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test_Numbers.py
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# # SelfTest/Math/test_Numbers.py: Self-test for Numbers module # # =================================================================== # # Copyright (c) 2014, Legrandin <helderijs@gmail.com> # All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions # are met: # # 1. Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # 2. Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in # the documentation and/or other materials provided with the # distribution. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS # "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT # LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS # FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE # COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, # INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, # BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; # LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER # CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT # LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN # ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE # POSSIBILITY OF SUCH DAMAGE. # =================================================================== """Self-test for Math.Numbers""" import sys import unittest from Crypto.SelfTest.st_common import list_test_cases from Crypto.Util.py3compat import * from Crypto.Math._IntegerNative import IntegerNative class TestIntegerBase(unittest.TestCase): def setUp(self): raise NotImplementedError("To be implemented") def Integers(self, *arg): return map(self.Integer, arg) def test_init_and_equality(self): Integer = self.Integer v1 = Integer(23) v2 = Integer(v1) v3 = Integer(-9) self.assertRaises(ValueError, Integer, 1.0) v4 = Integer(10**10) v5 = Integer(-10**10) v6 = Integer(0xFFFF) v7 = Integer(0xFFFFFFFF) v8 = Integer(0xFFFFFFFFFFFFFFFF) self.assertEqual(v1, v1) self.assertEqual(v1, 23) self.assertEqual(v1, v2) self.assertEqual(v3, -9) self.assertEqual(v4, 10 ** 10) self.assertEqual(v5, -10 ** 10) self.assertEqual(v6, 0xFFFF) self.assertEqual(v7, 0xFFFFFFFF) self.assertEqual(v8, 0xFFFFFFFFFFFFFFFF) self.assertFalse(v1 == v4) # Init and comparison between Integer's v6 = Integer(v1) self.assertEqual(v1, v6) self.assertFalse(Integer(0) == None) def test_conversion_to_int(self): v1, v2 = self.Integers(-23, 2 ** 1000) self.assertEqual(int(v1), -23) self.assertEqual(int(v2), 2 ** 1000) def test_equality_with_ints(self): v1, v2, v3 = self.Integers(23, -89, 2 ** 1000) self.assertTrue(v1 == 23) self.assertTrue(v2 == -89) self.assertFalse(v1 == 24) self.assertTrue(v3 == 2 ** 1000) def test_conversion_to_str(self): v1, v2, v3, v4 = self.Integers(20, 0, -20, 2 ** 1000) self.assertTrue(str(v1) == "20") self.assertTrue(str(v2) == "0") self.assertTrue(str(v3) == "-20") self.assertTrue(str(v4) == "10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376") def test_repr(self): v1, v2 = self.Integers(-1, 2**80) self.assertEqual(repr(v1), "Integer(-1)") self.assertEqual(repr(v2), "Integer(1208925819614629174706176)") def