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108 lines
4.3 KiB
108 lines
4.3 KiB
# Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Tests prime functions."""
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import unittest
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import rsa.prime
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import rsa.randnum
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class PrimeTest(unittest.TestCase):
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def test_is_prime(self):
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"""Test some common primes."""
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# Test some trivial numbers
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self.assertFalse(rsa.prime.is_prime(-1))
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self.assertFalse(rsa.prime.is_prime(0))
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self.assertFalse(rsa.prime.is_prime(1))
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self.assertTrue(rsa.prime.is_prime(2))
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self.assertFalse(rsa.prime.is_prime(42))
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self.assertTrue(rsa.prime.is_prime(41))
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# Test some slightly larger numbers
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self.assertEqual(
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[907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997],
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[x for x in range(901, 1000) if rsa.prime.is_prime(x)]
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)
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# Test around the 50th millionth known prime.
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self.assertTrue(rsa.prime.is_prime(982451653))
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self.assertFalse(rsa.prime.is_prime(982451653 * 961748941))
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def test_miller_rabin_primality_testing(self):
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"""Uses monkeypatching to ensure certain random numbers.
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This allows us to predict/control the code path.
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"""
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randints = []
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def fake_randint(maxvalue):
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return randints.pop(0)
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orig_randint = rsa.randnum.randint
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rsa.randnum.randint = fake_randint
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try:
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# 'n is composite'
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randints.append(2630484832) # causes the 'n is composite' case with n=3784949785
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self.assertEqual(False, rsa.prime.miller_rabin_primality_testing(2787998641, 7))
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self.assertEqual([], randints)
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# 'Exit inner loop and continue with next witness'
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randints.extend([
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2119139098, # causes 'Exit inner loop and continue with next witness'
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# the next witnesses for the above case:
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3051067716, 3603501763, 3230895847, 3687808133, 3760099987, 4026931495, 3022471882,
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])
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self.assertEqual(True, rsa.prime.miller_rabin_primality_testing(2211417913,
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len(randints)))
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self.assertEqual([], randints)
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finally:
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rsa.randnum.randint = orig_randint
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def test_mersenne_primes(self):
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"""Tests first known Mersenne primes.
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Mersenne primes are prime numbers that can be written in the form
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`Mn = 2**n - 1` for some integer `n`. For the list of known Mersenne
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primes, see:
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https://en.wikipedia.org/wiki/Mersenne_prime#List_of_known_Mersenne_primes
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"""
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# List of known Mersenne exponents.
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known_mersenne_exponents = [
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2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279,
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2203, 2281, 4423,
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]
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# Test Mersenne primes.
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for exp in known_mersenne_exponents:
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self.assertTrue(rsa.prime.is_prime(2**exp - 1))
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def test_get_primality_testing_rounds(self):
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"""Test round calculation for primality testing."""
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self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 63), 10)
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self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 127), 10)
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self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 255), 10)
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self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 511), 7)
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self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 767), 7)
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self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 1023), 4)
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self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 1279), 4)
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self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 1535), 3)
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self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 2047), 3)
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self.assertEqual(rsa.prime.get_primality_testing_rounds(1 << 4095), 3)
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