def keygen(self, secparam):
while True:
p, q = randomPrime(secparam), randomPrime(secparam)
print("p,q=>", p, q)
if isPrime(p) and isPrime(q) and p != q:
N = p * q
phi_N = N - p - q + 1
break
pk = {'secparam': secparam, 'N': N, 'phi_N': phi_N}
sk = {'p': p, 'q': q}
return (pk, sk)
def keygen(self, secparam=1024):
while True:
p, q = randomPrime(secparam), randomPrime(secparam)
if isPrime(p) and isPrime(q) and gcd(p * q, (p - 1) * (q - 1)) == 1:
break
n = p * q
g = n + 1
n2 = n ** 2
lam = lcm(p - 1, q - 1)
u = (self.L(((g % n2) ** lam), n) % n) ** -1
pk = {'n': n, 'g': g, 'n2': n2}
sk = {'lam': lam, 'u': u}
return pk, sk
def keygen(self, secparam=1024):
while True:
p, q = randomPrime(secparam), randomPrime(secparam)
if isPrime(p) and isPrime(q) and gcd(p * q,
(p - 1) * (q - 1)) == 1:
break
n = p * q
g = n + 1
n2 = n**2
lam = lcm(p - 1, q - 1)
u = (self.L(((g % n2)**lam), n) % n)**-1
pk = {'n': n, 'g': g, 'n2': n2}
sk = {'lam': lam, 'u': u}
return pk, sk
def hash(self, pk, sk, message, r=0):
# generate ephemeral trapdoors(p1,q1)
while True:
p1, q1 = randomPrime(pk['secparam']), randomPrime(pk['secparam'])
# print("p1,q1=>",p1,q1)
if isPrime(p1) and isPrime(q1) and p1 != q1:
N1 = p1 * q1
if not gcd(N1, pk['N']) == 1:
continue
break
if r == 0:
r = random(N1 * pk['N'])
# print("r=>",r)
# print("(p1,q1,N1)=>", (p1,q1,N1))
# print("N*N1=>",N1 * pk['N'])
phi_NN1 = pk['phi_N'] * (N1 - p1 - q1 + 1)
# print("phi_NN1=>", phi_NN1)
# find e inverse mod N1 * N, so gcd(e,phi_NN1)==1
while True:
e = random(phi_NN1)
if not gcd(e, phi_NN1) == 1:
continue
break
M = Conversion.bytes2integer(message)
# print("M =>",M)
# to set hash modular N * N1()
group.q = N1 * pk['N']
group.p = group.q * 2 + 1
# print("q=>",group.q)
# print("M hash=>", group.hash(M))
h = (group.hash(M) * (r**e)) % (N1 * pk['N'])
xi = {'h': h, 'r': r, 'N1': N1, 'p1': p1, 'q1': q1, 'e': e}
# print("e=>",xi['e'])
return xi