bitcoin/policies: show provably unspendable Taproot internal keys

In Taproot policies, it is a common pattern to use an unspendable
internal public key if one only wants to use script path spends, e.g.

    tr(UNSPENDABLE,{...})

https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki#constructing-and-spending-taproot-outputs
decribes that one could use the NUMS point for that:

> One example of such a point is H = lift_x(0x50929b74c1a04954b78b4b6035e97a5e078a5a0f28ec96d547bfee9ace803ac0)
which is constructed by taking the hash of the standard uncompressed
encoding of the secp256k1 base point G as X coordinate.

Wallet policy keys however must be xpubs, and also it is not desirable
to use the NUMS point, as described in
https://delvingbitcoin.org/t/unspendable-keys-in-descriptors/304:

> 1. unspendable keys should be indistinguishable from a random key for
an external observer;
> 2. in a descriptor with the range operator (like the wallet policies
> compatible with most known wallet account formats), each
> change/address_index combination must generate a different unspendable
> pubkey, and they should not be relatable to each other (in order to
> avoid fingerprinting);

The proposal in
https://delvingbitcoin.org/t/unspendable-keys-in-descriptors/304/21 to
use an xpub with the NUMS public key and a chain_code derived as the
hash from the xpubs in the descriptor was adopted by Liana
wallet. This commit implements this. Note that even though this
proposal it not a standard yet, it is still provably unspendable, so
we can display this info to the user. A future standard to achieve the
same can be included later.

src/rust/bitbox02-rust/src/hww/api/bitcoin/policies.rs

@@ -425,8 +425,11 @@ impl<'a> ParsedPolicy<'a> {
             BtcCoin::Tbtc | BtcCoin::Tltc => bip32::XPubType::Tpub,
         };
         let num_keys = policy.keys.len();
+
+        let taproot_is_unspendable_internal_key = self.taproot_is_unspendable_internal_key()?;
+
         for (i, key) in policy.keys.iter().enumerate() {
-            let key_str = match key {
+            let mut key_str = match key {
                 pb::KeyOriginInfo {
                     root_fingerprint,
                     keypath,
@@ -450,14 +453,14 @@ impl<'a> ParsedPolicy<'a> {
                 }
                 _ => return Err(Error::InvalidInput),
             };
+            if self.is_our_key[i] {
+                key_str = format!("This device: {}", key_str)
+            } else if i == 0 && taproot_is_unspendable_internal_key {
+                key_str = format!("Provably unspendable: {}", key_str)
+            }
             confirm::confirm(&confirm::Params {
                 title: &format!("Key {}/{}", i + 1, num_keys),
-                body: (if self.is_our_key[i] {
-                    format!("This device: {}", key_str)
-                } else {
-                    key_str
-                })
-                .as_str(),
+                body: key_str.as_str(),
                 scrollable: true,
                 longtouch: i == num_keys - 1 && matches!(mode, Mode::Advanced),
                 accept_is_nextarrow: true,
@@ -571,6 +574,74 @@ impl<'a> ParsedPolicy<'a> {
             _ => Err(Error::Generic),
         }
     }
+
+    /// Returns true if this is a Taproot policy and the Taproot internal key is provably
+    /// unspendable ,and false otherwise.
+    ///
+    /// We consider it provably unspendable if the internal xpub's public key is the NUMS point and
+    /// the xpub's chain code is the sha256() of the concatenation of all the public keys (33 byte
+    /// compressed) in the taptree left-to-right.
+    ///
+    /// See https://delvingbitcoin.org/t/unspendable-keys-in-descriptors/304/21
+    ///
+    /// This is not a standard yet, but it is provably unspendable in any case, so showing this info
+    /// to the user can't hurt.
+    fn taproot_is_unspendable_internal_key(&self) -> Result<bool, Error> {
+        match &self.descriptor {
+            Descriptor::Tr(tr) => {
+                // The internal key is always the first key in the keys list, enforced by
+                // `validate_keys()` (keys are referenced in order).
+                let internal_xpub = self
+                    .policy
+                    .keys
+                    .first()
+                    .ok_or(Error::InvalidInput)?
+                    .xpub
+                    .as_ref()
+                    .ok_or(Error::InvalidInput)?;
+
+                // See
+                // https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki#constructing-and-spending-taproot-outputs:
+                // > One example of such a point is H =
+                // > lift_x(0x50929b74c1a04954b78b4b6035e97a5e078a5a0f28ec96d547bfee9ace803ac0) which is constructed
+                // > by taking the hash of the standard uncompressed encoding of the secp256k1 base point G as X
+                // > coordinate.
+                const NUMS: [u8; 33] = [
+                    0x02, 0x50, 0x92, 0x9b, 0x74, 0xc1, 0xa0, 0x49, 0x54, 0xb7, 0x8b, 0x4b, 0x60,
+                    0x35, 0xe9, 0x7a, 0x5e, 0x07, 0x8a, 0x5a, 0x0f, 0x28, 0xec, 0x96, 0xd5, 0x47,
+                    0xbf, 0xee, 0x9a, 0xce, 0x80, 0x3a, 0xc0,
+                ];
+
+                if internal_xpub.depth != [0u8; 1]
+                    || internal_xpub.parent_fingerprint.as_slice() != [0u8; 4]
+                    || internal_xpub.child_num != 0
+                    || internal_xpub.public_key.as_slice() != NUMS
+                {
+                    return Ok(false);
+                }
+
+                let chain_code: [u8; 32] = {
+                    let mut hasher = Sha256::new();
+                    for pk in tr.inner.iter_scripts().flat_map(|(_, ms)| ms.iter_pk()) {
+                        let (key_index, _, _) =
+                            parse_wallet_policy_pk(&pk).map_err(|_| Error::InvalidInput)?;
+                        let key_info =
+                            self.policy.keys.get(key_index).ok_or(Error::InvalidInput)?;
+                        hasher.update(
+                            &key_info
+                                .xpub
+                                .as_ref()
+                                .ok_or(Error::InvalidInput)?
+                                .public_key,
+                        );
+                    }
+                    hasher.finalize().into()
+                };
+                Ok(chain_code == internal_xpub.chain_code.as_slice())
+            }
+            _ => Ok(false),
+        }
+    }
 }
 