test_conversion_to_bytes(self): Integer = self.Integer v1 = Integer(0x17) self.assertEqual(b("\x17"), v1.to_bytes()) v2 = Integer(0xFFFE) self.assertEqual(b("\xFF\xFE"), v2.to_bytes()) self.assertEqual(b("\x00\xFF\xFE"), v2.to_bytes(3)) self.assertRaises(ValueError, v2.to_bytes, 1) self.assertEqual(b("\xFE\xFF"), v2.to_bytes(byteorder='little')) self.assertEqual(b("\xFE\xFF\x00"), v2.to_bytes(3, byteorder='little')) v3 = Integer(-90) self.assertRaises(ValueError, v3.to_bytes) self.assertRaises(ValueError, v3.to_bytes, byteorder='bittle') def test_conversion_from_bytes(self): Integer = self.Integer v1 = Integer.from_bytes(b"\x00") self.assertTrue(isinstance(v1, Integer)) self.assertEqual(0, v1) v2 = Integer.from_bytes(b"\x00\x01") self.assertEqual(1, v2) v3 = Integer.from_bytes(b"\xFF\xFF") self.assertEqual(0xFFFF, v3) v4 = Integer.from_bytes(b"\x00\x01", 'big') self.assertEqual(1, v4) v5 = Integer.from_bytes(b"\x00\x01", byteorder='big') self.assertEqual(1, v5) v6 = Integer.from_bytes(b"\x00\x01", byteorder='little') self.assertEqual(0x0100, v6) self.assertRaises(ValueError, Integer.from_bytes, b'\x09', 'bittle') def test_inequality(self): # Test Integer!=Integer and Integer!=int v1, v2, v3, v4 = self.Integers(89, 89, 90, -8) self.assertTrue(v1 != v3) self.assertTrue(v1 != 90) self.assertFalse(v1 != v2) self.assertFalse(v1 != 89) self.assertTrue(v1 != v4) self.assertTrue(v4 != v1) self.assertTrue(self.Integer(0) != None) def test_less_than(self): # Test Integer<Integer and Integer<int v1, v2, v3, v4, v5 = self.Integers(13, 13, 14, -8, 2 ** 10) self.assertTrue(v1 < v3) self.assertTrue(v1 < 14) self.assertFalse(v1 < v2) self.assertFalse(v1 < 13) self.assertTrue(v4 < v1) self.assertFalse(v1 < v4) self.assertTrue(v1 < v5) self.assertFalse(v5 < v1) def test_less_than_or_equal(self): # Test Integer<=Integer and Integer<=int v1, v2, v3, v4, v5 = self.Integers(13, 13, 14, -4, 2 ** 10) self.assertTrue(v1 <= v1) self.assertTrue(v1 <= 13) self.assertTrue(v1 <= v2) self.assertTrue(v1 <= 14) self.assertTrue(v1 <= v3) self.assertFalse(v1 <= v4) self.assertTrue(v1 <= v5) self.assertFalse(v5 <= v1) def test_more_than(self): # Test Integer>Integer and Integer>int v1, v2, v3, v4, v5 = self.Integers(13, 13, 14, -8, 2 ** 10) self.assertTrue(v3 > v1) self.assertTrue(v3 > 13) self.assertFalse(v1 > v1) self.assertFalse(v1 > v2) self.assertFalse(v1 > 13) self.assertTrue(v1 > v4) self.assertFalse(v4 > v1) self.assertTrue(v5 > v1) self.assertFalse(v1 > v5) def test_more_than_or_equal(self): # Test Integer>=Integer and Integer>=int v1, v2, v3, v4 = self.Integers(13, 13, 14, -4) self.assertTrue(v3 >= v1) self.assertTrue(v3 >= 13) self.assertTrue(v1 >= v2) self.assertTrue(v1 >= v1) self.assertTrue(v1 >= 13) self.assertFalse(v4 >= v1) def test_bool(self): v1, v2, v3, v4 = self.Integers(0, 10, -9, 2 ** 10) self.assertFalse(v1) self.assertFalse(bool(v1)) self.assertTrue(v2) self.assertTrue(bool(v2)) self.assertTrue(v3) self.assertTrue(v4) def test_is_negative(self): v1, v2, v3, v4, v5 = self.Integers(-3 ** 100, -3, 0, 3, 3**100) self.assertTrue(v1.is_negative()) self.assertTrue(v2.is_negative()) self.assertFalse(v4.is_negative()) self.assertFalse(v5.is_negative()) def