How to use the ecdsa.ellipticcurve.Point function in ecdsa

from struct import pack
from hashlib import sha1, sha256
from util import *
import ecdsa


# Brainpool P-256-r1
_a = 0x7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9
_b = 0x26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6
_p = 0xA9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377
_Gx = 0x8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262
_Gy = 0x547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997
_q = 0xA9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7

curve_brainpoolp256r1 = ecdsa.ellipticcurve.CurveFp( _p, _a, _b)
generator_brainpoolp256r1 = ecdsa.ellipticcurve.Point( curve_brainpoolp256r1, _Gx, _Gy, _q)

# Brainpool P-384-r1
_a = 0x7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F90F8AA5814A503AD4EB04A8C7DD22CE2826
_b = 0x04A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62D57CB4390295DBC9943AB78696FA504C11
_p = 0x8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A71874700133107EC53
_Gx = 0x1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10E8E826E03436D646AAEF87B2E247D4AF1E
_Gy = 0x8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129280E4646217791811142820341263C5315
_q = 0x8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565

curve_brainpoolp384r1 = ecdsa.ellipticcurve.CurveFp( _p, _a, _b)
generator_brainpoolp384r1 = ecdsa.ellipticcurve.Point( curve_brainpoolp384r1, _Gx, _Gy, _q)

# Brainpool P-512-r1
_a = 0x7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA
_b = 0x3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723
_p = 0xAADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3

elif _is_ecdsa(rrsig.algorithm):
            if rrsig.algorithm == ECDSAP256SHA256:
                curve = ecdsa.curves.NIST256p
                key_len = 32
            elif rrsig.algorithm == ECDSAP384SHA384:
                curve = ecdsa.curves.NIST384p
                key_len = 48
            else:
                # shouldn't happen
                raise ValidationFailure('unknown ECDSA curve')
            keyptr = candidate_key.key
            x = ecdsa.util.string_to_number(keyptr[0:key_len])
            y = ecdsa.util.string_to_number(keyptr[key_len:key_len * 2])
            assert ecdsa.ecdsa.point_is_valid(curve.generator, x, y)
            point = ecdsa.ellipticcurve.Point(curve.curve, x, y, curve.order)
            verifying_key = ecdsa.keys.VerifyingKey.from_public_point(point, curve)
            r = rrsig.signature[:key_len]
            s = rrsig.signature[key_len:]
            sig = ecdsa.ecdsa.Signature(ecdsa.util.string_to_number(r),
                                        ecdsa.util.string_to_number(s))

        else:
            raise ValidationFailure('unknown algorithm %u' % rrsig.algorithm)

        hash.update(_to_rdata(rrsig, origin)[:18])
        hash.update(rrsig.signer.to_digestable(origin))

        if rrsig.labels < len(rrname) - 1:
            suffix = rrname.split(rrsig.labels + 1)[1]
            rrname = dns.name.from_text('*', suffix)
        rrnamebuf = rrname.to_digestable(origin)

# use ecdsa for NIST-384p -- not currently supported by pycryptodome

            keyptr = candidate_key.key

            if rrsig.algorithm == ECDSAP256SHA256:
                curve = ecdsa.curves.NIST256p
                key_len = 32
            elif rrsig.algorithm == ECDSAP384SHA384:
                curve = ecdsa.curves.NIST384p
                key_len = 48

            x = number.bytes_to_long(keyptr[0:key_len])
            y = number.bytes_to_long(keyptr[key_len:key_len * 2])
            if not ecdsa.ecdsa.point_is_valid(curve.generator, x, y):
                raise ValidationFailure('invalid ECDSA key')
            point = ecdsa.ellipticcurve.Point(curve.curve, x, y, curve.order)
            verifying_key = ecdsa.keys.VerifyingKey.from_public_point(point,
                                                                      curve)
            pubkey = ECKeyWrapper(verifying_key, key_len)
            r = rrsig.signature[:key_len]
            s = rrsig.signature[key_len:]
            sig = ecdsa.ecdsa.Signature(number.bytes_to_long(r),
                                        number.bytes_to_long(s))

        else:
            raise ValidationFailure('unknown algorithm %u' % rrsig.algorithm)

        hash.update(_to_rdata(rrsig, origin)[:18])
        hash.update(rrsig.signer.to_digestable(origin))

        if rrsig.labels < len(rrname) - 1:
            suffix = rrname.split(rrsig.labels + 1)[1]

if rrsig.algorithm == ECDSAP256SHA256:
                curve = ecdsa.curves.NIST256p
                key_len = 32
                digest_len = 32
            elif rrsig.algorithm == ECDSAP384SHA384:
                curve = ecdsa.curves.NIST384p
                key_len = 48
                digest_len = 48
            else:
                # shouldn't happen
                raise ValidationFailure('unknown ECDSA curve')
            keyptr = candidate_key.key
            x = ecdsa.util.string_to_number(keyptr[0:key_len])
            y = ecdsa.util.string_to_number(keyptr[key_len:key_len * 2])
            assert ecdsa.ecdsa.point_is_valid(curve.generator, x, y)
            point = ecdsa.ellipticcurve.Point(curve.curve, x, y, curve.order)
            verifying_key = ecdsa.keys.VerifyingKey.from_public_point(point, curve)
            r = rrsig.signature[:key_len]
            s = rrsig.signature[key_len:]
            sig = ecdsa.ecdsa.Signature(ecdsa.util.string_to_number(r),
                                        ecdsa.util.string_to_number(s))

