def reenc_return_r(self):
"""
Reencryption with fresh randomness, which is returned.
"""
r = random.mpz_lt(self.pk.q)
new_c = self.reenc_with_r(r)
return [new_c, r]
def prove_decryption(self, ciphertext):
"""
given g, y, alpha, beta/(encoded m), prove equality of discrete log
with Chaum Pedersen, and that discrete log is x, the secret key.
Prover sends a=g^w, b=alpha^w for random w
Challenge c = sha1(a,b) with and b in decimal form
Prover sends t = w + xc
Verifier will check that g^t = a * y^c
and alpha^t = b * beta/m ^ c
"""
m = (inverse(pow(ciphertext.alpha, self.x, self.pk.p), self.pk.p) *
ciphertext.beta) % self.pk.p
beta_over_m = (ciphertext.beta * inverse(m, self.pk.p)) % self.pk.p
# pick a random w
w = random.mpz_lt(self.pk.q)
a = pow(self.pk.g, w, self.pk.p)
b = pow(ciphertext.alpha, w, self.pk.p)
c = int(
SHA1.new(bytes(str(a) + "," + str(b), 'utf-8')).hexdigest(), 16)
t = (w + self.x * c) % self.pk.q
return m, {
'commitment': {
'A': str(a),
'B': str(b)
},
'challenge': str(c),
'response': str(t)
}
def encrypt_return_r(self, plaintext):
"""
Encrypt a plaintext and return the randomness just generated and used.
"""
r = random.mpz_lt(self.q)
ciphertext = self.encrypt_with_r(plaintext, r)
return [ciphertext, r]
def generate(self, p, q, g):
"""
Generate an ElGamal keypair
"""
self.pk.g = g
self.pk.p = p
self.pk.q = q
self.sk.x = random.mpz_lt(q)
self.pk.y = pow(g, self.sk.x, p)
self.sk.public_key = self.pk
def prove_sk(self, challenge_generator):
"""
Generate a PoK of the secret key
Prover generates w, a random integer modulo q, and computes commitment = g^w mod p.
Verifier provides challenge modulo q.
Prover computes response = w + x*challenge mod q, where x is the secret key.
"""
w = random.mpz_lt(self.pk.q)
commitment = pow(self.pk.g, w, self.pk.p)
challenge = challenge_generator(commitment) % self.pk.q
response = (w + (self.x * challenge)) % self.pk.q
return DLogProof(commitment, challenge, response)
def simulate_encryption_proof(self, plaintext, challenge=None):
# generate a random challenge if not provided
if not challenge:
challenge = random.mpz_lt(self.pk.q)
proof = ZKProof()
proof.challenge = challenge
# compute beta/plaintext, the completion of the DH tuple
beta_over_plaintext = (self.beta *
inverse(plaintext.m, self.pk.p)) % self.pk.p
# random response, does not even need to depend on the challenge
proof.response = random.mpz_lt(self.pk.q)
# now we compute A and B
proof.commitment['A'] = (
inverse(pow(self.alpha, proof.challenge, self.pk.p), self.pk.p) *
pow(self.pk.g, proof.response, self.pk.p)) % self.pk.p
proof.commitment['B'] = (inverse(
pow(beta_over_plaintext, proof.challenge, self.pk.p),
self.pk.p) * pow(self.pk.y, proof.response, self.pk.p)) % self.pk.p
return proof
def generate_encryption_proof(self, plaintext, randomness,
challenge_generator):
"""
Generate the disjunctive encryption proof of encryption
"""
# random W
w = random.mpz_lt(self.pk.q)
# build the proof
proof = ZKProof()
# compute A=g^w, B=y^w
proof.commitment['A'] = pow(self.pk.g, w, self.pk.p)
proof.commitment['B'] = pow(self.pk.y, w, self.pk.p)
# generate challenge
proof.challenge = challenge_generator(proof.commitment)
# Compute response = w + randomness * challenge
proof.response = (w + (randomness * proof.challenge)) % self.pk.q
return proof
def generate(cls, little_g, little_h, x, p, q, challenge_generator):
"""
generate a DDH tuple proof, where challenge generator is
almost certainly EG_fiatshamir_challenge_generator
"""
# generate random w
w = random.mpz_lt(q)
# create proof instance
proof = cls()
# compute A = little_g^w, B=little_h^w
proof.commitment['A'] = pow(little_g, w, p)
proof.commitment['B'] = pow(little_h, w, p)
# get challenge
proof.challenge = challenge_generator(proof.commitment)
# compute response
proof.response = (w + (x * proof.challenge)) % q
# return proof
return proof