test_addition(self): # Test Integer+Integer and Integer+int v1, v2, v3 = self.Integers(7, 90, -7) self.assertTrue(isinstance(v1 + v2, self.Integer)) self.assertEqual(v1 + v2, 97) self.assertEqual(v1 + 90, 97) self.assertEqual(v1 + v3, 0) self.assertEqual(v1 + (-7), 0) self.assertEqual(v1 + 2 ** 10, 2 ** 10 + 7) def test_subtraction(self): # Test Integer-Integer and Integer-int v1, v2, v3 = self.Integers(7, 90, -7) self.assertTrue(isinstance(v1 - v2, self.Integer)) self.assertEqual(v2 - v1, 83) self.assertEqual(v2 - 7, 83) self.assertEqual(v2 - v3, 97) self.assertEqual(v1 - (-7), 14) self.assertEqual(v1 - 2 ** 10, 7 - 2 ** 10) def test_multiplication(self): # Test Integer-Integer and Integer-int v1, v2, v3, v4 = self.Integers(4, 5, -2, 2 ** 10) self.assertTrue(isinstance(v1 * v2, self.Integer)) self.assertEqual(v1 * v2, 20) self.assertEqual(v1 * 5, 20) self.assertEqual(v1 * -2, -8) self.assertEqual(v1 * 2 ** 10, 4 * (2 ** 10)) def test_floor_div(self): v1, v2, v3 = self.Integers(3, 8, 2 ** 80) self.assertTrue(isinstance(v1 // v2, self.Integer)) self.assertEqual(v2 // v1, 2) self.assertEqual(v2 // 3, 2) self.assertEqual(v2 // -3, -3) self.assertEqual(v3 // 2 ** 79, 2) self.assertRaises(ZeroDivisionError, lambda: v1 // 0) def test_remainder(self): # Test Integer%Integer and Integer%int v1, v2, v3 = self.Integers(23, 5, -4) self.assertTrue(isinstance(v1 % v2, self.Integer)) self.assertEqual(v1 % v2, 3) self.assertEqual(v1 % 5, 3) self.assertEqual(v3 % 5, 1) self.assertEqual(v1 % 2 ** 10, 23) self.assertRaises(ZeroDivisionError, lambda: v1 % 0) self.assertRaises(ValueError, lambda: v1 % -6) def test_simple_exponentiation(self): v1, v2, v3 = self.Integers(4, 3, -2) self.assertTrue(isinstance(v1 ** v2, self.Integer)) self.assertEqual(v1 ** v2, 64) self.assertEqual(pow(v1, v2), 64) self.assertEqual(v1 ** 3, 64) self.assertEqual(pow(v1, 3), 64) self.assertEqual(v3 ** 2, 4) self.assertEqual(v3 ** 3, -8) self.assertRaises(ValueError, pow, v1, -3) def test_modular_exponentiation(self): v1, v2, v3 = self.Integers(23, 5, 17) self.assertTrue(isinstance(pow(v1, v2, v3), self.Integer)) self.assertEqual(pow(v1, v2, v3), 7) self.assertEqual(pow(v1, 5, v3), 7) self.assertEqual(pow(v1, v2, 17), 7) self.assertEqual(pow(v1, 5, 17), 7) self.assertEqual(pow(v1, 0, 17), 1) self.assertEqual(pow(v1, 1, 2 ** 80), 23) self.assertEqual(pow(v1, 2 ** 80, 89298), 17689) self.assertRaises(ZeroDivisionError, pow, v1, 5, 0) self.assertRaises(ValueError, pow, v1, 5, -4) self.assertRaises(ValueError, pow, v1, -3, 8) def test_inplace_exponentiation(self): v1 = self.Integer(4) v1.inplace_pow(2) self.assertEqual(v1, 16) v1 = self.Integer(4) v1.inplace_pow(2, 15) self.assertEqual(v1, 1) def test_abs(self): v1, v2, v3, v4, v5 = self.Integers(-2 ** 100, -2, 0, 2, 2 ** 100) self.assertEqual(abs(v1), 2 ** 100) self.assertEqual(abs(v2), 2) self.assertEqual(abs(v3), 0) self.assertEqual(abs(v4), 2) self.assertEqual(abs(v5), 2 ** 100) def test_sqrt(self): v1, v2, v3, v4 = self.Integers(-2, 0, 49, 10**100) self.assertRaises(ValueError, v1.sqrt) self.assertEqual(v2.sqrt(), 