How to verify a signature made by trezor wallet

Question

I want to verify a message signed by my trezor hardware wallet. Basically I have these information.

.venv/bin/trezorctl btc get-public-node -n 0
Passphrase required: 
Confirm your passphrase: 
node.depth: 1
node.fingerprint: ea66f037
node.child_num: 0
node.chain_code: e02030f2a7dfb474d53a96cb26febbbe3bd3b9756f4e0a820146ff1fb4e0bd99
node.public_key: 026b4cc594c849a0d9a124725997604bc6a0ec8f100b621b1eaed4c6094619fc46
xpub: xpub69cRfCiJ5BVzesfFdsTgEb29SskY74wYfjTRw5kdctGN2xp1HF4udTP21t68PAQ4CBq1Rn3wAsWr84wiDiRmmSZLwkEkv4qK5T5Y7EXebyQ

$ .venv/bin/trezorctl btc sign-message 'aaa' -n 0
Please confirm action on your Trezor device
Passphrase required: 
Confirm your passphrase: 
message: aaa
address: 17DB2Q3oZVkQAffkpFvF4cwsXggu39iKdQ
signature: IHQ7FDJy6zjwMImIsFcHGdhVxAH7ozoEoelN2EfgKZZ0JVAbvnGN/w8zxiMivqkO8ijw8fXeCMDt0K2OW7q2GF0=

I wanted to use python3-ecdsa. When I want to verify the signature with any valid public key, I get an AssertionError: (65, 64), because the base64.b64decode of the signature is 65 bytes, but should be 64. When I want to load the node.public_key into a ecdsa.VerifyingKey, I get an AssertionError: (32, 64), because the bytes.fromhex return 32 bytes, but every example I found uses 64 bytes for the public key. Probably I need to convert the bip32 xpub to a public key, but I really dont know how.

Solutiion

python-ecdsa needs to be at version 0.14 or greater to handle compressed format of the public key.

import ecdsa
import base64
import hashlib

class DoubleSha256:

    def __init__(self, *args, **kwargs):
        self._m = hashlib.sha256(*args, **kwargs)

    def __getattr__(self, attr):
        if attr == 'digest':
            return self.double_digest
        return getattr(self._m, attr)

    def double_digest(self):
        m = hashlib.sha256()
        m.update(self._m.digest())
        return m.digest()


def pad_message(message):
    return "\x18Bitcoin Signed Message:\n".encode('UTF-8') + bytes([len(message)]) + message.encode('UTF-8')


public_key_hex = '026b4cc594c849a0d9a124725997604bc6a0ec8f100b621b1eaed4c6094619fc46'
public_key = bytes.fromhex(public_key_hex)
message = pad_message('aaa')
sig = base64.b64decode('IHQ7FDJy6zjwMImIsFcHGdhVxAH7ozoEoelN2EfgKZZ0JVAbvnGN/w8zxiMivqkO8ijw8fXeCMDt0K2OW7q2GF0=')

vk = ecdsa.VerifyingKey.from_string(public_key, curve=ecdsa.SECP256k1)
print(vk.verify(sig[1:], message, hashfunc=DoubleSha256))

Answer 1

Public-key. Mathematically an elliptic curve public key is a point on the curve. For the elliptic curve used by Bitcoin, secp256k1, as well as other X9-style (Weierstrass form) curves, there are (in practice) two standard representations originally established by X9.62 and reused by many others:

• uncompressed format: consists of one octet with value 0x04, followed by two blocks of size equal to the curve order size containing the (affine) X and Y coordinates. For secp256k1 this is 1+32x2 = 65 octets

• compressed format: consists of one octet with value 0x02 or 0x03 indicating the parity of the Y coordinate, followed by a block of size equal tot he curve order containing the X coordinate. For secp256k1 this is 1+32 = 33 octets

The public key output by your trezor is the second form, 0x02 + 32 octets = 33 octets. Not 32.

I've never seen an X9EC library (ECDSA and/or ECDH) that doesn't accept at least the standard uncompressed form, and usually both. It is conceivable your python library expects only the uncompressed form without the leading 0x04, but if so this gratuitous and rather risky nonstandardness, unless a very good explanation is provided in the doc or code, would make me suspicious of its quality. If you do need to convert the compressed form to uncompressed you must implement the curve equation, which for secp256k1 can be found in standard references, not to mention many implementations. Compute x^3 + a*x + b, take the square root in F_p, and choose either the positive or negative value that has the correct parity (agreeing with the leading byte here 0x02).

The 'xpub' is a base58check encoding of a hierarchical deterministic key, which is not just an EC(DSA) key but adds metadata for the key derivation process. If you base58 decode it and remove the check, you get (in hex):

0488B21E01EA66F03700000000E02030F2A7DFB474D53A96CB26FEBBBE3BD3B9756F4E0A820146FF1FB4E0BD99026B4CC594C849A0D9A124725997604BC6A0EC8F100B621B1EAED4C6094619FC46good

which breaks down exactly as your display showed:

0488B21E  fixed prefix 
01  .depth 
EA66F037  .fingerprint
00000000  .child_num
E02030F2A7DFB474D53A96CB26FEBBBE3BD3B9756F4E0A820146FF1FB4E0BD99  .chain_code
026B4CC594C849A0D9A124725997604BC6A0EC8F100B621B1EAED4C6094619FC46  .public_key

Confirming this, the ripemd160 of sha256 of (the bytes that are shown in hex as) 026B4CC594C849A0D9A124725997604BC6A0EC8F100B621B1EAED4C6094619FC46 is (the bytes shown in hex as) 441e1d2adf9ff2a6075d71d0d8782228e0df47f8, and prefixing the version byte 00 for mainnet to that and base58check encoding gives the address 17DB2Q3oZVkQAffkpFvF4cwsXggu39iKdQ as shown.

Signature. Mathematically an X9.62-type ECDSA signature is two integers, called r and s. There are two different standards for representing them, and Bitcoin uses both with variations:

• ASN.1 DER format. DER is a general purpose encoding that contains 'tag' and 'length' metadata and variable length data depending on the numeric values, here r and s; for secp256k1 in general this encoding is usually 70 to 72 octets but occasionally less. However, to avoid certain 'malleability' attacks current Bitcoin requires use of 's' values less than half the curve order, commonly called 'low-s', which reduces the maximum length of the ASN.1 DER encoding to 71 octets. Bitcoin uses this for transaction signatures, and adds a 'sighash' byte immediately following it (in the 'scriptsig' aka redeem script) indicating certain options on how the signature was computed (and thus should be verified).

• 'plain' or P1363 format. This is fixed length and consists simply of the r and s values as fixed-length blocks; for secp256k1 this is 64 octets. Bitcoin uses this for message signatures but it adds a 'recovery' byte' to the beginning that allows determining the publickey from the message and signature if necessary, making the total 65 octets.

See https://bitcoin.stackexchange.com/questions/38351/ecdsa-v-r-s-what-is-v/38909 and https://bitcoin.stackexchange.com/questions/12554/why-the-signature-is-always-65-13232-bytes-long .

If your python library is designed for general purpose ECDSA, not Bitcoin, and wants a 64-byte signature, that almost certainly is the 'plain' format which corresponds to the Bitcoin message signature (here decoded from base64) with the first byte removed.