addition modulo $7$, we would still generate the entire group. This is a special property of groups with a prime number of elements. **Generator of Multiplicative Group** -For the multiplicative group of integers modulo a prime $p$, the group $G$ consists of the integers ${1, 2, 3, \ldots, p-1}$, where the operation is multiplication modulo $p$. We'll choose a small prime to make it simple, say $p = 7$. So, our group $(G^*_7, .)$ under multiplication modulo 7 consists of the elements ${1, 2, 3, 4, 5, 6}$. Remember, division by zero element is not excluded, that's why we have $G^*_7 as notation. +For the multiplicative group of integers modulo a prime $p$, the group ($\mathbb G_p, .)$ consists of the integers ${1, 2, 3, \ldots, p-1}$, where the operation is multiplication modulo $p$. We'll choose a small prime to make it simple, say $p = 7$. So, our group ($\mathbb G^*_7, .)$ under multiplication modulo $7$ consists of the elements ${1, 2, 3, 4, 5, 6}$. Remember, division by zero element is excluded, that's why we have `*` in the notation. Here's the group structure: @@ -161,7 +161,7 @@ Let's verify that each element is indeed a generator by multiplying it repeatedl - $3^5 = 243 \equiv 5 \mod 7$ - $3^6 = 729 \equiv 1 \mod 7$ (and since we've reached the identity after hitting all elements, $3$ is a generator) -You can verify that $5$ is also a generator for our multiplicative group $G^*_7$ modulo $7$. +You can verify that $5$ is also a generator for our multiplicative group ($\mathbb G^*_7, .)$ modulo $7$. In the next section, you will learn how generators enable the KZG commitment scheme to function as an efficient, secure, and verifiable method of committing to polynomials, making it a powerful tool for cryptographic protocols, particularly in blockchain technologies where these qualities are very important. From 883d0eae6abbe1e02858c70e53d8c8be8b0a2fe4 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 16:41:35 +0800 Subject: [PATCH 047/101] KZG - 08 fixed the format errors. --- docs/wiki/Cryptography/KZG.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 815f074c..d9142bf7 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -88,7 +88,7 @@ We need to know: ### [Finite Field of order prime p](#finite-field-of-order-prime) -A finite field of order prime $p$, we denote it by $\mathbb F_p$, is a special set of numbers, $\{1, 2, 3, \ldots, p-1\}$, where you can do all the usual math operations (addition, subtraction, multiplication, and division, except by zero) and still follow the rules of arithmetic. +A finite field of order prime $p$, we denote it by $\mathbb F_p$, is a special set of numbers, { $\{1, 2, 3, \ldots, p-1\}$ }, where you can do all the usual math operations (addition, subtraction, multiplication, and division, except by zero) and still follow the rules of arithmetic. The "order" of this set is the number of elements it contains, and for a finite field of order prime $p$, this number is a prime number. The most common way to create a $\mathbb F_p$ is by taking the set of all integers greathan or equal to $0$ and dividing them by $p$, keeping only the remainders. This gives us a set of numbers from $0$ to $p-1$ that can be used for arithmetic operations. For example, if $p = 5$, the set would be {0, 1, 2, 3, 4}, and you can add, subtract, multiply, and divide these numbers in a way that follows the rules of arithmetic. This set is a finite field of order 5, we denote this by $\mathbb F_5$, because it has exactly 5 elements, and it's a prime number. @@ -110,11 +110,11 @@ In mathematical sense, if you have a group ($\mathbb G, .)$ and an element $g$ This concept is best explained with an example. -We will work with ($\mathbb G_7, +)$ and ($\mathbb G^*_7, .)$, the group of elements ${0,1,2,3,4,5,6}$ and ${1,2,3,4,5,6}$ respectively. +We will work with ($\mathbb G_7, +)$ and ($\mathbb G^*_7, .)$, and their the group elements { ${0,1,2,3,4,5,6}$ } and { ${1,2,3,4,5,6}$ } respectively. **Generator of Additive Group** -Our set ($\mathbb G_7, +)$ with elements ${0,1,2,3,4,5,6}$ is a Group because it satisfies the definition of a Group. +Our set ($\mathbb G_7, +)$ with elements { ${0,1,2,3,4,5,6}$ } is a Group because it satisfies the definition of a Group. **Closure:** When you add any two numbers in the set and take the remainder when divided by $7$, you end up with a result that's still in the set. **Associativity:** For any numbers $a, b$ and $c$ in the set, $(a+b)+c$ is always the same as $a+(b+c)$, even with modulo $7$. From b7df0ce904349ac7e5e3884d1241776340dec4db Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 16:58:35 +0800 Subject: [PATCH 048/101] KZG - 09 Why choosing a prime number for modulo operations in finite field section is added. --- docs/wiki/Cryptography/KZG.md | 26 ++++++++++++++++++++++---- 1 file changed, 22 insertions(+), 4 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index d9142bf7..dfe77c74 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -106,11 +106,11 @@ A generator is an element within a group that, when combined with itself repeate In mathematical sense, if you have a group ($\mathbb G, .)$ and an element $g$ in $\mathbb G$ we say that $g$ is a generator of $\mathbb G$ if the set of all powers of $g$, $(g, g^2, g^3, ...)$, is equal to $\mathbb G$ for a finite group, or covers all elements of $\mathbb G$ through this repeated operation in the case of an infinite group. -*Remember, a group only has one operation* +*Remember, a group only has one operation.* This concept is best explained with an example. -We will work with ($\mathbb G_7, +)$ and ($\mathbb G^*_7, .)$, and their the group elements { ${0,1,2,3,4,5,6}$ } and { ${1,2,3,4,5,6}$ } respectively. +We will work with ($\mathbb G_7, +)$ of group elements { ${0,1,2,3,4,5,6}$ } and ($\mathbb G^*_7, .)$ of group elements { ${1,2,3,4,5,6}$ } with modulo $7$ to find the generator of the Groups. **Generator of Additive Group** @@ -136,7 +136,7 @@ As you can see, by repeatedly adding $1$ modulo $7$, we can generate every other **Generator of Multiplicative Group** -For the multiplicative group of integers modulo a prime $p$, the group ($\mathbb G_p, .)$ consists of the integers ${1, 2, 3, \ldots, p-1}$, where the operation is multiplication modulo $p$. We'll choose a small prime to make it simple, say $p = 7$. So, our group ($\mathbb G^*_7, .)$ under multiplication modulo $7$ consists of the elements ${1, 2, 3, 4, 5, 6}$. Remember, division by zero element is excluded, that's why we have `*` in the notation. +For the multiplicative group of integers modulo a prime $p$, the group ($\mathbb G_p, .)$ consists of the integers { ${1, 2, 3, \ldots, p-1}$ }, where the operation is multiplication modulo $p$. We'll choose a small prime to make it simple, say $p = 7$. So, our group ($\mathbb G^*_7, .)$ under multiplication modulo $7$ consists of the elements ${1, 2, 3, 4, 5, 6}$. Remember, division by zero element is excluded, that's why we have `*` in the notation. Here's the group structure: @@ -163,11 +163,29 @@ Let's verify that each element is indeed a generator by multiplying it repeatedl You can verify that $5$ is also a generator for our multiplicative group ($\mathbb G^*_7, .)$ modulo $7$. -In the next section, you will learn how generators enable the KZG commitment scheme to function as an efficient, secure, and verifiable method of committing to polynomials, making it a powerful tool for cryptographic protocols, particularly in blockchain technologies where these qualities are very important. +In the next section, we will learn how generators enable the KZG commitment scheme to function as an efficient, secure, and verifiable method of committing to polynomials, making it a powerful tool for cryptographic protocols, particularly in blockchain technologies where these qualities are very important. ### [Why choosing a prime number for modulo operations in finite fields](#why-choosing-a-prime-number-for-modulo-operations-in-finite-fields) +Choosing a prime number as the modulus for operations in a finite field offers several benefits and simplifies various aspects of field arithmetic: + +1. **Well-defined Division:** In a finite field, every non-zero element must have a multiplicative inverse. If the modulus is prime, every number in the set { ${1, 2, 3, \ldots, p-1}$ } has a multiplicative inverse modulo $p$. This property allows for well-defined division operations within the field, which wouldn't be possible if the modulus wasn't prime (except in special cases like Galois fields of order $p^n$, where $p$ is prime). + +2. **Simplicity of Construction:** When the modulus is a prime number, the field's construction is straightforward. The elements of the field are simply the set of integers { ${1, 2, 3, \ldots, p-1}$ }, and the field operations (addition, subtraction, multiplication, and division) are performed modulo $p$. For non-prime moduli, constructing a field requires more complex structures, such as polynomial rings. + +3. **Guaranteed Field Properties:** The use of a prime modulus guarantees the satisfaction of field properties. A finite field (also known as a Galois field) is a field that contains a finite number of elements. For a set to be a field, it must satisfy several properties, including the existence of additive and multiplicative identities, the existence of additive and multiplicative inverses for every element, and the commutative, associative, and distributive laws for addition and multiplication. A prime modulus ensures all these properties are met. + +4. **Uniform Distribution of Non-zero Elements:** In a finite field with a prime modulus, the non-zero elements have a uniform distribution with respect to multiplication. This means that the multiplication table of the field does not have any 'gaps' and every element appears exactly once in each row and column of the multiplication table (except the row and column for the zero element). + +5. **Simplified Algorithms:** Many algorithms in number theory and cryptography are simpler and more efficient when working with prime fields. For example, finding multiplicative inverses can be done efficiently using the Extended Euclidean Algorithm, and there's no need for complex polynomial arithmetic that is necessary in non-prime fields. + +6. **Cryptographic Security:** In the context of cryptography, the difficulty of certain problems, such as the discrete logarithm problem, is well-understood in prime fields. This difficulty is crucial for the security of cryptographic systems. For composite moduli (especially when the factors are not known), the structure can introduce vulnerabilities or make the problem's difficulty less predictable. +7. **Optimization in Computation:** Some prime numbers, like 31 or primes of the form $2^n - 1$, are easily optimized by CPUs for multiplication operations. This optimization can lead to faster computation times, which is beneficial in applications where performance is a critical factor. + +Using a prime number as the modulus for finite fields simplifies the field arithmetic and ensures that all field properties are satisfied, which is essential for both theoretical and practical applications, particularly in cryptography. + + ### [Cryptographic Assumptions needed for KZG Scheme](#cryptographic-assumptions-needed-for-kzg-scheme) **Discrete Logarithm** From 489194e041849c42281fe2ccd8567140daff8570 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 17:16:52 +0800 Subject: [PATCH 049/101] KZG - 10 Discrete Logarithm section is added. --- docs/wiki/Cryptography/KZG.md | 14 +++++++++++++- 1 file changed, 13 insertions(+), 1 deletion(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index dfe77c74..76166e0a 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -68,7 +68,7 @@ Moreover, the KZG commitment scheme is not only limited to Ethereum but has broa ## [Goal](#goal) Now that we are motivated to learn PCS, let us get started with defining what is our goal i.e. what is the exact problem we want to solve with KZG scheme. -Say we have a function or polynomial $f(x)$ defined as $f(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^t$. +Say we have a function or polynomial $f(x)$ defined as $f(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^t$. The degree of $f(x)$ is $t$. Our main goal with KZG scheme is that we want to prove to someone that we know this polynomial without revealing the polynomial. What do we mean by without revealing by polynomial? We meant that without revealing the coefficients of the polynomial. @@ -188,8 +188,20 @@ Using a prime number as the modulus for finite fields simplifies the field arith ### [Cryptographic Assumptions needed for KZG Scheme](#cryptographic-assumptions-needed-for-kzg-scheme) +In order to work with KZG commitment scheme, we need two additional assumptions. We won't go deep into why these assumptions are needed but we will give an intuition to why these cryptographic assumptions are needed to make KZG more secure. + **Discrete Logarithm** +Say we have a generator $g$ in $\mathbb G^*_p$ and $a$ and $g^a$ are any two elements in the finite field $\mathbb F^*_p$. The Discrete Logarithm assumption says that it is practically impossible to find $a$, for given $g$ and $g^a$. This means we can't easily find the exponent $a$ that will give us these elements. + +**Developing an intuition for Discrete Logarithm Problem** + +Imagine you have a special kind of lock that works with numbers (let's call this lock a "generator", and we'll name it $g$). This lock is part of a magic set of locks and keys, all living in a magical land called $\mathbb G^*_p$. Now, you pick a secret number $a$ and use it to turn your lock $g$ a certain number of times. The lock ends up in a new position, let's call this $g^a$. + +If someone walks by and sees your lock at $g^a$, even if they know it started at $g$ and the magical land it belongs to, figuring out how many times you turned it (finding your secret number $a$) is incredibly difficult. + +In simpler terms, the Discrete Logarithm problem tells us that even though it's easy to turn the lock around if you know your secret number, going backwards — seeing the result and trying to guess the secret number — is like finding a needle in a haystack. This concept is crucial in cryptography, ensuring that some secrets are incredibly hard to uncover. + **String Diffie-Hellman** ### [Pairing Function](#pairing-function) From 1c0a7379d24d179157fd0f3b3a130fc8cedb5018 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 17:26:39 +0800 Subject: [PATCH 050/101] KZG - 11 format erors fixed. --- docs/wiki/Cryptography/KZG.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 76166e0a..14c8bf8b 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -192,11 +192,11 @@ In order to work with KZG commitment scheme, we need two additional assumptions. **Discrete Logarithm** -Say we have a generator $g$ in $\mathbb G^*_p$ and $a$ and $g^a$ are any two elements in the finite field $\mathbb F^*_p$. The Discrete Logarithm assumption says that it is practically impossible to find $a$, for given $g$ and $g^a$. This means we can't easily find the exponent $a$ that will give us these elements. +Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a$ and $g^a$ are any two elements in the finite field $\mathbb F^*_p$. The Discrete Logarithm assumption says that it is practically impossible to find $a$, for given $g$ and $g^a$. This means we can't easily find the exponent $a$ that will give us these elements. **Developing an intuition for Discrete Logarithm Problem** -Imagine you have a special kind of lock that works with numbers (let's call this lock a "generator", and we'll name it $g$). This lock is part of a magic set of locks and keys, all living in a magical land called $\mathbb G^*_p$. Now, you pick a secret number $a$ and use it to turn your lock $g$ a certain number of times. The lock ends up in a new position, let's call this $g^a$. +Imagine you have a special kind of lock that works with numbers (let's call this lock a "generator", and we'll name it $g$). This lock is part of a magic set of locks and keys, all living in a magical land called $\mathbb G^\*_p$. Now, you pick a secret number $a$ and use it to turn your lock $g$ a certain number of times. The lock ends up in a new position, let's call this $g^a$. If someone walks by and sees your lock at $g^a$, even if they know it started at $g$ and the magical land it belongs to, figuring out how many times you turned it (finding your secret number $a$) is incredibly difficult. From af63bff5237af3879389fb5dbfe12e96aa727bce Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 17:42:44 +0800 Subject: [PATCH 051/101] KZG - 12 Strong Diffie-Hellman section is added. --- docs/wiki/Cryptography/KZG.md | 18 ++++++++++++++++-- 1 file changed, 16 insertions(+), 2 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 14c8bf8b..b9dfc143 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -192,7 +192,7 @@ In order to work with KZG commitment scheme, we need two additional assumptions. **Discrete Logarithm** -Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a$ and $g^a$ are any two elements in the finite field $\mathbb F^*_p$. The Discrete Logarithm assumption says that it is practically impossible to find $a$, for given $g$ and $g^a$. This means we can't easily find the exponent $a$ that will give us these elements. +Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a$ is any element in the finite field $\mathbb F^*_p$ and $g^a$ is some element in the group $\mathbb G^\*_p$. The Discrete Logarithm assumption says that it is practically impossible to find $a$, for given $g$ and $g^a$. This means we can't easily find the exponent $a$ that will give us these elements. **Developing an intuition for Discrete Logarithm Problem** @@ -202,7 +202,21 @@ If someone walks by and sees your lock at $g^a$, even if they know it started at In simpler terms, the Discrete Logarithm problem tells us that even though it's easy to turn the lock around if you know your secret number, going backwards — seeing the result and trying to guess the secret number — is like finding a needle in a haystack. This concept is crucial in cryptography, ensuring that some secrets are incredibly hard to uncover. -**String Diffie-Hellman** +**Strong Diffie-Hellman** + +Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a, b$ are any elements in the finite field $\mathbb F^*_p$ and $g^a, g^b$ are some elements in the group $\mathbb G^\*_p$. The Strong Diffie-Hellman assumption says that $g^a and g^b$ are indistinguishable from $g^{ab}$. This means we can't extract any extra information aboout $g^{ab}$ given $g^a and g^b$. + + +**Developing an intuition for Strong Diffie-Hellman** + +Imagine you're in a world, famous for its magical cookies, and there's a secret ingredient (our "generator", $g$) that makes them special. Two master bakers, Alice and Bob, each know a unique twist to using this ingredient, represented by their own secret recipes $a$ and $b$, respectively. + +When Alice bakes her cookies using her secret recipe, she creates a special batch $g^a$). Bob does the same with his recipe, resulting in another unique batch $g^b$. + +Now, suppose Alice and Bob decide to collaborate and combine their secret recipes to create a super-secret batch of cookies $g^{ab}$. The Strong Diffie-Hellman assumption is saying that even if someone has tasted both Alice's and Bob's individual batches, they can't decipher what their combined super-secret batch would taste like. The flavors of the combined recipe are indistinguishable from any other batch without knowing the exact combination of Alice's and Bob's recipes. + +So, in essence, the Strong Diffie-Hellman assumption tells us that just knowing the outcomes of individual secrets (recipes) doesn't help anyone crack the result of combining those secrets. This is a cornerstone of secure communication, ensuring that even if someone knows the separate pieces, the combined secret remains safe and unguessable. + ### [Pairing Function](#pairing-function) From e6a274f7e82ea362bc9adcb318d60f002fa13af0 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 18:22:50 +0800 Subject: [PATCH 052/101] KZG - 13 Pairing function section is added. --- docs/wiki/Cryptography/KZG.md | 36 +++++++++++++++++++++++++++++++++-- 1 file changed, 34 insertions(+), 2 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index b9dfc143..d489deb7 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -204,14 +204,14 @@ In simpler terms, the Discrete Logarithm problem tells us that even though it's **Strong Diffie-Hellman** -Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a, b$ are any elements in the finite field $\mathbb F^*_p$ and $g^a, g^b$ are some elements in the group $\mathbb G^\*_p$. The Strong Diffie-Hellman assumption says that $g^a and g^b$ are indistinguishable from $g^{ab}$. This means we can't extract any extra information aboout $g^{ab}$ given $g^a and g^b$. +Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a, b$ are any elements in the finite field $\mathbb F^*_p$ and $g^a$, $g^b$ are some elements in the group $\mathbb G^\*_p$. The Strong Diffie-Hellman assumption says that $g^a$ and $g^b$ are indistinguishable from $g^{ab}$. This means we can't extract any extra information aboout $g^{ab}$ given $g^a$ and $g^b$. **Developing an intuition for Strong Diffie-Hellman** Imagine you're in a world, famous for its magical cookies, and there's a secret ingredient (our "generator", $g$) that makes them special. Two master bakers, Alice and Bob, each know a unique twist to using this ingredient, represented by their own secret recipes $a$ and $b$, respectively. -When Alice bakes her cookies using her secret recipe, she creates a special batch $g^a$). Bob does the same with his recipe, resulting in another unique batch $g^b$. +When Alice bakes her cookies using her secret recipe, she creates a special batch $g^a$. Bob does the same with his recipe, resulting in another unique batch $g^b$. Now, suppose Alice and Bob decide to collaborate and combine their secret recipes to create a super-secret batch of cookies $g^{ab}$. The Strong Diffie-Hellman assumption is saying that even if someone has tasted both Alice's and Bob's individual batches, they can't decipher what their combined super-secret batch would taste like. The flavors of the combined recipe are indistinguishable from any other batch without knowing the exact combination of Alice's and Bob's recipes. @@ -219,6 +219,38 @@ So, in essence, the Strong Diffie-Hellman assumption tells us that just knowing ### [Pairing Function](#pairing-function) +Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a, b$ are any elements in the finite field $\mathbb F^*_p$ and $g^a$, $g^b$ are some elements in the group $\mathbb G^\*_p$. + +A pairing function is a special kind of function that takes two inputs and produces a single output with two important properties, biliner and non-degenrate. + +Bilinear means, we can move around in a reversible way. +Non-degenerate means, if we apply pairing function to teh same element, it doesn't result in the identity element of the Group. + +Let's define these properties a bit more rigorously. + +A pairing function $e:$ $\mathbb G_1 X \mathbb G_2 \rightarrow \mathbb G_T$ such that it satisfies, +Bilinear property: $e(g^a, g^b) = e(g, g^{ab}) = e(g^{ab}, g) = e(g,g)^{ab}$ +Non-degenerate property: $e(g,g) \neq 1$, means it is not an identity element. + +When $\mathbb G_1$ and $\mathbb G_2$ are the same Group, we call this symmetric pairing function. Otherwise, it is a assymetric pairing function. + +**Developing an intuition for Pairing function** + +Imagine two separate islands, each inhabited by a unique species of magical creatures. The first island is home to Unicorns, each with a distinct color, and the second island is inhabited by Dragons, each with a unique fire color. A pairing function is like a magical bridge that connects a Unicorn with a Dragon, creating a unique, new magical creature, a Dracorn, that embodies characteristics of both. + +Here's how to think about this pairing function without getting bogged down by technicalities: + +- **Two Groups:** Think of the Unicorns and Dragons as belonging to two different groups (in mathematical terms, these are usually called groups $\mathbb G_1$ and $\mathbb G_2$. +- **Pairing Function:** The magical bridge acts as the pairing function. When a Unicorn and a Dragon meet on this bridge, the pairing function combines them into a Dracorn. This Dracorn has a special glow that uniquely corresponds to the combination of that specific Unicorn and Dragon (reversable). +- **Unique Outcome:** Just like every Unicorn and Dragon pair produces a Dracorn with a unique glow, in mathematics, a pairing function takes one element from each group and produces a unique output in a third group (often denoted as $\mathbb G_T$)). + +**Why is this magical?