Bitcoin sign recover address

openssl_verify.py

from pybitcointools import bitcoin as btctools
import time, hashlib
priv = "5JsunC55XGVqFQj5kPGK4MWgTL26jKbnPhjnmchSNPo75XXCwtk"
address = "1N2XWu5soeppX2qUjvrf81rpdbShKJrjTr"
sign = btctools.ecdsa_sign("hello", priv)  

import base64

def VerifyMessage(address, hash, sig):
	sig = base64.b64decode(sig)

	pubkey = recover_compact(hash, sig)
	return btctools.pubkey_to_address(pubkey) == address


def msg_magic(message):
	return "\x18Bitcoin Signed Message:\n" + chr( len(message) ) + message

import ctypes
import ctypes.util
_bchr = chr
_bord = ord
_ssl = ctypes.cdll.LoadLibrary(ctypes.util.find_library('ssl') or 'libeay32')


# this specifies the curve used with ECDSA.
_NID_secp256k1 = 714 # from openssl/obj_mac.h

# Thx to Sam Devlin for the ctypes magic 64-bit fix.
def _check_result (val, func, args):
    if val == 0:
        raise ValueError
    else:
        return ctypes.c_void_p(val)

_ssl.EC_KEY_new_by_curve_name.restype = ctypes.c_void_p
_ssl.EC_KEY_new_by_curve_name.errcheck = _check_result

# From openssl/ecdsa.h
class ECDSA_SIG_st(ctypes.Structure):
     _fields_ = [("r", ctypes.c_void_p),
                ("s", ctypes.c_void_p)] 

class CECKey:
    """Wrapper around OpenSSL's EC_KEY"""

    POINT_CONVERSION_COMPRESSED = 2
    POINT_CONVERSION_UNCOMPRESSED = 4

    def __init__(self):
        self.k = _ssl.EC_KEY_new_by_curve_name(_NID_secp256k1)

    def __del__(self):
        if _ssl:
            _ssl.EC_KEY_free(self.k)
        self.k = None

    def set_secretbytes(self, secret):
        priv_key = _ssl.BN_bin2bn(secret, 32, _ssl.BN_new())
        group = _ssl.EC_KEY_get0_group(self.k)
        pub_key = _ssl.EC_POINT_new(group)
        ctx = _ssl.BN_CTX_new()
        if not _ssl.EC_POINT_mul(group, pub_key, priv_key, None, None, ctx):
            raise ValueError("Could not derive public key from the supplied secret.")
        _ssl.EC_POINT_mul(group, pub_key, priv_key, None, None, ctx)
        _ssl.EC_KEY_set_private_key(self.k, priv_key)
        _ssl.EC_KEY_set_public_key(self.k, pub_key)
        _ssl.EC_POINT_free(pub_key)
        _ssl.BN_CTX_free(ctx)
        return self.k

    def set_privkey(self, key):
        self.mb = ctypes.create_string_buffer(key)
        return _ssl.d2i_ECPrivateKey(ctypes.byref(self.k), ctypes.byref(ctypes.pointer(self.mb)), len(key))

    def set_pubkey(self, key):
        self.mb = ctypes.create_string_buffer(key)
        return _ssl.o2i_ECPublicKey(ctypes.byref(self.k), ctypes.byref(ctypes.pointer(self.mb)), len(key))

    def get_privkey(self):
        size = _ssl.i2d_ECPrivateKey(self.k, 0)
        mb_pri = ctypes.create_string_buffer(size)
        _ssl.i2d_ECPrivateKey(self.k, ctypes.byref(ctypes.pointer(mb_pri)))
        return mb_pri.raw

    def get_pubkey(self):
        size = _ssl.i2o_ECPublicKey(self.k, 0)
        mb = ctypes.create_string_buffer(size)
        _ssl.i2o_ECPublicKey(self.k, ctypes.byref(ctypes.pointer(mb)))
        return mb.raw

    def get_raw_ecdh_key(self, other_pubkey):
        ecdh_keybuffer = ctypes.create_string_buffer(32)
        r = _ssl.ECDH_compute_key(ctypes.pointer(ecdh_keybuffer), 32,
                                 _ssl.EC_KEY_get0_public_key(other_pubkey.k),
                                 self.k, 0)
        if r != 32:
            raise Exception('CKey.get_ecdh_key(): ECDH_compute_key() failed')
        return ecdh_keybuffer.raw

    def get_ecdh_key(self, other_pubkey, kdf=lambda k: hashlib.sha256(k).digest()):
        # FIXME: be warned it's not clear what the kdf should be as a default
        r = self.get_raw_ecdh_key(other_pubkey)
        return kdf(r)

    def sign(self, hash):
        if not isinstance(hash, bytes):
            raise TypeError('Hash must be bytes instance; got %r' % hash.__class__)
        if len(hash) != 32:
            raise ValueError('Hash must be exactly 32 bytes long')