        else:
            raise ValidationFailure('unknown algorithm %u' % rrsig.algorithm)

        hash.update(_to_rdata(rrsig, origin)[:18])
        hash.update(rrsig.signer.to_digestable(origin))

        if rrsig.labels < len(rrname) - 1:
            suffix = rrname.split(rrsig.labels + 1)[1]
            rrname = dns.name.from_text('*', suffix)
        rrnamebuf = rrname.to_digestable(origin)

def ser_to_point(Aser):
    curve = curve_secp256k1
    generator = generator_secp256k1
    _r  = generator.order()
    assert Aser[0] in [0x02, 0x03, 0x04]
    if Aser[0] == 0x04:
        return Point( curve, string_to_number(Aser[1:33]), string_to_number(Aser[33:]), _r )
    Mx = string_to_number(Aser[1:])
    return Point( curve, Mx, ECC_YfromX(Mx, curve, Aser[0] == 0x03)[0], _r )

import time

import jsonical
import json
import custom_exceptions

if ecdsa:
    # secp256k1, http://www.oid-info.com/get/1.3.132.0.10
    _p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2FL
    _r = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141L
    _b = 0x0000000000000000000000000000000000000000000000000000000000000007L
    _a = 0x0000000000000000000000000000000000000000000000000000000000000000L
    _Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798L
    _Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8L
    curve_secp256k1 = ecdsa.ellipticcurve.CurveFp(_p, _a, _b)
    generator_secp256k1 = ecdsa.ellipticcurve.Point(curve_secp256k1, _Gx, _Gy, _r)
    oid_secp256k1 = (1,3,132,0,10)
    SECP256k1 = ecdsa.curves.Curve("SECP256k1", curve_secp256k1, generator_secp256k1, oid_secp256k1 )
    
    # Register SECP256k1 to ecdsa library
    curves.curves.append(SECP256k1)

def generate_keypair():
    if not ecdsa:
        raise custom_exceptions.SigningNotAvailableException("ecdsa not installed")
    
    private_key = ecdsa.SigningKey.generate(curve=SECP256k1)
    public_key = private_key.get_verifying_key()
    return (private_key, public_key)
    
def load_privkey_pem(filename):
    return ecdsa.SigningKey.from_pem(open(filename, 'r').read().strip())

def test_double( c, x1, y1, x3, y3 ):
        """We expect that on curve c, 2*(x1,y1) = (x3, y3)."""
        p1 = Point( c, x1, y1 )
        p3 = p1.double()
        print "%s doubled = %s" % ( p1, p3 ),
        if p3.x() != x3 or p3.y() != y3:
            raise FailedTest("Failure: should give (%d,%d)." % ( x3, y3 ))
        else:
            print " Good."

def test_add( c, x1, y1, x2,  y2, x3, y3 ):
        """We expect that on curve c, (x1,y1) + (x2, y2 ) = (x3, y3)."""
        p1 = Point( c, x1, y1 )
        p2 = Point( c, x2, y2 )
        p3 = p1 + p2
        print "%s + %s = %s" % ( p1, p2, p3 ),
        if p3.x() != x3 or p3.y() != y3:
            raise FailedTest("Failure: should give (%d,%d)." % ( x3, y3 ))
        else:
            print " Good."

raise ValueError('pubkey must be 33 bytes')
        if pubkey[0] not in (2, 3):
            raise ValueError('invalid pubkey prefix byte')
        curve = cls.CURVE.curve

        is_odd = pubkey[0] == 3
        x = bytes_to_int(pubkey[1:])

        # p is the finite field order
        a, b, p = curve.a(), curve.b(), curve.p()
        y2 = pow(x, 3, p) + b
        assert a == 0  # Otherwise y2 += a * pow(x, 2, p)
        y = NT.square_root_mod_prime(y2 % p, p)
        if bool(y & 1) != is_odd:
            y = p - y
        point = EC.Point(curve, x, y)

        return ecdsa.VerifyingKey.from_public_point(point, curve=cls.CURVE)

raise BaseException("Bad encoding")
        if nV >= 31:
            compressed = True
            nV -= 4
        else:
            compressed = False

        recid = nV - 27
        # 1.1
        x = r + (recid/2) * order
        # 1.3
        alpha = ( x * x * x  + curve.a() * x + curve.b() ) % curve.p()
        beta = msqr.modular_sqrt(alpha, curve.p())
        y = beta if (beta - recid) % 2 == 0 else curve.p() - beta
        # 1.4 the constructor checks that nR is at infinity
        R = ellipticcurve.Point(curve, x, y, order)
        # 1.5 compute e from message:
        h = Hash( self.msg_magic( message ) )
        e = string_to_number(h)
        minus_e = -e % order
        # 1.6 compute Q = r^-1 (sR - eG)
        inv_r = numbertheory.inverse_mod(r,order)
        Q = inv_r * ( s * R + minus_e * G )
        public_key = ecdsa.VerifyingKey.from_public_point( Q, curve = SECP256k1 )
        # check that Q is the public key
        public_key.verify_digest( sig[1:], h, sigdecode = ecdsa.util.sigdecode_string)
        # check that we get the original signing address
        addr = public_key_to_bc_address( encode_point(public_key, compressed) )
        if address != addr:
            raise BaseException("Bad signature")