** Because even though there are countless possible combinations of Unicorns and Dragons, each combination (pairing) produces a unique Dracorn. This is powerful in cryptography because it allows for complex operations that underpin many security protocols, ensuring that each combination is distinct and traceable to its original pair. + +**In simpler terms,** imagine you have two sets of keys (Unicorns and Dragons), and when you combine one key from each set, you get a unique lock (Dracorn). The magic is in how predictable yet secure this combination is, allowing for secure interactions that rely on the certainty of these unique outcomes without revealing the original keys. + +Pairing functions enable advanced cryptographic techniques, such as those used in certain types of digital signatures and encryption, by allowing this kind of "cross-group" interaction to occur securely and predictably. + + ## [Important Properties of Commitments](#important-properties-of-commitments) From 93fc7ddcc1b207b4176be6ae1fa2d7707e57a4e9 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 19:21:55 +0800 Subject: [PATCH 053/101] KZG - 14 KZG protocol flow section is added. --- docs/wiki/Cryptography/KZG.md | 89 ++++++++++++++++++++++++++++++----- 1 file changed, 76 insertions(+), 13 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index d489deb7..702b8ca0 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -22,11 +22,9 @@ The KZG commitment scheme is like a cryptographic vault for securely locking awa - [Cryptographic Assumptions needed for KZG Scheme](#cryptographic-assumptions-needed-for-kzg-scheme) - [Pairing Function](#pairing-function) - [Important Properties of Commitments](#important-properties-of-commitments) - - [Binding Property](#binding-property) - - [Hiding Property](#hiding-property) - [KZG Protocol Flow](#kzg-protocol-flow) - - [Initial Configuration](#initial-configuration) - [Trusted Setup](#trusted-setup) + - [Initial Configuration](#initial-configuration) - [Commitment of the polynomial](#commitment-of-the-polynomial) - [Opening](#opening) - [Verification](#verification) @@ -229,10 +227,12 @@ Non-degenerate means, if we apply pairing function to teh same element, it doesn Let's define these properties a bit more rigorously. A pairing function $e:$ $\mathbb G_1 X \mathbb G_2 \rightarrow \mathbb G_T$ such that it satisfies, + Bilinear property: $e(g^a, g^b) = e(g, g^{ab}) = e(g^{ab}, g) = e(g,g)^{ab}$ -Non-degenerate property: $e(g,g) \neq 1$, means it is not an identity element. -When $\mathbb G_1$ and $\mathbb G_2$ are the same Group, we call this symmetric pairing function. Otherwise, it is a assymetric pairing function. +Non-degenerate property: $e(g,g) \neq 1$, means the output is not an identity element. + +When $\mathbb G_1$ and $\mathbb G_2$ are the same Group, we call this symmetric pairing function. Otherwise, it is an assymetric pairing function. **Developing an intuition for Pairing function** @@ -242,7 +242,7 @@ Here's how to think about this pairing function without getting bogged down by t - **Two Groups:** Think of the Unicorns and Dragons as belonging to two different groups (in mathematical terms, these are usually called groups $\mathbb G_1$ and $\mathbb G_2$. - **Pairing Function:** The magical bridge acts as the pairing function. When a Unicorn and a Dragon meet on this bridge, the pairing function combines them into a Dracorn. This Dracorn has a special glow that uniquely corresponds to the combination of that specific Unicorn and Dragon (reversable). -- **Unique Outcome:** Just like every Unicorn and Dragon pair produces a Dracorn with a unique glow, in mathematics, a pairing function takes one element from each group and produces a unique output in a third group (often denoted as $\mathbb G_T$)). +- **Unique Outcome:** Just like every Unicorn and Dragon pair produces a Dracorn with a unique glow, in mathematics, a pairing function takes one element from each group and produces a unique output in a third group (often denoted as $\mathbb G_T$). **Why is this magical?** Because even though there are countless possible combinations of Unicorns and Dragons, each combination (pairing) produces a unique Dracorn. This is powerful in cryptography because it allows for complex operations that underpin many security protocols, ensuring that each combination is distinct and traceable to its original pair. @@ -254,27 +254,90 @@ Pairing functions enable advanced cryptographic techniques, such as those used i ## [Important Properties of Commitments](#important-properties-of-commitments) -Let $F(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^d$ +Commitment schemes are like the secret-keeping wizards of the digital world. They let someone make a promise about a piece of information (we'll call this the secret message) in a way that ties them to their promise without letting anyone else know what the secret is. Here's how it works: -$F(a) = f_0 + f_1a + f_2a^2 + \ldots + f_da^d$ +1. **Making the Promise (Commitment):** You decide on a secret message and use a special spell (the commitment scheme) to create a magic seal (the commitment). This seal proves you have a secret, but it keeps the secret hidden. -So $C_F = F(a) \cdot G = (f_0 + f_1a + f_2a^2 + \ldots + f_da^d) \cdot G$ +2. **Keeping It Secret (Hiding):** Even though you've made this seal, nobody else can see what your secret message is. It's like you've locked it in a chest and only you have the key. -$C_F = f_0 \cdot G + f_1a \cdot G + f_2a^2 \cdot G + \ldots + f_da^d \cdot G$ +3. **Proving You're Honest (Binding):** The magic of the commitment is that you can't change your secret message later without breaking the seal. This means once you've made your commitment, you're bound to it. + +Later, when the time comes to reveal your secret, you can show the original message and prove that it matches the seal you made before. This lets someone else (the verifier) check and confirm that your secret message is the same one you committed to in the beginning, proving that you kept your word. + +The Binding and Hiding properties are extremely important and they tie back to the above cryptographic assumptions we made with the Discrete Logarithm and Strong Diffie-Hellman assumptions. -### [Binding Property](#binding-property) +But for now, we don't need to go deep into the technicalities. -### [Hiding Property](#hiding-property) +With this background, we are ready to explain KZG protocol flow and understand its construction. ## [KZG Protocol Flow](#kzg-protocol-flow) -### [Initial Configuration](#initial-configuration) +Let us reiterate on what is the problem we are solving with KZG protocol. + +We want prove that we know a specific evaluation of a function or polynomial at a point $x=a$ without revealing it. + +In the KZG commitment scheme, the roles of the Trusted Third Party, Prover, and Verifier are critical to its function and security. Here's how each contributes to the process: + +1. **Trusted Third Party (Setup Authority):** This entity is responsible for the initial setup phase of the KZG scheme. They generate the public parameters (PP) that will be used in the commitments and proofs, based on a secret that only they know. This secret is crucial for the construction of commitments but must be discarded (or kept extremely secure) after the setup to ensure the system's integrity. The trust in this party is fundamental because if the secret is mishandled or leaked, it could compromise the entire system. + +2. **Prover:** The Prover is the one who wants to commit to a certain piece of data (like a polynomial) without revealing it. Using the public parameters provided by the Trusted Third Party, the Prover computes a commitment to their data. When it's time to prove certain properties of their data (like a polynomial evaluation at a specific point), the Prover can generate a proof based on their commitment. This proof shows that their data has certain properties without revealing the data itself. + +3. **Verifier:** The Verifier is the party interested in checking the Prover's claims about their secret data. The Verifier uses the proof provided by the Prover, along with the public parameters from the Trusted Third Party, to verify that the Prover's claim about their data is true. This is done without the Verifier ever directly accessing the secret data. The strength of the KZG scheme ensures that if the proof verifies correctly, the Verifier can be confident in the Prover's claim, assuming the Trusted Third Party has correctly performed their role and the secret has not been compromised. + +This interaction between the three parties allows for secure and efficient verification of data properties in a variety of cryptographic applications, including blockchain protocols and secure computation, providing a balance between transparency and privacy. + +Below is a detailed sequence diagram that explains the flow in a typical KZG protocol. + +```mermaid +sequenceDiagram + autonumber + participant TP as Trusted Party + Actor P as Prover + Actor V as Verifier + rect rgb(255, 190, 152) + note right of TP: Generates a ∈ F_p,
      computes PP =
      and DELETES a + TP->>P: Sends PP + TP->>V: Sends PP + rect rgb(128,182,223) + note right of P: P Chooses f(x) ∈ F_p[X] and computes C(f(a)) = g^f(a) ∈ F_p using PP. + P->>V: Sends C(f(a)) + V-->>P: Asks to open at b ∈ F_p + rect rgb(224,128,135) + note right of P: P Computes Q_b(x) = (f(x) - f(b)) / (x - b) and computes C(Q_b) = g^Q_b(a). + P->>V: Sends (b, f(b), C(Q_b)) + V->>P: Checks if e(C(f), g) == e(C(Q_b), g^(a-b)) * e(g, g)^f(b) + end + end + end +``` ### [Trusted Setup](#trusted-setup) + +### [Initial Configuration](#initial-configuration) + +Say we have a function or polynomial $f(x)$ defined as $f(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^t$ in a finite field $\mathbb F_p$. The degree of $f(x)$ is $t$ which is less than $p$, the order of the finite field $\mathbb F_p$. + +We often denote this as $f(x) \in \mathbb{F}_p[x]$. + +Often, the prime order $p$ is choosen such that $p \gt 2^k$, for some security parameter k. The prime number $p$ is very large in practice. + +Prover also picks a pairing function that satisfies both bilinear and non-degenerate properties. + +To simplify this step, Prover picks a polynomial f(x) \in \mathbb{F}_p[x]$, the degree of $f(x)$ is at most $t$ which is less than $p$, the order of the finite field $\mathbb{F}_p$. Prover also picks a pairing function $e$. + + ### [Commitment of the polynomial](#commitment-of-the-polynomial) + +$F(a) = f_0 + f_1a + f_2a^2 + \ldots + f_da^d$ + +So $C_F = F(a) \cdot G = (f_0 + f_1a + f_2a^2 + \ldots + f_da^d) \cdot G$ + +$C_F = f_0 \cdot G + f_1a \cdot G + f_2a^2 \cdot G + \ldots + f_da^d \cdot G$ + + ### [Opening](#opening) ### [Verification](#verification) From 7f5f296ed66bb9da9b6ef6649da72571f9749e65 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 20:15:51 +0800 Subject: [PATCH 054/101] KZG - 15 Trusted setup section is added. --- docs/wiki/Cryptography/KZG.md | 11 ++++++++++- 1 file changed, 10 insertions(+), 1 deletion(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 702b8ca0..41ea21f6 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -312,8 +312,17 @@ sequenceDiagram end end ``` + ### [Trusted Setup](#trusted-setup) +A trusted third party picks a random element $a \in \mathbb{F}_p$. They compute the public parameter (PP) or common reference string (CRS)., as < $g, g^{a^1}, g^{a^2}, \ldots, g^{a^t}$ >. Then, they **delete** $a$. This step of deleteing $a$ is extremely important to secure the system. + +Then, the trusted party sends the public paramters to the Prover and the Verifier. + +In practice, this process is wrapped around a multi-party computation (MPC) where a secret is generated in such a way that, as long as at least one participant remains honest, the randomness of the secret can be guaranteed. + +The trusted setup is a one-time procedure that generates a piece of data necessary for the cryptographic protocol to function. This data must be used every time the protocol is run, but once generated and the secrets are forgotten, no further participation from the creators of the ceremony is required. The trust in the setup comes from the fact that the secrets used to generate the data are securely discarded after the setup, ensuring that the data remains secure for future use +Modern protocols often use a powers-of-tau setup, which involves hundreds of participants. The security of the final output depends on the honesty of at least one participant who does not publish their secret. This approach is considered "close enough to trustless" in practice, making it a practical solution for cryptographic protocols that require a trusted setup ### [Initial Configuration](#initial-configuration) @@ -325,7 +334,7 @@ Often, the prime order $p$ is choosen such that $p \gt 2^k$, for some security p Prover also picks a pairing function that satisfies both bilinear and non-degenerate properties. -To simplify this step, Prover picks a polynomial f(x) \in \mathbb{F}_p[x]$, the degree of $f(x)$ is at most $t$ which is less than $p$, the order of the finite field $\mathbb{F}_p$. Prover also picks a pairing function $e$. +To simplify this step, Prover picks a polynomial $f(x) \in \mathbb{F}_p[x]$, the degree of $f(x)$ is at most $t$ which is less than $p$, the order of the finite field $\mathbb{F}_p$. Prover also picks a pairing function $e$. ### [Commitment of the polynomial](#commitment-of-the-polynomial) From 98c63450c0a4485afda54f9245ce485e19b1364e Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 26 Mar 2024 21:08:16 +0800 Subject: [PATCH 055/101] KZG - 16 Commitment of the Polynomial section is added. --- docs/wiki/Cryptography/KZG.md | 28 +++++++++++++++++++--------- 1 file changed, 19 insertions(+), 9 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 41ea21f6..cbcd9e9b 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -25,7 +25,7 @@ The KZG commitment scheme is like a cryptographic vault for securely locking awa - [KZG Protocol Flow](#kzg-protocol-flow) - [Trusted Setup](#trusted-setup) - [Initial Configuration](#initial-configuration) - - [Commitment of the polynomial](#commitment-of-the-polynomial) + - [Commitment of the Polynomial](#commitment-of-the-polynomial) - [Opening](#opening) - [Verification](#verification) - [KZG by Hands](#kzg-by-hands) @@ -314,7 +314,7 @@ sequenceDiagram ``` ### [Trusted Setup](#trusted-setup) -A trusted third party picks a random element $a \in \mathbb{F}_p$. They compute the public parameter (PP) or common reference string (CRS)., as < $g, g^{a^1}, g^{a^2}, \ldots, g^{a^t}$ >. Then, they **delete** $a$. This step of deleteing $a$ is extremely important to secure the system. +A trusted third party picks a random element $a \in \mathbb{F}_p$. They compute the public parameter (PP) or common reference string (CRS), as < $g, g^{a^1}, g^{a^2}, \ldots, g^{a^t}$ >. Then, they **delete** $a$. This step of deleteing $a$ is extremely important to secure the system. Then, the trusted party sends the public paramters to the Prover and the Verifier. @@ -326,26 +326,36 @@ Modern protocols often use a powers-of-tau setup, which involves hundreds of par ### [Initial Configuration](#initial-configuration) -Say we have a function or polynomial $f(x)$ defined as $f(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^t$ in a finite field $\mathbb F_p$. The degree of $f(x)$ is $t$ which is less than $p$, the order of the finite field $\mathbb F_p$. +Say the Prover has a function or polynomial $f(x)$ defined as $f(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^t$ in a finite field $\mathbb F_p$. The degree of $f(x)$ is $t$ which is less than $p$, the order of the finite field $\mathbb F_p$. We often denote this as $f(x) \in \mathbb{F}_p[x]$. +$\mathbb{G}_p$ is an Elliptic Curve group of order $p$ with a generator $g$. + Often, the prime order $p$ is choosen such that $p \gt 2^k$, for some security parameter k. The prime number $p$ is very large in practice. -Prover also picks a pairing function that satisfies both bilinear and non-degenerate properties. +Prover also picks a pairing function that satisfies both bilinear and non-degenerate properties. The pairing is denoted as below: + +$e:$ $\mathbb G_1 X \mathbb G_2 \rightarrow \mathbb G_T$ + +To simplify this step, Prover picks a polynomial $f(x) \in \mathbb{F}_p[x]$, the degree of $f(x)$ is at most $t$ which is less than $p$, the order of the finite field $\mathbb{F}_p$. Prover also picks a pairing function $e$ on the Elliptic Curve group $\mathbb{G}_p$. + -To simplify this step, Prover picks a polynomial $f(x) \in \mathbb{F}_p[x]$, the degree of $f(x)$ is at most $t$ which is less than $p$, the order of the finite field $\mathbb{F}_p$. Prover also picks a pairing function $e$. +### [Commitment of the Polynomial](#commitment-of-the-polynomial) +Say, the commitment of the polynomial $f(x)$ is denoted as $C_f$. The commitment is like hash function. -### [Commitment of the polynomial](#commitment-of-the-polynomial) +So $C_f = g ^ {f(a)} = g^{(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)}$. Here $f(a)$ is the polynomial evaluted at $x=a$. +Though, the Prover doesn't know $a$, he or she can still cmpute the commitment of the polynomial at $x=a$. -$F(a) = f_0 + f_1a + f_2a^2 + \ldots + f_da^d$ +So we have, $C_f = g ^ {f(a)} = g^{(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)}$. -So $C_F = F(a) \cdot G = (f_0 + f_1a + f_2a^2 + \ldots + f_da^d) \cdot G$ +$C_f = g^{f_0} \cdot g^{f_1a} \cdot g^{f_2a^2} \ldots g^{f_ta^t}$. -$C_F = f_0 \cdot G + f_1a \cdot G + f_2a^2 \cdot G + \ldots + f_da^d \cdot G$ +$C_f = (g)^{f_0} \cdot (g^a)^{f_1} \cdot (g^{a^2})^{f_2} \ldots (g^{a^t})^{f_t}$. +From the CRS, the Prover knows these values < $g, g^{a^1}, g^{a^2}, \ldots, g^{a^t}$ >, he or she can compute this value as commitment of the polynomial, $C_f$ and sends to the Verifier. ### [Opening](#opening) From 7923fc5ea7873e553df7053313c35e454c55943d Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 09:08:50 +0800 Subject: [PATCH 056/101] KZG - 17 Opening of the Polynomial section is added. --- docs/wiki/Cryptography/KZG.md | 36 ++++++++++++++++++++++++++++++----- 1 file changed, 31 insertions(+), 5 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index cbcd9e9b..2c01dad1 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -26,13 +26,13 @@ The KZG commitment scheme is like a cryptographic vault for securely locking awa - [Trusted Setup](#trusted-setup) - [Initial Configuration](#initial-configuration) - [Commitment of the Polynomial](#commitment-of-the-polynomial) - - [Opening](#opening) + - [Opening of the Polynomial](#opening-of-the-polynomial) - [Verification](#verification) - [KZG by Hands](#kzg-by-hands) - [KZG by Hands - Initial Configuration](#kzg-by-hands---initial-configuration) - [KZG by Hands - Trusted Setup](#kzg-by-hands---trusted-setup) - [KZG by Hands - Commitment of the polynomial](#kzg-by-hands---commitment-of-the-polynomial) - - [KZG by Hands - Opening](#kzg-by-hands---opening) + - [KZG by Hands - Opening of the Polynomial](#kzg-by-hands---opening-of-the-polynomial) - [KZG by Hands - Verification](#kzg-by-hands---verification) - [Security of KZG - Deleting the toxic waste](#security-of-kzg---deleting-the-toxic-waste) - [Implementing KZG in Sagemath](#implementing-kzg-in-sagemath) @@ -134,7 +134,7 @@ As you can see, by repeatedly adding $1$ modulo $7$, we can generate every other **Generator of Multiplicative Group** -For the multiplicative group of integers modulo a prime $p$, the group ($\mathbb G_p, .)$ consists of the integers { ${1, 2, 3, \ldots, p-1}$ }, where the operation is multiplication modulo $p$. We'll choose a small prime to make it simple, say $p = 7$. So, our group ($\mathbb G^*_7, .)$ under multiplication modulo $7$ consists of the elements ${1, 2, 3, 4, 5, 6}$. Remember, division by zero element is excluded, that's why we have `*` in the notation. +For the multiplicative group of integers modulo a prime $p$, the group ($\mathbb G_p, .$) consists of the integers { ${1, 2, 3, \ldots, p-1}$ }, where the operation is multiplication modulo $p$. We'll choose a small prime to make it simple, say $p = 7$. So, our group ($\mathbb G^*_7, .)