49 lines
1.4 KiB
Python
49 lines
1.4 KiB
Python
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import random
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from sympy import isprime
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def generate_large_prime(bits=512):
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"""Generate a large prime number of specified bit length."""
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p = 1
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while not isprime(p):
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p = random.getrandbits(bits)
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return p
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def blum_blum_shub(p, q, seed, length):
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"""Blum-Blum-Shub PRNG for generating nonces."""
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n = p * q
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x = seed ** 2 % n
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output_bits = []
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for _ in range(length):
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x = x ** 2 % n
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output_bits.append(x % 2)
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return int(''.join(map(str, output_bits)), 2)
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def generate_keys():
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"""Generate public and private keys for the Schnorr signature scheme."""
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p = generate_large_prime()
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q = generate_large_prime()
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n = p * q
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g = 0o12341234 # Example
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x = 0o12341234 # Example
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y = pow(g, x, n)
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return (p, q, g, n, x, y)
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def schnorr_sign(message, p, q, g, n, x):
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"""Generate a Schnorr signature for a message."""
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k = blum_blum_shub(p, q, random.randint(2, 2), 256)
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r = pow(g, k, n)
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s = (k - x * hash(message)) % (n-1)
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return (r, s)
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def main():
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p, q, g, n, x, y = generate_keys()
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message = "Sign this message!"
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signature1 = schnorr_sign(message, p, q, g, n, x)
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signature2 = schnorr_sign(message, p, q, g, n, x)
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print("Public Key:", y)
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print("Signature 1:", signature1)
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print("Signature 2:", signature2)
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if __name__ == "__main__":
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main()
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