JCMathLib is an open-source library for the JavaCard platform that aims to enable low-level cryptographic computations unavailable in the standard JavaCard API. In particular, it focuses on providing efficient modular arithmetic and elliptic curve operations.

If you want to get into the technical details of JCMathLib, you can find them in this paper: https://arxiv.org/abs/1810.01662.

When citing our work, please use the following reference:

@inproceedings{mavroudis2020jcmathlib,
  title={JCMathLib: wrapper cryptographic library for transparent and certifiable JavaCard applets},
  author={Mavroudis, Vasilios and Svenda, Petr},
  booktitle={2020 IEEE European Symposium on Security and Privacy Workshops (EuroS\&PW)},
  pages={89--96},
  year={2020},
  organization={IEEE}
}

Table of Contents

• Features and Limitations
• Getting Started
• Integration With Your Applet
• Community

Features and Limitations

JCMathLib includes the following features:

• BigNat arithmetic including modular operations
• Elliptic curve point addition and multiplication
• Option to accelerate computation by utilizing int native type on smartcards that support it ( branch ints)
• No dependencies on proprietary interfaces (only public JavaCard API)
• Selection of appropriate algorithm implementation based on the card's algorithm support (OperationSupport)
• Resource management (ObjectAllocator, ObjectLocker)
• Predefined common elliptic curves (SecP256r1, SecP256k1, SecP512r1)
• Tool for packaging JCMathLib into a single file for easy integration

Although higher-level cryptographic primitives and protocols can be constructed using JCMathLib, they are not included in the library. In case you need a higher-level implementation, you may try looking for projects building on top of JCMathLib (e.g., see our users).

As JCMathLib is implemented for the JavaCard Platform and relies only on public JavaCard API, it is not as efficient as a native implementation could be. This approach has a number of advantages, like easy portability and the possibility to open-source code. However, it makes it much harder (if not impossible) to perform the operations in constant time, and we do not aim to. The library is thus vulnerable to timing side-channel attacks and is NOT suited for production use.

Getting Started

Clone this repository:

git clone --recurse-submodules https://github.com/OpenCryptoProject/JCMathLib.git

For compilation for JavaCards, you need to obtain JavaCard SDKs, which are included as submodule. If you did not use --recurse-submodules in the previous command and your libs-sdks folder is empty, run:

git submodule update --init --recursive

Before using JCMathLib in your projects, you should test that it works properly on your smartcard. For that, you may want to run UnitTests. If you plan to work only with a simulator, you can skip to the last step of the following section.

Running unit tests

1. Set your card type in the JCMathLib/applet/src/main/java/opencrypto/jcmathlib/UnitTests class. The supported options are listed in class OperationSupport.{SIMULATOR, JCOP21, JCOP3_P60, JCOP4_P71, GD60, GD70, SECORA}.

public class UnitTests extends Applet {
    public final static short CARD_TYPE = OperationSupport.SIMULATOR; // TODO set your card here

2. OPTIONAL (depending on card selected in step 1). Change the JavaCard API version in applet/build.gradle file if you wish to run the code on cards with a JavaCard API version different from 3.0.5.

// JC310b43 supports building also for lower versions (cap.targetsdk).
// If another SDK is selected, please comment the cap.targetsdk setting.
final def JC_SELECTED = JC310b43 <----
...
// JC310b43 supports compilation targeting for lower API versions.
// Here you can specify path to the SDK you want to use.
// Only JC304 and higher are supported for targeting.
// If JC310b43 is not used, targetsdk cannot be set.
targetsdk JC305  <----

If you would like to build for lower versions, comment out line with targetsdk JC305 and set final def JC_SELECTED = JC310b43 to other value like final def JC_SELECTED = JC222.

The list of settings is summarized here:

Card	OperationSupport	JC_SELECTED	targetsdk	Notes
jCardSim simulator	SIMULATOR	--	--	(JavaCard API settings are ignored)
NXP J2E145G	JCOP21	JC303	remove
NXP JCOP3 J3H145 P60	JCOP3_P60	JC310b43	JC304
NXP JCOP4 J3Rxxx P71	JCOP4_P71	JC310b43	JC305
G+D Sm@rtcafe 6.0	GD60	JC303	remove
G+D Sm@rtcafe 7.0	GD70	JC310b43	JC304
Infineon Secora ID S	SECORA	JC310b43	JC305	(may require AES256 GP keys)

3. Build the applet by running the following command.

./gradlew buildJavaCard

4. If the build completes successfully, you may install it on a card by running the following command. In case you encounter some issues, you may want to try using GlobalPlatformPro directly and install the built cap file applet/build/javacard/unit_tests.cap.

./gradlew installJavaCard

If the installation completes successfully, you can run the tests. If the UnitTests contain your card type, the following command will try to run the tests with a connected card. Otherwise, it will run the tests just in a simulator.

./gradlew --rerun-tasks test

If you have multiple readers connected to your device, you may need to adjust the reader index (runCfg.setTargetReaderIndex in JCMathLib/applet/src/test/java/tests/BaseTest).

Example usage

For an example usage of the library, see the Example applet.

Integration With Your Applet

To enable easy integration of JCMathLib with your applet, we provide a Python script that bundles JCMathLib into a single .java that can be included in your code.

The script provides the following interface, allowing to specify which parts of JCMathLib to include (to save memory).

$ python package.py -h
usage: package.py [-h] [-d DIR] [-k] [-c {SecP256k1,SecP256r1,SecP512r1} [{SecP256k1,SecP256r1,SecP512r1} ...]] [-p PACKAGE] [-o OUTPUT]

Package the JCMathLib library into a single file.

options:
  -h, --help            show this help message and exit
  -d DIR, --dir DIR     Directory to package
  -k, --keep-locks      Keep locks
  -c {SecP256k1,SecP256r1,SecP512r1} [{SecP256k1,SecP256r1,SecP512r1} ...], --curves {SecP256k1,SecP256r1,SecP512r1} [{SecP256k1,SecP256r1,SecP512r1} ...]
                        Curves to include
  -p PACKAGE, --package PACKAGE
                        Package name
  -o OUTPUT, --output OUTPUT
                        Output file

For example, to bundle JCMathLib for your applet test in which you use curve SecP256k1, use the following. The output will be stored in jcmathlib.java file.

$ python package.py -p test -c SecP256k1 -o jcmathlib.java

Community

JCMathLib is kindly supported by:

How to contribute

We welcome all contributions, but we especially appreciate contributions in the following form:

• Code improvements. If you discover a bug or have an idea for improving the code, please, submit the change in a Pull Request.
• Features. If you wish certain feature was included in JCMathLib, let us know via Issues or implement it yourself and submit a Pull Request.
• Testing on cards. If you have a smart card model that is not yet included in JCMathLib and you manage to get it working, please, create a pull request with the corresponding OperationSupport configuration and include information about the smart card. Also consider submitting your card results to JCAlgTest.

Our users

• Myst: Secure Multiparty Key Generation, Signature and Decryption JavaCard applet and host application
• BioID: a Privacy-Friendly Identity Document
• JCEd25519: a JavaCard implementation of Ed25519 signing

(If you can't find yourself here, please let us know via Issues)