1 # -*- coding: utf-8 -*- 2 # 3 # Copyright 2011 Sybren A. Stvel <sybren (at] stuvel.eu> 4 # 5 # Licensed under the Apache License, Version 2.0 (the "License"); 6 # you may not use this file except in compliance with the License. 7 # You may obtain a copy of the License at 8 # 9 # http://www.apache.org/licenses/LICENSE-2.0 10 # 11 # Unless required by applicable law or agreed to in writing, software 12 # distributed under the License is distributed on an "AS IS" BASIS, 13 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 # See the License for the specific language governing permissions and 15 # limitations under the License. 16 17 """Tests prime functions.""" 18 19 import unittest 20 21 from rsa._compat import range 22 import rsa.prime 23 import rsa.randnum 24 25 26 class PrimeTest(unittest.TestCase): 27 def test_is_prime(self): 28 """Test some common primes.""" 29 30 # Test some trivial numbers 31 self.assertFalse(rsa.prime.is_prime(-1)) 32 self.assertFalse(rsa.prime.is_prime(0)) 33 self.assertFalse(rsa.prime.is_prime(1)) 34 self.assertTrue(rsa.prime.is_prime(2)) 35 self.assertFalse(rsa.prime.is_prime(42)) 36 self.assertTrue(rsa.prime.is_prime(41)) 37 38 # Test some slightly larger numbers 39 self.assertEqual( 40 [907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997], 41 [x for x in range(901, 1000) if rsa.prime.is_prime(x)] 42 ) 43 44 # Test around the 50th millionth known prime. 45 self.assertTrue(rsa.prime.is_prime(982451653)) 46 self.assertFalse(rsa.prime.is_prime(982451653 * 961748941)) 47 48 def test_miller_rabin_primality_testing(self): 49 """Uses monkeypatching to ensure certain random numbers. 50 51 This allows us to predict/control the code path. 52 """ 53 54 randints = [] 55 56 def fake_randint(maxvalue): 57 return randints.pop(0) 58 59 orig_randint = rsa.randnum.randint 60 rsa.randnum.randint = fake_randint 61 try: 62 # 'n is composite' 63 randints.append(2630484832) # causes the 'n is composite' case with n=3784949785 64 self.assertEqual(False, rsa.prime.miller_rabin_primality_testing(2787998641, 7)) 65 self.assertEqual([], randints) 66 67 # 'Exit inner loop and continue with next witness' 68 randints.extend([ 69 2119139098, # causes 'Exit inner loop and continue with next witness' 70 # the next witnesses for the above case: 71 3051067716, 3603501763, 3230895847, 3687808133, 3760099987, 4026931495, 3022471882, 72 ]) 73 self.assertEqual(True, rsa.prime.miller_rabin_primality_testing(2211417913, 74 len(randints))) 75 self.assertEqual([], randints) 76 finally: 77 rsa.randnum.randint = orig_randint 78 79 def test_mersenne_primes(self): 80 """Tests first known Mersenne primes. 81 82 Mersenne primes are prime numbers that can be written in the form 83 `Mn = 2**n - 1` for some integer `n`. For the list of known Mersenne 84 primes, see: 85 https://en.wikipedia.org/wiki/Mersenne_prime#List_of_known_Mersenne_primes 86 """ 87 88 # List of known Mersenne exponents. 89 known_mersenne_exponents = [ 90 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 91 2203, 2281, 4423, 92 ] 93 94 # Test Mersenne primes. 95 for exp in known_mersenne_exponents: 96 self.assertTrue(rsa.prime.is_prime(2**exp - 1)) 97 98 def test_get_primality_testing_rounds(self): 99 """Test round calculation for primality testing.""" 100 101 self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 63), 10) 102 self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 127), 10) 103 self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 255), 10) 104 self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 511), 7) 105 self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 767), 7) 106 self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 1023), 4) 107 self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 1279), 4) 108 self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 1535), 3) 109 self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 2047), 3) 110 self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 4095), 3) 111
