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diff --git a/lib/Crypto/SelfTest/Math/test_Numbers.py b/lib/Crypto/SelfTest/Math/test_Numbers.py
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+++ b/lib/Crypto/SelfTest/Math/test_Numbers.py
@@ -0,0 +1,797 @@
+#
+#  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')