 /// Parses a policy as specified by 'Wallet policies': https://github.com/bitcoin/bips/pull/1389.
@@ -1529,4 +1600,29 @@ mod tests {
             "6160dc5cf72b79380e9e715c75ae54573b81dcb4ed8ab2e90fde5d661e443781",
         );
     }
+
+    #[test]
+    fn test_tr_unspendable_internal_key() {
+        mock_unlocked_using_mnemonic(
+            "sudden tenant fault inject concert weather maid people chunk youth stumble grit",
+            "",
+        );
+
+        let policy_str = "tr(@0/<0;1>/*,{and_v(v:multi_a(1,@1/<2;3>/*,@2/<2;3>/*),older(2)),multi_a(2,@1/<0;1>/*,@2/<0;1>/*)})";
+
+        let k0 = pb::KeyOriginInfo {
+            root_fingerprint: vec![],
+            keypath: vec![],
+            xpub: Some(parse_xpub("tpubD6NzVbkrYhZ4WNrreqKvZr3qeJR7meg2BgaGP9upLkt7bp5SY6AAhY8vaN8ThfCjVcK6ZzE6kZbinszppNoGKvypeTmhyQ6uvUptXEXqknv").unwrap()),
+        };
+        let k1 = pb::KeyOriginInfo {
+            root_fingerprint: hex::decode("ffd63c8d").unwrap(),
+            keypath: vec![48 + HARDENED, 1 + HARDENED, 0 + HARDENED, 2 + HARDENED],
+            xpub: Some(parse_xpub("tpubDExA3EC3iAsPxPhFn4j6gMiVup6V2eH3qKyk69RcTc9TTNRfFYVPad8bJD5FCHVQxyBT4izKsvr7Btd2R4xmQ1hZkvsqGBaeE82J71uTK4N").unwrap()),
+        };
+        let k2 = make_our_key(KEYPATH_ACCOUNT);
+        let policy = make_policy(policy_str, &[k0, k1, k2]);
+        let parsed_policy = parse(&policy, BtcCoin::Tbtc).unwrap();
+        assert!(parsed_policy.taproot_is_unspendable_internal_key().unwrap());
+    }
 }

src/rust/bitbox02-rust/src/hww/api/bitcoin/signtx.rs

@@ -3135,6 +3135,103 @@ mod tests {
         assert!(unsafe { !PREVTX_REQUESTED });
     }
 
