Miller-Rabin素性检验

miller-rabin.py

import random
import argparse

smallPrimeList = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139,
149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229,
233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421,
431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521,
523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619,
631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733,
739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953,
967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049,
1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129,
1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231,
1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319,
1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439,
1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523,
1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709,
1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913,
1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999]

def MillerRabin(n, times):
    m = n - 1
    k = 0
    while m % 2 == 0:
        m = m // 2  # m = int(m / 2) is not acceptable
        k += 1
    # print(m, k)
    for i in range(0, times):
        isPrime = False
        a = random.randint(1, n - 1)
        b = pow(a, m, n)
        b = b % n
        if b == 1:
            isPrime = True
        for j in range(0, k):
            if b == n - 1:
                isPrime = True
                break
            b = (b * b) % n
        if not isPrime:
            return False
        else:
            print("Passed Miller-Rabin Test Round " + str(i))
    return True

def PrimalityTest(n):
    for prime in smallPrimeList:
        if n % prime == 0:
            return False
    print("Passed small prime test")
    return MillerRabin(n, 13)
    # If use the error rate 1/4, it seems that 40 is appropriate (see https://stackoverflow.com/questions/4159333/rsa-and-prime-generator-algorithms/4160517#4160517)
    # But actually the bound can be tighter
    # see paper "Average case error estimates for the strong probable prime test" (https://www.math.dartmouth.edu/~carlp/PDF/paper88.pdf)

parser = argparse.ArgumentParser()
parser.add_argument('--single', type=int, help='Test the primality of a single number')
args = parser.parse_args()

if args.single:
    print(PrimalityTest(args.single))

else:
    f = open('result.txt', 'w')
    cnt = 0
    while (cnt < 500):
        number = random.getrandbits(512)
        if (number % 2 == 0):
            continue
        else:
            isPrime = PrimalityTest(number)
            print(str(isPrime) + ' ' + str(number))
            f.write(str(isPrime) + ' ' + str(number) + '\n')
            cnt += 1
    f.close()

直接调用python miller-rabin.py会在当前目录下输出result.txt，其中每行内容为是否为素数（True/False） 被检测的512位奇数。调用python miller-rabin.py --single [number]可以检测number是否为素数。