$ under multiplication modulo $7$ consists of the elements { ${1, 2, 3, 4, 5, 6}$ }. Remember, division by zero element is excluded, that's why we have `*` in the notation. Here's the group structure: @@ -357,10 +357,36 @@ $C_f = (g)^{f_0} \cdot (g^a)^{f_1} \cdot (g^{a^2})^{f_2} \ldots (g^{a^t})^{f_ From the CRS, the Prover knows these values < $g, g^{a^1}, g^{a^2}, \ldots, g^{a^t}$ >, he or she can compute this value as commitment of the polynomial, $C_f$ and sends to the Verifier. -### [Opening](#opening) +### [Opening of the Polynomial](#opening-of-the-polynomial) + +Upon receiving a commitment to a polynomial, denoted by $C_f$, from the Prover, the Verifier takes the next step in the protocol by selecting a random point, which we'll call $b$, from the field $\mathbb F_p$. The Verifier then requests the Prover to open or reveal the value of the polynomial at this specific point. + +**What does 'opening the polynomial' mean?** +Opening the polynomial at $x=b$ involves calculating the value of the polynomial at that point, which is mathematically represented as $f(b)$. This is done by evaluating the polynomial using the chosen point $b$: + +$f(b) = f_0 + f_1b + f_2b^2 + \ldots + f_tb^t$. + +Let's assume that this computation results in $f(b) = d$. The Prover's task is now to provide the Verifier with an Evaluation Proof, which is evidence that $f(b)$ truly equals $d$. + +Let's unpack this step by step. + +**Calculating the Evaluation Proof:** +The Prover determines the Quotient polynomial, which we will denote as $Q(x)$, and computes a commitment to it. This step is essential for creating a verifiable proof. Since we know $f(b)=d$, the polynomial $(f(x)−d)$ will have a root at $x=b$, meaning that $(f(x)−d)$ is divisible by $x−b$ with no remainder—this is a consequence of Little Bezout’s Theorem. + +Expressed in mathematical terms, the Quotient polynomial is: +$Q(x) = \frac{f(x) - f(b)}{x - b} = \frac{f(x) - d}{x - b}$ + +The commitment to the Quotient Polynomial, $Q(x)$, is represented by $C_Q$. Using the Common Reference String (CRS) provided during the Trusted Setup, the Prover calculates $C_Q$: +$C_Q = g^{Q(a)}$. + +The Prover can calculate $C_Q$ as long as $(f(x) - f(b))$ is divisible by $(x−b)$. If this were not the case, $Q(x)$ would not be a proper polynomial i.e. the Quotient polynomial will have a denominator and some negative exponents, and the Prover could not compute the Evaluation Proof $C_Q$ using only the CRS. + +Finally, the Prover sends the tuple < $b, f(b), C_Q$ > to the Verifier, completing this stage of the protocol. + ### [Verification](#verification) + ## [KZG by Hands](#kzg-by-hands) ### [KZG by Hands - Initial Configuration](#kzg-by-hands---initial-configuration) @@ -369,7 +395,7 @@ From the CRS, the Prover knows these values < $g, g^{a^1}, g^{a^2}, \ldots, g^{a ### [KZG by Hands - Commitment of the polynomial](#kzg-by-hands---commitment-of-the-polynomial) -### [KZG by Hands - Opening](#kzg-by-hands---opening) +### [KZG by Hands - Opening of the Polynomial](#kzg-by-hands---opening-of-the-polynomial) ### [KZG by Hands - Verification](#kzg-by-hands---verification) From 19355e591945f3b692e2de5edf357b06324d0ad5 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 11:56:13 +0800 Subject: [PATCH 057/101] KZG - 18 Verification Proof section is added. --- docs/wiki/Cryptography/KZG.md | 135 +++++++++++++++++++++------------- 1 file changed, 83 insertions(+), 52 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 2c01dad1..709a8582 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -5,43 +5,6 @@ ## [TLDR](#tldr) The KZG commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. -**Table of Contents** -- [KZG Commitments Unveiled: A Beginner's Guide](#kzg-commitments-unveiled-a-beginners-guide) - - [\[DRAFT MODE - WORK IN PROGRESS\]](#draft-mode---work-in-progress) - - [TLDR](#tldr) - - [Motivation](#motivation) - - [ZKSNARKs](#zksnarks) - - [Ethereum Danksharding](#ethereum-danksharding) - - [Goal](#goal) - - [What we need to know before we discuss KZG](#what-we-need-to-know-before-we-discuss-kzg) - - [Modular Arithmetic](#modular-arithmetic) - - [Finite Field of order prime p](#finite-field-of-order-prime-p) - - [Group](#group) - - [Generator of a Group](#generator-of-a-group) - - [Why choosing a prime number for modulo operations in finite fields](#why-choosing-a-prime-number-for-modulo-operations-in-finite-fields) - - [Cryptographic Assumptions needed for KZG Scheme](#cryptographic-assumptions-needed-for-kzg-scheme) - - [Pairing Function](#pairing-function) - - [Important Properties of Commitments](#important-properties-of-commitments) - - [KZG Protocol Flow](#kzg-protocol-flow) - - [Trusted Setup](#trusted-setup) - - [Initial Configuration](#initial-configuration) - - [Commitment of the Polynomial](#commitment-of-the-polynomial) - - [Opening of the Polynomial](#opening-of-the-polynomial) - - [Verification](#verification) - - [KZG by Hands](#kzg-by-hands) - - [KZG by Hands - Initial Configuration](#kzg-by-hands---initial-configuration) - - [KZG by Hands - Trusted Setup](#kzg-by-hands---trusted-setup) - - [KZG by Hands - Commitment of the polynomial](#kzg-by-hands---commitment-of-the-polynomial) - - [KZG by Hands - Opening of the Polynomial](#kzg-by-hands---opening-of-the-polynomial) - - [KZG by Hands - Verification](#kzg-by-hands---verification) - - [Security of KZG - Deleting the toxic waste](#security-of-kzg---deleting-the-toxic-waste) - - [Implementing KZG in Sagemath](#implementing-kzg-in-sagemath) - - [KZG using Assymetic Pairing Fuctions](#kzg-using-assymetic-pairing-fuctions) - - [KZG Batch Mode Single Polynomial, multiple points](#kzg-batch-mode-single-polynomial-multiple-points) - - [KZG Batch Mode Multiple Polynomials, same point](#kzg-batch-mode-multiple-polynomials-same-point) - - [KZG Batch Mode Multiple Polynomials, multiple points](#kzg-batch-mode-multiple-polynomials-multiple-points) - - ## [Motivation](#motivation) ### [ZKSNARKs](#zksnarks) @@ -297,24 +260,24 @@ sequenceDiagram Actor V as Verifier rect rgb(255, 190, 152) - note right of TP: Generates a ∈ F_p,
      computes PP =
      and DELETES a + note right of TP: Generates a ∈ F_p,
      computes PP =
      and DELETES a TP->>P: Sends PP TP->>V: Sends PP rect rgb(128,182,223) - note right of P: P Chooses f(x) ∈ F_p[X] and computes C(f(a)) = g^f(a) ∈ F_p using PP. - P->>V: Sends C(f(a)) - V-->>P: Asks to open at b ∈ F_p + note right of P: P Chooses f(x) ∈ F_p[X] and computes C_f = C(f(a)) = f(a).g ∈ F_p using PP. + P->>V: Sends C_f + V-->>P: V Asks to open at b ∈ F_p rect rgb(224,128,135) - note right of P: P Computes Q_b(x) = (f(x) - f(b)) / (x - b) and computes C(Q_b) = g^Q_b(a). - P->>V: Sends (b, f(b), C(Q_b)) - V->>P: Checks if e(C(f), g) == e(C(Q_b), g^(a-b)) * e(g, g)^f(b) + note right of P: P Computes Q_b(x) = (f(x) - f(b)) / (x - b) and computes C_Q = C(Q_b) = Q_b(a).g. + P->>V: Sends (b, f(b), C_Q) + V->>P: Checks if e(C_f - f(b).g, g) == e(C_Q, ag - bg) end end end ``` ### [Trusted Setup](#trusted-setup) -A trusted third party picks a random element $a \in \mathbb{F}_p$. They compute the public parameter (PP) or common reference string (CRS), as < $g, g^{a^1}, g^{a^2}, \ldots, g^{a^t}$ >. Then, they **delete** $a$. This step of deleteing $a$ is extremely important to secure the system. +A trusted third party picks a random element $a \in \mathbb{F}_p$. They compute the public parameter (PP) or common reference string (CRS), as < $g, {a^1}.g, {a^2}.g, \ldots, {a^t}.g$ >. Then, they **delete** $a$. This step of deleteing $a$ is extremely important to secure the system. Then, the trusted party sends the public paramters to the Prover and the Verifier. @@ -345,17 +308,17 @@ To simplify this step, Prover picks a polynomial $f(x) \in \mathbb{F}_p[x]$, the Say, the commitment of the polynomial $f(x)$ is denoted as $C_f$. The commitment is like hash function. -So $C_f = g ^ {f(a)} = g^{(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)}$. Here $f(a)$ is the polynomial evaluted at $x=a$. +So $C_f = {f(a)} \cdot g = {(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)} \cdot g$. Here $f(a)$ is the polynomial evaluted at $x=a$. Though, the Prover doesn't know $a$, he or she can still cmpute the commitment of the polynomial at $x=a$. -So we have, $C_f = g ^ {f(a)} = g^{(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)}$. +So we have, $C_f = {f(a)} \cdot g = {(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)} \cdot g$. -$C_f = g^{f_0} \cdot g^{f_1a} \cdot g^{f_2a^2} \ldots g^{f_ta^t}$. +$C_f = {f_0} \cdot g + {f_1a} \cdot g + {f_2a^2} \cdot g + \ldots + {f_ta^t} \cdot g $. -$C_f = (g)^{f_0} \cdot (g^a)^{f_1} \cdot (g^{a^2})^{f_2} \ldots (g^{a^t})^{f_t}$. +$C_f = {f_0} \cdot g + {f_1} \cdot (ag) + {f_2} \cdot ({a^2}g) + \ldots + {f_t} \cdot ({a^t}g)$. -From the CRS, the Prover knows these values < $g, g^{a^1}, g^{a^2}, \ldots, g^{a^t}$ >, he or she can compute this value as commitment of the polynomial, $C_f$ and sends to the Verifier. +From the CRS, the Prover knows these values < $g, {a^1}.g, {a^2}.g, \ldots, {a^t}.g$ >, he or she can compute this value as commitment of the polynomial, $C_f$ and sends to the Verifier. ### [Opening of the Polynomial](#opening-of-the-polynomial) @@ -377,14 +340,82 @@ Expressed in mathematical terms, the Quotient polynomial is: $Q(x) = \frac{f(x) - f(b)}{x - b} = \frac{f(x) - d}{x - b}$ The commitment to the Quotient Polynomial, $Q(x)$, is represented by $C_Q$. Using the Common Reference String (CRS) provided during the Trusted Setup, the Prover calculates $C_Q$: -$C_Q = g^{Q(a)}$. +$C_Q = {Q(a)} \cdot g$. The Prover can calculate $C_Q$ as long as $(f(x) - f(b))$ is divisible by $(x−b)$. If this were not the case, $Q(x)$ would not be a proper polynomial i.e. the Quotient polynomial will have a denominator and some negative exponents, and the Prover could not compute the Evaluation Proof $C_Q$ using only the CRS. Finally, the Prover sends the tuple < $b, f(b), C_Q$ > to the Verifier, completing this stage of the protocol. -### [Verification](#verification) +### [Verification Proof](#verification-proof) +Let's first summarize what data does the Verifier has so far in the protocol. + +**Data in hand:** The Verifier knows: +- The commitment of the polynomial, $C_f$. +- The opening point $b$. +- The value of the polynomial at $b$, denoted as $f(b)$. +- The commitment to the Quotient polynomial at $b$, denoted as $C_Q = {Q(a)} \cdot g$. + +**Properties of a commitment scheme:** +- **Completeness:** A commitment scheme is said to be **complete** if anything which is true is provable. +- **Soundness:** It is said to be **sound** if everything which is provable is true - i.e. anything which is false cannot be proven by the scheme. + +**Quotient polynomial and verification:** + +Recall that the Quotient polynomial is given by +$Q(x) = \frac{f(x) - f(b)}{x - b} = \frac{f(x) - d}{x - b}$. + +So, $(x - b) \cdot Q(x) = f(x) - d$ + +Evaluating this at $x=a$, we get +$(a - b) \cdot Q(a) = f(a) - d$ + +Multiplying both sides by the generator $g$, we get + +$(a−b) \cdot Q(a) \cdot g = f(a) \cdot g − d \cdot g$ + +Now, the Verifier knows that $C_Q = Q(a) \cdot g$ and $C_f = f(a) \cdot g$. + +So substituting, we get + +$(a−b) \cdot C_Q = C_f − d \cdot g$ + +If the verifier can confirm the validity of the above equality, it means the commitment has been verified. However, since the verifier is unaware of the value of $a$, they cannot directly validate the truth of this equality. + +However, the Verifier can use Elliptic Curve Pairings as outlined above to verify the equality constraint even without knowing $a$. Remember that the pairing function is denoted as: + +$e:$ $\mathbb G_1 X \mathbb G_2 \rightarrow \mathbb G_T$ such that it satisfies, + +Bilinear property: $e(g^a, g^b) = e(g, g^{ab}) = e(g^{ab}, g) = e(g,g)^{ab}$ + +Non-degenerate property: $e(g,g) \neq 1$, means the output is not an identity element. + +Let us for now, use a symmetric pairing function where $e:$ $\mathbb G X \mathbb G \rightarrow \mathbb G_T$ + +The Prover has to check he equality $(a−b) \cdot C_Q = C_f − d \cdot g$. + +The pairing function takes any two elements from the group $\mathbb G$ and maps it to an element in $\mathbb G_T$. + +- A commitment, like $C_f$ or $C_Q$, is obtained by multiplying a number (a scalar) with the group's generator, $g$. +- Since both $C_f$ and $C_Q$) are the result of this operation, they belong to the group $\mathbb G$. +- When we multiply $C_Q$ by the difference of two numbers $a$ and $b$, which is also a scalar, the result, $(a−b) \cdot C_Q$, stays within the group $\mathbb G$. +- Similarly, $C_f$ is a group element, and so is $d \cdot g$ because it's the generator multiplied by a scalar. +- Subtracting $d \cdot g$ from $C_f$ gives us another element in the group, $C_f − d \cdot g$. +- All these resulting elements are part of the group $\mathbb G$ and can be used in the pairing function. + +So, applying the pairing function on the both sides using the generator $g$ as the second parameter, the equality constraint becomes, + +$e((a−b) \cdot C_Q, g) = e(C_f − d \cdot g, g)$ + +We still can't calculate $a-b$ as nobody knows $a$. But we can use the bilinear property of the pairing function + +$e(g^a, g^b) = e(g, g^{ab}) = e(g^{ab}, g) = e(g,g)^{ab}$ + +So we can rewrite the equality constraint as +$e(C_Q, (a−b) \cdot g) = e(C_f − d \cdot g, g)$ +$e(C_Q, a \cdot g − b \cdot g) = e(C_f − d \cdot g, g)$ + +Though the Verifier doesn’t know $a$, he or she knows $a \cdot g$ from the Common Reference String. So now the Verifier can check whether the above equality is true or not. This ends the verification of the Evaluation Proof. ## [KZG by Hands](#kzg-by-hands) From 5d1cd1f349c391bb0e1ad67047f3222add0fb5b8 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 12:16:53 +0800 Subject: [PATCH 058/101] KZG - 19 fixed some format errors. --- docs/wiki/Cryptography/KZG.md | 23 +++++++++++++++++------ 1 file changed, 17 insertions(+), 6 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 709a8582..43f6d70d 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -58,7 +58,7 @@ When we do modular arithmetic operations in the finite field $\mathbb F_p$, we h In genral, when we define a finite field, we define, the order $p$ of the field and an arithemetic operation like addition or multiplication. If it is addition, we denote the field by $(\mathbb F_p, +)$. If it is multiplication, we denote it by $(\mathbb F^*_p, +)$. The `*` is telling us to exclude the zero element from our field so that we can satisfy all the required properties of the finite field i.e. mainly we can divide the numbers and find inverse of all elements. If we include the zero element, we can't find the inverse of zero element. ### [Group](#group) -The group is a similar concept as finite field with some small changes. In a Group, we only have one arithmetic operation on the set, usually addition or multiplication as opposed to in a finite field we have addition and multiplication both and this group must satisfy few properties which we will below with an example. We denote a Group by ($\mathbb G, +)$ for a Group with addition as the group operation, ($\mathbb G^*, .)$ for Group with multiplication operation; the `*` is telling to exclude zero element to avoid division by zero. +A Group is a similar concept as finite field with some small changes. In a Group, we only have one arithmetic operation on the set, usually addition or multiplication as opposed to in a finite field we have addition and multiplication both and this group must satisfy few properties which we will discuss below with an example. We denote a Group by ($\mathbb G, +)$ for a Group with addition as the group operation, ($\mathbb G^*, .)$ for Group with multiplication operation; the `*` is telling to exclude zero element to avoid division by zero. In the next section we use an example to define a Group. This will help develop an intuition on when we call a set of numbers a Group. @@ -67,8 +67,6 @@ A generator is an element within a group that, when combined with itself repeate In mathematical sense, if you have a group ($\mathbb G, .)$ and an element $g$ in $\mathbb G$ we say that $g$ is a generator of $\mathbb G$ if the set of all powers of $g$, $(g, g^2, g^3, ...)$, is equal to $\mathbb G$ for a finite group, or covers all elements of $\mathbb G$ through this repeated operation in the case of an infinite group. -*Remember, a group only has one operation.* - This concept is best explained with an example. We will work with ($\mathbb G_7, +)$ of group elements { ${0,1,2,3,4,5,6}$ } and ($\mathbb G^*_7, .)$ of group elements { ${1,2,3,4,5,6}$ } with modulo $7$ to find the generator of the Groups. @@ -242,11 +240,11 @@ We want prove that we know a specific evaluation of a function or polynomial at In the KZG commitment scheme, the roles of the Trusted Third Party, Prover, and Verifier are critical to its function and security. Here's how each contributes to the process: -1. **Trusted Third Party (Setup Authority):** This entity is responsible for the initial setup phase of the KZG scheme. They generate the public parameters (PP) that will be used in the commitments and proofs, based on a secret that only they know. This secret is crucial for the construction of commitments but must be discarded (or kept extremely secure) after the setup to ensure the system's integrity. The trust in this party is fundamental because if the secret is mishandled or leaked, it could compromise the entire system. +1. **Trusted Third Party (Setup Authority):** This entity is responsible for the initial setup phase of the KZG scheme. They generate the public parameters (PP) or Common Reference String (CRS) that will be used in the commitments and proofs, based on a secret that only they know. This secret is crucial for the construction of commitments but must be discarded (or kept extremely secure) after the setup to ensure the system's integrity. The trust in this party is fundamental because if the secret is mishandled or leaked, it could compromise the entire system. -2. **Prover:** The Prover is the one who wants to commit to a certain piece of data (like a polynomial) without revealing it. Using the public parameters provided by the Trusted Third Party, the Prover computes a commitment to their data. When it's time to prove certain properties of their data (like a polynomial evaluation at a specific point), the Prover can generate a proof based on their commitment. This proof shows that their data has certain properties without revealing the data itself. +2. **Prover:** The Prover is the one who wants to commit to a certain piece of data (like a polynomial) without revealing it. Using the CRS provided by the Trusted Third Party, the Prover computes a commitment to their data. When it's time to prove certain properties of their data (like a polynomial evaluation at a specific point), the Prover can generate a proof based on their commitment. This proof shows that their data has certain properties without revealing the data itself. -3. **Verifier:** The Verifier is the party interested in checking the Prover's claims about their secret data. The Verifier uses the proof provided by the Prover, along with the public parameters from the Trusted Third Party, to verify that the Prover's claim about their data is true. This is done without the Verifier ever directly accessing the secret data. The strength of the KZG scheme ensures that if the proof verifies correctly, the Verifier can be confident in the Prover's claim, assuming the Trusted Third Party has correctly performed their role and the secret has not been compromised. +3. **Verifier:** The Verifier is the party interested in checking the Prover's claims about their secret data. The Verifier uses the proof provided by the Prover, along with the CRS from the Trusted Third Party, to verify that the Prover's claim about their data is true. This is done without the Verifier ever directly accessing the secret data. The strength of the KZG scheme ensures that if the proof verifies correctly, the Verifier can be confident in the Prover's claim, assuming the Trusted Third Party has correctly performed their role and the secret has not been compromised. This interaction between the three parties allows for secure and efficient verification of data properties in a variety of cryptographic applications, including blockchain protocols and secure computation, providing a balance between transparency and privacy. @@ -417,6 +415,19 @@ $e(C_Q, a \cdot g − b \cdot g) = e(C_f − d \cdot g, g)$ Though the Verifier doesn’t know $a$, he or she knows $a \cdot g$ from the Common Reference String. So now the Verifier can check whether the above equality is true or not. This ends the verification of the Evaluation Proof. +**Full Opening VS Partial Opening of the polynomial** + +- **Full Open Process:** + - The Prover sends the complete polynomial to the Verifier. + - Using the CRS, the Verifier independently computes the polynomial's commitment. + - The Verifier then checks if this independently computed commitment matches the one originally sent by the Prover. + +- **Partial Open Process in KZG:** + - Instead of opening the whole polynomial, the Prover can opt for a partial open. + - This means the Prover reveals the polynomial's value at a single specific point. + - This partial revelation is known as the Evaluation Proof. + + ## [KZG by Hands](#kzg-by-hands) From 489bf5c6a490c6bc5c772525f9c6b354ed7f1522 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 13:33:53 +0800 Subject: [PATCH 059/101] KZG - 20 KZG by Hands section is added. --- docs/wiki/Cryptography/KZG.md | 39 +++++++++++++++++++++++++++++++++-- 1 file changed, 37 insertions(+), 2 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 43f6d70d..53ec75bc 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -410,7 +410,9 @@ We still can't calculate $a-b$ as nobody knows $a$. But we can use the bilinear $e(g^a, g^b) = e(g, g^{ab}) = e(g^{ab}, g) = e(g,g)^{ab}$ So we can rewrite the equality constraint as + $e(C_Q, (a−b) \cdot g) = e(C_f − d \cdot g, g)$ + $e(C_Q, a \cdot g − b \cdot g) = e(C_f − d \cdot g, g)$ Though the Verifier doesn’t know $a$, he or she knows $a \cdot g$ from the Common Reference String. So now the Verifier can check whether the above equality is true or not. This ends the verification of the Evaluation Proof. @@ -427,19 +429,52 @@ Though the Verifier doesn’t know $a$, he or she knows $a \cdot g$ from the Com - This means the Prover reveals the polynomial's value at a single specific point. - This partial revelation is known as the Evaluation Proof. - - ## [KZG by Hands](#kzg-by-hands) +Now, let us practically dervie the steps in KZG protocol using a small finite field. We can compute all finite field operations and pairing operations by hand and get a feel for the KZG protocol flow and verifying polynomial commitments. ### [KZG by Hands - Initial