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[ci skip] It is *not* the case that a discrete log exists when the base and modulus are coprime. Take 4^x = 2 mod 5 as a counterexample. Change API accordingly.

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This commit is contained in:
Nick Thompson
2018-02-10 17:51:59 -06:00
parent 4f4f3eda37
commit faa61cd911
3 changed files with 50 additions and 48 deletions
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73
test/discrete_log_test.cpp
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@ -17,7 +17,7 @@ using boost::integer::bsgs_discrete_log;
template<class Z>
void test_trial_multiplication_discrete_log()
{
std::cout << "Testing basic trial multiplication discrete logarithm on type " << boost::typeindex::type_id<Z>().pretty_name() << "\n";
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);
@ -59,18 +59,42 @@ void test_trial_multiplication_discrete_log()
template<class Z>
void test_bsgs_discrete_log()
{
std::cout << "Testing basic baby-step giant-step discrete logarithm on type " << boost::typeindex::type_id<Z>().pretty_name() << "\n";
bsgs_discrete_log<Z> dl_7(7, 41);
BOOST_CHECK_EQUAL(dl_7(7), 1);
BOOST_CHECK_EQUAL(dl_7(8), 2);
BOOST_CHECK_EQUAL(dl_7(15), 3);
BOOST_CHECK_EQUAL(dl_7(23), 4);
BOOST_CHECK_EQUAL(dl_7(38), 5);
BOOST_CHECK_EQUAL(dl_7(20), 6);
BOOST_CHECK_EQUAL(dl_7(7).value(), 1);
BOOST_CHECK_EQUAL(dl_7(8).value(), 2);
BOOST_CHECK_EQUAL(dl_7(15).value(), 3);
BOOST_CHECK_EQUAL(dl_7(23).value(), 4);
BOOST_CHECK_EQUAL(dl_7(38).value(), 5);
BOOST_CHECK_EQUAL(dl_7(20).value(), 6);
}
template<class Z>
void test_trial_multiplication_with_prime_base()
void test_trial_multiplication_with_prime_modulus()
{
std::cout << "Testing trial multiplication with prime modulus on type " << boost::typeindex::type_id<Z>().pretty_name() << "\n";
for (Z i = 0; i < boost::math::max_prime; ++i)
{
Z modulus = boost::math::prime(i);
for (Z base = 2; base < modulus; ++base)
{
for (Z arg = 1; arg < modulus; ++arg)
{
boost::optional<Z> dl = trial_multiplication_discrete_log(base, arg, modulus);
if (dl)
{
BOOST_CHECK_EQUAL(arg, boost::multiprecision::powm(base, dl.value(), modulus));
}
}
}
}
}
template<class Z>
void test_bsgs_with_prime_modulus()
{
std::cout << "Testing baby-step, giant-step with prime modulus on type " << boost::typeindex::type_id<Z>().pretty_name() << "\n";
for (Z i = 0; i < boost::math::max_prime; ++i)
{
Z p = boost::math::prime(i);
@ -79,39 +103,20 @@ void test_trial_multiplication_with_prime_base()
bsgs_discrete_log<Z> dl_j(j, p);
for (Z k = 1; k < p; ++k)
{
boost::optional<Z> dl = trial_multiplication_discrete_log(j, k, p);
// It is guaranteed to exist with the modulus is prime:
BOOST_ASSERT(dl);
BOOST_CHECK_EQUAL(k, boost::multiprecision::powm(j, dl.value(), p));
boost::optional<Z> dl = dl_j(k);
if (dl)
{
BOOST_CHECK_EQUAL(k, boost::multiprecision::powm(j, dl.value(), p));
}
}
}
}
}
template<class Z>
void test_bsgs_with_prime_base()
{
for (Z i = 0; i < boost::math::max_prime; ++i)
{
Z p = boost::math::prime(i);
for (Z j = 2; j < p; ++j)
{
bsgs_discrete_log<Z> dl_j(j, p);
for (Z k = 1; k < p; ++k)
{
Z dl = dl_j(k);
BOOST_CHECK_EQUAL(k, boost::multiprecision::powm(j, dl, p));
}
}
}
}
BOOST_AUTO_TEST_CASE(discrete_log_test)
{
test_trial_multiplication_discrete_log<size_t>();
test_bsgs_discrete_log<int>();
test_trial_multiplication_with_prime_base<long long>();
test_bsgs_with_prime_base<long long>();
test_trial_multiplication_with_prime_modulus<long long>();
test_bsgs_with_prime_modulus<long long>();
}