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Filename : test_modexp.py
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#
#  SelfTest/Math/test_modexp.py: Self-test for module exponentiation
#
# ===================================================================
#
# Copyright (c) 2017, Helder Eijs <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
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#
# 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
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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# ===================================================================

"""Self-test for the custom module exponentiation"""

import unittest

from Cryptodome.SelfTest.st_common import list_test_cases

from Cryptodome.Util.number import long_to_bytes, bytes_to_long

from Cryptodome.Util.py3compat import *

from Cryptodome.Util._raw_api import (load_pycryptodome_raw_lib,
                                  create_string_buffer,
                                  get_raw_buffer,
                                  c_size_t,
                                  c_ulonglong)

from Cryptodome.Hash import SHAKE128
from Cryptodome.Math.Numbers import Integer
from Cryptodome.Math._IntegerCustom import _raw_montgomery

from Cryptodome.Random.random import StrongRandom


def create_rng(tag):
    rng = StrongRandom(SHAKE128.new(data=tag))
    return rng

class ExceptionModulus(ValueError):
    pass

def monty_pow(base, exp, modulus):
    max_len = len(long_to_bytes(max(base, exp, modulus)))

    base_b, exp_b, modulus_b = [ long_to_bytes(x, max_len) for x in
                                 (base, exp, modulus) ]

    out = create_string_buffer(max_len)
    error = _raw_montgomery.monty_pow(
                out,
                base_b,
                exp_b,
                modulus_b,
                c_size_t(max_len),
                c_ulonglong(32)
                )

    if error == 17:
        raise ExceptionModulus()
    if error:
        raise ValueError("monty_pow failed with error: %d" % error)

    result = bytes_to_long(get_raw_buffer(out))
    return result

exponent1 = 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
modulus1 = 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


class TestModExp(unittest.TestCase):

    def test_small(self):
        self.assertEqual(1, monty_pow(11,12,19))

    def test_large_1(self):
        base = 0xfffffffffffffffffffffffffffffffffffffffffffffffffff
        expected = pow(base, exponent1, modulus1)
        result = monty_pow(base, exponent1, modulus1)
        self.assertEqual(result, expected)

    def test_zero_exp(self):
        base = 0xfffffffffffffffffffffffffffffffffffffffffffffffffff
        result = monty_pow(base, 0, modulus1)
        self.assertEqual(result, 1)

    def test_zero_base(self):
        result = monty_pow(0, exponent1, modulus1)
        self.assertEqual(result, 0)

    def test_zero_modulus(self):
        base = 0xfffffffffffffffffffffffffffffffffffffffffffffffff
        self.assertRaises(ExceptionModulus, monty_pow, base, exponent1, 0)
        self.assertRaises(ExceptionModulus, monty_pow, 0, 0, 0)

    def test_larger_exponent(self):
        base = modulus1 - 0xFFFFFFF
        expected = pow(base, modulus1<<64, modulus1)
        result = monty_pow(base, modulus1<<64, modulus1)
        self.assertEqual(result, expected)

    def test_even_modulus(self):
        base = modulus1 >> 4
        self.assertRaises(ExceptionModulus, monty_pow, base, exponent1, modulus1-1)

    def test_several_lengths(self):
        prng = SHAKE128.new().update(b('Test'))
        for length in range(1, 100):
            modulus2 = Integer.from_bytes(prng.read(length)) | 1
            base = Integer.from_bytes(prng.read(length)) % modulus2
            exponent2 = Integer.from_bytes(prng.read(length))

            expected = pow(base, exponent2, modulus2)
            result = monty_pow(base, exponent2, modulus2)
            self.assertEqual(result, expected)

    def test_variable_exponent(self):
        prng = create_rng(b('Test variable exponent'))
        for i in range(20):
            for j in range(7):
                modulus = prng.getrandbits(8*30) | 1
                base = prng.getrandbits(8*30) % modulus
                exponent = prng.getrandbits(i*8+j)

                expected = pow(base, exponent, modulus)
                result = monty_pow(base, exponent, modulus)
                self.assertEqual(result, expected)

                exponent ^= (1 << (i*8+j)) - 1

                expected = pow(base, exponent, modulus)
                result = monty_pow(base, exponent, modulus)
                self.assertEqual(result, expected)

    def test_stress_63(self):
        prng = create_rng(b('Test 63'))
        length = 63
        for _ in range(2000):
            modulus  = prng.getrandbits(8*length) | 1
            base     = prng.getrandbits(8*length) % modulus
            exponent = prng.getrandbits(8*length)

            expected = pow(base, exponent, modulus)
            result = monty_pow(base, exponent, modulus)
            self.assertEqual(result, expected)

    def test_stress_64(self):
        prng = create_rng(b('Test 64'))
        length = 64
        for _ in range(2000):
            modulus  = prng.getrandbits(8*length) | 1
            base     = prng.getrandbits(8*length) % modulus
            exponent = prng.getrandbits(8*length)

            expected = pow(base, exponent, modulus)
            result = monty_pow(base, exponent, modulus)
            self.assertEqual(result, expected)

    def test_stress_65(self):
        prng = create_rng(b('Test 65'))
        length = 65
        for _ in range(2000):
            modulus  = prng.getrandbits(8*length) | 1
            base     = prng.getrandbits(8*length) % modulus
            exponent = prng.getrandbits(8*length)

            expected = pow(base, exponent, modulus)
            result = monty_pow(base, exponent, modulus)
            self.assertEqual(result, expected)


def get_tests(config={}):
    tests = []
    tests += list_test_cases(TestModExp)
    return tests


if __name__ == '__main__':
    suite = lambda: unittest.TestSuite(get_tests())
    unittest.main(defaultTest='suite')