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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
# 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
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# ===================================================================
"""Self-test for the custom module exponentiation"""
import unittest
from Crypto.SelfTest.st_common import list_test_cases
from Crypto.Util.number import long_to_bytes, bytes_to_long
from Crypto.Util.py3compat import *
from Crypto.Util._raw_api import (load_pycryptodome_raw_lib,
create_string_buffer,
get_raw_buffer,
c_size_t,
c_ulonglong)
from Crypto.Hash import SHAKE128
from Crypto.Math.Numbers import Integer
from Crypto.Math._IntegerCustom import _raw_montgomery
from Crypto.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 = 0xd66691b20071be4d66d4b71032b37fa007cfabf579fcb91e50bfc2753b3f0ce7be74e216aef7e26d4ae180bc20d7bd3ea88a6cbf6f87380e613c8979b5b043b200a8ff8856a3b12875e36e98a7569f3852d028e967551000b02c19e9fa52e83115b89309aabb1e1cf1e2cb6369d637d46775ce4523ea31f64ad2794cbc365dd8a35e007ed3b57695877fbf102dbeb8b3212491398e494314e93726926e1383f8abb5889bea954eb8c0ca1c62c8e9d83f41888095c5e645ed6d32515fe0c58c1368cad84694e18da43668c6f43e61d7c9bca633ddcda7aef5b79bc396d4a9f48e2a9abe0836cc455e435305357228e93d25aaed46b952defae0f57339bf26f5a9
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')
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