def verify_knowledge_exponent(u, w, z, Q, r, n):
g = pow(65537, hash_to_length(concat(u, w)), n)
l, nonce = hash_to_prime(concat(u, w, z))
alpha = hash_to_length(concat(u, w, z, l))
# print((pow(Q, l, n) * pow(u*pow(g,alpha,n), r, n)) % n)
# print((w * pow(z, alpha, n)) % n )
return (pow(Q, l, n) * pow(u*pow(g,alpha,n), r, n)) % n == (w * pow(z, alpha, n)) % n
def prove_knowledge_exponent(x, u, w, n):
g = pow(65537, hash_to_length(concat(u, w)), n)
z = pow(g, x, n)
l, nonce = hash_to_prime(concat(u, w, z)) # Fiat-Shamir instead of interactive challenge
alpha = hash_to_length(concat(u, w, z, l))
q = x // l
r = x % l
Q = pow(u*pow(g,alpha,n), q, n)
return z, Q, r
def __verify_exponentiation_test(Q, u, x, w, n):
# start_time = datetime.datetime.now()
l = hash_to_prime(x=(concat(x, u, w)))[0]
# end_time = datetime.datetime.now()
# print((end_time - start_time))
# start_time = datetime.datetime.now()
r = x % l
# end_time = datetime.datetime.now()
# print((end_time - start_time))
# check (Q^l)(u^r) == w
return pow(Q, l, n) * pow(u, r, n) % n == w
def prove_exponentiation_test(u, x, w, n):
l, nonce = hash_to_prime(concat(x, u, w)) # Fiat-Shamir instead of interactive challenge
q = x // l
Q = pow(u, q, n)
return Q
def __verify_exponentiation(Q, l_nonce, u, x, w, n):
l = hash_to_prime(x=(concat(x, u, w)), nonce=l_nonce)[0]
r = x % l
# check (Q^l)(u^r) == w
return (pow(Q, l, n) % n) * (pow(u, r, n) % n) % n == w