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91 righe
1.7 KiB
91 righe
1.7 KiB
import random, sys
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def miller_rabin_pass(a, s, d, n):
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'''
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n is an odd number with
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n-1 = (2^s)d, and d odd
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and a is the base: 1 < a < n-1
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returns True iff n passes the MillerRabinTest for a
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'''
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a_to_power = pow(a, d, n)
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i=0
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#Invariant: a_to_power = a^(d*2^i) mod n
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# we test whether (a^d) = 1 mod n
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if a_to_power == 1:
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return True
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# we test whether a^(d*2^i) = n-1 mod n
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# for 0<=i<=s-1
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while(i < s-1):
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if a_to_power == n - 1:
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return True
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a_to_power = (a_to_power * a_to_power) % n
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i+=1
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# we reach here if the test failed until i=s-2
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return a_to_power == n - 1
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def miller_rabin(n):
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'''
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Applies the MillerRabin Test to n (odd)
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returns True iff n passes the MillerRabinTest for
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K random bases
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'''
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#Compute s and d such that n-1 = (2^s)d, with d odd
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d = n-1
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s = 0
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while d%2 == 0:
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d >>= 1
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s+=1
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#Applies the test K times
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#The probability of a false positive is less than (1/4)^K
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K = 20
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i=1
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while(i<=K):
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# 1 < a < n-1
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a = random.randrange(2,n-1)
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if not miller_rabin_pass(a, s, d, n):
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return False
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i += 1
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return True
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def gen_prime(nbits):
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'''
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Generates a prime of b bits using the
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miller_rabin_test
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'''
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while True:
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p = random.getrandbits(nbits)
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#force p to have nbits and be odd
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p |= 2**nbits | 1
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if miller_rabin(p):
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return p
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break
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def gen_prime_range(start, stop):
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'''
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Generates a prime within the given range
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using the miller_rabin_test
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'''
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while True:
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p = random.randrange(start,stop-1)
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p |= 1
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if miller_rabin(p):
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return p
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break
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if __name__ == "__main__":
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if sys.argv[1] == "test":
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n = sys.argv[2]
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print (miller_rabin(n) and "PRIME" or "COMPOSITE")
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elif sys.argv[1] == "genprime":
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nbits = int(sys.argv[2])
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print(gen_prime(nbits))
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