def RSASP1(k:golberg_key, m) -> any :
#Second form of the key. Step 2
s_1 = fastModularExponentation(m, k.d_np, k.p)
s_2 = fastModularExponentation(m, k.d_nq, k.q)
h = ((s_1 - s_2) * k.q_inv) % k.p
return s_2 + k.q * h
def millerRabin_2(n: int, a: int) -> bool:
if a > n - 2 or a < 2:
print('random a must be between 2 and n-2')
#Step 1
prev_n = n - 1
s = round(log2(prev_n))
if s == 1:
return False
d = int(prev_n / s)
# n - 1 must be even
if (prev_n % 2 > 0):
return False
#Step 2. (seed() function has not be called, so random function's seed is by default 1970)
#Step 3.
x = pow(a, d, n)
aux = x % n
if (aux == 1 or aux == -1):
return True
r = 1
#Step 4
while True:
x = fastModularExponentation(a, int((2 ^ r) * d), n)
if x == 1:
return False
elif x == -1:
return True
r += 1
if (r < s - 1):
break
#Step 5: r == s-1
x = fastModularExponentation(a, int((2 ^ (s - 1)) * d), n)
if x == -1:
return True
return False
def gen(self, k: int):
# Pick p, q primes such that p | q - 1, that is equvalent to
# say that q = r*p + 1 for some r
#p is prime of length k
p = number.getPrime(k)
r = 1
while True:
q = r * p + 1
if number.isPrime(q):
break
r += 1
# Compute elements of G = {i^r mod q | i in Z_q*}
G = []
ctr = 0
self.t = q
#Choose two random elements inside G
last_i = 0
while True:
i = random.randint(1, q)
if i != last_i:
aux = pow(i, r, q)
if aux != 1:
G.append(aux)
ctr += 1
last_i = i
if ctr == 2:
break
# Since the order of G is prime, any element of G except 1 is a generator
self.g = G[0]
self.sk = G[1]
# pk= g^s
self.pk = fastModularExponentation(self.g, self.sk, q)
def sign_sk_provided(self, m: int, sk: int):
if m + sk == 0:
return 1
# g ^ 1/(x+sk)
return fastModularExponentation(self.g, 1 / m + sk, self.t)