forked from lthn/blockchain
666 lines
18 KiB
C++
666 lines
18 KiB
C++
// Copyright (c) 2021 Zano Project
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// Distributed under the MIT/X11 software license, see the accompanying
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// file COPYING or http://www.opensource.org/licenses/mit-license.php.
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#pragma once
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TEST(crypto, primitives)
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{
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struct helper
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{
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static void make_rnd_indicies(std::vector<size_t>& v, size_t size)
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{
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v.resize(size);
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for (size_t i = 0; i < size; ++i)
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v[i] = i;
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std::shuffle(v.begin(), v.end(), crypto::uniform_random_bit_generator());
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};
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};
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struct timer_t
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{
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std::chrono::high_resolution_clock::time_point m_tp{};
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uint64_t m_t{};
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uint64_t m_div_coeff{ 1 };
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void start(uint64_t div_coeff = 1) { m_tp = std::chrono::high_resolution_clock::now(); m_div_coeff = div_coeff; }
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void stop() { m_t = std::chrono::duration_cast<std::chrono::microseconds>(std::chrono::high_resolution_clock::now() - m_tp).count(); }
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uint64_t get_time_mcs() { return m_div_coeff == 1 ? m_t : m_t / m_div_coeff; }
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};
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typedef uint64_t(*run_func_t)(timer_t& t, size_t rounds);
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auto run = [](const std::string& title, size_t rounds, run_func_t cb)
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{
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uint64_t result;
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timer_t t_warmup, t, t_total;
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t_total.start();
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result = cb(t_warmup, rounds);
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result += cb(t, rounds);
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t_total.stop();
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double run_time_mcs_x_100 = double(uint64_t(t.get_time_mcs() / (rounds / 100)));
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LOG_PRINT_L0(std::left << std::setw(40) << title << std::setw(7) << rounds << " rnds -> "
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<< std::right << std::setw(7) << std::fixed << std::setprecision(2) << run_time_mcs_x_100 / 100.0 << " mcs avg. (gross: "
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<< std::fixed << std::setprecision(2) << double(t_total.get_time_mcs()) / 1000.0 << " ms), result hash: " << result);
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};
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#define HASH_64_VEC(vec_var_name) hash_64(vec_var_name.data(), vec_var_name.size() * sizeof(vec_var_name[0]))
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LOG_PRINT_L0(ENDL << "native crypto primitives:");
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run("sc_reduce", 30000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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struct bytes64
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{
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unsigned char b[64];
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};
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std::vector<bytes64> scalars_64(rounds);
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for (size_t i = 0; i < scalars_64.size(); ++i)
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crypto::generate_random_bytes(sizeof(bytes64), scalars_64[i].b);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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sc_reduce(scalars_64[rnd_indecies[i]].b);
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}
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t.stop();
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return HASH_64_VEC(scalars_64);
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});
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run("sc_reduce32", 30000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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std::vector<crypto::ec_scalar> scalars(rounds);
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for (size_t i = 0; i < scalars.size(); ++i)
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crypto::generate_random_bytes(sizeof(crypto::ec_scalar), scalars[i].data);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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sc_reduce32((unsigned char*)&scalars[rnd_indecies[i]].data);
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}
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t.stop();
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return HASH_64_VEC(scalars);
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});
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run("sc_mul", 50000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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std::vector<scalar_t> a(rounds), b(rounds);
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for (size_t i = 0; i < rounds; ++i)
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{
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a[i].make_random();
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b[i].make_random();
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}
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std::vector<scalar_t> result(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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sc_mul(result[rnd_indecies[i]].m_s, a[rnd_indecies[i]].m_s, b[rnd_indecies[i]].m_s);
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t.stop();
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return HASH_64_VEC(result);
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});
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run("sc_add", 50000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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std::vector<scalar_t> a(rounds), b(rounds);
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for (size_t i = 0; i < rounds; ++i)
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{
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a[i].make_random();
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b[i].make_random();
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}
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std::vector<scalar_t> result(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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sc_add(result[i].m_s, a[rnd_indecies[i]].m_s, b[rnd_indecies[i]].m_s);