+    // Tests that unspendable internal Taproot keys are displayed as such.
+    #[test]
+    fn test_policy_tr_unspendable_internal_key() {
+        let transaction = alloc::rc::Rc::new(core::cell::RefCell::new(Transaction::new_policy()));
+
+        mock_host_responder(transaction.clone());
+
+        let policy_str = "tr(@0/<0;1>/*,{and_v(v:multi_a(1,@1/<2;3>/*,@2/<2;3>/*),older(2)),multi_a(2,@1/<0;1>/*,@2/<0;1>/*)})";
+
+        static mut UI_COUNTER: u32 = 0;
+        mock(Data {
+            ui_confirm_create: Some(Box::new(move |params| {
+                match unsafe {
+                    UI_COUNTER += 1;
+                    UI_COUNTER
+                } {
+                    1 => {
+                        assert_eq!(params.title, "Spend from");
+                        assert_eq!(params.body, "BTC Testnet\npolicy with\n3 keys");
+                    }
+                    2 => {
+                        assert_eq!(params.title, "Name");
+                        assert_eq!(params.body, "test policy account name");
+                    }
+                    3 => {
+                        assert_eq!(params.title, "");
+                        assert_eq!(params.body, "Show policy\ndetails?");
+                    }
+                    4 => {
+                        assert_eq!(params.title, "Policy");
+                        assert_eq!(params.body, policy_str);
+                    }
+                    5 => {
+                        assert_eq!(params.title, "Key 1/3");
+                        assert_eq!(params.body, "Provably unspendable: tpubD6NzVbkrYhZ4WNrreqKvZr3qeJR7meg2BgaGP9upLkt7bp5SY6AAhY8vaN8ThfCjVcK6ZzE6kZbinszppNoGKvypeTmhyQ6uvUptXEXqknv");
+                    }
+                    6 => {
+                        assert_eq!(params.title, "Key 2/3");
+                        assert_eq!(params.body, "[ffd63c8d/48'/1'/0'/2']tpubDExA3EC3iAsPxPhFn4j6gMiVup6V2eH3qKyk69RcTc9TTNRfFYVPad8bJD5FCHVQxyBT4izKsvr7Btd2R4xmQ1hZkvsqGBaeE82J71uTK4N");
+                    }
+                    7 => {
+                        assert_eq!(params.title, "Key 3/3");
+                        assert_eq!(params.body, "This device: [93531fa9/48'/1'/0'/3']tpubDEjJGD6BCCuA7VHrbk3gMeQ5HocbZ4eSQ121DcvCkC8xaeRFjyoJC9iVrSz1bWfNwAY5K2Vfz5bnHR3y4RrqVpkc5ikz4trfhSyosZPrcnk");
+                    }
+                    _ => {}
+                }
+                true
+            })),
+            ui_transaction_address_create: Some(Box::new(move |_amount, _address| true)),
+            ui_transaction_fee_create: Some(Box::new(|_total, _fee, _longtouch| true)),
+            ..Default::default()
+        });
+
+        mock_unlocked_using_mnemonic(
+            "sudden tenant fault inject concert weather maid people chunk youth stumble grit",
+            "",
+        );
+        bitbox02::random::mock_reset();
+        // For the policy registration below.
+        mock_memory();
+
+        let keypath_account = &[48 + HARDENED, 1 + HARDENED, 0 + HARDENED, 3 + HARDENED];
+
+        let policy = pb::btc_script_config::Policy {
+            policy: policy_str.into(),
+            keys: vec![
+                pb::KeyOriginInfo {
+                    root_fingerprint: vec![],
+                    keypath: vec![],
+                    xpub: Some(parse_xpub("tpubD6NzVbkrYhZ4WNrreqKvZr3qeJR7meg2BgaGP9upLkt7bp5SY6AAhY8vaN8ThfCjVcK6ZzE6kZbinszppNoGKvypeTmhyQ6uvUptXEXqknv").unwrap()),
+                },
+                pb::KeyOriginInfo {
+                    root_fingerprint: hex::decode("ffd63c8d").unwrap(),
+                    keypath: vec![48 + HARDENED, 1 + HARDENED, 0 + HARDENED, 2 + HARDENED],
+                    xpub: Some(parse_xpub("tpubDExA3EC3iAsPxPhFn4j6gMiVup6V2eH3qKyk69RcTc9TTNRfFYVPad8bJD5FCHVQxyBT4izKsvr7Btd2R4xmQ1hZkvsqGBaeE82J71uTK4N").unwrap()),
+                },
+                pb::KeyOriginInfo {
+                    root_fingerprint: crate::keystore::root_fingerprint().unwrap(),
+                    keypath: keypath_account.to_vec(),
+                    xpub: Some(crate::keystore::get_xpub(keypath_account).unwrap().into()),
+                },
+            ],
+        };
+
+        // Register policy.
+        let policy_hash = super::super::policies::get_hash(pb::BtcCoin::Tbtc, &policy).unwrap();
+        bitbox02::memory::multisig_set_by_hash(&policy_hash, "test policy account name").unwrap();
+
+        assert!(block_on(process(
+            &transaction
+                .borrow()
+                .init_request_policy(policy, keypath_account),
+        ))
+        .is_ok());
+        assert!(unsafe { UI_COUNTER >= 7 });
+    }
+
     /// Test that a policy with derivations other than `/**` work.
     #[test]
     fn test_policy_different_multipath_derivations() {