Simple_RSA_Tool/Cryptodome/SelfTest/Math/test_Numbers.py

#
#  SelfTest/Math/test_Numbers.py: Self-test for Numbers module
#
# ===================================================================
#
# Copyright (c) 2014, Legrandin <helderijs@gmail.com>
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# modification, are permitted provided that the following conditions
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#
# 1. Redistributions of source code must retain the above copyright
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# 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.
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"""Self-test for Math.Numbers"""

import sys
import unittest

from Cryptodome.SelfTest.st_common import list_test_cases

from Cryptodome.Util.py3compat import *

from Cryptodome.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(0xFFFF)
        self.assertEqual(b("\xFF\xFF"), v2.to_bytes())
        self.assertEqual(b("\x00\xFF\xFF"), v2.to_bytes(3))
        self.assertRaises(ValueError, v2.to_bytes, 1)

        v3 = Integer(-90)
        self.assertRaises(ValueError, v3.to_bytes)

    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\x00"))
        self.assertEqual(0, v2)

        v3 = Integer.from_bytes(b("\xFF\xFF"))
        self.assertEqual(0xFFFF, v3)

    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 Cryptodome.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 Cryptodome.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')