transactions.py 文件源码

def recover_public_key(self, digest, signature, i):
        """ Recover the public key from the the signature
        """
        # See http: //www.secg.org/download/aid-780/sec1-v2.pdf section 4.1.6 primarily
        curve = ecdsa.SECP256k1.curve
        G = ecdsa.SECP256k1.generator
        order = ecdsa.SECP256k1.order
        yp = (i % 2)
        r, s = ecdsa.util.sigdecode_string(signature, order)
        # 1.1
        x = r + (i // 2) * order
        # 1.3. This actually calculates for either effectively 02||X or 03||X depending on 'k' instead of always for 02||X as specified.
        # This substitutes for the lack of reversing R later on. -R actually is defined to be just flipping the y-coordinate in the elliptic curve.
        alpha = ((x * x * x) + (curve.a() * x) + curve.b()) % curve.p()
        beta = ecdsa.numbertheory.square_root_mod_prime(alpha, curve.p())
        y = beta if (beta - yp) % 2 == 0 else curve.p() - beta
        # 1.4 Constructor of Point is supposed to check if nR is at infinity.
        R = ecdsa.ellipticcurve.Point(curve, x, y, order)
        # 1.5 Compute e
        e = ecdsa.util.string_to_number(digest)
        # 1.6 Compute Q = r^-1(sR - eG)
        Q = ecdsa.numbertheory.inverse_mod(r, order) * (s * R + (-e % order) * G)
        # Not strictly necessary, but let's verify the message for paranoia's sake.
        if not ecdsa.VerifyingKey.from_public_point(Q, curve=ecdsa.SECP256k1).verify_digest(signature, digest,
                                                                                            sigdecode=ecdsa.util.sigdecode_string):
            return None
        return ecdsa.VerifyingKey.from_public_point(Q, curve=ecdsa.SECP256k1)