Python ecdsa.numbertheory.square_root_mod_prime() Examples

def __uncompress_public_key(public_key: bytes) -> bytes:
        """
        Uncompress the compressed public key.
        :param public_key: compressed public key
        :return: uncompressed public key
        """
        is_even = public_key.startswith(b'\x02')
        x = string_to_number(public_key[1:])

        curve = NIST256p.curve
        order = NIST256p.order
        p = curve.p()
        alpha = (pow(x, 3, p) + (curve.a() * x) + curve.b()) % p
        beta = square_root_mod_prime(alpha, p)
        if is_even == bool(beta & 1):
            y = p - beta
        else:
            y = beta
        point = Point(curve, x, y, order)
        return b''.join([number_to_string(point.x(), order), number_to_string(point.y(), order)]) 

def from_bytes(cls, data: bytes):
        """ Generates either a HDPublicKey from the underlying bytes.

        The serialization must conform to the description in:
        https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki#serialization-format
        """
        if len(data) < 78:
            raise ValueError("b must be at least 78 bytes long.")

        version = int.from_bytes(data[:4], 'big')
        depth = data[4]
        parent_fingerprint = data[5:9]
        index = int.from_bytes(data[9:13], 'big')
        chain_code = data[13:45]
        key_bytes = data[45:78]

        if version != HDPublicKey.__VERSION:
            raise ValueError('invalid HD Public Key.')

        if key_bytes[0] != 0x02 and key_bytes[0] != 0x03:
            raise ValueError("First byte of public key must be 0x02 or 0x03!")

        # The curve of points satisfying y^2 = x^3 + a*x + b (mod p).
        curve = ecdsa.curve_256
        x = util.string_to_number(key_bytes[1:])
        y = (x * x * x + curve.a() * x + curve.b()) % curve.p()
        y = numbertheory.square_root_mod_prime(y, curve.p())
        if (key_bytes[0] == 0x03 and y % 2 == 0) or (key_bytes[0] == 0x02 and y % 2 != 0):
            y = (y * -1) % curve.p()
        order = curves.NIST256p.order
        s_key = util.number_to_string(x, order) + util.number_to_string(y, order)

        public_key = VerifyingKey.from_string(string=s_key, curve=curves.NIST256p)
        rv = cls(
            public_key=public_key,
            chain_code=chain_code,
            index=index,
            depth=depth,
            parent_fingerprint=parent_fingerprint)
        return rv 

def from_hex_key(cls, key, network=BitcoinMainNet):
        """Load the PublicKey from a compressed or uncompressed hex key.

        This format is defined in PublicKey.get_key()
        """
        if len(key) == 130 or len(key) == 66:
            # It might be a hexlified byte array
            try:
                key = unhexlify(key)
            except TypeError:
                pass
        key = ensure_bytes(key)

        compressed = False
        id_byte = key[0]
        if not isinstance(id_byte, six.integer_types):
            id_byte = ord(id_byte)
        if id_byte == 4:
            # Uncompressed public point
            # 1B ID + 32B x coord + 32B y coord = 65 B
            if len(key) != 65:
                raise KeyParseError("Invalid key length")
            public_pair = PublicPair(
                long_or_int(hexlify(key[1:33]), 16),
                long_or_int(hexlify(key[33:]), 16))
        elif id_byte in [2, 3]:
            # Compressed public point!
            compressed = True
            if len(key) != 33:
                raise KeyParseError("Invalid key length")
            y_odd = bool(id_byte & 0x01)  # 0 even, 1 odd
            x = long_or_int(hexlify(key[1:]), 16)
            # The following x-to-pair algorithm was lifted from pycoin
            # I still need to sit down an understand it. It is also described
            # in http://www.secg.org/collateral/sec1_final.pdf
            curve = SECP256k1.curve
            p = curve.p()
            # For SECP256k1, curve.a() is 0 and curve.b() is 7, so this is
            # effectively (x ** 3 + 7) % p, but the full equation is kept
            # for just-in-case-the-curve-is-broken future-proofing
            alpha = (pow(x, 3, p) + curve.a() * x + curve.b()) % p
            beta = square_root_mod_prime(alpha, p)
            y_even = not y_odd
            if y_even == bool(beta & 1):
                public_pair = PublicPair(x, p - beta)
            else:
                public_pair = PublicPair(x, beta)
        else:
            raise KeyParseError("The given key is not in a known format.")
        return cls.from_public_pair(public_pair, network=network,
                                    compressed=compressed) 

def from_hex_key(cls, key, network=BitcoinMainNet):
        """Load the PublicKey from a compressed or uncompressed hex key.

