feat(core): Implement extend_mnemonics() for SLIP-39.

[no changelog]

core/src/trezor/crypto/slip39.py

@@ -247,6 +247,69 @@ def split_ems(
     return mnemonics
 
 
+def extend_mnemonics(
+    share_count: int,  # The number of shares to create.
+    mnemonics: list[str],  # A threshold set of the old mnemonics.
+) -> list[str]:
+    """
+    Extends a set of mnemonics to the desired share_count, while maintaining the threshold. This,
+    for example, allows extending a 2-of-2 backup to 2-of-3, where the first two shares remain the
+    same. It also allows reconstructing lost shares by providing any threshold number of shares and
+    requesting the original share_count. The current implementation is limited to Slip39_Basic,
+    i.e. single group.
+
+    It is not possible to tell how many shares the user originally created, so if share_count is
+    less than the original number of shares, then this function will return the first share_count
+    shares.
+    """
+
+    if not mnemonics:
+        raise MnemonicError("The list of mnemonics is empty.")
+
+    (
+        identifier,
+        extendable,
+        iteration_exponent,
+        group_threshold,
+        group_count,
+        groups,
+    ) = _decode_mnemonics(mnemonics)
+
+    if group_threshold != 1 or group_count != 1 or len(groups) != 1:
+        raise MnemonicError("Extending advanced backups is not supported.")
+
+    threshold = groups[0][0]
+    shares = groups[0][1]
+    if len(shares) != threshold:
+        raise MnemonicError(
+            f"Wrong number of mnemonics. Expected {threshold} mnemonics, but {len(shares)} were provided."
+        )
+
+    if threshold == 1 and share_count > 1:
+        raise ValueError(
+            "Creating multiple member shares with member threshold 1 is not allowed. Use 1-of-1 member sharing instead."
+        )
+
+    shares = _extend_shares(share_count, list(shares))
+
+    mnemonics = []
+    for index, value in shares:
+        mnemonics.append(
+            _encode_mnemonic(
+                identifier,
+                extendable,
+                iteration_exponent,
+                group_index=0,
+                group_threshold=1,
+                group_count=1,
+                member_index=index,
+                member_threshold=threshold,
+                value=value,
+            )
+        )
+    return mnemonics
+
+
 def recover_ems(mnemonics: list[str]) -> tuple[int, bool, int, bytes]:
     """
     Combines mnemonic shares to obtain the encrypted master secret which was previously
@@ -457,9 +520,7 @@ def _create_digest(random_data: bytes, shared_secret: bytes) -> bytes:
     return hmac(hmac.SHA256, random_data, shared_secret).digest()[:_DIGEST_LENGTH_BYTES]
 
 
-def _split_secret(
+def _check_parameters(threshold: int, share_count: int) -> None:
-    threshold: int, share_count: int, shared_secret: bytes
-) -> list[tuple[int, bytes]]:
     if threshold < 1:
         raise ValueError(
             f"The requested threshold ({threshold}) must be a positive integer."
@@ -475,6 +536,12 @@ def _split_secret(
             f"The requested number of shares ({share_count}) must not exceed {MAX_SHARE_COUNT}."
         )
 
+
+def _split_secret(
+    threshold: int, share_count: int, shared_secret: bytes
+) -> list[tuple[int, bytes]]:
+    _check_parameters(threshold, share_count)
+
     # If the threshold is 1, then the digest of the shared secret is not used.
     if threshold == 1:
         return [(i, shared_secret) for i in range(share_count)]
@@ -499,6 +566,13 @@ def _split_secret(
     return shares
 
 
+def _extend_shares(
+    share_count: int, old_shares: list[tuple[int, bytes]]
+) -> list[tuple[int, bytes]]:
+    _check_parameters(len(old_shares), share_count)
+    return [(i, shamir.interpolate(old_shares, i)) for i in range(share_count)]
+
+
 def _recover_secret(threshold: int, shares: list[tuple[int, bytes]]) -> bytes:
     # If the threshold is 1, then the digest of the shared secret is not used.
     if threshold == 1:

core/tests/test_trezor.crypto.slip39.py

@@ -37,6 +37,16 @@ class TestCryptoSlip39(unittest.TestCase):
                 slip39.recover_ems(mnemonics[:3]), slip39.recover_ems(mnemonics[2:])
             )
 
+    def test_basic_sharing_extend(self):
+        identifier = slip39.generate_random_identifier()
+        for extendable in (False, True):
+            mnemonics = slip39.split_ems(1, [(2, 3)], identifier, extendable, 1, self.EMS)
+            mnemonics = mnemonics[0]
+            extended_mnemonics = slip39.extend_mnemonics(4, mnemonics[1:])
+            self.assertEqual(mnemonics, extended_mnemonics[:3])
+            for i in range(3):
+                self.assertEqual(slip39.recover_ems([extended_mnemonics[3], mnemonics[i]])[3], self.EMS)
+
     def test_basic_sharing_fixed(self):
         for extendable in (False, True):
             generated_identifier = slip39.generate_random_identifier()