Configuration](#kzg-by-hands---initial-configuration) +- We will work with the finite field $(\mathbb F_{11}, + )$. So, the prime order $p = 11$. This means all finite field operations are done modulo 11. +- The finite field set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. +- The generator $g = 2$ in $(\mathbb G_{11}, +)$. +- This means that the group operation is addition with modulo 11. +- The Prover selects the polynomial $f(x) = 3x^2 + 5x + 7$. +- Then we have the degree of the polynomial $f(x)$ as $t = 2$. +- The pairing function $e(x, y) = xy$ over $(\mathbb G_{11}, +)$. ### [KZG by Hands - Trusted Setup](#kzg-by-hands---trusted-setup) +- The Trusted Party choses a secret number randomly. Say, $a = 3$ is the secret number. +- They generate the public parameter or the common reference string (CRS) < $g, {a^1}.g, {a^2}.g, \ldots, {a^t}.g$ >. +- This is equal to < $2, 3 \cdot 2, {3^2} \cdot 2$ > which is equal to < $2, 6, 7$ > after applying modulo 11. +- The Trusted Party **deletes** the secret number $a$. +- The Trusted Party sends the CRS to the Prover and Verifier. ### [KZG by Hands - Commitment of the polynomial](#kzg-by-hands---commitment-of-the-polynomial) +- The Prover calculates the commitment of the polynomial, $C_f$. +- $C_f = f(a) \cdot g = {f_0} \cdot g + {f_1} \cdot (ag) + {f_2} \cdot ({a^2}g) $. +- $C_f = 7 \cdot g + 5 \cdot (ag) + 3 \cdot a^2g = 7.2 + 5.6 + 3.7 = 65 = 10$ (mod 11). +- The Provers sends the commitment of the polynomial $C_f = 10$ to the Verifier. ### [KZG by Hands - Opening of the Polynomial](#kzg-by-hands---opening-of-the-polynomial) +- The Verifier asks the Prover to open the polynomial at $x = 1$. +- The Prover computes the Quotient polynomial $Q(x) = \frac{f(x) - f(1)}{x - 1} = \frac{f(x) - d}{x - b}$. +- Compute $f(1) = d = 3.1^2 + 5.1 + 7 = 4$ (mod $11$). +- $Q(x) = \frac{3x^2 + 5x + 7 - 4}{x - 1} = \frac{3x^2 + 5x + 3}{x - 1}$. +- **Divide the Leading Term:** $3x^2$ divided by $x$ gives us $3x$. We write $3x$ above the division bar. +- **Multiply the Divisor by the Quotient's Leading Term:** Multiply $x - 1$ by $3x$ to get $3x^2 - 3x$. +- **Subtract from the Polynomial:** Subtract $3x^2 - 3x$ from $3x^2 + 5x$ to get $8x$. +- **Bring Down the Next Term:** Bring down the $+3$ to get $8x + 3$. +- **Divide the Next Term:** $8x$ divided by $x$ is $8$. Write $+8$ above the division bar next to $3x$. +- **Multiply Again:** Multiply $x - 1$ by $8$ to get $8x - 8$. +- **Subtract Subtract:** $8x - 8$ from $8x + 3$ to get $11$. +- **Apply Modulo 11:** We reduce each term modulo $11$. Since $11$ is $0$ modulo $11$, the remainder is $0$. +- The Prover computes the commitment of $C_Q = Q(a) \cdot g = 3 \cdot ag + 8 \cdot g = 3.6 + 8.2 = 34 = 1$ (mod 11). +- The Prover sends to the Verifier < $1, f(1), C_Q$ > = < $1, 4, 1$ >. ### [KZG by Hands - Verification](#kzg-by-hands---verification) +- The Verified must check the pairing constraint $e(C_Q, a \cdot g − b \cdot g) = e(C_f − d \cdot g, g)$ +- L.H.S (left hand side): $e(1, 6 - 1.2) = e(1, 4) = 1.4 = 4 (mod 11)$ +- R.H.S (right hand side): $e(10 - 4.2, 2) = e(2, 2) = 2.2 = 4 (mod 11)$. +- This proves the equality constraint is true, hence the Evaluation Proof is verified. ## [Security of KZG - Deleting the toxic waste](#security-of-kzg---deleting-the-toxic-waste) From 82793bd97a0df68d71a3386943fd6c79555f6c62 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 13:50:36 +0800 Subject: [PATCH 060/101] KZG - 20 Security of KZG section is added. --- docs/wiki/Cryptography/KZG.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 53ec75bc..39f4c7de 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -395,7 +395,7 @@ The Prover has to check he equality $(a−b) \cdot C_Q = C_f − d \cdot g$. The pairing function takes any two elements from the group $\mathbb G$ and maps it to an element in $\mathbb G_T$. - A commitment, like $C_f$ or $C_Q$, is obtained by multiplying a number (a scalar) with the group's generator, $g$. -- Since both $C_f$ and $C_Q$) are the result of this operation, they belong to the group $\mathbb G$. +- Since both $C_f$ and $C_Q$ are the result of this operation, they belong to the group $\mathbb G$. - When we multiply $C_Q$ by the difference of two numbers $a$ and $b$, which is also a scalar, the result, $(a−b) \cdot C_Q$, stays within the group $\mathbb G$. - Similarly, $C_f$ is a group element, and so is $d \cdot g$ because it's the generator multiplied by a scalar. - Subtracting $d \cdot g$ from $C_f$ gives us another element in the group, $C_f − d \cdot g$. @@ -477,6 +477,11 @@ Now, let us practically dervie the steps in KZG protocol using a small finite fi - This proves the equality constraint is true, hence the Evaluation Proof is verified. ## [Security of KZG - Deleting the toxic waste](#security-of-kzg---deleting-the-toxic-waste) +- Imagine the Prover somehow finds out the secret number $a$ or the Trusted Party leaks $a$ to a malicious Prover. +- The Prover computes $f_1(x) = 3x^2 + 5x + 7$ at $x=3$. So we get, $f_1(2) = 3.3^2 + 5.3 + 7 = 49 = 5 mod(11)$ +- The Prover computes $f_2(x) = 2x^2 + 7x + 10$ at $x=3$. So we get, $f_2(2) = 2.3^2 + 7.3 + 10 = 49 = 5 mod(11)$ +- This breaks the binding property of the commitment scheme leading to fradulent proofs by the malicious Prover. +- Hence, it is extremely important to **delete** the secret number $a$ by the Trusted Party after generating the CRS. ## [Implementing KZG in Sagemath](#implementing-kzg-in-sagemath) From 4ff03c9d9e3b33987ec649a1ada01859bb840769 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 14:14:24 +0800 Subject: [PATCH 061/101] KZG - 21 Assymetic Pairing section is added. --- docs/wiki/Cryptography/KZG.md | 23 +++++++++++++++++++++-- 1 file changed, 21 insertions(+), 2 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 39f4c7de..a812191c 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -483,9 +483,28 @@ Now, let us practically dervie the steps in KZG protocol using a small finite fi - This breaks the binding property of the commitment scheme leading to fradulent proofs by the malicious Prover. - Hence, it is extremely important to **delete** the secret number $a$ by the Trusted Party after generating the CRS. -## [Implementing KZG in Sagemath](#implementing-kzg-in-sagemath) - ## [KZG using Assymetic Pairing Fuctions](#kzg-using-assymetic-pairing-fuctions) +An assymetric pairing function is denoted as: + +$e:$ $\mathbb G_1 X \mathbb G_2 \rightarrow \mathbb G_T$. + +Let the generators of $\mathbb G_1$ be $g_1$ and $\mathbb G_2$ be $g_2$. + +The Prover has to check the equality $(a−b) \cdot Q(a) = f(a) − d$. + +Multiplying both sides by $g_1$, we get +$(a−b) \cdot Q(a) \cdot g_1 = f(a) \cdot g_1 − d \cdot g_1$ +$(a−b) \cdot C_Q = C_f − d \cdot g_1$ + +Applying the assymetric pairing function on both sides, we get +$e((a−b) \cdot C_Q, g_2) = e(C_f − d \cdot g_1, g_2)$ + +Using the bilinear property, we get +$e(C_Q, (a−b) \cdot g_2) = e(C_f − d \cdot g_1, g_2)$ +$e(C_Q, a \cdot g_2 − b \cdot g_2 ) = e(C_f − d \cdot g_1, g_2)$ + +Here $a \cdot g_2$ will be the part of CRS of $\mathbb G_2$ and everything else can be either computed or part of CRS of $\mathbb G_1$. + ## [KZG Batch Mode Single Polynomial, multiple points](#kzg-batch-mode-single-polynomial-multiple-points) From fac2e1449825d6b36f62c27990ace937b1ac319a Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 14:15:39 +0800 Subject: [PATCH 062/101] KZG - 22 fixed some formatting errors. --- docs/wiki/Cryptography/KZG.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index a812191c..b7c4626e 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -494,6 +494,7 @@ The Prover has to check the equality $(a−b) \cdot Q(a) = f(a) − d$. Multiplying both sides by $g_1$, we get $(a−b) \cdot Q(a) \cdot g_1 = f(a) \cdot g_1 − d \cdot g_1$ + $(a−b) \cdot C_Q = C_f − d \cdot g_1$ Applying the assymetric pairing function on both sides, we get @@ -501,6 +502,7 @@ $e((a−b) \cdot C_Q, g_2) = e(C_f − d \cdot g_1, g_2)$ Using the bilinear property, we get $e(C_Q, (a−b) \cdot g_2) = e(C_f − d \cdot g_1, g_2)$ + $e(C_Q, a \cdot g_2 − b \cdot g_2 ) = e(C_f − d \cdot g_1, g_2)$ Here $a \cdot g_2$ will be the part of CRS of $\mathbb G_2$ and everything else can be either computed or part of CRS of $\mathbb G_1$. From 18efe280ea5f7d344f7c7430060f092f01d8a3e1 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 14:17:00 +0800 Subject: [PATCH 063/101] KZG - 23 fixed some formatting errors. --- docs/wiki/Cryptography/KZG.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index b7c4626e..0cc40446 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -493,14 +493,17 @@ Let the generators of $\mathbb G_1$ be $g_1$ and $\mathbb G_2$ be $g_2$. The Prover has to check the equality $(a−b) \cdot Q(a) = f(a) − d$. Multiplying both sides by $g_1$, we get + $(a−b) \cdot Q(a) \cdot g_1 = f(a) \cdot g_1 − d \cdot g_1$ $(a−b) \cdot C_Q = C_f − d \cdot g_1$ Applying the assymetric pairing function on both sides, we get + $e((a−b) \cdot C_Q, g_2) = e(C_f − d \cdot g_1, g_2)$ Using the bilinear property, we get + $e(C_Q, (a−b) \cdot g_2) = e(C_f − d \cdot g_1, g_2)$ $e(C_Q, a \cdot g_2 − b \cdot g_2 ) = e(C_f − d \cdot g_1, g_2)$ From 4969e952a85ba5ff071e988317bc4aebcf4770f6 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 14:31:47 +0800 Subject: [PATCH 064/101] KZG - 24 KZG Compactness. --- docs/wiki/Cryptography/KZG.md | 13 ++++--------- 1 file changed, 4 insertions(+), 9 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 0cc40446..10a9f4b2 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -5,6 +5,8 @@ ## [TLDR](#tldr) The KZG commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. +The KZG Polynomial Commitment Scheme ensures that both commitments and evaluation proofs are of a fixed size, regardless of the polynomial's length, offering consistent and space-efficient cryptographic operations. + ## [Motivation](#motivation) ### [ZKSNARKs](#zksnarks) @@ -510,14 +512,7 @@ $e(C_Q, a \cdot g_2 − b \cdot g_2 ) = e(C_f − d \cdot g_1, g_2)$ Here $a \cdot g_2$ will be the part of CRS of $\mathbb G_2$ and everything else can be either computed or part of CRS of $\mathbb G_1$. - -## [KZG Batch Mode Single Polynomial, multiple points](#kzg-batch-mode-single-polynomial-multiple-points) - -## [KZG Batch Mode Multiple Polynomials, same point](#kzg-batch-mode-multiple-polynomials-same-point) - -## [KZG Batch Mode Multiple Polynomials, multiple points](#kzg-batch-mode-multiple-polynomials-multiple-points) - - - +### [Unwavering Compactness](#unwavering-compactness) +One key benefit of the KZG Polynomial Commitment Scheme is its efficient use of space. No matter the length or complexity of the polynomial we're working with, the commitment to that polynomial—essentially its cryptographic "footprint"—is always a single, fixed-size element within a mathematical group, $\mathbb G$. This means that as the polynomial grows in degree, the size of the commitment does not increase. The same principle applies to the evaluation proof, which is the evidence we provide to show that our commitment is accurate. Whether we're verifying just one value or many at once (in batch mode), the proof will always be of a consistent size. This consistency in size translates to predictable and efficient storage requirements, an important feature for practical applications in cryptography. From a8cb30d708c08b115fb548b862322b1ac790b576 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 14:32:54 +0800 Subject: [PATCH 065/101] KZG - 25 fixed some formatting errors. --- docs/wiki/Cryptography/KZG.md | 2 -- 1 file changed, 2 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 10a9f4b2..1c87f3ed 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -1,7 +1,5 @@ # KZG Commitments Unveiled: A Beginner's Guide -## [DRAFT MODE - WORK IN PROGRESS] - ## [TLDR](#tldr) The KZG commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. From 3f3dbcf90d99e89d23b8f91fa287fd3452089702 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 14:34:01 +0800 Subject: [PATCH 066/101] KZG - 26 fixed some formatting errors. --- docs/wiki/Cryptography/KZG.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 1c87f3ed..16563366 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -1,4 +1,4 @@ -# KZG Commitments Unveiled: A Beginner's Guide +# KZG Polynomial Commitment Scheme ## [TLDR](#tldr) The KZG commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. From d2f33a2efad76aac58be4f8e5fe65ba4fd319054 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 15:31:43 +0800 Subject: [PATCH 067/101] KZG - 27 Added references. --- docs/wiki/Cryptography/KZG.md | 46 ++++++++++++++++++++--------------- 1 file changed, 27 insertions(+), 19 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 16563366..52918f97 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -3,7 +3,7 @@ ## [TLDR](#tldr) The KZG commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. -The KZG Polynomial Commitment Scheme ensures that both commitments and evaluation proofs are of a fixed size, regardless of the polynomial's length, offering consistent and space-efficient cryptographic operations. +The KZG Polynomial Commitment Scheme ensures that both commitments and evaluation proofs are of a fixed size, regardless of the polynomial's length, offering consistent and space-efficient cryptographic operations[^5]. ## [Motivation](#motivation) @@ -75,10 +75,10 @@ We will work with ($\mathbb G_7, +)$ of group elements { ${0,1,2,3,4,5,6}$ } and Our set ($\mathbb G_7, +)$ with elements { ${0,1,2,3,4,5,6}$ } is a Group because it satisfies the definition of a Group. -**Closure:** When you add any two numbers in the set and take the remainder when divided by $7$, you end up with a result that's still in the set. -**Associativity:** For any numbers $a, b$ and $c$ in the set, $(a+b)+c$ is always the same as $a+(b+c)$, even with modulo $7$. -**Identity element:** The number $0$ acts as an identity element because when you add $0$ to any number in the set, you get the same number back. -**Inverse elements:** Every number in the set has an inverse such that when you add them together, you end up back at the identity element $0$. For example, the inverse of $3$ is $4$ because $3 + 4 = 7$, which is $0$ modulo $7$. +- **Closure:** When you add any two numbers in the set and take the remainder when divided by $7$, you end up with a result that's still in the set. +- **Associativity:** For any numbers $a, b$ and $c$ in the set, $(a+b)+c$ is always the same as $a+(b+c)$, even with modulo $7$. +- **Identity element:** The number $0$ acts as an identity element because when you add $0$ to any number in the set, you get the same number back. +- **Inverse elements:** Every number in the set has an inverse such that when you add them together, you end up back at the identity element $0$. For example, the inverse of $3$ is $4$ because $3 + 4 = 7$, which is $0$ modulo $7$. Now, for the generator. Since our group has a prime order $7$, any element except for the identity element $0$ is a generator. Let's pick the element $1$ as our generator i.e $g = 1$. Since we are working with an additive group, our group elements with generator g will be $\{0, g, 2g, 3g, 4g, 5g, 6g\}$. @@ -91,7 +91,7 @@ Starting with $1$ and adding it to itself modulo $7$, we get: - $1 + 1 + 1 + 1 + 1 + 1 = 6$ (which is $6*1$ modulo 7) - $1 + 1 + 1 + 1 + 1 + 1 + 1 = 7$, which is $0$ modulo 7 (which is $7*1$ modulo 7) -As you can see, by repeatedly adding $1$ modulo $7$, we can generate every other element in the group. Hence, $1$ is a generator of the group ($\mathbb G_7, +)$. Similarly, we could pick $2, 3, 4, 5, or 6$ as our generator, and by performing repeated addition modulo $7$, we would still generate the entire group. This is a special property of groups with a prime number of elements. +As you can see, by repeatedly adding $1$ modulo $7$, we can generate every other element in the group. Hence, $1$ is a generator of the group ($\mathbb G_7, +)$. Similarly, we could pick any number in $2, 3, 4, 5, 6$ as our generator, and by performing repeated addition modulo $7$, we would still generate the entire group. This is a special property of groups with a prime number of elements. **Generator of Multiplicative Group** @@ -183,7 +183,7 @@ Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a, b$ are any ele A pairing function is a special kind of function that takes two inputs and produces a single output with two important properties, biliner and non-degenrate. Bilinear means, we can move around in a reversible way. -Non-degenerate means, if we apply pairing function to teh same element, it doesn't result in the identity element of the Group. +Non-degenerate means, if we apply pairing function to the same element, it doesn't result in the identity element of the Group. Let's define these properties a bit more rigorously. @@ -195,13 +195,15 @@ Non-degenerate property: $e(g,g) \neq 1$, means the output is not an identity el When $\mathbb G_1$ and $\mathbb G_2$ are the same Group, we call this symmetric pairing function. Otherwise, it is an assymetric pairing function. +Here is a great resource to learn more about pairing functions from a practical POV[^3]. + **Developing an intuition for Pairing function** Imagine two separate islands, each inhabited by a unique species of magical creatures. The first island is home to Unicorns, each with a distinct color, and the second island is inhabited by Dragons, each with a unique fire color. A pairing function is like a magical bridge that connects a Unicorn with a Dragon, creating a unique, new magical creature, a Dracorn, that embodies characteristics of both. Here's how to think about this pairing function without getting bogged down by technicalities: -- **Two Groups:** Think of the Unicorns and Dragons as belonging to two different groups (in mathematical terms, these are usually called groups $\mathbb G_1$ and $\mathbb G_2$. +- **Two Groups:** Think of the Unicorns and Dragons as belonging to two different groups (in mathematical terms, these are usually called groups $\mathbb G_1$ and $\mathbb G_2$). - **Pairing Function:** The magical bridge acts as the pairing function. When a Unicorn and a Dragon meet on this bridge, the pairing function combines them into a Dracorn. This Dracorn has a special glow that uniquely corresponds to the combination of that specific Unicorn and Dragon (reversable). - **Unique Outcome:** Just like every Unicorn and Dragon pair produces a Dracorn with a unique glow, in mathematics, a pairing function takes one element from each group and produces a unique output in a third group (often denoted as $\mathbb G_T$). @@ -217,17 +219,15 @@ Pairing functions enable advanced cryptographic techniques, such as those used i Commitment schemes are like the secret-keeping wizards of the digital world. They let someone make a promise about a piece of information (we'll call this the secret message) in a way that ties them to their promise without letting anyone else know what the secret is. Here's how it works: -1. **Making the Promise (Commitment):** You decide on a secret message and use a special spell (the commitment scheme) to create a magic seal (the commitment). This seal proves you have a secret, but it keeps the secret hidden. - -2. **Keeping It Secret (Hiding):** Even though you've made this seal, nobody else can see what your secret message is. It's like you've locked it in a chest and only you have the key. +- **Making the Promise (Commitment):** You decide on a secret message and use a special spell (the commitment scheme) to create a magic seal (the commitment). This seal proves you have a secret, but it keeps the secret hidden. +- **Keeping It Secret (Hiding):** Even though you've made this seal, nobody else can see what your secret message is. It's like you've locked it in a chest and only you have the key. +- **Proving You're Honest (Binding):** The magic of the commitment is that you can't change your secret message later without breaking the seal. This means once you've made your commitment, you're bound to it. -3. **Proving You're Honest (Binding):** The magic of the commitment is that you can't change your secret message later without breaking the seal. This means once you've made your commitment, you're bound to it. - -Later, when the time comes to reveal your secret, you can show the original message and prove that it matches the seal you made before. This lets someone else (the verifier) check and confirm that your secret message is the same one you committed to in the beginning, proving that you kept your word. +Later, when the time comes to reveal your secret, you can show the original message and prove that it matches the seal you made before. This lets someone else (the Verifier) check and confirm that your secret message is the same one you committed to in the beginning, proving that you kept your word. The Binding and Hiding properties are extremely important and they tie back to the above cryptographic assumptions we made with the Discrete Logarithm and Strong Diffie-Hellman assumptions. -But for now, we don't need to go deep into the technicalities. +But for now, we don't need to go deep into the technicalities. In case, you want to learn more, here is a great resource for PCS from Prof. Dan Boneh[^4]. With this background, we are ready to explain KZG protocol flow and understand its construction. @@ -277,13 +277,15 @@ sequenceDiagram ### [Trusted Setup](#trusted-setup) A trusted third party picks a random element $a \in \mathbb{F}_p$. They compute the public parameter (PP) or common reference string (CRS), as < $g, {a^1}.g, {a^2}.g, \ldots, {a^t}.g$ >. Then, they **delete** $a$. This step of deleteing $a$ is extremely important to secure the system. -Then, the trusted party sends the public paramters to the Prover and the Verifier. +Then, the trusted party sends the CRS to the Prover and the Verifier. In practice, this process is wrapped around a multi-party computation (MPC) where a secret is generated in such a way that, as long as at least one participant remains honest, the randomness of the secret can be guaranteed. The trusted setup is a one-time procedure that generates a piece of data necessary for the cryptographic protocol to function. This data must be used every time the protocol is run, but once generated and the secrets are forgotten, no further participation from the creators of the ceremony is required. The trust in the setup comes from the fact that the secrets used to generate the data are securely discarded after the setup, ensuring that the data remains secure for future use -Modern protocols often use a powers-of-tau setup, which involves hundreds of participants. The security of the final output depends on the honesty