        This format is defined in PublicKey.get_key()
        """
        if len(key) == 130 or len(key) == 66:
            # It might be a hexlified byte array
            try:
                key = unhexlify(ensure_bytes(key))
            except (TypeError, binascii.Error):
                pass
        key = ensure_bytes(key)

        compressed = False
        id_byte = key[0]
        if not isinstance(id_byte, six.integer_types):
            id_byte = ord(id_byte)
        if id_byte == 4:
            # Uncompressed public point
            # 1B ID + 32B x coord + 32B y coord = 65 B
            if len(key) != 65:
                raise KeyParseError("Invalid key length")
            public_pair = PublicPair(
                long_or_int(hexlify(key[1:33]), 16),
                long_or_int(hexlify(key[33:]), 16))
        elif id_byte in [2, 3]:
            # Compressed public point!
            compressed = True
            if len(key) != 33:
                raise KeyParseError("Invalid key length")
            y_odd = bool(id_byte & 0x01)  # 0 even, 1 odd
            x = long_or_int(hexlify(key[1:]), 16)
            # The following x-to-pair algorithm was lifted from pycoin
            # I still need to sit down an understand it. It is also described
            # in http://www.secg.org/collateral/sec1_final.pdf
            curve = SECP256k1.curve
            p = curve.p()
            # For SECP256k1, curve.a() is 0 and curve.b() is 7, so this is
            # effectively (x ** 3 + 7) % p, but the full equation is kept
            # for just-in-case-the-curve-is-broken future-proofing
            alpha = (pow(x, 3, p) + curve.a() * x + curve.b()) % p
            beta = square_root_mod_prime(alpha, p)
            y_even = not y_odd
            if y_even == bool(beta & 1):
                public_pair = PublicPair(x, p - beta)
            else:
                public_pair = PublicPair(x, beta)
        else:
            raise KeyParseError("The given key is not in a known format.")
        return cls.from_public_pair(public_pair, network=network,
                                    compressed=compressed) 

def from_hex_key(cls, key, network=BitcoinMainNet):
        """Load the PublicKey from a compressed or uncompressed hex key.

        This format is defined in PublicKey.get_key()
        """
        if len(key) == 130 or len(key) == 66:
            # It might be a hexlified byte array
            try:
                key = unhexlify(key)
            except TypeError:
                pass
        key = ensure_bytes(key)

        compressed = False
        id_byte = key[0]
        if not isinstance(id_byte, six.integer_types):
            id_byte = ord(id_byte)
        if id_byte == 4:
            # Uncompressed public point
            # 1B ID + 32B x coord + 32B y coord = 65 B
            if len(key) != 65:
                raise KeyParseError("Invalid key length")
            public_pair = PublicPair(
                long_or_int(hexlify(key[1:33]), 16),
                long_or_int(hexlify(key[33:]), 16))
        elif id_byte in [2, 3]:
            # Compressed public point!
            compressed = True
            if len(key) != 33:
                raise KeyParseError("Invalid key length")
            y_odd = bool(id_byte & 0x01)  # 0 even, 1 odd
            x = long_or_int(hexlify(key[1:]), 16)
            # The following x-to-pair algorithm was lifted from pycoin
            # I still need to sit down an understand it. It is also described
            # in http://www.secg.org/collateral/sec1_final.pdf
            curve = SECP256k1.curve
            p = curve.p()
            # For SECP256k1, curve.a() is 0 and curve.b() is 7, so this is
            # effectively (x ** 3 + 7) % p, but the full equation is kept
            # for just-in-case-the-curve-is-broken future-proofing
            alpha = (pow(x, 3, p) + curve.a() * x + curve.b()) % p
            beta = square_root_mod_prime(alpha, p)
            y_even = not y_odd
            if y_even == bool(beta & 1):
                public_pair = PublicPair(x, p - beta)
            else:
                public_pair = PublicPair(x, beta)
        else:
            raise KeyParseError("The given key is not in a known format.")
        return cls.from_public_pair(public_pair, network=network,
                                    compressed=compressed) 

def fromExtendedKey(xkey, public=False):
        """
        Create a BIP32Key by importing from extended private or public key string

        If public is True, return a public-only key regardless of input type.
        """
        # Sanity checks
        raw = Base58.check_decode(xkey)
        if len(raw) != 78:
            raise ValueError("extended key format wrong length")

        # Verify address version/type
        version = raw[:4]
        if version == EX_MAIN_PRIVATE:
            keytype = 'xprv'
        elif version == EX_MAIN_PUBLIC:
            keytype = 'xpub'
        else:
            raise ValueError("unknown extended key version")

        # Extract remaining fields
        depth = ord(raw[4])
        fpr = raw[5:9]
        child = struct.unpack(">L", raw[9:13])[0]
        chain = raw[13:45]
        secret = raw[45:78]

        # Extract private key or public key point
        if keytype == 'xprv':
            secret = secret[1:]
        else:
            # Recover public curve point from compressed key
            lsb = ord(secret[0]) & 1
            x = string_to_int(secret[1:])
            ys = (x**3+7) % FIELD_ORDER # y^2 = x^3 + 7 mod p
            y = sqrt_mod(ys, FIELD_ORDER)
            if y & 1 != lsb:
                y = FIELD_ORDER-y
            point = ecdsa.ellipticcurve.Point(SECP256k1.curve, x, y)
            secret = ecdsa.VerifyingKey.from_public_point(point, curve=SECP256k1)

        is_pubkey = (keytype == 'xpub')
        key = BIP32Key(secret=secret, chain=chain, depth=depth, index=child, fpr=fpr, public=is_pubkey)
        if not is_pubkey and public:
            key = key.SetPublic()
        return key


    # Normal class initializer