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148 lines
5.5 KiB
Python
148 lines
5.5 KiB
Python
# This file is part of the Trezor project.
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#
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# Copyright (C) 2012-2022 SatoshiLabs and contributors
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#
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# This library is free software: you can redistribute it and/or modify
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# it under the terms of the GNU Lesser General Public License version 3
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# as published by the Free Software Foundation.
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#
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# This library is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU Lesser General Public License for more details.
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#
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# You should have received a copy of the License along with this library.
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# If not, see <https://www.gnu.org/licenses/lgpl-3.0.html>.
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from functools import reduce
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from typing import Iterable, Sequence, Tuple
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from . import _ed25519
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# XXX, these could be NewType's, but that would infect users of the cosi module with these types as well.
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# Unsure if we want that.
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Ed25519PrivateKey = bytes
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Ed25519PublicPoint = bytes
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Ed25519Signature = bytes
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def combine_keys(pks: Iterable[Ed25519PublicPoint]) -> Ed25519PublicPoint:
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"""Combine a list of Ed25519 points into a "global" CoSi key."""
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P = [_ed25519.decodepoint(pk) for pk in pks]
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combine = reduce(_ed25519.edwards_add, P)
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return Ed25519PublicPoint(_ed25519.encodepoint(combine))
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def combine_sig(
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global_R: Ed25519PublicPoint, sigs: Iterable[Ed25519Signature]
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) -> Ed25519Signature:
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"""Combine a list of signatures into a single CoSi signature."""
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S = [_ed25519.decodeint(si) for si in sigs]
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s = sum(S) % _ed25519.l
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sig = global_R + _ed25519.encodeint(s)
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return Ed25519Signature(sig)
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def get_nonce(
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sk: Ed25519PrivateKey, data: bytes, ctr: int = 0
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) -> Tuple[int, Ed25519PublicPoint]:
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"""Calculate CoSi nonces for given data.
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These differ from Ed25519 deterministic nonces in that there is a counter appended at end.
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Returns both the private point `r` and the partial signature `R`.
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`r` is returned for performance reasons: :func:`sign_with_privkey`
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takes it as its `nonce` argument so that it doesn't repeat the `get_nonce` call.
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`R` should be combined with other partial signatures through :func:`combine_keys`
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to obtain a "global commitment".
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"""
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# r = hash(hash(sk)[b .. 2b] + M + ctr)
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# R = rB
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h = _ed25519.H(sk)
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bytesize = _ed25519.b // 8
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assert len(h) == bytesize * 2
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r = _ed25519.Hint(h[bytesize:] + data + ctr.to_bytes(4, "big"))
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R = _ed25519.scalarmult(_ed25519.B, r)
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return r, Ed25519PublicPoint(_ed25519.encodepoint(R))
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def verify_combined(
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signature: Ed25519Signature, digest: bytes, pub_key: Ed25519PublicPoint
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) -> None:
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"""Verify Ed25519 signature. Raise exception if the signature is invalid.
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A CoSi combined signature is equivalent to a plain Ed25519 signature with a public
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key that is a combination of the cosigners' public keys. This function takes the
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combined public key and performs simple Ed25519 verification.
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"""
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# XXX this *might* change to bool function
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_ed25519.checkvalid(signature, digest, pub_key)
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def verify(
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signature: Ed25519Signature,
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digest: bytes,
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sigs_required: int,
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keys: Sequence[Ed25519PublicPoint],
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mask: int,
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) -> None:
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"""Verify a CoSi multi-signature. Raise exception if the signature is invalid.
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This function verifies a M-of-N signature scheme. The arguments are:
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- the minimum number M of signatures required
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- public keys of all N possible cosigners
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- a bitmask specifying which of the N cosigners have produced the signature.
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The verification checks that the mask specifies at least M cosigners, then combines
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the selected public keys and verifies the signature against the combined key.
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"""
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if sigs_required < 1:
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raise ValueError("At least one signer must be specified.")
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if mask.bit_length() > len(keys):
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raise ValueError("Sigmask specifies more public keys than provided.")
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selected_keys = [key for i, key in enumerate(keys) if mask & (1 << i)]
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if len(selected_keys) < sigs_required:
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raise _ed25519.SignatureMismatch("Insufficient number of signatures.")
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global_pk = combine_keys(selected_keys)
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verify_combined(signature, digest, global_pk)
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def pubkey_from_privkey(privkey: Ed25519PrivateKey) -> Ed25519PublicPoint:
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"""Interpret 32 bytes of data as an Ed25519 private key.
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Calculate and return the corresponding public key.
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"""
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return Ed25519PublicPoint(_ed25519.publickey_unsafe(privkey))
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def sign_with_privkey(
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digest: bytes,
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privkey: Ed25519PrivateKey,
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global_pubkey: Ed25519PublicPoint,
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nonce: int,
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global_commit: Ed25519PublicPoint,
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) -> Ed25519Signature:
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"""Create a CoSi signature of `digest` with the supplied private key.
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This function needs to know the global public key and global commitment.
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"""
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h = _ed25519.H(privkey)
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a = _ed25519.decodecoord(h)
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S = (nonce + _ed25519.Hint(global_commit + global_pubkey + digest) * a) % _ed25519.l
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return Ed25519Signature(_ed25519.encodeint(S))
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def sign_with_privkeys(digest: bytes, privkeys: Sequence[bytes]) -> bytes:
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"""Locally produce a CoSi signature from a list of private keys."""
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pubkeys = [pubkey_from_privkey(sk) for sk in privkeys]
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nonces = [get_nonce(sk, digest, i) for i, sk in enumerate(privkeys)]
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global_pk = combine_keys(pubkeys)
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global_R = combine_keys(R for _, R in nonces)
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sigs = [
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sign_with_privkey(digest, sk, global_pk, r, global_R)
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for sk, (r, _) in zip(privkeys, nonces)
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]
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return combine_sig(global_R, sigs)
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