0) self.assertEqual(v3.sqrt(), 7) self.assertEqual(v4.sqrt(), 10**50) def test_sqrt_module(self): # Invalid modulus (non positive) self.assertRaises(ValueError, self.Integer(5).sqrt, 0) self.assertRaises(ValueError, self.Integer(5).sqrt, -1) # Simple cases assert self.Integer(0).sqrt(5) == 0 assert self.Integer(1).sqrt(5) in (1, 4) # Test with all quadratic residues in several fields for p in (11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53): for i in range(0, p): square = i**2 % p res = self.Integer(square).sqrt(p) assert res in (i, p - i) # 2 is a non-quadratic reside in Z_11 self.assertRaises(ValueError, self.Integer(2).sqrt, 11) # 10 is not a prime self.assertRaises(ValueError, self.Integer(4).sqrt, 10) # 5 is square residue of 4 and 7 assert self.Integer(5 - 11).sqrt(11) in (4, 7) assert self.Integer(5 + 11).sqrt(11) in (4, 7) def test_in_place_add(self): v1, v2 = self.Integers(10, 20) v1 += v2 self.assertEqual(v1, 30) v1 += 10 self.assertEqual(v1, 40) v1 += -1 self.assertEqual(v1, 39) v1 += 2 ** 1000 self.assertEqual(v1, 39 + 2 ** 1000) def test_in_place_sub(self): v1, v2 = self.Integers(10, 20) v1 -= v2 self.assertEqual(v1, -10) v1 -= -100 self.assertEqual(v1, 90) v1 -= 90000 self.assertEqual(v1, -89910) v1 -= -100000 self.assertEqual(v1, 10090) def test_in_place_mul(self): v1, v2 = self.Integers(3, 5) v1 *= v2 self.assertEqual(v1, 15) v1 *= 2 self.assertEqual(v1, 30) v1 *= -2 self.assertEqual(v1, -60) v1 *= 2 ** 1000 self.assertEqual(v1, -60 * (2 ** 1000)) def test_in_place_modulus(self): v1, v2 = self.Integers(20, 7) v1 %= v2 self.assertEqual(v1, 6) v1 %= 2 ** 1000 self.assertEqual(v1, 6) v1 %= 2 self.assertEqual(v1, 0) def t(): v3 = self.Integer(9) v3 %= 0 self.assertRaises(ZeroDivisionError, t) def test_and(self): v1, v2, v3 = self.Integers(0xF4, 0x31, -0xF) self.assertTrue(isinstance(v1 & v2, self.Integer)) self.assertEqual(v1 & v2, 0x30) self.assertEqual(v1 & 0x31, 0x30) self.assertEqual(v1 & v3, 0xF0) self.assertEqual(v1 & -0xF, 0xF0) self.assertEqual(v3 & -0xF, -0xF) self.assertEqual(v2 & (2 ** 1000 + 0x31), 0x31) def test_or(self): v1, v2, v3 = self.Integers(0x40, 0x82, -0xF) self.assertTrue(isinstance(v1 | v2, self.Integer)) self.assertEqual(v1 | v2, 0xC2) self.assertEqual(v1 | 0x82, 0xC2) self.assertEqual(v2 | v3, -0xD) self.assertEqual(v2 | 2 ** 1000, 2 ** 1000 + 0x82) def test_right_shift(self): v1, v2, v3 = self.Integers(0x10, 1, -0x10) self.assertEqual(v1 >> 0, v1) self.assertTrue(isinstance(v1 >> v2, self.Integer)) self.assertEqual(v1 >> v2, 0x08) self.assertEqual(v1 >> 1, 0x08) self.assertRaises(ValueError, lambda: v1 >> -1) self.assertEqual(v1 >> (2 ** 1000), 0) self.assertEqual(v3 >> 1, -0x08) self.assertEqual(v3 >> (2 ** 1000), -1) def test_in_place_right_shift(self): v1, v2, v3 = self.Integers(0x10, 1, -0x10) v1 >>= 0 self.assertEqual(v1, 0x10) v1 >>= 1 self.assertEqual(v1, 0x08) v1 >>= v2 self.assertEqual(v1, 0x04) v3 >>= 1 self.assertEqual(v3, -0x08) def l(): v4 = self.Integer(0x90) v4 >>= -1 self.assertRaises(ValueError, l) def m1(): v4 = self.Integer(0x90) v4 >>= 2 ** 1000 return v4 self.assertEqual(0, m1()) def m2(): v4 = self.Integer(-1) v4 >>= 2 ** 