of at least one participant who does not publish their secret. This approach is considered "close enough to trustless" in practice, making it a practical solution for cryptographic protocols that require a trusted setup +Modern protocols often use a powers-of-tau setup, which involves hundreds of participants. The security of the final output depends on the honesty of at least one participant who does not publish their secret. This approach is considered "close enough to trustless" in practice, making it a practical solution for cryptographic protocols that require a trusted setup. + +Ethereum has a very detailed documentation of the Trusted Setup ceremony for more detail[^2]. ### [Initial Configuration](#initial-configuration) @@ -308,7 +310,7 @@ Say, the commitment of the polynomial $f(x)$ is denoted as $C_f$. The commitment So $C_f = {f(a)} \cdot g = {(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)} \cdot g$. Here $f(a)$ is the polynomial evaluted at $x=a$. -Though, the Prover doesn't know $a$, he or she can still cmpute the commitment of the polynomial at $x=a$. +Though, the Prover doesn't know $a$, he or she can still compute the commitment of the polynomial at $x=a$. So we have, $C_f = {f(a)} \cdot g = {(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)} \cdot g$. @@ -332,7 +334,7 @@ Let's assume that this computation results in $f(b) = d$. The Prover's task is n Let's unpack this step by step. **Calculating the Evaluation Proof:** -The Prover determines the Quotient polynomial, which we will denote as $Q(x)$, and computes a commitment to it. This step is essential for creating a verifiable proof. Since we know $f(b)=d$, the polynomial $(f(x)−d)$ will have a root at $x=b$, meaning that $(f(x)−d)$ is divisible by $x−b$ with no remainder—this is a consequence of Little Bezout’s Theorem. +The Prover determines the Quotient polynomial, which we will denote as $Q(x)$, and computes a commitment to it. This step is essential for creating a verifiable proof. Since we know $f(b)=d$, the polynomial $(f(x)−d)$ will have a root at $x=b$, meaning that $(f(x)−d)$ is divisible by $x−b$ with no remainder—this is a consequence of Little Bezout’s Theorem[^1]. Expressed in mathematical terms, the Quotient polynomial is: $Q(x) = \frac{f(x) - f(b)}{x - b} = \frac{f(x) - d}{x - b}$ @@ -514,3 +516,9 @@ Here $a \cdot g_2$ will be the part of CRS of $\mathbb G_2$ and everything else One key benefit of the KZG Polynomial Commitment Scheme is its efficient use of space. No matter the length or complexity of the polynomial we're working with, the commitment to that polynomial—essentially its cryptographic "footprint"—is always a single, fixed-size element within a mathematical group, $\mathbb G$. This means that as the polynomial grows in degree, the size of the commitment does not increase. The same principle applies to the evaluation proof, which is the evidence we provide to show that our commitment is accurate. Whether we're verifying just one value or many at once (in batch mode), the proof will always be of a consistent size. This consistency in size translates to predictable and efficient storage requirements, an important feature for practical applications in cryptography. +## [References](#references) +[^1] https://en.wikipedia.org/wiki/Polynomial_remainder_theorem +[^2] https://github.com/ethereum/kzg-ceremony +[^3] https://www.rareskills.io/post/bilinear-pairing +[^4] https://www.youtube.com/watch?v=WyT5KkKBJUw +[^5] https://www.iacr.org/archive/asiacrypt2010/6477178/6477178.pdf From 7e47b112492a44b6e08aba89ac7186dc02776fe0 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 15:34:14 +0800 Subject: [PATCH 068/101] KZG - 28 fixed some formatting errors. --- docs/wiki/Cryptography/KZG.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 52918f97..1f001320 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -517,8 +517,8 @@ One key benefit of the KZG Polynomial Commitment Scheme is its efficient use of ## [References](#references) -[^1] https://en.wikipedia.org/wiki/Polynomial_remainder_theorem -[^2] https://github.com/ethereum/kzg-ceremony -[^3] https://www.rareskills.io/post/bilinear-pairing -[^4] https://www.youtube.com/watch?v=WyT5KkKBJUw -[^5] https://www.iacr.org/archive/asiacrypt2010/6477178/6477178.pdf +[^1]: https://en.wikipedia.org/wiki/Polynomial_remainder_theorem +[^2]: https://github.com/ethereum/kzg-ceremony +[^3]: https://www.rareskills.io/post/bilinear-pairing +[^4]: https://www.youtube.com/watch?v=WyT5KkKBJUw +[^5]: https://www.iacr.org/archive/asiacrypt2010/6477178/6477178.pdf From c641c86a709f76504b1014112c6553dec710414f Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Wed, 27 Mar 2024 17:53:02 +0800 Subject: [PATCH 069/101] KZG - 29 fixed some formatting errors. --- docs/wiki/Cryptography/KZG.md | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 1f001320..a4e80e03 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -3,7 +3,7 @@ ## [TLDR](#tldr) The KZG commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. -The KZG Polynomial Commitment Scheme ensures that both commitments and evaluation proofs are of a fixed size, regardless of the polynomial's length, offering consistent and space-efficient cryptographic operations[^5]. +The KZG Polynomial Commitment Scheme ensures that both commitments and evaluation proofs are of a fixed size, regardless of the polynomial's length, offering consistent and space-efficient cryptographic operations[^5][^6][^7]. ## [Motivation](#motivation) @@ -195,7 +195,7 @@ Non-degenerate property: $e(g,g) \neq 1$, means the output is not an identity el When $\mathbb G_1$ and $\mathbb G_2$ are the same Group, we call this symmetric pairing function. Otherwise, it is an assymetric pairing function. -Here is a great resource to learn more about pairing functions from a practical POV[^3]. +Here are some great resources to learn more about pairing functions from a practical POV[^3][^8][^9]. **Developing an intuition for Pairing function** @@ -522,3 +522,7 @@ One key benefit of the KZG Polynomial Commitment Scheme is its efficient use of [^3]: https://www.rareskills.io/post/bilinear-pairing [^4]: https://www.youtube.com/watch?v=WyT5KkKBJUw [^5]: https://www.iacr.org/archive/asiacrypt2010/6477178/6477178.pdf +[^6]: https://dankradfeist.de/ethereum/2020/06/16/kate-polynomial-commitments.html +[^7]: https://www.youtube.com/watch?v=uGeIDNEwHjs&t=520s +[^8]: https://www.youtube.com/watch?v=8WDOpzxpnTE +[^9]: https://vitalik.eth.limo/general/2017/01/14/exploring_ecp.html From f5d38e0f9cc2ca064c0a97738f0d2fc91ba8e32a Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Fri, 29 Mar 2024 11:28:40 +0800 Subject: [PATCH 070/101] added changes based on review 1. --- docs/wiki/Cryptography/KZG.md | 45 ++++++++++++++++++++++------------- 1 file changed, 28 insertions(+), 17 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index a4e80e03..1fe7185f 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -1,9 +1,10 @@ # KZG Polynomial Commitment Scheme ## [TLDR](#tldr) -The KZG commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. +The KZG (Kate, Zaverucha, and Goldwasser) commitment scheme is like a cryptographic vault for securely locking away polynomials (mathematical equations) so that you can later prove you have them without giving away their secrets. It's like making a sealed promise that you can validate without ever having to open it up and show the contents. Using advanced math based on elliptic curves, it enables efficient, verifiable commitments that are a key part of making blockchain transactions more private and scalable. This scheme is especially important for Ethereum's upgrades, where it helps to verify transactions quickly and securely without compromising on privacy. + +KZG is a powerful cryptographic tool that supports a wide range of applications within the Ethereum ecosystem and other cryptographic applications. Its distinctive features are leveraged in proving schemes to enhance scalability and privacy in various applications. -The KZG Polynomial Commitment Scheme ensures that both commitments and evaluation proofs are of a fixed size, regardless of the polynomial's length, offering consistent and space-efficient cryptographic operations[^5][^6][^7]. ## [Motivation](#motivation) @@ -12,18 +13,23 @@ Learning about Polynomial Commitment Schemes (PCS) is important because they pla *Modern ZKSNARK = Functional Commitment Scheme + Compatible Interactive Oracle Proof (IOP)* -PCS is a way to prove that you know a secret function (represented by a polynomial) without showing the function itself. It's like promising to show a secret recipe to someone, but you only show them the final dish without revealing the recipe. This is crucial for ZKSNARKs because it allows the prover to prove they know a secret function without revealing it. - -IOP is another method that helps in proving that you know a secret value without revealing it. It's used along with PCS to make a ZKSNARK. The IOP helps in proving the knowledge, while PCS makes the proof short and easy to check. This combination allows for creating efficient ZKSNARKs that can be used in many areas, like blockchain and privacy-preserving computations. - -To make ZKSNARKs, you need to choose a PCS and IOP that work well together. The PCS is used to commit to a polynomial and prove the evaluation of the polynomial at a certain point without revealing the polynomial. The IOP is used to create a proof of knowledge, which is then turned into a non-interactive proof using a method called the Fiat-Shamir heuristic. This makes it possible to generate and verify the proof without needing to communicate in real-time, making ZKSNARKs useful for blockchain and distributed systems. ### [Ethereum Danksharding](#ethereum-danksharding) KZG commitment scheme has emerged as a pivotal technology in the Ethereum ecosystem, particularly in the context of Proto-Danksharding and its anticipated evolution into Danksharding. This commitment scheme is a cornerstone of many Zero-Knowledge (ZK) related applications within Ethereum, enabling efficient and secure verification of data without revealing the underlying information. -The adoption of KZG commitments in Proto-Danksharding and its future application in Danksharding represents a significant step towards Ethereum's full sharding implementation. Sharding is a long-term scaling solution for Ethereum, aiming to improve the network's scalability and capacity by dividing the network into smaller, more manageable pieces. The KZG commitment scheme plays a vital role in this process by facilitating the efficient verification of data across shards, thereby enhancing the overall security and performance of the Ethereum network. +Ethereum-based applications utilizing the KZG (Kate, Zaverucha, and Goldberg) scheme include: + +- **Proto-Danksharding (EIP-4844)**: This proposal aims to reduce the cost of posting data on Ethereum's Layer 1 for rollups by using KZG for its polynomial commitment scheme. It introduces a "blob-carrying transaction" type to accommodate substantial data blobs, with only a commitment to the data blob being accessible from the execution layer. + +- **Data Availability Sampling**: PCS enable a critical feature known as Data Availability Sampling (DAS) in Ethereum roadmap, which allows validators to confirm the correctness and availability of data blobs without downloading the entire data. This capability is facilitated by the unique properties of PCS, enabling efficient verification processes in blockchain applications like Ethereum's Danksharding. + +- **PSE's Summa, Proof of Solvenecy Protocol**: Ethereum Foundation's PSE group project Summa, Proof of Solvency protocol, uses KZG commitments to proove the centralized exchanges and other custodians total assets are greater than their liabilities without revealing any information about users' balances. + +- **Scroll's zkRollups**: Scroll, a native zkEVM Layer 2 for Ethereum, uses KZG to generate commitments to a collection of polynomials that encapsulate computations. This allows verifiers to request evaluations at random points to validate the accuracy of the computation represented by the polynomials. -Moreover, the KZG commitment scheme is not only limited to Ethereum but has broader applications in the blockchain and cryptographic communities. Its ability to commit to a polynomial and verify evaluations of the polynomial without revealing the polynomial itself makes it a versatile tool for various cryptographic protocols and applications. +- **Jellyfish**: Jellyfish employs the KZG commitment scheme to generate commitments to polynomials during the commitment phase. It leverages the homomorphic properties of KZG for efficient evaluation of the polynomial at any point without revealing its coefficients. + +- **Hyperplonk**: Hyperplonk utilizes the multi-linear KZG commitment, indicating its application in scenarios requiring multi-linear polynomial commitments. ## [Goal](#goal) @@ -31,21 +37,21 @@ Now that we are motivated to learn PCS, let us get started with defining what is Say we have a function or polynomial $f(x)$ defined as $f(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^t$. The degree of $f(x)$ is $t$. -Our main goal with KZG scheme is that we want to prove to someone that we know this polynomial without revealing the polynomial. What do we mean by without revealing by polynomial? We meant that without revealing the coefficients of the polynomial. +Our main goal with KZG scheme is that we want to prove to someone that we know this polynomial without revealing the polynomial, i.e. coefficients of the polynomial. In practice what we exactly do is that we prove that we know a specific evaluation of this polynomial at a point $x=a$. We write this, $f(a)$, for some $x=a$. -## [What we need to know before we discuss KZG](#what-we-need-to-know-before-we-discuss-kzg) +## [Prerequisite Knowledge](#prerequisite-knowledge) There are some important concepts we need to know before we can move further to understand KZG scheme. Fortunately, we can get an Engineering level understanding of the KZG scheme from just enough high school mathematics. We will try to gain some intuition on advanced concepts and their important properties without knowing them intimately. This can help us see the KZG protocol flow without bogged down by the advanced mathematics. We need to know: ### [Modular Arithmetic](#modular-arithmetic) -- Can you read a clock? Can you add/subtract two time values? In general can you do clock arithmetic? This is called Modular arithmetic. We only need to know how to add, subtract, multiply or divide numbers and apply modulus operation (the clock scale). -- We usually write this mod $p$ to mean modulo $p$, where $p$ is some number. +An analog clock illustrates modular arithmetic as hours cycle back after reaching their limit. For KZG, it's enough to know simple arithmetic—adding, subtracting, multiplying, and dividing—along with using the modulus operation, just like a clock resets after 12 or 24 hours. + ### [Finite Field of order prime p](#finite-field-of-order-prime) @@ -125,7 +131,7 @@ You can verify that $5$ is also a generator for our multiplicative group ($\math In the next section, we will learn how generators enable the KZG commitment scheme to function as an efficient, secure, and verifiable method of committing to polynomials, making it a powerful tool for cryptographic protocols, particularly in blockchain technologies where these qualities are very important. -### [Why choosing a prime number for modulo operations in finite fields](#why-choosing-a-prime-number-for-modulo-operations-in-finite-fields) +### [Why Primes for Modulo Operations in Fields](#why-primes-for-modulo-operations-in-fields) Choosing a prime number as the modulus for operations in a finite field offers several benefits and simplifies various aspects of field arithmetic: @@ -145,7 +151,7 @@ Choosing a prime number as the modulus for operations in a finite field offers s Using a prime number as the modulus for finite fields simplifies the field arithmetic and ensures that all field properties are satisfied, which is essential for both theoretical and practical applications, particularly in cryptography. -### [Cryptographic Assumptions needed for KZG Scheme](#cryptographic-assumptions-needed-for-kzg-scheme) +### [Cryptographic Assumptions](#cryptographic-assumptions) In order to work with KZG commitment scheme, we need two additional assumptions. We won't go deep into why these assumptions are needed but we will give an intuition to why these cryptographic assumptions are needed to make KZG more secure. @@ -478,14 +484,16 @@ Now, let us practically dervie the steps in KZG protocol using a small finite fi - R.H.S (right hand side): $e(10 - 4.2, 2) = e(2, 2) = 2.2 = 4 (mod 11)$. - This proves the equality constraint is true, hence the Evaluation Proof is verified. -## [Security of KZG - Deleting the toxic waste](#security-of-kzg---deleting-the-toxic-waste) +## [Security of KZG](#security-of-kzg) +**Deleting toxic waste during the Trusted Setup Ceremony** + - Imagine the Prover somehow finds out the secret number $a$ or the Trusted Party leaks $a$ to a malicious Prover. - The Prover computes $f_1(x) = 3x^2 + 5x + 7$ at $x=3$. So we get, $f_1(2) = 3.3^2 + 5.3 + 7 = 49 = 5 mod(11)$ - The Prover computes $f_2(x) = 2x^2 + 7x + 10$ at $x=3$. So we get, $f_2(2) = 2.3^2 + 7.3 + 10 = 49 = 5 mod(11)$ - This breaks the binding property of the commitment scheme leading to fradulent proofs by the malicious Prover. - Hence, it is extremely important to **delete** the secret number $a$ by the Trusted Party after generating the CRS. -## [KZG using Assymetic Pairing Fuctions](#kzg-using-assymetic-pairing-fuctions) +## [Assymetic Pairing Fuctions](#assymetic-pairing-fuctions) An assymetric pairing function is denoted as: $e:$ $\mathbb G_1 X \mathbb G_2 \rightarrow \mathbb G_T$. @@ -513,6 +521,9 @@ $e(C_Q, a \cdot g_2 − b \cdot g_2 ) = e(C_f − d \cdot g_1, g_2)$ Here $a \cdot g_2$ will be the part of CRS of $\mathbb G_2$ and everything else can be either computed or part of CRS of $\mathbb G_1$. ### [Unwavering Compactness](#unwavering-compactness) + +The KZG Polynomial Commitment Scheme ensures that both commitments and evaluation proofs are of a fixed size, regardless of the polynomial's length, offering consistent and space-efficient cryptographic operations[^5][^6][^7]. + One key benefit of the KZG Polynomial Commitment Scheme is its efficient use of space. No matter the length or complexity of the polynomial we're working with, the commitment to that polynomial—essentially its cryptographic "footprint"—is always a single, fixed-size element within a mathematical group, $\mathbb G$. This means that as the polynomial grows in degree, the size of the commitment does not increase. The same principle applies to the evaluation proof, which is the evidence we provide to show that our commitment is accurate. Whether we're verifying just one value or many at once (in batch mode), the proof will always be of a consistent size. This consistency in size translates to predictable and efficient storage requirements, an important feature for practical applications in cryptography. From 5539f998f3a6a352a657cf07b99d18438dde8b5b Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Fri, 29 Mar 2024 11:35:27 +0800 Subject: [PATCH 071/101] typos fixed. --- docs/wiki/Cryptography/KZG.md | 8 +++----- 1 file changed, 3 insertions(+), 5 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 1fe7185f..d9208faa 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -14,7 +14,7 @@ Learning about Polynomial Commitment Schemes (PCS) is important because they pla *Modern ZKSNARK = Functional Commitment Scheme + Compatible Interactive Oracle Proof (IOP)* -### [Ethereum Danksharding](#ethereum-danksharding) +### [Use cases in Ethereum Ecosystem](#use-cases-in-ethereum-ecosystem) KZG commitment scheme has emerged as a pivotal technology in the Ethereum ecosystem, particularly in the context of Proto-Danksharding and its anticipated evolution into Danksharding. This commitment scheme is a cornerstone of many Zero-Knowledge (ZK) related applications within Ethereum, enabling efficient and secure verification of data without revealing the underlying information. Ethereum-based applications utilizing the KZG (Kate, Zaverucha, and Goldberg) scheme include: @@ -23,7 +23,7 @@ Ethereum-based applications utilizing the KZG (Kate, Zaverucha, and Goldberg) sc - **Data Availability Sampling**: PCS enable a critical feature known as Data Availability Sampling (DAS) in Ethereum roadmap, which allows validators to confirm the correctness and availability of data blobs without downloading the entire data. This capability is facilitated by the unique properties of PCS, enabling efficient verification processes in blockchain applications like Ethereum's Danksharding. -- **PSE's Summa, Proof of Solvenecy Protocol**: Ethereum Foundation's PSE group project Summa, Proof of Solvency protocol, uses KZG commitments to proove the centralized exchanges and other custodians total assets are greater than their liabilities without revealing any information about users' balances. +- **PSE's Summa, Proof of Solvenecy Protocol**: Ethereum Foundation's PSE group project, Summa, leverages KZG commitments in its Proof of Solvency protocol. This allows centralized exchanges and custodians to demonstrate that their total assets exceed their liabilities, all while keeping user balance information private. - **Scroll's zkRollups**: Scroll, a native zkEVM Layer 2 for Ethereum, uses KZG to generate commitments to a collection of polynomials that encapsulate computations. This allows verifiers to request evaluations at random points to validate the accuracy of the computation represented by the polynomials. @@ -219,9 +219,7 @@ Here's how to think about this pairing function without getting bogged down by t Pairing functions enable advanced cryptographic techniques, such as those used in certain types of digital signatures and encryption, by allowing this kind of "cross-group" interaction to occur securely and predictably. - - -## [Important Properties of Commitments](#important-properties-of-commitments) +## [Properties of Commitments](#properties-of-commitments) Commitment schemes are like the secret-keeping wizards of the digital world. They let someone make a promise about a piece of information (we'll call this the secret message) in a way that ties them to their promise without letting anyone else know what the secret is. Here's how it works: From 16bb6dec1bb4a6c857d2a368abd69dfbb43f7393 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 30 Mar 2024 08:16:33 +0800 