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Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: John Law <johnlaw.po@gmail.com>
224 lines
3.2 KiB
Python
224 lines
3.2 KiB
Python
# Primality Testing with the Rabin-Miller Algorithm
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import random
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def rabinMiller(num: int) -> bool:
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s = num - 1
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t = 0
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while s % 2 == 0:
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s = s // 2
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t += 1
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for trials in range(5):
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a = random.randrange(2, num - 1)
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v = pow(a, s, num)
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if v != 1:
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i = 0
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while v != (num - 1):
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if i == t - 1:
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return False
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else:
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i = i + 1
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v = (v ** 2) % num
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return True
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def isPrime(num: int) -> bool:
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if num < 2:
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return False
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lowPrimes = [
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2,
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3,
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5,
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7,
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11,
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13,
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17,
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19,
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23,
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29,
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31,
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37,
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41,
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43,
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47,
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53,
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59,
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61,
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67,
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71,
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73,
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79,
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83,
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89,
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97,
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101,
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103,
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107,
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109,
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113,
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127,
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131,
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137,
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139,
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149,
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151,
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157,
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163,
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167,
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173,
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179,
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181,
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191,
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193,
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197,
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199,
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211,
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223,
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227,
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229,
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233,
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239,
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241,
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251,
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257,
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263,
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269,
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271,
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277,
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281,
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283,
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293,
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307,
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311,
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313,
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317,
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331,
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337,
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347,
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349,
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353,
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359,
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367,
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373,
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379,
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383,
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389,
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397,
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401,
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409,
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419,
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421,
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431,
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433,
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439,
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443,
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449,
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457,
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461,
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463,
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467,
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479,
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487,
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491,
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499,
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503,
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509,
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521,
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523,
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541,
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547,
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557,
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563,
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569,
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571,
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577,
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587,
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593,
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599,
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601,
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607,
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613,
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617,
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619,
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631,
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641,
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643,
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647,
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653,
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659,
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661,
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673,
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677,
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683,
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691,
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701,
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709,
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719,
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727,
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733,
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739,
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743,
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751,
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757,
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761,
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769,
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773,
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787,
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797,
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809,
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811,
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821,
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823,
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827,
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829,
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839,
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853,
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857,
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859,
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863,
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877,
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881,
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883,
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887,
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907,
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911,
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919,
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929,
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937,
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941,
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947,
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953,
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967,
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971,
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977,
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983,
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991,
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997,
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]
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if num in lowPrimes:
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return True
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for prime in lowPrimes:
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if (num % prime) == 0:
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return False
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return rabinMiller(num)
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def generateLargePrime(keysize: int = 1024) -> int:
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while True:
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num = random.randrange(2 ** (keysize - 1), 2 ** (keysize))
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if isPrime(num):
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return num
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if __name__ == "__main__":
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num = generateLargePrime()
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print(("Prime number:", num))
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print(("isPrime:", isPrime(num)))
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