1000 return v4 self.assertEqual(-1, m2()) def _test_left_shift(self): v1, v2, v3 = self.Integers(0x10, 1, -0x10) self.assertEqual(v1 << 0, v1) self.assertTrue(isinstance(v1 << v2, self.Integer)) self.assertEqual(v1 << v2, 0x20) self.assertEqual(v1 << 1, 0x20) self.assertEqual(v3 << 1, -0x20) self.assertRaises(ValueError, lambda: v1 << -1) self.assertRaises(ValueError, lambda: v1 << (2 ** 1000)) def test_in_place_left_shift(self): v1, v2, v3 = self.Integers(0x10, 1, -0x10) v1 <<= 0 self.assertEqual(v1, 0x10) v1 <<= 1 self.assertEqual(v1, 0x20) v1 <<= v2 self.assertEqual(v1, 0x40) v3 <<= 1 self.assertEqual(v3, -0x20) def l(): v4 = self.Integer(0x90) v4 <<= -1 self.assertRaises(ValueError, l) def m(): v4 = self.Integer(0x90) v4 <<= 2 ** 1000 self.assertRaises(ValueError, m) def test_get_bit(self): v1, v2, v3 = self.Integers(0x102, -3, 1) self.assertEqual(v1.get_bit(0), 0) self.assertEqual(v1.get_bit(1), 1) self.assertEqual(v1.get_bit(v3), 1) self.assertEqual(v1.get_bit(8), 1) self.assertEqual(v1.get_bit(9), 0) self.assertRaises(ValueError, v1.get_bit, -1) self.assertEqual(v1.get_bit(2 ** 1000), 0) self.assertRaises(ValueError, v2.get_bit, -1) self.assertRaises(ValueError, v2.get_bit, 0) self.assertRaises(ValueError, v2.get_bit, 1) self.assertRaises(ValueError, v2.get_bit, 2 * 1000) def test_odd_even(self): v1, v2, v3, v4, v5 = self.Integers(0, 4, 17, -4, -17) self.assertTrue(v1.is_even()) self.assertTrue(v2.is_even()) self.assertFalse(v3.is_even()) self.assertTrue(v4.is_even()) self.assertFalse(v5.is_even()) self.assertFalse(v1.is_odd()) self.assertFalse(v2.is_odd()) self.assertTrue(v3.is_odd()) self.assertFalse(v4.is_odd()) self.assertTrue(v5.is_odd()) def test_size_in_bits(self): v1, v2, v3, v4 = self.Integers(0, 1, 0x100, -90) self.assertEqual(v1.size_in_bits(), 1) self.assertEqual(v2.size_in_bits(), 1) self.assertEqual(v3.size_in_bits(), 9) self.assertRaises(ValueError, v4.size_in_bits) def test_size_in_bytes(self): v1, v2, v3, v4, v5, v6 = self.Integers(0, 1, 0xFF, 0x1FF, 0x10000, -9) self.assertEqual(v1.size_in_bytes(), 1) self.assertEqual(v2.size_in_bytes(), 1) self.assertEqual(v3.size_in_bytes(), 1) self.assertEqual(v4.size_in_bytes(), 2) self.assertEqual(v5.size_in_bytes(), 3) self.assertRaises(ValueError, v6.size_in_bits) def test_perfect_square(self): self.assertFalse(self.Integer(-9).is_perfect_square()) self.assertTrue(self.Integer(0).is_perfect_square()) self.assertTrue(self.Integer(1).is_perfect_square()) self.assertFalse(self.Integer(2).is_perfect_square()) self.assertFalse(self.Integer(3).is_perfect_square()) self.assertTrue(self.Integer(4).is_perfect_square()) self.assertTrue(self.Integer(39*39).is_perfect_square()) self.assertFalse(self.Integer(39*39+1).is_perfect_square()) for x in range(100, 1000): self.assertFalse(self.Integer(x**2+1).is_perfect_square()) self.assertTrue(self.Integer(x**2).is_perfect_square()) def test_fail_if_divisible_by(self): v1, v2, v3 = self.Integers(12, -12, 4) # No failure expected v1.fail_if_divisible_by(7) v2.fail_if_divisible_by(7) v2.fail_if_divisible_by(2 ** 80) # Failure expected self.assertRaises(ValueError, v1.fail_if_divisible_by, 