Subject: [PATCH 072/101] Applied the suggestions from review 2. --- docs/wiki/Cryptography/KZG.md | 41 ++++++++++++++++++----------------- 1 file changed, 21 insertions(+), 20 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index d9208faa..5430166b 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -57,14 +57,18 @@ An analog clock illustrates modular arithmetic as hours cycle back after reachin A finite field of order prime $p$, we denote it by $\mathbb F_p$, is a special set of numbers, { $\{1, 2, 3, \ldots, p-1\}$ }, where you can do all the usual math operations (addition, subtraction, multiplication, and division, except by zero) and still follow the rules of arithmetic. -The "order" of this set is the number of elements it contains, and for a finite field of order prime $p$, this number is a prime number. The most common way to create a $\mathbb F_p$ is by taking the set of all integers greathan or equal to $0$ and dividing them by $p$, keeping only the remainders. This gives us a set of numbers from $0$ to $p-1$ that can be used for arithmetic operations. For example, if $p = 5$, the set would be {0, 1, 2, 3, 4}, and you can add, subtract, multiply, and divide these numbers in a way that follows the rules of arithmetic. This set is a finite field of order 5, we denote this by $\mathbb F_5$, because it has exactly 5 elements, and it's a prime number. +The "order" of this set is the number of elements it contains, and for a finite field of order prime $p$, this number is a prime number. The most common way to create a $\mathbb F_p$ is by taking the set of all integers greater than or equal to $0$ and dividing them by $p$, keeping only the remainders. This gives us a set of numbers from $0$ to $p-1$ that can be used for arithmetic operations. For example, if $p = 5$, the set would be {0, 1, 2, 3, 4}, and you can add, subtract, multiply, and divide these numbers in a way that follows the rules of arithmetic. This set is a finite field of order 5, we denote this by $\mathbb F_5$, because it has exactly 5 elements, and it's a prime number. When we do modular arithmetic operations in the finite field $\mathbb F_p$, we have a nice "wrap around" property i.e. the field behaves as if it "wraps around" after reaching $(p - 1)$. In genral, when we define a finite field, we define, the order $p$ of the field and an arithemetic operation like addition or multiplication. If it is addition, we denote the field by $(\mathbb F_p, +)$. If it is multiplication, we denote it by $(\mathbb F^*_p, +)$. The `*` is telling us to exclude the zero element from our field so that we can satisfy all the required properties of the finite field i.e. mainly we can divide the numbers and find inverse of all elements. If we include the zero element, we can't find the inverse of zero element. +In the next section, we will learn how generators of a Group enable the KZG commitment scheme to function as an efficient, secure, and verifiable method of committing to polynomials, making it a powerful tool for cryptographic protocols, particularly in blockchain technologies where these properties are very important. + ### [Group](#group) -A Group is a similar concept as finite field with some small changes. In a Group, we only have one arithmetic operation on the set, usually addition or multiplication as opposed to in a finite field we have addition and multiplication both and this group must satisfy few properties which we will discuss below with an example. We denote a Group by ($\mathbb G, +)$ for a Group with addition as the group operation, ($\mathbb G^*, .)$ for Group with multiplication operation; the `*` is telling to exclude zero element to avoid division by zero. +A Group is conceptually similar to a finite field, although with a few minor variations. An important difference is that in a group, we only have one arithmetic operation on the set, typically addition or multiplication as opposed to finite field with both addition and multiplication. Similarly to finite field, group elements must have an inverse and meet all its requirements, explained in the example below. + +The notation is ($\mathbb G, +)$ for a Group with addition as the group operation, ($\mathbb G^*, .)$ for Group with multiplication operation; the `*` is telling to exclude zero element to avoid division by zero. In the next section we use an example to define a Group. This will help develop an intuition on when we call a set of numbers a Group. @@ -128,9 +132,6 @@ Let's verify that each element is indeed a generator by multiplying it repeatedl You can verify that $5$ is also a generator for our multiplicative group ($\mathbb G^*_7, .)$ modulo $7$. -In the next section, we will learn how generators enable the KZG commitment scheme to function as an efficient, secure, and verifiable method of committing to polynomials, making it a powerful tool for cryptographic protocols, particularly in blockchain technologies where these qualities are very important. - - ### [Why Primes for Modulo Operations in Fields](#why-primes-for-modulo-operations-in-fields) Choosing a prime number as the modulus for operations in a finite field offers several benefits and simplifies various aspects of field arithmetic: @@ -139,7 +140,7 @@ Choosing a prime number as the modulus for operations in a finite field offers s 2. **Simplicity of Construction:** When the modulus is a prime number, the field's construction is straightforward. The elements of the field are simply the set of integers { ${1, 2, 3, \ldots, p-1}$ }, and the field operations (addition, subtraction, multiplication, and division) are performed modulo $p$. For non-prime moduli, constructing a field requires more complex structures, such as polynomial rings. -3. **Guaranteed Field Properties:** The use of a prime modulus guarantees the satisfaction of field properties. A finite field (also known as a Galois field) is a field that contains a finite number of elements. For a set to be a field, it must satisfy several properties, including the existence of additive and multiplicative identities, the existence of additive and multiplicative inverses for every element, and the commutative, associative, and distributive laws for addition and multiplication. A prime modulus ensures all these properties are met. +3. **Guaranteed Field Properties:** The use of a prime modulus guarantees the satisfaction of required field properties. These include - the existence of additive and multiplicative identities, the existence of additive and multiplicative inverses for every element, and the commutative, associative, and distributive laws for addition and multiplication. A prime modulus ensures all these properties are met. 4. **Uniform Distribution of Non-zero Elements:** In a finite field with a prime modulus, the non-zero elements have a uniform distribution with respect to multiplication. This means that the multiplication table of the field does not have any 'gaps' and every element appears exactly once in each row and column of the multiplication table (except the row and column for the zero element). @@ -186,10 +187,10 @@ So, in essence, the Strong Diffie-Hellman assumption tells us that just knowing ### [Pairing Function](#pairing-function) Say we have a generator $g$ in the group $\mathbb G^\*_p$ and $a, b$ are any elements in the finite field $\mathbb F^*_p$ and $g^a$, $g^b$ are some elements in the group $\mathbb G^\*_p$. -A pairing function is a special kind of function that takes two inputs and produces a single output with two important properties, biliner and non-degenrate. +A pairing function is a mathematical function that takes two inputs and produces a single output by mapping distinct pairs of inputs to a distinct value. It has two important properties, bilinearity and non-degeneracy. -Bilinear means, we can move around in a reversible way. -Non-degenerate means, if we apply pairing function to the same element, it doesn't result in the identity element of the Group. +- Bilinearity means, we can move around in a reversible way. +- Non-degeneracy means, if we apply pairing function to the same element, it doesn't result in the identity element of the Group. Let's define these properties a bit more rigorously. @@ -244,7 +245,7 @@ We want prove that we know a specific evaluation of a function or polynomial at In the KZG commitment scheme, the roles of the Trusted Third Party, Prover, and Verifier are critical to its function and security. Here's how each contributes to the process: -1. **Trusted Third Party (Setup Authority):** This entity is responsible for the initial setup phase of the KZG scheme. They generate the public parameters (PP) or Common Reference String (CRS) that will be used in the commitments and proofs, based on a secret that only they know. This secret is crucial for the construction of commitments but must be discarded (or kept extremely secure) after the setup to ensure the system's integrity. The trust in this party is fundamental because if the secret is mishandled or leaked, it could compromise the entire system. +1. **Trusted Third Party (Setup Authority):** This entity is responsible for the initial setup phase of the KZG scheme. They generate the public parameters (PP) or Common Reference String (CRS) that will be used in the commitments and proofs, based on a secret that only they know. This secret is crucial for the construction of commitments but must be discarded (or kept extremely secure) after the setup to ensure the system's integrity. The trust in this party is fundamental because if the secret is mishandled or leaked, it could compromise the entire system. This party's role ends after generating CRS and sharing it with the Prover and Verifier i.e. they no longer involved in either proving or verifying steps of the protocol flow. 2. **Prover:** The Prover is the one who wants to commit to a certain piece of data (like a polynomial) without revealing it. Using the CRS provided by the Trusted Third Party, the Prover computes a commitment to their data. When it's time to prove certain properties of their data (like a polynomial evaluation at a specific point), the Prover can generate a proof based on their commitment. This proof shows that their data has certain properties without revealing the data itself. @@ -287,7 +288,7 @@ In practice, this process is wrapped around a multi-party computation (MPC) wher The trusted setup is a one-time procedure that generates a piece of data necessary for the cryptographic protocol to function. This data must be used every time the protocol is run, but once generated and the secrets are forgotten, no further participation from the creators of the ceremony is required. The trust in the setup comes from the fact that the secrets used to generate the data are securely discarded after the setup, ensuring that the data remains secure for future use -Modern protocols often use a powers-of-tau setup, which involves hundreds of participants. The security of the final output depends on the honesty of at least one participant who does not publish their secret. This approach is considered "close enough to trustless" in practice, making it a practical solution for cryptographic protocols that require a trusted setup. +Modern protocols often use a powers-of-tau setup, which involves even thousands of participants. The security of the final output depends on the honesty of at least one participant who does not publish their secret. This approach is considered "close enough to trustless" in practice, making it a practical solution for cryptographic protocols that require a trusted setup. Ethereum has a very detailed documentation of the Trusted Setup ceremony for more detail[^2]. @@ -465,19 +466,19 @@ Now, let us practically dervie the steps in KZG protocol using a small finite fi - The Prover computes the Quotient polynomial $Q(x) = \frac{f(x) - f(1)}{x - 1} = \frac{f(x) - d}{x - b}$. - Compute $f(1) = d = 3.1^2 + 5.1 + 7 = 4$ (mod $11$). - $Q(x) = \frac{3x^2 + 5x + 7 - 4}{x - 1} = \frac{3x^2 + 5x + 3}{x - 1}$. -- **Divide the Leading Term:** $3x^2$ divided by $x$ gives us $3x$. We write $3x$ above the division bar. -- **Multiply the Divisor by the Quotient's Leading Term:** Multiply $x - 1$ by $3x$ to get $3x^2 - 3x$. -- **Subtract from the Polynomial:** Subtract $3x^2 - 3x$ from $3x^2 + 5x$ to get $8x$. -- **Bring Down the Next Term:** Bring down the $+3$ to get $8x + 3$. -- **Divide the Next Term:** $8x$ divided by $x$ is $8$. Write $+8$ above the division bar next to $3x$. -- **Multiply Again:** Multiply $x - 1$ by $8$ to get $8x - 8$. -- **Subtract Subtract:** $8x - 8$ from $8x + 3$ to get $11$. -- **Apply Modulo 11:** We reduce each term modulo $11$. Since $11$ is $0$ modulo $11$, the remainder is $0$. +- Divide the Leading Term: $3x^2$ divided by $x$ gives us $3x$. We write $3x$ above the division bar. +- Multiply the Divisor by the Quotient's Leading Term: Multiply $x - 1$ by $3x$ to get $3x^2 - 3x$. +- Subtract from the Polynomial: Subtract $3x^2 - 3x$ from $3x^2 + 5x$ to get $8x$. +- Bring Down the Next Term: Bring down the $+3$ to get $8x + 3$. +- Divide the Next Term: $8x$ divided by $x$ is $8$. Write $+8$ above the division bar next to $3x$. +- Multiply Again: Multiply $x - 1$ by $8$ to get $8x - 8$. +- Subtract Subtract: $8x - 8$ from $8x + 3$ to get $11$. +- Apply Modulo $11$: We reduce each term modulo $11$. Since $11$ is $0$ modulo $11$, the remainder is $0$. - The Prover computes the commitment of $C_Q = Q(a) \cdot g = 3 \cdot ag + 8 \cdot g = 3.6 + 8.2 = 34 = 1$ (mod 11). - The Prover sends to the Verifier < $1, f(1), C_Q$ > = < $1, 4, 1$ >. ### [KZG by Hands - Verification](#kzg-by-hands---verification) -- The Verified must check the pairing constraint $e(C_Q, a \cdot g − b \cdot g) = e(C_f − d \cdot g, g)$ +- The Verifier must check the pairing constraint $e(C_Q, a \cdot g − b \cdot g) = e(C_f − d \cdot g, g)$ - L.H.S (left hand side): $e(1, 6 - 1.2) = e(1, 4) = 1.4 = 4 (mod 11)$ - R.H.S (right hand side): $e(10 - 4.2, 2) = e(2, 2) = 2.2 = 4 (mod 11)$. - This proves the equality constraint is true, hence the Evaluation Proof is verified. From 148c216fc36c1b6ec16a676ac55fe9ea2bd1e988 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 30 Mar 2024 08:19:24 +0800 Subject: [PATCH 073/101] fixed some grammar errors. --- docs/wiki/Cryptography/KZG.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 5430166b..f4dbee51 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -286,7 +286,7 @@ Then, the trusted party sends the CRS to the Prover and the Verifier. In practice, this process is wrapped around a multi-party computation (MPC) where a secret is generated in such a way that, as long as at least one participant remains honest, the randomness of the secret can be guaranteed. -The trusted setup is a one-time procedure that generates a piece of data necessary for the cryptographic protocol to function. This data must be used every time the protocol is run, but once generated and the secrets are forgotten, no further participation from the creators of the ceremony is required. The trust in the setup comes from the fact that the secrets used to generate the data are securely discarded after the setup, ensuring that the data remains secure for future use +The trusted setup is a one-time procedure that generates a piece of data necessary for the cryptographic protocol to function. This data must be used every time the protocol is run, but once generated and the secrets are forgotten, no further participation from the creators of the ceremony is required. The trust in the setup comes from the fact that the secrets used to generate the data are securely discarded after the setup, ensuring that the data remains secure for future use. Modern protocols often use a powers-of-tau setup, which involves even thousands of participants. The security of the final output depends on the honesty of at least one participant who does not publish their secret. This approach is considered "close enough to trustless" in practice, making it a practical solution for cryptographic protocols that require a trusted setup. From a196800304c4089e4a8c65d4b9783ecbe478b5b4 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 30 Mar 2024 18:34:29 +0800 Subject: [PATCH 074/101] KZG Batch mode section - part 1 is added. --- docs/wiki/Cryptography/KZG.md | 41 +++++++++++++++++++++++++++++++++-- 1 file changed, 39 insertions(+), 2 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index f4dbee51..aa542400 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -245,7 +245,7 @@ We want prove that we know a specific evaluation of a function or polynomial at In the KZG commitment scheme, the roles of the Trusted Third Party, Prover, and Verifier are critical to its function and security. Here's how each contributes to the process: -1. **Trusted Third Party (Setup Authority):** This entity is responsible for the initial setup phase of the KZG scheme. They generate the public parameters (PP) or Common Reference String (CRS) that will be used in the commitments and proofs, based on a secret that only they know. This secret is crucial for the construction of commitments but must be discarded (or kept extremely secure) after the setup to ensure the system's integrity. The trust in this party is fundamental because if the secret is mishandled or leaked, it could compromise the entire system. This party's role ends after generating CRS and sharing it with the Prover and Verifier i.e. they no longer involved in either proving or verifying steps of the protocol flow. +1. **Trusted Third Party (Setup Authority):** This entity is responsible for the initial setup phase of the KZG scheme. They generate the public parameters (PP) or Common Reference String (CRS) that will be used in the commitments and proofs, based on a secret that only they know. This secret is crucial for the construction of commitments but must be discarded (or kept extremely secure) after the setup to ensure the system's integrity. The trust in this party is fundamental because if the secret is mishandled or leaked, it could compromise the entire system. The role of this party concludes once they have generated the CRS and distributed it to both the Prover and the Verifier. After this point, they are not involved in any further steps of the protocol, whether it be in proving or verifying. 2. **Prover:** The Prover is the one who wants to commit to a certain piece of data (like a polynomial) without revealing it. Using the CRS provided by the Trusted Third Party, the Prover computes a commitment to their data. When it's time to prove certain properties of their data (like a polynomial evaluation at a specific point), the Prover can generate a proof based on their commitment. This proof shows that their data has certain properties without revealing the data itself. @@ -519,12 +519,49 @@ $e(C_Q, a \cdot g_2 − b \cdot g_2 ) = e(C_f − d \cdot g_1, g_2)$ Here $a \cdot g_2$ will be the part of CRS of $\mathbb G_2$ and everything else can be either computed or part of CRS of $\mathbb G_1$. -### [Unwavering Compactness](#unwavering-compactness) +## [Unwavering Compactness](#unwavering-compactness) The KZG Polynomial Commitment Scheme ensures that both commitments and evaluation proofs are of a fixed size, regardless of the polynomial's length, offering consistent and space-efficient cryptographic operations[^5][^6][^7]. One key benefit of the KZG Polynomial Commitment Scheme is its efficient use of space. No matter the length or complexity of the polynomial we're working with, the commitment to that polynomial—essentially its cryptographic "footprint"—is always a single, fixed-size element within a mathematical group, $\mathbb G$. This means that as the polynomial grows in degree, the size of the commitment does not increase. The same principle applies to the evaluation proof, which is the evidence we provide to show that our commitment is accurate. Whether we're verifying just one value or many at once (in batch mode), the proof will always be of a consistent size. This consistency in size translates to predictable and efficient storage requirements, an important feature for practical applications in cryptography. +## [KZG Batch Mode] + +KZG commitments can also be opened and verified at multiple points or using multiple polynmials or any combination of them. This is called batch mode in practice. + +### [Batch Mode Single Polynomial, Multiple Points] + +In batch mode, the Verifier requests the Prover to validate a set of points $B =$ { $b_1, b_2, b_3, \ldots, b_n$ } with $n < t$, where $t$ is the degree of the polynomial $f(x)$. For these points, the Prover computes the values $f(b_1) = d_1, f(b_2) = d_2, \ldots, f(b_n) = d_n$ and forms the set $D =$ { $d_1, d_2, d_3, \ldots, d_n$ }. + +The Prover then creates a Polynomial $P(x) = (x - b_1)(x - b_2)\ldots(x - b_n)$. Given that $n < t$, it's possible to divide $f(x)$ by $P(x)$, resulting in $f(x) = P(x)Q(x) + R(x)$, where $Q(x)$ is the quotient polynomial and $R(x)$ is the remainder. This division suggests that $f(x)$ can be represented as such, not implying direct divisibility by $Q(x)$. + +The commitment for $Q(x)$, denoted as $C_Q$, alongside the set $B$, is sent to the Verifier by the Prover. Optionally, the Prover may also send the remainder polynomial $R(x)$ to the Verifier. However, the Verifier has the capability to independently compute $R(x)$, considering that for any $b_i$ in $B$, $P(x)$ evaluates to zero, leading to $f(x) = R(x)$ for all $b_i$ in $B$. + +As the degree of $Q(x)$ is $n$ and $R(x)$'s degree is less than $n$, the Verifier, knowing $R(x)$'s evaluation at $n$ points, can determine $R(x)$ via Lagrange’s Interpolation. + +The Verifier also computes the polynomials $P(x)$ and $R(x)$, alongside their commitments $C_P = P(a) \cdot g$ and $C_R = R(a) \cdot g$. They proceed to verify the Batch Evaluation by ensuring that $f(b_i) = R(b_i)$ for all $b_i$ in $B$ and that the equality $f(x) = P(x)Q(x) + R(x)$ holds. + +The Verifier needs to evaluate the above constraint to verify the proof. However, since the secret opening at $x = a$ is unknown, hence she or he cannot evaluate it directly. But like before, the Verifier can use pairings to solve this. + +To verify, the Verifier checks: +- $f(b_i) = R(b_i)$ for each $b_i$ in $B$, comparing the Prover's provided $D$ values with their computation of $R(x)$ at each $b_i$. + +- The equality $f(x) \cdot g - R(x) \cdot g = P(x)Q(x) \cdot g$ when evaluated at $x = a$, simplifying to $C_f - C_R = P(a) \cdot C_Q$ using known commitments and the secret $a$. + +Despite not knowing $a$, the Verifier utilizes pairings to assess the proof: +- Since both $C_f$ and $C_R$ belong to $\mathbb G$, their difference does too. +- Given $C_Q$'s membership in $\mathbb G$ and $P(a)$ as a scalar, $P(a) \cdot C_Q$ remains within $\mathbb G$. + +Applying the pairing function yields: + +$e(C_f − C_R, g) = e(P(a) \cdot C_Q, g)$ + +Applying the bilinearity property, we get + +$e(C_f - C_R, g) = e(C_Q, C_P)$ + +where $C_P = P(a) \cdot g$. Given this, the Verifier can confirm the truth of the equality, thereby verifying the proof. + ## [References](#references) [^1]: https://en.wikipedia.org/wiki/Polynomial_remainder_theorem From cf27fcb2817ff294f709730a2ebc9253bca4f3a5 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 30 Mar 2024 18:35:38 +0800 Subject: [PATCH 075/101] header format is fixed. --- docs/wiki/Cryptography/KZG.