Initial

Author: harshildarji

other/rabin_miller.py

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+# Primality Testing with the Rabin-Miller Algorithm
+
+import random
+
+def rabinMiller(num):
+    s = num - 1
+    t = 0
+
+    while s % 2 == 0:
+        s = s // 2
+        t += 1
+
+    for trials in range(5):
+        a = random.randrange(2, num - 1)
+        v = pow(a, s, num)
+        if v != 1:
+            i = 0
+            while v != (num - 1):
+                if i == t - 1:
+                    return False
+                else:
+                    i = i + 1
+                    v = (v ** 2) % num
+    return True
+
+def isPrime(num):
+    if (num < 2):
+        return False
+
+    lowPrimes = [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]
+
+    if num in lowPrimes:
+        return True
+
+    for prime in lowPrimes:
+        if (num % prime) == 0:
+            return False
+
+    return rabinMiller(num)
+
+def generateLargePrime(keysize = 1024):
+    while True:
+        num = random.randrange(2 ** (keysize - 1), 2 ** (keysize))
+        if isPrime(num):
+            return num
+
+if __name__ == '__main__':
+    num = generateLargePrime()
+    print('Prime number:', num)
+    print('isPrime:', isPrime(num))