4) self.assertRaises(ValueError, v1.fail_if_divisible_by, v3) def test_multiply_accumulate(self): v1, v2, v3 = self.Integers(4, 3, 2) v1.multiply_accumulate(v2, v3) self.assertEqual(v1, 10) v1.multiply_accumulate(v2, 2) self.assertEqual(v1, 16) v1.multiply_accumulate(3, v3) self.assertEqual(v1, 22) v1.multiply_accumulate(1, -2) self.assertEqual(v1, 20) v1.multiply_accumulate(-2, 1) self.assertEqual(v1, 18) v1.multiply_accumulate(1, 2 ** 1000) self.assertEqual(v1, 18 + 2 ** 1000) v1.multiply_accumulate(2 ** 1000, 1) self.assertEqual(v1, 18 + 2 ** 1001) def test_set(self): v1, v2 = self.Integers(3, 6) v1.set(v2) self.assertEqual(v1, 6) v1.set(9) self.assertEqual(v1, 9) v1.set(-2) self.assertEqual(v1, -2) v1.set(2 ** 1000) self.assertEqual(v1, 2 ** 1000) def test_inverse(self): v1, v2, v3, v4, v5, v6 = self.Integers(2, 5, -3, 0, 723872, 3433) self.assertTrue(isinstance(v1.inverse(v2), self.Integer)) self.assertEqual(v1.inverse(v2), 3) self.assertEqual(v1.inverse(5), 3) self.assertEqual(v3.inverse(5), 3) self.assertEqual(v5.inverse(92929921), 58610507) self.assertEqual(v6.inverse(9912), 5353) self.assertRaises(ValueError, v2.inverse, 10) self.assertRaises(ValueError, v1.inverse, -3) self.assertRaises(ValueError, v4.inverse, 10) self.assertRaises(ZeroDivisionError, v2.inverse, 0) def test_inplace_inverse(self): v1, v2 = self.Integers(2, 5) v1.inplace_inverse(v2) self.assertEqual(v1, 3) def test_gcd(self): v1, v2, v3, v4 = self.Integers(6, 10, 17, -2) self.assertTrue(isinstance(v1.gcd(v2), self.Integer)) self.assertEqual(v1.gcd(v2), 2) self.assertEqual(v1.gcd(10), 2) self.assertEqual(v1.gcd(v3), 1) self.assertEqual(v1.gcd(-2), 2) self.assertEqual(v4.gcd(6), 2) def test_lcm(self): v1, v2, v3, v4, v5 = self.Integers(6, 10, 17, -2, 0) self.assertTrue(isinstance(v1.lcm(v2), self.Integer)) self.assertEqual(v1.lcm(v2), 30) self.assertEqual(v1.lcm(10), 30) self.assertEqual(v1.lcm(v3), 102) self.assertEqual(v1.lcm(-2), 6) self.assertEqual(v4.lcm(6), 6) self.assertEqual(v1.lcm(0), 0) self.assertEqual(v5.lcm(0), 0) def test_jacobi_symbol(self): data = ( (1001, 1, 1), (19, 45, 1), (8, 21, -1), (5, 21, 1), (610, 987, -1), (1001, 9907, -1), (5, 3439601197, -1) ) js = self.Integer.jacobi_symbol # Jacobi symbol is always 1 for k==1 or n==1 for k in range(1, 30): self.assertEqual(js(k, 1), 1) for n in range(1, 30, 2): self.assertEqual(js(1, n), 1) # Fail if n is not positive odd self.assertRaises(ValueError, js, 6, -2) self.assertRaises(ValueError, js, 6, -1) self.assertRaises(ValueError, js, 6, 0) self.assertRaises(ValueError, js, 0, 0) self.assertRaises(ValueError, js, 6, 2) self.assertRaises(ValueError, js, 6, 4) self.assertRaises(ValueError, js, 6, 6) self.assertRaises(ValueError, js, 6, 8) for tv in data: self.assertEqual(js(tv[0], tv[1]), tv[2]) self.assertEqual(js(self.Integer(tv[0]), tv[1]), tv[2]) self.assertEqual(js(tv[0], self.Integer(tv[1])), tv[2]) def test_jacobi_symbol_wikipedia(self): # Test vectors from https://en.wikipedia.org/wiki/Jacobi_symbol tv = [ (3, [(1, 1), (2, -1), (3, 0), (4, 1), (5, -1), (6, 0), (7, 1), (8, -1), (9, 0), (10, 1), (11, -1), (12, 0), (13, 1), (14, -1), (15, 0), (16, 