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index aa542400..916506f6 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -525,11 +525,11 @@ The KZG Polynomial Commitment Scheme ensures that both commitments and evaluatio One key benefit of the KZG Polynomial Commitment Scheme is its efficient use of space. No matter the length or complexity of the polynomial we're working with, the commitment to that polynomial—essentially its cryptographic "footprint"—is always a single, fixed-size element within a mathematical group, $\mathbb G$. This means that as the polynomial grows in degree, the size of the commitment does not increase. The same principle applies to the evaluation proof, which is the evidence we provide to show that our commitment is accurate. Whether we're verifying just one value or many at once (in batch mode), the proof will always be of a consistent size. This consistency in size translates to predictable and efficient storage requirements, an important feature for practical applications in cryptography. -## [KZG Batch Mode] +## KZG Batch Mode KZG commitments can also be opened and verified at multiple points or using multiple polynmials or any combination of them. This is called batch mode in practice. -### [Batch Mode Single Polynomial, Multiple Points] +### Batch Mode Single Polynomial, Multiple Points In batch mode, the Verifier requests the Prover to validate a set of points $B =$ { $b_1, b_2, b_3, \ldots, b_n$ } with $n < t$, where $t$ is the degree of the polynomial $f(x)$. For these points, the Prover computes the values $f(b_1) = d_1, f(b_2) = d_2, \ldots, f(b_n) = d_n$ and forms the set $D =$ { $d_1, d_2, d_3, \ldots, d_n$ }. From 3eae027cdc6f86cce23398dc190f361119bdaa4d Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 30 Mar 2024 18:36:48 +0800 Subject: [PATCH 076/101] header format is fixed. --- docs/wiki/Cryptography/KZG.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 916506f6..20b01f68 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -525,11 +525,11 @@ The KZG Polynomial Commitment Scheme ensures that both commitments and evaluatio One key benefit of the KZG Polynomial Commitment Scheme is its efficient use of space. No matter the length or complexity of the polynomial we're working with, the commitment to that polynomial—essentially its cryptographic "footprint"—is always a single, fixed-size element within a mathematical group, $\mathbb G$. This means that as the polynomial grows in degree, the size of the commitment does not increase. The same principle applies to the evaluation proof, which is the evidence we provide to show that our commitment is accurate. Whether we're verifying just one value or many at once (in batch mode), the proof will always be of a consistent size. This consistency in size translates to predictable and efficient storage requirements, an important feature for practical applications in cryptography. -## KZG Batch Mode +## [KZG Batch Mode](#kzg-batch-mode) KZG commitments can also be opened and verified at multiple points or using multiple polynmials or any combination of them. This is called batch mode in practice. -### Batch Mode Single Polynomial, Multiple Points +### [Single Polynomial, Multiple Points](#single-polynomial-multiple-points) In batch mode, the Verifier requests the Prover to validate a set of points $B =$ { $b_1, b_2, b_3, \ldots, b_n$ } with $n < t$, where $t$ is the degree of the polynomial $f(x)$. For these points, the Prover computes the values $f(b_1) = d_1, f(b_2) = d_2, \ldots, f(b_n) = d_n$ and forms the set $D =$ { $d_1, d_2, d_3, \ldots, d_n$ }. From 8b6a6e4dba69a6fd5ad591371626375a21cddbe0 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 30 Mar 2024 18:53:08 +0800 Subject: [PATCH 077/101] Lagrange interpolation reference is added. --- docs/wiki/Cryptography/KZG.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 20b01f68..6efd0e1b 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -537,7 +537,7 @@ The Prover then creates a Polynomial $P(x) = (x - b_1)(x - b_2)\ldots(x - b_n)$. The commitment for $Q(x)$, denoted as $C_Q$, alongside the set $B$, is sent to the Verifier by the Prover. Optionally, the Prover may also send the remainder polynomial $R(x)$ to the Verifier. However, the Verifier has the capability to independently compute $R(x)$, considering that for any $b_i$ in $B$, $P(x)$ evaluates to zero, leading to $f(x) = R(x)$ for all $b_i$ in $B$. -As the degree of $Q(x)$ is $n$ and $R(x)$'s degree is less than $n$, the Verifier, knowing $R(x)$'s evaluation at $n$ points, can determine $R(x)$ via Lagrange’s Interpolation. +As the degree of $Q(x)$ is $n$ and $R(x)$'s degree is less than $n$, the Verifier, knowing $R(x)$'s evaluation at $n$ points, can determine $R(x)$ via Lagrange’s Interpolation[^10]. The Verifier also computes the polynomials $P(x)$ and $R(x)$, alongside their commitments $C_P = P(a) \cdot g$ and $C_R = R(a) \cdot g$. They proceed to verify the Batch Evaluation by ensuring that $f(b_i) = R(b_i)$ for all $b_i$ in $B$ and that the equality $f(x) = P(x)Q(x) + R(x)$ holds. @@ -573,3 +573,4 @@ where $C_P = P(a) \cdot g$. Given this, the Verifier can confirm the truth of th [^7]: https://www.youtube.com/watch?v=uGeIDNEwHjs&t=520s [^8]: https://www.youtube.com/watch?v=8WDOpzxpnTE [^9]: https://vitalik.eth.limo/general/2017/01/14/exploring_ecp.html +[^10]: https://en.wikipedia.org/wiki/Lagrange_polynomial \ No newline at end of file From f977990b14655186c142af6e75ca7f6b421ba12d Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Sat, 30 Mar 2024 19:19:52 +0800 Subject: [PATCH 078/101] Fixed uneven header spacing issue. --- docs/wiki/Cryptography/KZG.md | 12 ------------ 1 file changed, 12 deletions(-) diff --git a/docs/wiki/Cryptography/KZG.md b/docs/wiki/Cryptography/KZG.md index 6efd0e1b..2587aafe 100644 --- a/docs/wiki/Cryptography/KZG.md +++ b/docs/wiki/Cryptography/KZG.md @@ -44,7 +44,6 @@ In practice what we exactly do is that we prove that we know a specific evaluati We write this, $f(a)$, for some $x=a$. ## [Prerequisite Knowledge](#prerequisite-knowledge) - There are some important concepts we need to know before we can move further to understand KZG scheme. Fortunately, we can get an Engineering level understanding of the KZG scheme from just enough high school mathematics. We will try to gain some intuition on advanced concepts and their important properties without knowing them intimately. This can help us see the KZG protocol flow without bogged down by the advanced mathematics. We need to know: @@ -54,7 +53,6 @@ An analog clock illustrates modular arithmetic as hours cycle back after reachin ### [Finite Field of order prime p](#finite-field-of-order-prime) - A finite field of order prime $p$, we denote it by $\mathbb F_p$, is a special set of numbers, { $\{1, 2, 3, \ldots, p-1\}$ }, where you can do all the usual math operations (addition, subtraction, multiplication, and division, except by zero) and still follow the rules of arithmetic. The "order" of this set is the number of elements it contains, and for a finite field of order prime $p$, this number is a prime number. The most common way to create a $\mathbb F_p$ is by taking the set of all integers greater than or equal to $0$ and dividing them by $p$, keeping only the remainders. This gives us a set of numbers from $0$ to $p-1$ that can be used for arithmetic operations. For example, if $p = 5$, the set would be {0, 1, 2, 3, 4}, and you can add, subtract, multiply, and divide these numbers in a way that follows the rules of arithmetic. This set is a finite field of order 5, we denote this by $\mathbb F_5$, because it has exactly 5 elements, and it's a prime number. @@ -133,7 +131,6 @@ Let's verify that each element is indeed a generator by multiplying it repeatedl You can verify that $5$ is also a generator for our multiplicative group ($\mathbb G^*_7, .)$ modulo $7$. ### [Why Primes for Modulo Operations in Fields](#why-primes-for-modulo-operations-in-fields) - Choosing a prime number as the modulus for operations in a finite field offers several benefits and simplifies various aspects of field arithmetic: 1. **Well-defined Division:** In a finite field, every non-zero element must have a multiplicative inverse. If the modulus is prime, every number in the set { ${1, 2, 3, \ldots, p-1}$ } has a multiplicative inverse modulo $p$. This property allows for well-defined division operations within the field, which wouldn't be possible if the modulus wasn't prime (except in special cases like Galois fields of order $p^n$, where $p$ is prime). @@ -153,7 +150,6 @@ Using a prime number as the modulus for finite fields simplifies the field arith ### [Cryptographic Assumptions](#cryptographic-assumptions) - In order to work with KZG commitment scheme, we need two additional assumptions. We won't go deep into why these assumptions are needed but we will give an intuition to why these cryptographic assumptions are needed to make KZG more secure. **Discrete Logarithm** @@ -221,7 +217,6 @@ Here's how to think about this pairing function without getting bogged down by t Pairing functions enable advanced cryptographic techniques, such as those used in certain types of digital signatures and encryption, by allowing this kind of "cross-group" interaction to occur securely and predictably. ## [Properties of Commitments](#properties-of-commitments) - Commitment schemes are like the secret-keeping wizards of the digital world. They let someone make a promise about a piece of information (we'll call this the secret message) in a way that ties them to their promise without letting anyone else know what the secret is. Here's how it works: - **Making the Promise (Commitment):** You decide on a secret message and use a special spell (the commitment scheme) to create a magic seal (the commitment). This seal proves you have a secret, but it keeps the secret hidden. @@ -238,7 +233,6 @@ With this background, we are ready to explain KZG protocol flow and understand i ## [KZG Protocol Flow](#kzg-protocol-flow) - Let us reiterate on what is the problem we are solving with KZG protocol. We want prove that we know a specific evaluation of a function or polynomial at a point $x=a$ without revealing it. @@ -293,7 +287,6 @@ Modern protocols often use a powers-of-tau setup, which involves even thousands Ethereum has a very detailed documentation of the Trusted Setup ceremony for more detail[^2]. ### [Initial Configuration](#initial-configuration) - Say the Prover has a function or polynomial $f(x)$ defined as $f(x) = f_0 + f_1x + f_2x^2 + \ldots + f_dx^t$ in a finite field $\mathbb F_p$. The degree of $f(x)$ is $t$ which is less than $p$, the order of the finite field $\mathbb F_p$. We often denote this as $f(x) \in \mathbb{F}_p[x]$. @@ -310,7 +303,6 @@ To simplify this step, Prover picks a polynomial $f(x) \in \mathbb{F}_p[x]$, the ### [Commitment of the Polynomial](#commitment-of-the-polynomial) - Say, the commitment of the polynomial $f(x)$ is denoted as $C_f$. The commitment is like hash function. So $C_f = {f(a)} \cdot g = {(f_0 + f_1a + f_2a^2 + \ldots + f_ta^t)} \cdot g$. Here $f(a)$ is the polynomial evaluted at $x=a$. @@ -326,7 +318,6 @@ $C_f = {f_0} \cdot g + {f_1} \cdot (ag) + {f_2} \cdot ({a^2}g) + \ldots + {f_ From the CRS, the Prover knows these values < $g, {a^1}.g, {a^2}.g, \ldots, {a^t}.g$ >, he or she can compute this value as commitment of the polynomial, $C_f$ and sends to the Verifier. ### [Opening of the Polynomial](#opening-of-the-polynomial) - Upon receiving a commitment to a polynomial, denoted by $C_f$, from the Prover, the Verifier takes the next step in the protocol by selecting a random point, which we'll call $b$, from the field $\mathbb F_p$. The Verifier then requests the Prover to open or reveal the value of the polynomial at this specific point. **What does 'opening the polynomial' mean?** @@ -520,17 +511,14 @@ $e(C_Q, a \cdot g_2 − b \cdot g_2 ) = e(C_f − d \cdot g_1, g_2)$ Here $a \cdot g_2$ will be the part of CRS of $\mathbb G_2$ and everything else can be either computed or part of CRS of $\mathbb G_1$. ## [Unwavering Compactness](#unwavering-compactness) - The KZG Polynomial Commitment Scheme ensures that both commitments and evaluation proofs are of a fixed size, regardless of the polynomial's length, offering consistent and space-efficient cryptographic operations[^5][^6][^7]. One key benefit of the KZG Polynomial Commitment Scheme is its efficient use of space. No matter the length or complexity of the polynomial we're working with, the commitment to that polynomial—essentially its cryptographic "footprint"—is always a single, fixed-size element within a mathematical group, $\mathbb G$. This means that as the polynomial grows in degree, the size of the commitment does not increase. The same principle applies to the evaluation proof, which is the evidence we provide to show that our commitment is accurate. Whether we're verifying just one value or many at once (in batch mode), the proof will always be of a consistent size. This consistency in size translates to predictable and efficient storage requirements, an important feature for practical applications in cryptography. ## [KZG Batch Mode](#kzg-batch-mode) - KZG commitments can also be opened and verified at multiple points or using multiple polynmials or any combination of them. This is called batch mode in practice. ### [Single Polynomial, Multiple Points](#single-polynomial-multiple-points) - In batch mode, the Verifier requests the Prover to validate a set of points $B =$ { $b_1, b_2, b_3, \ldots, b_n$ } with $n < t$, where $t$ is the degree of the polynomial $f(x)$. For these points, the Prover computes the values $f(b_1) = d_1, f(b_2) = d_2, \ldots, f(b_n) = d_n$ and forms the set $D =$ { $d_1, d_2, d_3, \ldots, d_n$ }. The Prover then creates a Polynomial $P(x) = (x - b_1)(x - b_2)\ldots(x - b_n)$. Given that $n < t$, it's possible to divide $f(x)$ by $P(x)$, resulting in $f(x) = P(x)Q(x) + R(x)$, where $Q(x)$ is the quotient polynomial and $R(x)$ is the remainder. This division suggests that $f(x)$ can be represented as such, not implying direct divisibility by $Q(x)$. From a6c42c8ae5bed9b1430d12ba790c3c2ce529ce8d Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Mon, 8 Apr 2024 13:25:32 +0800 Subject: [PATCH 079/101] Preconfirmations - new page. --- .../Preconfirmations/Preconfirmations.md | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) create mode 100644 docs/wiki/research/Preconfirmations/Preconfirmations.md diff --git a/docs/wiki/research/Preconfirmations/Preconfirmations.md b/docs/wiki/research/Preconfirmations/Preconfirmations.md new file mode 100644 index 00000000..f3d1b404 --- /dev/null +++ b/docs/wiki/research/Preconfirmations/Preconfirmations.md @@ -0,0 +1,19 @@ + +# Ethereum Based Preconfirmations + +## [Overview](#overview) + +Based preconfirmations (preconfs) represent a significant advancement in Ethereum transaction processing, offering users swift and reliable execution. Through a combination of on-chain infrastructure, proposer accountability mechanisms, and flexible promise acquisition processes, preconfs stand to significantly enhance the user experience in Ethereum interactions. This technology not only reduces transaction latency but also introduces a layer of security and efficiency previously unseen in the ecosystem[^1]. + + +## [Construction of Preconfs](#construction-of-preconfs) + + +## [Key Elements of Preconfs](#key-elements-of-preconfs) + + +## [Preconfs Acquisition Process Flow](#preconfs-acquisition-process-flow) + + +## References +[^1]: https://ethresear.ch/t/based-preconfirmations/17353 From f24021d41b9ef8331ea32fdedd15678b1ba02a96 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Mon, 8 Apr 2024 19:20:54 +0800 Subject: [PATCH 080/101] Construction of promise section is added. --- .../Preconfirmations/Preconfirmations.md | 24 ++++++++++++++++++- 1 file changed, 23 insertions(+), 1 deletion(-) diff --git a/docs/wiki/research/Preconfirmations/Preconfirmations.md b/docs/wiki/research/Preconfirmations/Preconfirmations.md index f3d1b404..4b27a5c1 100644 --- a/docs/wiki/research/Preconfirmations/Preconfirmations.md +++ b/docs/wiki/research/Preconfirmations/Preconfirmations.md @@ -6,7 +6,29 @@ Based preconfirmations (preconfs) represent a significant advancement in Ethereum transaction processing, offering users swift and reliable execution. Through a combination of on-chain infrastructure, proposer accountability mechanisms, and flexible promise acquisition processes, preconfs stand to significantly enhance the user experience in Ethereum interactions. This technology not only reduces transaction latency but also introduces a layer of security and efficiency previously unseen in the ecosystem[^1]. -## [Construction of Preconfs](#construction-of-preconfs) +## [Construction of Preconf Promises](#construction-of-preconf-promises) + +Preconfirmation promises, or "preconfs," reply on two foundational on-chain infrastructure components: + +- **Proposer Slashing:** Proposers can opt into additional slashing conditions to ensure reliability and accountability. This approach draws inspiration from EigenLayer's model, which employs restaking as a means of enforcing these slashing mechanisms. + +- **Proposer Forced Inclusions:** To ensure the seamless execution of transactions, proposers have the authority to mandate the inclusion of specific transactions on-chain. This capability is necessary in situations where the separation between proposers and builders (PBS) renders self-building impractical. The implementation of this mechanism typically involves the use of inclusion lists. + + +When a L1 proposer decides to become a "preconfer," they are essentially agreeing to adhere to two distinct slashing conditions related to preconf promises. In return for their service, preconfers issue signed promises to users and are compensated with tips for successfully fulfilling these promises. The hierarchy among preconfers is determined based on their position in the slot order, with precedence given to those with earlier slot assignments. + +A transaction that secures a preconf promise gains the eligibility for immediate inclusion and execution on-chain by any proposer positioned before the issuer of the promise (preconfer). The primary obligation of the preconfer is to honor all such promises during their designated slot, utilizing the inclusion list to facilitate this process. + +There are two main types of promise-related faults, each carrying the potential for slashing: + +1. **Liveness Faults:** These faults occur when a preconfer fails to include a promised transaction on the chain because their designated slot was missed. + +2. **Safety Faults:** These arise when the preconfer includes transactions on-chain that directly contradict the promises made, despite not missing their slot. + + +To ensure that transactions with preconf promises are given priority, a specific execution queue is established for transactions lacking such promises. This arrangement guarantees that preconfed transactions are executed ahead of others. + +Preconfers are not limited to a single type of preconfirmation promise. They can offer a spectrum of promises, ranging from strict execution guarantees based on specific state roots to simpler promises of transaction inclusion. This flexibility allows preconfers to cater to a wide array of user needs and preferences. ## [Key Elements of Preconfs](#key-elements-of-preconfs) From 0a9d77f2b724a058156298d6d18cae2036cbade4 Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 9 Apr 2024 05:23:07 +0800 Subject: [PATCH 081/101] Ket elements of preconf promise section is added. --- .../Preconfirmations/Preconfirmations.md | 27 +++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/docs/wiki/research/Preconfirmations/Preconfirmations.md b/docs/wiki/research/Preconfirmations/Preconfirmations.md index 4b27a5c1..782d717c 100644 --- a/docs/wiki/research/Preconfirmations/Preconfirmations.md +++ b/docs/wiki/research/Preconfirmations/Preconfirmations.md @@ -33,6 +33,33 @@ Preconfers are not limited to a single type of preconfirmation promise. They can ## [Key Elements of Preconfs](#key-elements-of-preconfs) +The process towards securing a preconfirmation promise for transactions within the Ethereum network is initiated by establishing a connection with the next available preconfer. This process entails a series of critical steps and factors, including: + +- **Endpoints:** Preconfers may offer direct API endpoints or utilize decentralized peer-to-peer (p2p) networks for the exchange of promises, striking a balance between quick response times and widespread availability. + +- **Latency:** Utilizing direct communication channels, the process aims to achieve preconfirmation times as swift as 100 milliseconds, ensuring rapid transaction handling. + +- **Bootstrapping:** A substantial participation rate among L1 validators as preconfers is crucial. This ensures that within the proposer lookahead window, there is always a significant chance of encountering a preconfer ready to issue promises. + +- **Liveness Fallback:** Users can enhance their transaction's reliability by securing promises from several preconfers, thus safeguarding against the possibility of any single preconfer failing to fulfill their promise due to missed slots. + +- **Parallelization:** The system accommodates various promise types, ranging from strict commitments on post-execution state to more flexible, intent-based promises. + +- **Replay Protection:** Ensures transactions are protected from replay attacks, vital for maintaining the integrity and security of preconf transactions. + +- **Single Secret Leader Election (SSLE):** This mechanism allows for the confidential identification of preconfers within the lookahead period, enabling them to validate their status without revealing their identity prematurely. + +- **Delegated Preconf:** Offers a provision for proposers constrained by limited network bandwidth or processing capability, allowing them to delegate their preconfirmation duties to ensure efficient processing of promises. + +- **Fair Exchange:** The system addresses the fair exchange dilemma between users and preconfers concerning promise requests and the collection of preconf tips. Solutions include public streaming of promises for transparency, intermediation by trusted relays, or the use of cryptographic fair exchange protocols to balance the interests of all parties involved. + +- **Tip Pricing:** The negotiation of preconf tips considers the transaction's potential impact on a proposer’s ability to extract MEV. Through mutual agreement or the assistance of trusted relays, users and preconfers can determine fair compensation for preconfirmations. + +- **Negative Tips:** Preconfers may accept negative tips for transactions that enhance their MEV opportunities, such as those affecting DEX prices and creating arbitrage prospects. + + +Each of these elements plays a crucial role in the functionality and efficiency of based preconfirmations, ensuring transactions are not only processed swiftly but also securely and fairly within the Ethereum ecosystem. + ## [Preconfs Acquisition Process Flow](#preconfs-acquisition-process-flow) From c9a7062beea96916a781fef97e64b1614660df3a Mon Sep 17 00:00:00 2001 From: Nagu Thogiti Date: Tue, 9 Apr 2024 05:42:22 +0800 Subject: [PATCH 082/101] Preconf process flow section is added. --- .../Preconfirmations/Preconfirmations.md | 79 ++++++++++++++++++ .../Preconfirmations-Acquisition-Flow.png | Bin 0 -> 339753 bytes 2 files changed, 79 insertions(+) create mode 100644 docs/wiki/research/img/preconfs/Preconfirmations-Acquisition-Flow.png diff --git a/docs/wiki/research/Preconfirmations/Preconfirmations.md b/docs/wiki/research/Preconfirmations/Preconfirmations.md index 782d717c..5bd0c76c 100644 --- a/docs/wiki/research/Preconfirmations/Preconfirmations.md +++ b/docs/wiki/research/Preconfirmations/Preconfirmations.md @@ -64,5 +64,84 @@ Each of these elements plays a crucial role in the functionality and efficiency ## [Preconfs Acquisition Process Flow](#preconfs-acquisition-process-flow) +*Figure: Preconfs Acquisition Process Flow* + +```mermaid +sequenceDiagram + participant User as User + participant Preconfer as Preconfer + participant Blockchain as Ethereum + + rect rgb(191, 223, 255) + User->>+Preconfer: Identify & send promise request + Note over User,Preconfer: User selects the next preconfer based on slot
