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103 lines
3.3 KiB
Python
103 lines
3.3 KiB
Python
# zkp-dh: Zero-knowledge proof generator and verifier for one party to show
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# to another that their Diffie-Hellman shared secret is correct.
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# See the Camenisch and Stadler paper for procedural specifics on ZKP
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# proof generation, such as knowledge of discrete logarithm.
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# Lining Wang, June 2014
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import random
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import hashlib
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import binascii
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import sys
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# DiffieHellman class enables construction of keys capable of performing
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# D-H exchanges, and interactive proof of knowledge
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class DiffieHellman:
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P = 101
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G = 51
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def __init__(self,secret=0):
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if (secret==0):
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self.secret = random.randrange(1 << (self.G.bit_length() - 1), self.G - 1)
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else:
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self.secret = secret
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self.public = pow(self.G, self.secret, self.P)
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# get shared secret: (g^b)^a mod p
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def get_shared_secret(self, remote_pub):
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return pow(remote_pub, self.secret, self.P)
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# Given the public key of B (remote_pub), shows that the shared secret
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# between A and B was generated by A.
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# Returns zero-knowledge proof of shared Diffie-Hellman secret between A & B.
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def prove_shared_secret(self, remote_pub):
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G = self.G; prover_pub = self.public; phi = self. P - 1;
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secret = self.get_shared_secret(remote_pub)
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# Random key in the group Z_q
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randKey = DiffieHellman() # random secret
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commit1 = randKey.public
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commit2 = randKey.get_shared_secret(remote_pub)
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# shift and hash
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concat = str(G) + str(prover_pub) + str(remote_pub) + str(secret) + str(commit1) + str(commit2)
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h = hashlib.md5()
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h.update(concat.encode("utf-8"))
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challenge = int(h.hexdigest(), 16)
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product = (self.secret * challenge) % phi
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response = (randKey.secret - product) % phi
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return (secret, challenge, response)
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# Verifies proof generated above. Verifier c is showing that
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# shared secret between A and B was generated by A.
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# returns 0 if if verification fails; returns shared secret otherwise
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def verify_shared_secret(self, prover_pub, remote_pub, secret, challenge,
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response):
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P = self.P; G = self.G ; public = self.public
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# g^r * (a's public key)^challenge
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commit1 = (pow(G, response, P) * pow(public, challenge, P)) % P
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# (b's public key)^response * (secret)^challenge
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commit2 = (pow(remote_pub, response, P) * pow(secret, challenge, P)) % P
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# Shift and hash
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hasher = hashlib.md5()
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concat = str(G) + str(prover_pub) + str(remote_pub) + str(secret) + str(commit1) + str(commit2)
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hasher.update(concat.encode("utf-8"))
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check = int(hasher.hexdigest(), 16)
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if challenge == check:
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return secret
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else:
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return 0
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x=3
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y=4
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a = DiffieHellman(x)
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b = DiffieHellman(y)
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print("G=",a.G)
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print("p=",a.P)
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print("x=",x)
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print("y=",y)
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print("\n============")
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print("a (pub,sec)=",a.public,a.secret)
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print("b (pub,sec)=",b.public,b.secret)
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shared=a.get_shared_secret(b.public)
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print("Shared=",shared)
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print("\nNow Bob will generate the secret, a challenge and a response")
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results = a.prove_shared_secret(b.public)
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print("(secret, challenge, response):",results)
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val=a.verify_shared_secret(a.public, b.public, results[0], results[1], results[2])
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print("\nAlice now checks")
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if (val==shared):
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print("Bob has proven he knows x")
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else:
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print("Bob has not proven that he knows x")
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