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t.stop();
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return HASH_64_VEC(result);
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});
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run("sc_mul + sc_add", 50000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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std::vector<scalar_t> a(rounds), b(rounds), c(rounds);
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for (size_t i = 0; i < rounds; ++i)
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{
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a[i].make_random();
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b[i].make_random();
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c[i].make_random();
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}
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std::vector<scalar_t> result(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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scalar_t tmp;
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sc_mul(tmp.m_s, a[rnd_indecies[i]].m_s, b[rnd_indecies[i]].m_s); // tmp = a * b
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sc_add(result[i].m_s, tmp.m_s, c[rnd_indecies[i]].m_s); // result = tmp + c
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}
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t.stop();
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return HASH_64_VEC(result);
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});
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run("sc_muladd", 50000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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std::vector<scalar_t> a(rounds), b(rounds), c(rounds);
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for (size_t i = 0; i < rounds; ++i)
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{
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a[i].make_random();
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b[i].make_random();
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c[i].make_random();
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}
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std::vector<scalar_t> result(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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sc_muladd(result[i].m_s, a[rnd_indecies[i]].m_s, b[rnd_indecies[i]].m_s, c[rnd_indecies[i]].m_s);
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t.stop();
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return HASH_64_VEC(result);
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});
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run("ge_p3_tobytes", 10000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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std::vector<ge_p3> points_p3(rounds);
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ge_scalarmult_base(&points_p3[0], c_scalar_1.data());
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for (size_t i = 1; i < points_p3.size(); ++i)
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ge_bytes_hash_to_ec_32(&points_p3[i], (const unsigned char*)&points_p3[i - 1].X); // P_{i+1} = Hp(P_i.X)
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std::vector<crypto::ec_point> points(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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ge_p3_tobytes((unsigned char*)points[i].data, &points_p3[rnd_indecies[i]]);
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}
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t.stop();
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return HASH_64_VEC(points);
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});
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run("ge_frombytes_vartime(p3)", 10000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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point_t P = c_point_G;
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std::vector<crypto::ec_point> points_p3_bytes(rounds);
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for (size_t i = 0; i < points_p3_bytes.size(); ++i)
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{
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P = hash_helper_t::hp(P);
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ge_p3_tobytes((unsigned char*)&points_p3_bytes[i], &P.m_p3);
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}
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std::vector<ge_p3> points(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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ge_frombytes_vartime(&points[i], (unsigned char*)&points_p3_bytes[rnd_indecies[i]]);
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}
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t.stop();
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return HASH_64_VEC(points);
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});
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run("ge_p3_to_cached(p3)", 10000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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std::vector<ge_p3> points_p3(rounds);
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ge_scalarmult_base(&points_p3[0], c_scalar_1.data());
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for (size_t i = 1; i < points_p3.size(); ++i)
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ge_bytes_hash_to_ec_32(&points_p3[i], (const unsigned char*)&points_p3[i - 1].X); // P_{i+1} = Hp(P_i.X)
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std::vector<ge_cached> points_cached(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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ge_p3_to_cached(&points_cached[i], &points_p3[rnd_indecies[i]]);
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}
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t.stop();
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return HASH_64_VEC(points_cached);
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});
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run("ge_add(p3 + p3)", 50000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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std::vector<ge_cached> points_cached(rounds);
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point_t p = scalar_t::random() * c_point_G;
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for (size_t i = 0; i < rnd_indecies.size(); ++i)
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{
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ge_p3_to_cached(&points_cached[i], &p.m_p3);
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p = p + p;
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}
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ge_p3 Q;
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ge_scalarmult_base(&Q, &scalar_t::random().m_s[0]);
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std::vector<ge_p1p1> results(rnd_indecies.size());
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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ge_add(&results[i], &Q, &points_cached[rnd_indecies[i]]);
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}
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t.stop();
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return HASH_64_VEC(results);
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});