      position and sends a transaction promise request. + + Preconfer->>-User: Evaluate request + Note over User,Preconfer: Preconfer assesses the request, considering network
      conditions, preconf tip, and MEV potential. + end + rect rgb(177,176,159) + Preconfer->>+User: Issue preconf promise + Note over User,Preconfer: If accepted, preconfer sends back a
      signed preconf promise to the user. + end + rect rgb(191, 223, 255) + User->>Preconfer: Transfer preconf tip + Note over User,Preconfer: User transfers the agreed preconf tip
      to the preconfer as compensation. + end + rect rgb(177,176,159) + Preconfer->>+Blockchain: Include & execute transaction + Note over Preconfer,Blockchain: In the assigned slot, preconfer includes the
      transaction in their block proposal for execution. + + Blockchain->>-User: Verify transaction execution + Note over User,Blockchain: Once executed on-chain, both user and preconfer verify the fulfillment of the promise. + end +``` + + +The promise acquisition process in the context of Ethereum's sequencing and pre-confirmation mechanism is a critical aspect, ensuring transactions receive a preconfirmation or "promise" from a proposer or sequencer. This process involves several steps, each integral to securing a promise that a transaction will be included and executed on-chain within a specified time frame. The above figure shows the preconf promise acquisition flow through a sequence of interactions. Below is a detailed explanation of the acquisition process flow: + +**1. User Identifies Next Preconfer** + +- **Starting Point:** A user or a smart contract initiates the process by identifying the next available preconfer (a proposer who has opted in to provide preconfirmation services) within the Ethereum network's proposer lookahead window. + +- **Selection Criteria:** The selection is based on the proposer's slot position in the proposer lookahead, where proposers have declared their capability and willingness to issue preconfirmations by posting collateral. + +**2. Promise Request Sent to Preconfer** + +- **Initiation:** The user sends a promise request to the identified preconfer. This request includes details of the transaction for which the preconfirmation is sought, along with any specific conditions or requirements. + +- **Communication Channel:** The request can be sent through various off-chain communication channels established by the preconfer, such as a dedicated API endpoint or a peer-to-peer messaging system. + +**3. Preconfer Evaluates the Request** + +- **Assessment:** Upon receiving the request, the preconfer evaluates it based on several factors, including the current network conditions, the preconf tip amount proposed by the user, and the overall risk of executing the transaction. + +- **Decision Making:** The preconfer decides whether to accept or reject the promise request. This decision may involve calculating the potential MEV and assessing whether the transaction aligns with the preconfer's criteria. + +**4. Issuance of Preconf Promise** + +- **Promise Generation:** If the preconfer decides to accept the request, they generate a signed preconf promise. This promise includes the preconfer's commitment to ensuring the transaction's inclusion and execution within their upcoming slot, adhering to the agreed conditions. + +- **Communication of Promise:** The preconf promise is then communicated back to the user, providing them with a guarantee of transaction execution. The communication method used is similar to that of the initial request, ensuring secure and verifiable delivery. + +**5. Payment of Preconf Tip** + +- **Tip Transfer:** Upon receipt of the preconf promise, the user transfers the agreed preconf tip to the preconfer. This tip serves as compensation for the service provided and incentivizes the preconfer to honor the commitment. + +- **Escrow Mechanisms:** In some implementations, the tip may be held in escrow until the promise is fulfilled, adding an extra layer of security for the user. + +**6. Inclusion and Execution of Transaction** + +- **On-Chain Fulfillment:** The preconfer includes the preconfirmed transaction in their proposed block during their assigned slot, executing it according to the terms outlined in the preconf promise. + +- **Verification of Fulfillment:** Once the transaction is included and executed on-chain, both the preconfer and the user can verify that the promise has been fulfilled, completing the process. + + +**Additional Considerations:** + +- **Fallback Mechanisms:** In case of unexpected issues or if the first preconfer fails to include the transaction, users may have fallback options, such as requesting promises from multiple preconfers in parallel. + +- **Dispute Resolution:** The system may include mechanisms for resolving disputes in cases where there's disagreement about whether the promise was adequately fulfilled. + + ## References [^1]: https://ethresear.ch/t/based-preconfirmations/17353 diff --git 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z!OAnN3)_Se`Q*=*+gsB-bh=%xA}tSK%XF^BPa6YmJfI(51Q~JPrSBuFS3Zs}n73}* zLHzs8MAJ!R5p%%ak+fTcJ^580B@T?b>N;r9`)?`f8m2VMyHk}>qrF(5xay|&>4gK9 z5wI7TQ)!tO2jSs_=YQ?I^2ex~M4k#@<z>% literal 0 HcmV?d00001 From 691395e0848a1ec0d25a828595457f01f7282eb7 Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Sun, 25 Feb 2024 22:17:43 +0100 Subject: [PATCH 011/101] :arrow_right_hook: Move The Merge to history --- docs/wiki/protocol/history.md | 19 +++++++++++++++++++ docs/wiki/research/scaling.md | 17 +---------------- 2 files changed, 20 insertions(+), 16 deletions(-) create mode 100644 docs/wiki/protocol/history.md diff --git a/docs/wiki/protocol/history.md b/docs/wiki/protocol/history.md new file mode 100644 index 00000000..f408814c --- /dev/null +++ b/docs/wiki/protocol/history.md @@ -0,0 +1,19 @@ +# History + +## The DAO Hack and Ethereum Classic(ETC) fork +TODO + +## The Merge. +On September 15, 2022, Ethereum implemented [EIP-3675](https://eips.ethereum.org/EIPS/eip-3675) (Upgrade consensus to Proof-of-Stake) through an event known as The Merge. The Merge has resulted in the deprecation of the Proof-of-Work consensus, which was previously implemented in the same logic layer as execution. Instead, it has been replaced by a much more complex and sophisticated Proof-of-Stake consensus that eliminates the need for energy-intensive mining. New Proof-of-Stake consensus Gasper runs on its own tech stack and p2p network, this new abstraction layer is known as Beacon Chain. The Beacon Chain has been running and achieving consensus since December 1st, 2020. After a prolonged period of consistent performance without any failures, it was deemed ready to become Ethereum's consensus provider, The Merge gets its name from the union of the two networks. + +- Consensus Layer (Beacon Chain): Specifically designed to be really good to reaching consensus. In Ethereum, time is divided up into twelve second units called **slots**, the consensus is reached when a valid block has been proposed in a specific slot. However, occasionally validators might be offline when called to propose a block, meaning slots can sometimes go empty. + +- Execution Layer (State and Transactional Ledger): Driven by the consensus layer, it specializes in managing the transactions mempool, the Ethereum state, and Ethereum block construction and execution. + +As result, an Ethereum node requires running two different software components: an execution client (or execution engine) driven by a consensus client through an internal communication protocol (Engine API). Note, that no additional trust assumptions need to be made for the execution Layer to follow and execute consensus decisions since each execution client receives information from the consensus Layer through its corresponding twin consensus client, and both clients operate within the same node’s trust domain. + +!["Ethereum Nodes"](./img/scaling/ethereum-nodes.png "Ethereum Nodes") + +Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. + +Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. \ No newline at end of file diff --git a/docs/wiki/research/scaling.md b/docs/wiki/research/scaling.md index 7e91b150..243c205b 100644 --- a/docs/wiki/research/scaling.md +++ b/docs/wiki/research/scaling.md @@ -47,27 +47,12 @@ Layer 2 scaling is the set of solutions built on top of Layer 1 blockchain proto !["Layer 2 Scaling"](./img/scaling/layer-2-scaling.png "Layer 2 Scaling") - The solution predominantly adopted by the Ethereum community to solve the scalability problem is a multi-rollup-centric approach. Here, Ethereum acts as fundamental secure layer of Settlement, and Data Availability, while the majority of Execution tasks are delegated to upper layers referred to as Rollups.R ollups bundle multiple Layer 2 transactions into a single Layer 1 transaction. These transactions are stored in Layer 1, but the their execution is delegated to off-chain mechanisms. This allows for significant scalability improvements without sacrificing security. Ethereum's high level of programmability makes possible to create scalable solutions on top of the platform through Ethereum smart contracts. As previously mentioned, to maintain a high level of decentralization, Ethereum imposes limitations on the computational and storage resources that can use the transactions included in the blocks through gas limitations. + The solution predominantly adopted by the Ethereum community to solve the scalability problem is a multi-rollup-centric approach. Here, Ethereum acts as fundamental secure layer of Settlement, and Data Availability, while the majority of Execution tasks are delegated to upper layers referred to as Rollups.Rollups bundle multiple Layer 2 transactions into a single Layer 1 transaction. These transactions are stored in Layer 1, but the their execution is delegated to off-chain mechanisms. This allows for significant scalability improvements without sacrificing security. Ethereum's high level of programmability makes possible to create scalable solutions on top of the platform through Ethereum smart contracts. As previously mentioned, to maintain a high level of decentralization, Ethereum imposes limitations on the computational and storage resources that transactions included in the blocks can use, through gas limitations. Therefore, the data stored in L1 is minimized, and only raw transactions are stored along with a hash root of the L2 state tree. > **Rollups can be seen as a way to compress transaction execution, reducing the computational burden on the Layer 1 blockchain, thereby providing the possibility to increase the TPS while still maintaining the security level of Layer 1 for the Layer2 transactions.** -#### Split consensus from execution (The Merge). -On September 15, 2022, Ethereum implemented [EIP-3675](https://eips.ethereum.org/EIPS/eip-3675) (Upgrade consensus to Proof-of-Stake) through an event known as The Merge. The Merge has resulted in the deprecation of the Proof-of-Work consensus, which was previously implemented in the same logic layer as execution. Instead, it has been replaced by a much more complex and sophisticated Proof-of-Stake consensus that eliminates the need for energy-intensive mining. New Proof-of-Stake consensus Gasper runs on its own tech stack and p2p network, this new abstraction layer is known as Beacon Chain. The Beacon Chain has been running and achieving consensus since December 1st, 2020. After a prolonged period of consistent performance without any failures, it was deemed ready to become Ethereum's consensus provider, The Merge gets its name from the union of the two networks. - -- Consensus Layer (Beacon Chain): Specifically designed to be really good to reaching consensus. In Ethereum, time is divided up into twelve second units called **slots**, the consensus is reached when a valid block has been proposed in a specific slot. However, occasionally validators might be offline when called to propose a block, meaning slots can sometimes go empty. - -- Execution Layer (State and Transactional Ledger): Driven by the consensus layer, it specializes in managing the transactions mempool, the Ethereum state, and Ethereum block construction and execution. - -As result, an Ethereum node requires running two different software components: an execution client (or execution engine) driven by a consensus client through an internal communication protocol (Engine API). Note, that no additional trust assumptions need to be made for the execution Layer to follow and execute consensus decisions since each execution client receives information from the consensus Layer through its corresponding twin consensus client, and both clients operate within the same node’s trust domain. - -!["Ethereum Nodes"](./img/scaling/ethereum-nodes.png "Ethereum Nodes") - -Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. - -Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. - #### EIP-4844: Shard Blob Transactions (Proto-DankSharding) TODO From 43c170cf732e4f3dcedf6c4e7a98fce4b6d0d4df Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Mon, 26 Feb 2024 17:18:29 +0100 Subject: [PATCH 012/101] :x: Delete History Section --- docs/wiki/protocol/history.md | 19 ------------------- 1 file changed, 19 deletions(-) delete mode 100644 docs/wiki/protocol/history.md diff --git a/docs/wiki/protocol/history.md b/docs/wiki/protocol/history.md deleted file mode 100644 index f408814c..00000000 --- a/docs/wiki/protocol/history.md +++ /dev/null @@ -1,19 +0,0 @@ -# History - -## The DAO Hack and Ethereum Classic(ETC) fork -TODO - -## The Merge. -On September 15, 2022, Ethereum implemented [EIP-3675](https://eips.ethereum.org/EIPS/eip-3675) (Upgrade consensus to Proof-of-Stake) through an event known as The Merge. The Merge has resulted in the deprecation of the Proof-of-Work consensus, which was previously implemented in the same logic layer as execution. Instead, it has been replaced by a much more complex and sophisticated Proof-of-Stake consensus that eliminates the need for energy-intensive mining. New Proof-of-Stake consensus Gasper runs on its own tech stack and p2p network, this new abstraction layer is known as Beacon Chain. The Beacon Chain has been running and achieving consensus since December 1st, 2020. After a prolonged period of consistent performance without any failures, it was deemed ready to become Ethereum's consensus provider, The Merge gets its name from the union of the two networks. - -- Consensus Layer (Beacon Chain): Specifically designed to be really good to reaching consensus. In Ethereum, time is divided up into twelve second units called **slots**, the consensus is reached when a valid block has been proposed in a specific slot. However, occasionally validators might be offline when called to propose a block, meaning slots can sometimes go empty. - -- Execution Layer (State and Transactional Ledger): Driven by the consensus layer, it specializes in managing the transactions mempool, the Ethereum state, and Ethereum block construction and execution. - -As result, an Ethereum node requires running two different software components: an execution client (or execution engine) driven by a consensus client through an internal communication protocol (Engine API). Note, that no additional trust assumptions need to be made for the execution Layer to follow and execute consensus decisions since each execution client receives information from the consensus Layer through its corresponding twin consensus client, and both clients operate within the same node’s trust domain. - -!["Ethereum Nodes"](./img/scaling/ethereum-nodes.png "Ethereum Nodes") - -Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. - -Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. \ No newline at end of file From ae3a908504250b8e9c43643b182df4c17746461b Mon Sep 17 00:00:00 2001 From: GianfrancoBazzani Date: Mon, 26 Feb 2024 17:18:29 +0100 Subject: [PATCH 013/101] :x: Delete History Section --- docs/wiki/protocol/history.md | 19 - .../img/scaling/ethereum-nodes.excalidraw | 1692 ----------------- .../research/img/scaling/ethereum-nodes.png | Bin 143272 -> 0 bytes docs/wiki/research/scaling.md | 2 - 4 files changed, 1713 deletions(-) delete mode 100644 docs/wiki/protocol/history.md delete mode 100644 docs/wiki/research/img/scaling/ethereum-nodes.excalidraw delete mode 100644 docs/wiki/research/img/scaling/ethereum-nodes.png diff --git a/docs/wiki/protocol/history.md b/docs/wiki/protocol/history.md deleted file mode 100644 index f408814c..00000000 --- a/docs/wiki/protocol/history.md +++ /dev/null @@ -1,19 +0,0 @@ -# History - -## The DAO Hack and Ethereum Classic(ETC) fork -TODO - -## The Merge. -On September 15, 2022, Ethereum implemented [EIP-3675](https://eips.ethereum.org/EIPS/eip-3675) (Upgrade consensus to Proof-of-Stake) through an event known as The Merge. The Merge has resulted in the deprecation of the Proof-of-Work consensus, which was previously implemented in the same logic layer as execution. Instead, it has been replaced by a much more complex and sophisticated Proof-of-Stake consensus that eliminates the need for energy-intensive mining. New Proof-of-Stake consensus Gasper runs on its own tech stack and p2p network, this new abstraction layer is known as Beacon Chain. The Beacon Chain has been running and achieving consensus since December 1st, 2020. After a prolonged period of consistent performance without any failures, it was deemed ready to become Ethereum's consensus provider, The Merge gets its name from the union of the two networks. - -- Consensus Layer (Beacon Chain): Specifically designed to be really good to reaching consensus. In Ethereum, time is divided up into twelve second units called **slots**, the consensus is reached when a valid block has been proposed in a specific slot. However, occasionally validators might be offline when called to propose a block, meaning slots can sometimes go empty. - -- Execution Layer (State and Transactional Ledger): Driven by the consensus layer, it specializes in managing the transactions mempool, the Ethereum state, and Ethereum block construction and execution. - -As result, an Ethereum node requires running two different software components: an execution client (or execution engine) driven by a consensus client through an internal communication protocol (Engine API). Note, that no additional trust assumptions need to be made for the execution Layer to follow and execute consensus decisions since each execution client receives information from the consensus Layer through its corresponding twin consensus client, and both clients operate within the same node’s trust domain. - -!["Ethereum Nodes"](./img/scaling/ethereum-nodes.png "Ethereum Nodes") - -Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. - -Open source and public specifications for each client enhance client diversity. This is because a node can be set up with different combinations of client implementations from various software companies and developer communities. The goal is to achieve a client diversity in which the network is not dominated by a specific combination of execution client + consensus client implementation. This enhances the resilience of the network in case of bugs in the client implementations. \ No newline at end of file diff --git a/docs/wiki/research/img/scaling/ethereum-nodes.excalidraw b/docs/wiki/research/img/scaling/ethereum-nodes.excalidraw deleted file mode 100644 index 4b8a53d8..00000000 --- a/docs/wiki/research/img/scaling/ethereum-nodes.excalidraw +++ /dev/null @@ -1,1692 +0,0 @@ -{ - "type": "excalidraw", - "version": 2, - "source": "https://excalidraw.com", - "elements": [ - { - "id": "Nb67fof541cwUGSaExFOn", - "type": "rectangle", - "x": 624.0888875325521, - "y": 229.88887532552076, - "width": 785.5999823676217, - "height": 610.933369954427, - "angle": 0, - "strokeColor": "#7877e6", - "backgroundColor": "transparent", - "fillStyle": "hachure", - "strokeWidth": 1, - "strokeStyle": "solid", - "roughness": 1, - "opacity": 100, - "groupIds": [], - "roundness": { - "type": 3 - }, - "seed": 1598975292, - "version": 747, - "versionNonce": 900749884, - "isDeleted": false, - 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