def decrypt(c, n, g, lamb, miu):
n2 = n * n
if integer.gcd(c, n2) != 1:
print("error")
if c < 1 or c >= n2 or integer.gcd(c, n2) != 1:
raise Exception("cipher c must be in Group Z_*_n^2")
m_bar = integer.mod(funcL(integer.fast_pow(c, lamb, n2), n) * miu, n)
return m_bar
def test_gcd(self):
actual = integer.gcd(4, 5)
expected = 1
assert actual == expected
actual = integer.gcd(3, 6)
expected = 3
assert actual == expected
def keyGen(sbit):
p = integer.randprime(int(sbit/2))
q = integer.randprime(int(sbit/2))
while integer.gcd(p*q, (p-1)*(q-1)) != 1:
p = integer.randprime(int(sbit/2))
q = integer.randprime(int(sbit/2))
n = p * q
n2 = n * n
lamb = integer.lcm(p - 1, q - 1)
g = sampleGen(n2)
while integer.gcd(funcL(integer.fast_pow(g, lamb, n2), n), n) != 1:
g = sampleGen(n2)
miu = integer.inverse(funcL(integer.fast_pow(g, lamb, n2), n), n)
'''
lamb = (p - 1) * (q - 1)
g = n + 1
miu = inverse(lamb, n, lamb)
'''
return n, g, lamb, miu
def encrypt(m, n, g):
if m < 0 or m >= n:
raise Exception("message m must be not less than 0 and less than n")
r = integer.random.randint(1, n - 1)
n2 = int(n**2)
while integer.gcd(r, n2) != 1:
r = integer.random.randint(1, n - 1)
'''
r = randprime(int(math.log2(n)))
while r > n - 1:
r = randprime(int(math.log2(n)))
n2 = n * n
'''
c = integer.mod(integer.fast_pow(g, m, n2) * integer.fast_pow(r, n, n2), n2)
return c
def sampleGen(n):
g = integer.random.randint(1, n - 1)
while integer.gcd(g, n) != 1:
g = integer.random.randint(1, n - 1)
return g