        sig_size0 = ctypes.c_uint32()
        sig_size0.value = _ssl.ECDSA_size(self.k)
        mb_sig = ctypes.create_string_buffer(sig_size0.value)
        result = _ssl.ECDSA_sign(0, hash, len(hash), mb_sig, ctypes.byref(sig_size0), self.k)
        assert 1 == result
        if bitcoin.core.script.IsLowDERSignature(mb_sig.raw[:sig_size0.value]):
            return mb_sig.raw[:sig_size0.value]
        else:
            return self.signature_to_low_s(mb_sig.raw[:sig_size0.value])

    def sign_compact(self, hash):
        if not isinstance(hash, bytes):
            raise TypeError('Hash must be bytes instance; got %r' % hash.__class__)
        if len(hash) != 32:
            raise ValueError('Hash must be exactly 32 bytes long')

        sig_size0 = ctypes.c_uint32()
        sig_size0.value = _ssl.ECDSA_size(self.k)
        mb_sig = ctypes.create_string_buffer(sig_size0.value)
        result = _ssl.ECDSA_sign(0, hash, len(hash), mb_sig, ctypes.byref(sig_size0), self.k)
        assert 1 == result

        if bitcoin.core.script.IsLowDERSignature(mb_sig.raw[:sig_size0.value]):
            sig = mb_sig.raw[:sig_size0.value]
        else:
            sig = self.signature_to_low_s(mb_sig.raw[:sig_size0.value])

        sig = bitcoin.core.DERSignature.deserialize(sig)

        r_val = sig.r
        s_val = sig.s

        # assert that the r and s are less than 32 long, excluding leading 0s
        assert len(r_val) <= 32 or r_val[0:-32] == b'\x00'
        assert len(s_val) <= 32 or s_val[0:-32] == b'\x00'

        # ensure r and s are always 32 chars long by 0padding
        r_val = ((b'\x00' * 32) + r_val)[-32:]
        s_val = ((b'\x00' * 32) + s_val)[-32:]

        # tmp pubkey of self, but always compressed
        pubkey = CECKey()
        pubkey.set_pubkey(self.get_pubkey())
        pubkey.set_compressed(True)

        # bitcoin core does <4, but I've seen other places do <2 and I've never seen a i > 1 so far
        for i in range(0, 4):
            cec_key = CECKey()
            cec_key.set_compressed(True)

            result = cec_key.recover(r_val, s_val, hash, len(hash), i, 1)
            if result == 1:
                if cec_key.get_pubkey() == pubkey.get_pubkey():
                    return r_val + s_val, i

        raise ValueError

    def signature_to_low_s(self, sig):
        der_sig = ECDSA_SIG_st()
        _ssl.d2i_ECDSA_SIG(ctypes.byref(ctypes.pointer(der_sig)), ctypes.byref(ctypes.c_char_p(sig)), len(sig))
        group = _ssl.EC_KEY_get0_group(self.k)
        order = _ssl.BN_new()
        halforder = _ssl.BN_new()
        ctx = _ssl.BN_CTX_new()
        _ssl.EC_GROUP_get_order(group, order, ctx)
        _ssl.BN_rshift1(halforder, order)

        # Verify that s is over half the order of the curve before we actually subtract anything from it
        if _ssl.BN_cmp(der_sig.s, halforder) > 0:
          _ssl.BN_sub(der_sig.s, order, der_sig.s)

        _ssl.BN_free(halforder)
        _ssl.BN_free(order)
        _ssl.BN_CTX_free(ctx)

        derlen = _ssl.i2d_ECDSA_SIG(ctypes.pointer(der_sig), 0)
        if derlen == 0:
            _ssl.ECDSA_SIG_free(der_sig)
            return None
        new_sig = ctypes.create_string_buffer(derlen)
        _ssl.i2d_ECDSA_SIG(ctypes.pointer(der_sig), ctypes.byref(ctypes.pointer(new_sig)))
        _ssl.BN_free(der_sig.r)
        _ssl.BN_free(der_sig.s)

        return new_sig.raw

    def verify(self, hash, sig):
        """Verify a DER signature"""
        if not sig:
          return false

        # New versions of OpenSSL will reject non-canonical DER signatures. de/re-serialize first.
        norm_sig = ctypes.c_void_p(0)
        _ssl.d2i_ECDSA_SIG(ctypes.byref(norm_sig), ctypes.byref(ctypes.c_char_p(sig)), len(sig))

        derlen = _ssl.i2d_ECDSA_SIG(norm_sig, 0)
        if derlen == 0:
            _ssl.ECDSA_SIG_free(norm_sig)
            return false

        norm_der = ctypes.create_string_buffer(derlen)
        _ssl.i2d_ECDSA_SIG(norm_sig, ctypes.byref(ctypes.pointer(norm_der)))
        _ssl.ECDSA_SIG_free(norm_sig)

