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118 lines
3.3 KiB
C++
118 lines
3.3 KiB
C++
/*
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* (C) Copyright Nick Thompson 2018.
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* Use, modification and distribution are subject to the
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* Boost Software License, Version 1.0. (See accompanying file
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* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#define BOOST_TEST_MODULE discrete_log_test
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#include <boost/test/included/unit_test.hpp>
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#include <boost/integer/discrete_log.hpp>
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#include <boost/math/special_functions/prime.hpp>
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using boost::integer::trial_multiplication_discrete_log;
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using boost::integer::bsgs_discrete_log;
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template<class Z>
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void test_trial_multiplication_discrete_log()
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{
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boost::optional<Z> x = trial_multiplication_discrete_log<Z>(2, 1, 3);
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BOOST_CHECK_EQUAL(0, x.value());
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x = trial_multiplication_discrete_log<Z>(2, 2, 3);
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BOOST_CHECK_EQUAL(1, x.value());
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x = trial_multiplication_discrete_log<Z>(2, 1, 4);
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BOOST_CHECK_EQUAL(0, x.value());
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x = trial_multiplication_discrete_log<Z>(2, 2, 4);
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BOOST_CHECK_EQUAL(1, x.value());
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// No solution to 2^^x mod 4 = 3:
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x = trial_multiplication_discrete_log<Z>(2, 3, 4);
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BOOST_TEST(!x);
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x = trial_multiplication_discrete_log<Z>(7, 7, 41);
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BOOST_CHECK_EQUAL(1, x.value());
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x = trial_multiplication_discrete_log<Z>(7, 8, 41);
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BOOST_CHECK_EQUAL(2, x.value());
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x = trial_multiplication_discrete_log<Z>(7, 15, 41);
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BOOST_CHECK_EQUAL(3, x.value());
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x = trial_multiplication_discrete_log<Z>(7, 23, 41);
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BOOST_CHECK_EQUAL(4, x.value());
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x = trial_multiplication_discrete_log<Z>(7, 38, 41);
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BOOST_CHECK_EQUAL(5, x.value());
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x = trial_multiplication_discrete_log<Z>(7, 20, 41);
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BOOST_CHECK_EQUAL(6, x.value());
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Z k = 1;
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for (Z i = 0; i < 40; ++i)
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{
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x = trial_multiplication_discrete_log<Z>(7, k, 41);
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BOOST_CHECK_EQUAL(i, x.value());
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k = (7*k) % 41;
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}
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}
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template<class Z>
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void test_bsgs_discrete_log()
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{
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bsgs_discrete_log<Z> dl_7(7, 41);
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BOOST_CHECK_EQUAL(dl_7(7), 1);
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BOOST_CHECK_EQUAL(dl_7(8), 2);
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BOOST_CHECK_EQUAL(dl_7(15), 3);
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BOOST_CHECK_EQUAL(dl_7(23), 4);
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BOOST_CHECK_EQUAL(dl_7(38), 5);
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BOOST_CHECK_EQUAL(dl_7(20), 6);
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}
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template<class Z>
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void test_trial_multiplication_with_prime_base()
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{
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for (Z i = 0; i < boost::math::max_prime; ++i)
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{
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Z p = boost::math::prime(i);
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for (Z j = 2; j < p; ++j)
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{
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bsgs_discrete_log<Z> dl_j(j, p);
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for (Z k = 1; k < p; ++k)
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{
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boost::optional<Z> dl = trial_multiplication_discrete_log(j, k, p);
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// It is guaranteed to exist with the modulus is prime:
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BOOST_ASSERT(dl);
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BOOST_CHECK_EQUAL(k, boost::multiprecision::powm(j, dl.value(), p));
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}
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}
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}
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}
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template<class Z>
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void test_bsgs_with_prime_base()
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{
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for (Z i = 0; i < boost::math::max_prime; ++i)
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{
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Z p = boost::math::prime(i);
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for (Z j = 2; j < p; ++j)
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{
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bsgs_discrete_log<Z> dl_j(j, p);
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for (Z k = 1; k < p; ++k)
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{
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Z dl = dl_j(k);
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BOOST_CHECK_EQUAL(k, boost::multiprecision::powm(j, dl, p));
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}
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}
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}
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}
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BOOST_AUTO_TEST_CASE(discrete_log_test)
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{
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test_trial_multiplication_discrete_log<size_t>();
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test_bsgs_discrete_log<int>();
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test_trial_multiplication_with_prime_base<long long>();
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test_bsgs_with_prime_base<long long>();
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}
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