def getPrimePair(bits=512):
assert bits % 4 == 0
p = MillerRabin.gen_prime(bits)
q = MillerRabin.gen_prime_range(p + 1, 2 * p)
return p, q
def gen_prime():
# 测试三次
prime = gen_random.pseudoprime_number()
flag1 = MillerRabin.millerrabin(prime)
flag2 = MillerRabin.millerrabin(prime)
flag3 = MillerRabin.millerrabin(prime)
if not (flag1 and flag2 and flag3):
prime = gen_prime()
'''if MillerRabin.millerrabin(prime) == False:
prime = gen_prime()'''
return prime
def generateKey():
global p, q, n, e, d, phiN
start = time.time()
p = mr.generateLargePrime(548)
q = mr.generateLargePrime(548)
n = p * q
phiN = (p-1) * (q-1)
e = random.randrange(3, phiN-1)
while (gcd(e, phiN) != 1):
e = random.randrange(2, phiN-1)
d = modinv(e, phiN)
def getPrimePair(bits=512):
'''
genera un par de primos p , q con
p de nbits y
p < q < 2p
'''
assert bits%4==0
p = MillerRabin.gen_prime(bits)
q = MillerRabin.gen_prime_range(p+1, 2*p)
return p,q
def getPrimePair(bits=512):
'''
genera un par de primos p , q con
p de nbits y
p < q < 2p
'''
assert bits%4==0
p = MillerRabin.gen_prime(bits)
q = MillerRabin.gen_prime_range(p+1, 2*p)
return p,q
def __init__(self,nonPrimePeriod):
while True:
if MillerRabin.miller_rabin(nonPrimePeriod):
self.period = nonPrimePeriod
break
else:
nonPrimePeriod = nonPrimePeriod + 1
def gen_prime(n):
if (n < 200):
n = 200
a = 10**n
b = a * 10
x = random.randrange(a, b)
x |= 1
while (pow(2, x - 1, x) != 1 or MillerRabin.is_Prime(x) == False):
x += 2
return x
def gen_RSApq(n):
x0 = gen_prime(n // 3)
a = 10**(n - n // 3)
b = a * 100
#on genere un grand nombre premier
#puis on en cherche un de la forme k*x+1
#ainsi p-1 ne sera pas seulement composé de petits facteurs
k = random.randrange(a, b)
x = k * x0 + 1
while (x & 1 and pow(2, x - 1, x) != 1 and not MillerRabin.is_Prime(x)):
x += x0
return x
def is_good_prime(self, p):
return p % 4 == 3 and MillerRabin.is_prime(p)
def generate_prime(num_bit):
x = generate_bbs(num_bit)
while not MillerRabin.is_prime(x):
x = generate_bbs(num_bit)
return x
import MillerRabin
import time
import sys
if __name__ == "__main__":
# some primes
lst = []
for i in range(2, 30):
if MillerRabin.miller_rabin(i):
lst.append(i)
print("{} are the primes up to 30".format(lst))
# some bigger primes
count = 0
for i in range(2, 10000):
if MillerRabin.miller_rabin(i):
count += 1
print("{} primes up to 10000 ({}%)".format(count, count/100))
# some time expensive calculation (takes ~18 secs)
t1 = time.time()
i = 2
count = 0
while i < 1000000:
if MillerRabin.miller_rabin(i):
count += 1
i += 1
if (i % 100000 == 0):
print("{}%".format(i/10000))
def generate_prime(rng, bits):
import MillerRabin
return MillerRabin.gen_prime(bits, rng)
#!/usr/bin/python3
import random
import math
import sys
import MillerRabin
import algo
factors = [int(nb) for nb in range(3, 100, 2) if MillerRabin.is_Prime(nb)]
def main():
lenNb = random.randint(200, 210)
eps = random.randint(1, 10)
p = gen_RSApq(lenNb)
q = gen_RSApq(lenNb + eps)
n = p * q
e = gen_exp(p, q)
d = congru_equation(e, 1, (p - 1) * (q - 1))
m = random.randint(10**100, 10**200)
print(m)
c = pow(m, e, n)
plain = pow(c, d, n)
print(plain == m)
def gen_exp(p, q):
e = 1
prod = (p - 1) * (q - 1)
def get_big_prime(bits):
return MillerRabin.gen_prime(bits)
def generate_prime(rng, bits): import MillerRabin return MillerRabin.gen_prime(bits, rng)
