import random
from sympy import isprime

def generate_large_prime(bits=512):
    """Generate a large prime number of specified bit length."""
    p = 1
    while not isprime(p):
        p = random.getrandbits(bits)
    return p

def blum_blum_shub(p, q, seed, length):
    """Blum-Blum-Shub PRNG for generating nonces."""
    n = p * q
    x = seed ** 2 % n
    output_bits = []
    for _ in range(length):
        x = x ** 2 % n
        output_bits.append(x % 2)
    return int(''.join(map(str, output_bits)), 2)

def generate_keys():
    """Generate public and private keys for the Schnorr signature scheme."""
    p = generate_large_prime()
    q = generate_large_prime()
    n = p * q
    g = 0o12341234 # Example
    x = 0o12341234 # Example
    y = pow(g, x, n)                 
    return (p, q, g, n, x, y)

def schnorr_sign(message, p, q, g, n, x):
    """Generate a Schnorr signature for a message."""
    k = blum_blum_shub(p, q, random.randint(2, 2), 256)
    r = pow(g, k, n)
    s = (k - x * hash(message)) % (n-1)
    return (r, s)

def main():
    p, q, g, n, x, y = generate_keys()
    message = "Sign this message!"
    signature1 = schnorr_sign(message, p, q, g, n, x)
    signature2 = schnorr_sign(message, p, q, g, n, x)
    print("Public Key:", y)
    print("Signature 1:", signature1)
    print("Signature 2:", signature2)

if __name__ == "__main__":
    main()