1), (17, -1), (18, 0), (19, 1), (20, -1), (21, 0), (22, 1), (23, -1), (24, 0), (25, 1), (26, -1), (27, 0), (28, 1), (29, -1), (30, 0)]), (5, [(1, 1), (2, -1), (3, -1), (4, 1), (5, 0), (6, 1), (7, -1), (8, -1), (9, 1), (10, 0), (11, 1), (12, -1), (13, -1), (14, 1), (15, 0), (16, 1), (17, -1), (18, -1), (19, 1), (20, 0), (21, 1), (22, -1), (23, -1), (24, 1), (25, 0), (26, 1), (27, -1), (28, -1), (29, 1), (30, 0)]), (7, [(1, 1), (2, 1), (3, -1), (4, 1), (5, -1), (6, -1), (7, 0), (8, 1), (9, 1), (10, -1), (11, 1), (12, -1), (13, -1), (14, 0), (15, 1), (16, 1), (17, -1), (18, 1), (19, -1), (20, -1), (21, 0), (22, 1), (23, 1), (24, -1), (25, 1), (26, -1), (27, -1), (28, 0), (29, 1), (30, 1)]), (9, [(1, 1), (2, 1), (3, 0), (4, 1), (5, 1), (6, 0), (7, 1), (8, 1), (9, 0), (10, 1), (11, 1), (12, 0), (13, 1), (14, 1), (15, 0), (16, 1), (17, 1), (18, 0), (19, 1), (20, 1), (21, 0), (22, 1), (23, 1), (24, 0), (25, 1), (26, 1), (27, 0), (28, 1), (29, 1), (30, 0)]), (11, [(1, 1), (2, -1), (3, 1), (4, 1), (5, 1), (6, -1), (7, -1), (8, -1), (9, 1), (10, -1), (11, 0), (12, 1), (13, -1), (14, 1), (15, 1), (16, 1), (17, -1), (18, -1), (19, -1), (20, 1), (21, -1), (22, 0), (23, 1), (24, -1), (25, 1), (26, 1), (27, 1), (28, -1), (29, -1), (30, -1)]), (13, [(1, 1), (2, -1), (3, 1), (4, 1), (5, -1), (6, -1), (7, -1), (8, -1), (9, 1), (10, 1), (11, -1), (12, 1), (13, 0), (14, 1), (15, -1), (16, 1), (17, 1), (18, -1), (19, -1), (20, -1), (21, -1), (22, 1), (23, 1), (24, -1), (25, 1), (26, 0), (27, 1), (28, -1), (29, 1), (30, 1)]), (15, [(1, 1), (2, 1), (3, 0), (4, 1), (5, 0), (6, 0), (7, -1), (8, 1), (9, 0), (10, 0), (11, -1), (12, 0), (13, -1), (14, -1), (15, 0), (16, 1), (17, 1), (18, 0), (19, 1), (20, 0), (21, 0), (22, -1), (23, 1), (24, 0), (25, 0), (26, -1), (27, 0), (28, -1), (29, -1), (30, 0)]), (17, [(1, 1), (2, 1), (3, -1), (4, 1), (5, -1), (6, -1), (7, -1), (8, 1), (9, 1), (10, -1), (11, -1), (12, -1), (13, 1), (14, -1), (15, 1), (16, 1), (17, 0), (18, 1), (19, 1), (20, -1), (21, 1), (22, -1), (23, -1), (24, -1), (25, 1), (26, 1), (27, -1), (28, -1), (29, -1), (30, 1)]), (19, [(1, 1), (2, -1), (3, -1), (4, 1), (5, 1), (6, 1), (7, 1), (8, -1), (9, 1), (10, -1), (11, 1), (12, -1), (13, -1), (14, -1), (15, -1), (16, 1), (17, 1), (18, -1), (19, 0), (20, 1), (21, -1), (22, -1), (23, 1), (24, 1), (25, 1), (26, 1), (27, -1), (28, 1), (29, -1), (30, 1)]), (21, [(1, 1), (2, -1), (3, 0), (4, 1), (5, 1), (6, 0), (7, 0), (8, -1), (9, 0), (10, -1), (11, -1), (12, 0), (13, -1), (14, 0), (15, 0), (16, 1), (17, 1), (18, 0), (19, -1), (20, 1), (21, 0), (22, 1), (23, -1), (24, 0), (25, 1), (26, 1), (27, 0), (28, 0), (29, -1), (30, 0)]), (23, [(1, 1), (2, 1), (3, 1), (4, 1), (5, -1), (6, 1), (7, -1), (8, 1), (9, 1), (10, -1), (11, -1), (12, 1), (13, 1), (14, -1), (15, -1), (16, 1), (17, -1), (18, 1), (19, -1), (20, -1), (21, -1), (22, -1), (23, 0), (24, 1), (25, 1), (26, 1), (27, 1), (28, -1), (29, 1), (30, -1)]), (25, [(1, 1), (2, 1), (3, 1), (4, 1), (5, 0), (6, 1), (7, 1), (8, 1), (9, 1), (10, 0), (11, 1), (12, 1), (13, 1), (14, 1), (15, 0), (16, 1), (17, 1), (18, 1), (19, 1), (20, 0), (21, 1), (22, 1), (23, 1), (24, 1), (25, 