ECDH using P-192 prime192v1

ecdh.py

#
# ECDH using P-192 prime192v1
#
# Runs very slow because of binary methods used.
#
import random

# Elliptic curve parameters P-192 prime192v1
p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff

a = 0xfffffffffffffffffffffffffffffffefffffffffffffffc
b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1

Gx = 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012
Gy = 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811
    
def addmod(a, b, m):
    return (a + b) % m

def submod(a, b, m):
    return (a - b) % m

def mulmod(a, b, m):
    r = 0
    a = a % m
    
    while b:
        if b & 1:
            r = addmod(r, a, m)
        a = addmod(a, a, m)
        b = b >> 1
    return r
    
def modexp(b, e, m):
    r = 1
    b = b % m
    
    while e:
        if e & 1:
            r = mulmod(r, b, m)
        b = mulmod(b, b, m)
        e = e >> 1
    return r

def modinv(a, m):
    return modexp(a, m - 2, m)

def ecpadd(P, Q):
    if (Q == (0, 0)):
        return P
    if (P == (0, 0)):
        return Q
        
    px, py = P
    qx, qy = Q
    
    if P != Q:
        t1 = submod(py, qy, p)
        t2 = submod(px, qx, p)
    else:
        t1 = mulmod(qx, qx, p)
        t1 = mulmod(3, t1, p)
        t1 = addmod(t1, a, p)
        t2 = addmod(qy, qy, p)
        
    t2 = modinv(t2, p)
    s = mulmod(t1, t2, p)
    t1 = mulmod(s, s, p)
    t2 = addmod(qx, px, p)
    rx = submod(t1, t2, p)

    t1 = submod(qx, rx, p)
    t1 = mulmod(s, t1, p)
    ry = submod(t1, qy, p)

    return (rx, ry)
    
def ecpmul(P, n):
    Q = (0, 0)
    for i in range(n.bit_length()):
        if (n >> i) & 1:
            Q = ecpadd(Q, P)
        P = ecpadd(P, P)
    return Q

def test():
    print(f"Running test...")
    
    sk  = 0xf17d3fea367b74d340851ca4270dcb24c271f445bed9d527
    pk_x = 0x42ea6dd9969dd2a61fea1aac7f8e98edcc896c6e55857cc0
    pk_y = 0xdfbe5d7c61fac88b11811bde328e8a0d12bf01a9d204b523
    secret = 0x803d8ab2e5b6e6fca715737c3a82f7ce3c783124f6d51cd0
    
    skey = ecpmul((pk_x, pk_y), sk)
    
    assert skey[0] == secret
    print(f"Passed.")
    
def main():
    #test()
    
    # Generate a private key from random numbers
    A_sk = random.randint(1, p-1)
    B_sk = random.randint(1, p-1)

    print(f"Private Key for Alice : {A_sk}")
    print(f"Private Key for Bob   : {B_sk}\n")

    # Generate public keys.
    A_pk = ecpmul((Gx, Gy), A_sk)
    B_pk = ecpmul((Gx, Gy), B_sk)

    print(f"Public Key for Alice : {A_pk}")
    print(f"Public Key for Bob   : {B_pk}\n")

    # Generate shared secrets
    A_secret = ecpmul(B_pk, A_sk)
    B_secret = ecpmul(A_pk, B_sk)

    print(f"Session Key for Alice : {A_secret}")
    print(f"Session Key for Bob   : {B_secret}\n")

    # Ensure both shared secrets are the same
    assert A_secret == B_secret

    print("Shared secret:", A_secret[0])

if __name__ == "__main__":
    main()