toy ECDSA

gistfile1.txt

# EC, Field are in http://afiodorov.github.io/2019/06/18/elliptic/

from dataclasses import dataclass
from random import randint

@dataclass
class Signature:
    sig: int
    pp: EC.Point
    randomx: int
        
    def __post_init__(self):
        self.sig = Field(o).n(self.sig)
        self.randomx = Field(o).n(self.randomx)
        
def sign(gen_point, secret, msg) -> Signature:
    k = randint(1, o)
    R = k * gen_point
    pp = gen_point * secret
    sig = (Field(o).n(msg) + R.x.a * secret) / k
    return Signature(sig.a, pp, R.x.a)


def verify(gen_point, msg, sig: Signature) -> bool:
    u = msg / sig.sig
    v = sig.randomx / sig.sig
    return (u.a * gen_point + v.a * sig.pp).x.a == sig.randomx.a
    
p = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 - 1
x = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
y = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
o = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141

point = EC(0, 7).point(Field(p).n(x), y)
assert (o * point).zero
assert (o - 1) * point == -point # this implies above

def S256Point(x, y):
    p = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 - 1
    return EC(0, 7).point(Field(p).n(x), y)
    
pp = S256Point(0x04519fac3d910ca7e7138f7013706f619fa8f033e6ec6e09370ea38cee6a7574,
               0x82b51eab8c27c66e26c858a079bcdf4f1ada34cec420cafc7eac1a42216fb6c4)
s = 0x8ca63759c1157ebeaec0d03cecca119fc9a75bf8e6d0fa65c841c8e2738cdaec
randomx = 0x37206a0610995c58074999cb9767b87af4c4978db68c06e8e6e81d282047a7c6
sig = Signature(s, pp, randomx)
msg = 0xbc62d4b80d9e36da29c16c5d4d9f11731f36052c72401a76c23c0fb5a9b74423
verify(point, msg, sig)

verify(point, 10, sign(point, 102301, 10))