        # -1 = error, 0 = bad sig, 1 = good
        return _ssl.ECDSA_verify(0, hash, len(hash), norm_der, derlen, self.k) == 1

    def set_compressed(self, compressed):
        if compressed:
            form = self.POINT_CONVERSION_COMPRESSED
        else:
            form = self.POINT_CONVERSION_UNCOMPRESSED
        _ssl.EC_KEY_set_conv_form(self.k, form)

    def recover(self, sigR, sigS, msg, msglen, recid, check):
        """
        Perform ECDSA key recovery (see SEC1 4.1.6) for curves over (mod p)-fields
        recid selects which key is recovered
        if check is non-zero, additional checks are performed
        """
        i = int(recid / 2)

        r = None
        s = None
        ctx = None
        R = None
        O = None
        Q = None

        assert len(sigR) == 32, len(sigR)
        assert len(sigS) == 32, len(sigS)

        try:
            r = _ssl.BN_bin2bn(bytes(sigR), len(sigR), _ssl.BN_new())
            s = _ssl.BN_bin2bn(bytes(sigS), len(sigS), _ssl.BN_new())

            group = _ssl.EC_KEY_get0_group(self.k)
            ctx = _ssl.BN_CTX_new()
            order = _ssl.BN_CTX_get(ctx)
            ctx = _ssl.BN_CTX_new()

            if not _ssl.EC_GROUP_get_order(group, order, ctx):
                return -2

            x = _ssl.BN_CTX_get(ctx)
            if not _ssl.BN_copy(x, order):
                return -1
            if not _ssl.BN_mul_word(x, i):
                return -1
            if not _ssl.BN_add(x, x, r):
                return -1

            field = _ssl.BN_CTX_get(ctx)
            if not _ssl.EC_GROUP_get_curve_GFp(group, field, None, None, ctx):
                return -2

            if _ssl.BN_cmp(x, field) >= 0:
                return 0

            R = _ssl.EC_POINT_new(group)
            if R is None:
                return -2
            if not _ssl.EC_POINT_set_compressed_coordinates_GFp(group, R, x, recid % 2, ctx):
                return 0

            if check:
                O = _ssl.EC_POINT_new(group)
                if O is None:
                    return -2
                if not _ssl.EC_POINT_mul(group, O, None, R, order, ctx):
                    return -2
                if not _ssl.EC_POINT_is_at_infinity(group, O):
                    return 0

            Q = _ssl.EC_POINT_new(group)
            if Q is None:
                return -2

            n = _ssl.EC_GROUP_get_degree(group)
            e = _ssl.BN_CTX_get(ctx)
            if not _ssl.BN_bin2bn(msg, msglen, e):
                return -1

            if 8 * msglen > n:
                _ssl.BN_rshift(e, e, 8 - (n & 7))

            zero = _ssl.BN_CTX_get(ctx)
            # if not _ssl.BN_zero(zero):
            #     return -1
            if not _ssl.BN_mod_sub(e, zero, e, order, ctx):
                return -1
            rr = _ssl.BN_CTX_get(ctx)
            if not _ssl.BN_mod_inverse(rr, r, order, ctx):
                return -1
            sor = _ssl.BN_CTX_get(ctx)
            if not _ssl.BN_mod_mul(sor, s, rr, order, ctx):
                return -1
            eor = _ssl.BN_CTX_get(ctx)
            if not _ssl.BN_mod_mul(eor, e, rr, order, ctx):
                return -1
            if not _ssl.EC_POINT_mul(group, Q, eor, R, sor, ctx):
                return -2

            if not _ssl.EC_KEY_set_public_key(self.k, Q):
                return -2

            return 1
        finally:
            if r: _ssl.BN_free(r)
            if s: _ssl.BN_free(s)
            if ctx: _ssl.BN_CTX_free(ctx)
            if R: _ssl.EC_POINT_free(R)
            if O: _ssl.EC_POINT_free(O)
            if Q: _ssl.EC_POINT_free(Q) 


def recover_compact(hash, sig):
	"""Recover a public key from a compact signature."""
	if len(sig) != 65:
		raise ValueError("Signature should be 65 characters, not [%d]" % (len(sig), ))

	recid = (_bord(sig[0]) - 27) & 3
	compressed = (_bord(sig[0]) - 27) & 4 != 0

	cec_key = CECKey()
	cec_key.set_compressed(compressed)

	sigR = sig[1:33]
	sigS = sig[33:65]

	result = cec_key.recover(sigR, sigS, hash, len(hash), recid, 0)

	if result < 1:
		return False

	pubkey = cec_key.get_pubkey()

	return pubkey


import time
s = time.time()
print 

for i in range(10):
	hash = hashlib.sha256(hashlib.sha256(msg_magic("hello")).digest()).digest()
	verified = VerifyMessage("1N2XWu5soeppX2qUjvrf81rpdbShKJrjTr", hash, sign)
print verified, time.time()-s