How to use ecdsa - 10 common examples

def _recover_key(self, digest, signature, i) :
        ''' Recover the public key from the sig
            http://www.secg.org/sec1-v2.pdf
        '''
        curve = ecdsa.SECP256k1.curve
        G = ecdsa.SECP256k1.generator
        order = ecdsa.SECP256k1.order
        yp = (i %2)
        r, s = ecdsa.util.sigdecode_string(signature, order)
        x = r + (i // 2 ) * order
        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
        # generate R
        R = ecdsa.ellipticcurve.Point(curve, x, y, order)
        e = ecdsa.util.string_to_number(digest)
        # compute Q
        Q = ecdsa.numbertheory.inverse_mod(r, order) * (s * R + (-e % order) * G)
        # verify message
        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)

curve = ecdsa.SECP256k1.curve
        G = ecdsa.SECP256k1.generator
        order = ecdsa.SECP256k1.order
        yp = (i %2)
        r, s = ecdsa.util.sigdecode_string(signature, order)
        x = r + (i // 2 ) * order
        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
        # generate R
        R = ecdsa.ellipticcurve.Point(curve, x, y, order)
        e = ecdsa.util.string_to_number(digest)
        # compute Q
        Q = ecdsa.numbertheory.inverse_mod(r, order) * (s * R + (-e % order) * G)
        # verify message
        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)

def recover_public_key(self, digest, signature, i):
        curve = ecdsa.SECP256k1.curve
        G = ecdsa.SECP256k1.generator
        order = ecdsa.SECP256k1.order
        yp = (i % 2)
        r, s = ecdsa.util.sigdecode_string(signature, order)
        x = r + (i // 2) * order
        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
        R = ecdsa.ellipticcurve.Point(curve, x, y, order)
        e = ecdsa.util.string_to_number(digest)
        Q = ecdsa.numbertheory.inverse_mod(r, order) * (s * R +
                                                        (-e % order) * G)
        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)

def recover_public_key(digest, signature, i, message=None):
    """ 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)

    if SECP256K1_MODULE == "cryptography" and message is not None:
        if not isinstance(message, bytes):

def _recover_key(self, digest, signature, i) :
        ''' Recover the public key from the sig
            http://www.secg.org/sec1-v2.pdf
        '''
        curve = ecdsa.SECP256k1.curve
        G = ecdsa.SECP256k1.generator
        order = ecdsa.SECP256k1.order
        yp = (i %2)
        r, s = ecdsa.util.sigdecode_string(signature, order)
        x = r + (i // 2 ) * order
        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
        # generate R
        R = ecdsa.ellipticcurve.Point(curve, x, y, order)
        e = ecdsa.util.string_to_number(digest)
        # compute Q
        Q = ecdsa.numbertheory.inverse_mod(r, order) * (s * R + (-e % order) * G)
        # verify message
        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)

recid = meta - 27

    j = recid // 2
    yp = 0 if (recid % 2) == 0 else 1

    ecdsa_signature = signature_bytes[1:]

    r, s = ecdsa.util.sigdecode_string(ecdsa_signature, order)
    
    # 1.1
    x = r + j * 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())
    if (beta - yp) % 2 == 0:
        y = beta
    else:
        y = 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
    h = double_sha256(format_message_for_signing(message))
    e = ecdsa.util.string_to_number(h)

    # 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.

def get_rpc_credentials(config: SimpleConfig) -> Tuple[str, str]:
    rpc_user = config.get('rpcuser', None)
    rpc_password = config.get('rpcpassword', None)
    if rpc_user is None or rpc_password is None:
        rpc_user = 'user'
        import ecdsa, base64
        bits = 128
        nbytes = bits // 8 + (bits % 8 > 0)
        pw_int = ecdsa.util.randrange(pow(2, bits))
        pw_b64 = base64.b64encode(
            pw_int.to_bytes(nbytes, 'big'), b'-_')
        rpc_password = to_string(pw_b64, 'ascii')
        config.set_key('rpcuser', rpc_user)
        config.set_key('rpcpassword', rpc_password, save=True)
    elif rpc_password == '':
        _logger.warning('RPC authentication is disabled.')
    return rpc_user, rpc_password

http://www.secg.org/sec1-v2.pdf
        '''
        curve = ecdsa.SECP256k1.curve
        G = ecdsa.SECP256k1.generator
        order = ecdsa.SECP256k1.order
        yp = (i %2)
        r, s = ecdsa.util.sigdecode_string(signature, order)
        x = r + (i // 2 ) * order
        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
        # generate R
        R = ecdsa.ellipticcurve.Point(curve, x, y, order)
        e = ecdsa.util.string_to_number(digest)
        # compute Q
        Q = ecdsa.numbertheory.inverse_mod(r, order) * (s * R + (-e % order) * G)
        # verify message
        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)

http://www.secg.org/sec1-v2.pdf
        '''
        curve = ecdsa.SECP256k1.curve
        G = ecdsa.SECP256k1.generator
        order = ecdsa.SECP256k1.order
        yp = (i %2)
        r, s = ecdsa.util.sigdecode_string(signature, order)
        x = r + (i // 2 ) * order
        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
        # generate R
        R = ecdsa.ellipticcurve.Point(curve, x, y, order)
        e = ecdsa.util.string_to_number(digest)
        # compute Q
        Q = ecdsa.numbertheory.inverse_mod(r, order) * (s * R + (-e % order) * G)
        # verify message
        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)

def recover_public_key(self, digest, signature, i):
        curve = ecdsa.SECP256k1.curve
        G = ecdsa.SECP256k1.generator
        order = ecdsa.SECP256k1.order
        yp = (i % 2)
        r, s = ecdsa.util.sigdecode_string(signature, order)
        x = r + (i // 2) * order
        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
        R = ecdsa.ellipticcurve.Point(curve, x, y, order)
        e = ecdsa.util.string_to_number(digest)
        Q = ecdsa.numbertheory.inverse_mod(r, order) * (s * R +
                                                        (-e % order) * G)
        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)