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[ci skip] Modular exponentiation, modular multiplicative inverse, extended Euclidean algorithm, discrete logarithm.

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Nick Thompson
2018-01-28 14:47:14 -06:00
parent 919c5277c1
commit fc4d657201
14 changed files with 768 additions and 39 deletions
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test/discrete_log_test.cpp Normal file
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/*
* (C) Copyright Nick Thompson 2018.
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
*/
#define BOOST_TEST_MODULE discrete_log_test
#include <boost/test/included/unit_test.hpp>
#include <boost/integer/discrete_log.hpp>
using boost::integer::trial_multiplication_discrete_log;
using boost::integer::baby_step_giant_step_discrete_log;
template<class Z>
void test_trial_multiplication_discrete_log()
{
boost::optional<Z> x = trial_multiplication_discrete_log<Z>(2, 1, 3);
BOOST_CHECK_EQUAL(0, x.value());
x = trial_multiplication_discrete_log<Z>(2, 2, 3);
BOOST_CHECK_EQUAL(1, x.value());
x = trial_multiplication_discrete_log<Z>(2, 1, 4);
BOOST_CHECK_EQUAL(0, x.value());
x = trial_multiplication_discrete_log<Z>(2, 2, 4);
BOOST_CHECK_EQUAL(1, x.value());
// No solution to 2^^x mod 4 = 3:
x = trial_multiplication_discrete_log<Z>(2, 3, 4);
BOOST_TEST(!x);
x = trial_multiplication_discrete_log<Z>(7, 7, 41);
BOOST_CHECK_EQUAL(1, x.value());
x = trial_multiplication_discrete_log<Z>(7, 8, 41);
BOOST_CHECK_EQUAL(2, x.value());
x = trial_multiplication_discrete_log<Z>(7, 15, 41);
BOOST_CHECK_EQUAL(3, x.value());
x = trial_multiplication_discrete_log<Z>(7, 23, 41);
BOOST_CHECK_EQUAL(4, x.value());
x = trial_multiplication_discrete_log<Z>(7, 38, 41);
BOOST_CHECK_EQUAL(5, x.value());
x = trial_multiplication_discrete_log<Z>(7, 20, 41);
BOOST_CHECK_EQUAL(6, x.value());
Z k = 1;
for (Z i = 0; i < 40; ++i)
{
x = trial_multiplication_discrete_log<Z>(7, k, 41);
BOOST_CHECK_EQUAL(i, x.value());
k = (7*k) % 41;
}
}
template<class Z>
void test_bsgs_discrete_log()
{
baby_step_giant_step_discrete_log<Z> dl(7, 41);
BOOST_CHECK_EQUAL(dl(7), 1);
BOOST_CHECK_EQUAL(dl(8), 2);
BOOST_CHECK_EQUAL(dl(15), 3);
BOOST_CHECK_EQUAL(dl(23), 4);
BOOST_CHECK_EQUAL(dl(38), 5);
BOOST_CHECK_EQUAL(dl(20), 6);
}
BOOST_AUTO_TEST_CASE(discrete_log_test)
{
test_trial_multiplication_discrete_log<size_t>();
test_bsgs_discrete_log<int>();
}