0), (26, 1), (27, 1), (28, 1), (29, 1), (30, 0)]), (27, [(1, 1), (2, -1), (3, 0), (4, 1), (5, -1), (6, 0), (7, 1), (8, -1), (9, 0), (10, 1), (11, -1), (12, 0), (13, 1), (14, -1), (15, 0), (16, 1), (17, -1), (18, 0), (19, 1), (20, -1), (21, 0), (22, 1), (23, -1), (24, 0), (25, 1), (26, -1), (27, 0), (28, 1), (29, -1), (30, 0)]), (29, [(1, 1), (2, -1), (3, -1), (4, 1), (5, 1), (6, 1), (7, 1), (8, -1), (9, 1), (10, -1), (11, -1), (12, -1), (13, 1), (14, -1), (15, -1), (16, 1), (17, -1), (18, -1), (19, -1), (20, 1), (21, -1), (22, 1), (23, 1), (24, 1), (25, 1), (26, -1), (27, -1), (28, 1), (29, 0), (30, 1)]), ] js = self.Integer.jacobi_symbol for n, kj in tv: for k, j in kj: self.assertEqual(js(k, n), j) def test_hex(self): v1, = self.Integers(0x10) self.assertEqual(hex(v1), "0x10") class TestIntegerInt(TestIntegerBase): def setUp(self): self.Integer = IntegerNative class testIntegerRandom(unittest.TestCase): def test_random_exact_bits(self): for _ in range(1000): a = IntegerNative.random(exact_bits=8) self.assertFalse(a < 128) self.assertFalse(a >= 256) for bits_value in range(1024, 1024 + 8): a = IntegerNative.random(exact_bits=bits_value) self.assertFalse(a < 2**(bits_value - 1)) self.assertFalse(a >= 2**bits_value) def test_random_max_bits(self): flag = False for _ in range(1000): a = IntegerNative.random(max_bits=8) flag = flag or a < 128 self.assertFalse(a>=256) self.assertTrue(flag) for bits_value in range(1024, 1024 + 8): a = IntegerNative.random(max_bits=bits_value) self.assertFalse(a >= 2**bits_value) def test_random_bits_custom_rng(self): class CustomRNG(object): def __init__(self): self.counter = 0 def __call__(self, size): self.counter += size return bchr(0) * size custom_rng = CustomRNG() a = IntegerNative.random(exact_bits=32, randfunc=custom_rng) self.assertEqual(custom_rng.counter, 4) def test_random_range(self): func = IntegerNative.random_range for x in range(200): a = func(min_inclusive=1, max_inclusive=15) self.assertTrue(1 <= a <= 15) for x in range(200): a = func(min_inclusive=1, max_exclusive=15) self.assertTrue(1 <= a < 15) self.assertRaises(ValueError, func, min_inclusive=1, max_inclusive=2, max_exclusive=3) self.assertRaises(ValueError, func, max_inclusive=2, max_exclusive=3) def get_tests(config={}): tests = [] tests += list_test_cases(TestIntegerInt) try: from Crypto.Math._IntegerGMP import IntegerGMP class TestIntegerGMP(TestIntegerBase): def setUp(self): self.Integer = IntegerGMP tests += list_test_cases(TestIntegerGMP) except (ImportError, OSError) as e: if sys.platform == "win32": sys.stdout.write("Skipping GMP tests on Windows\n") else: sys.stdout.write("Skipping GMP tests (%s)\n" % str(e) ) try: from Crypto.Math._IntegerCustom import IntegerCustom class TestIntegerCustomModexp(TestIntegerBase): def setUp(self): self.Integer = IntegerCustom tests += list_test_cases(TestIntegerCustomModexp) except (ImportError, OSError) as e: sys.stdout.write("Skipping custom modexp tests (%s)\n" % str(e) ) tests += list_test_cases(testIntegerRandom) return tests if __name__ == '__main__': suite = lambda: unittest.TestSuite(get_tests()) unittest.main(defaultTest='suite')