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run("ge_p1p1_to_p3(p1p1)", 50000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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ge_cached G;
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ge_p3_to_cached(&G, &c_point_G.m_p3);
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std::vector<ge_p1p1> points_p1p1(rounds);
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ge_add(&points_p1p1[0], &c_point_G.m_p3, &G);
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for (size_t i = 1; i < points_p1p1.size(); ++i)
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{
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ge_p3 p3;
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ge_p1p1_to_p3(&p3, &points_p1p1[i - 1]);
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ge_add(&points_p1p1[i], &p3, &G);
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}
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std::vector<ge_p3> points_p3(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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ge_p1p1_to_p3(&points_p3[i], &points_p1p1[rnd_indecies[i]]);
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}
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t.stop();
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return HASH_64_VEC(points_p3);
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});
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run("ge_scalarmult()", 5000, [](timer_t& t, size_t rounds) {
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//rounds -= rounds % 8;
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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scalar_t x;
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x.make_random();
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std::vector<crypto::ec_scalar> scalars(rounds);
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for (size_t i = 0; i < rounds; ++i)
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{
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//scalar_t x = x + x + x;
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scalar_t x;
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x.make_random();
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memcpy(&scalars[i].data, x.data(), 32);
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}
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point_t p = scalar_t::random() * c_point_G;
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//std::vector<ge_p2> points_p2(rounds);
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std::vector<ge_p3> points_p3(rounds);
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// warmup round
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//for (size_t i = 0; i < rounds; ++i)
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// ge_scalarmult((ge_p2*)&points_p3[i], (const unsigned char*)&scalars[rnd_indecies[i]], &p.m_p3);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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ge_scalarmult((ge_p2*)&points_p3[i], (const unsigned char*)&scalars[rnd_indecies[i]], &p.m_p3);
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//ge_scalarmult(&points_p2[i * 4 + 3], (const unsigned char*)&scalars[rnd_indecies[i * 4 + 3]], &p.m_p3);
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//ge_scalarmult(&points_p2[i * 4 + 0], (const unsigned char*)&scalars[rnd_indecies[i * 4 + 0]], &p.m_p3);
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//ge_scalarmult(&points_p2[i * 4 + 1], (const unsigned char*)&scalars[rnd_indecies[i * 4 + 1]], &p.m_p3);
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//ge_scalarmult(&points_p2[i * 4 + 2], (const unsigned char*)&scalars[rnd_indecies[i * 4 + 2]], &p.m_p3);
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}
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t.stop();
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return HASH_64_VEC(points_p3);
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});
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run("ge_scalarmult() (2)", 5000, [](timer_t& t, size_t rounds) {
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//rounds -= rounds % 8;
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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scalar_t x;
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x.make_random();
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std::vector<crypto::ec_scalar> scalars(rounds);
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for (size_t i = 0; i < rounds; ++i)
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{
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//scalar_t x = x + x + x;
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scalar_t x;
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x.make_random();
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memcpy(&scalars[i].data, x.data(), 32);
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}
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point_t p = scalar_t::random() * c_point_G;
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//std::vector<ge_p2> points_p2(rounds);
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std::vector<ge_p3> points_p3(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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ge_scalarmult((ge_p2*)&points_p3[i], (const unsigned char*)&scalars[rnd_indecies[i]], &p.m_p3);
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//ge_scalarmult(&points_p2[i * 4 + 3], (const unsigned char*)&scalars[rnd_indecies[i * 4 + 3]], &p.m_p3);
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//ge_scalarmult(&points_p2[i * 4 + 0], (const unsigned char*)&scalars[rnd_indecies[i * 4 + 0]], &p.m_p3);
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//ge_scalarmult(&points_p2[i * 4 + 1], (const unsigned char*)&scalars[rnd_indecies[i * 4 + 1]], &p.m_p3);
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//ge_scalarmult(&points_p2[i * 4 + 2], (const unsigned char*)&scalars[rnd_indecies[i * 4 + 2]], &p.m_p3);
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}
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t.stop();
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return HASH_64_VEC(points_p3);
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});
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run("ge_scalarmult_p3()", 5000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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scalar_t x;
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x.make_random();
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std::vector<crypto::ec_scalar> scalars(rounds);
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for (size_t i = 0; i < rounds; ++i)
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{
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//scalar_t x = x + x + x;
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scalar_t x;
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x.make_random();
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memcpy(&scalars[i].data, x.data(), 32);
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}
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point_t p = scalar_t::random() * c_point_G;
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std::vector<ge_p3> points_p3(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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ge_scalarmult_p3(&points_p3[i], (const unsigned char*)&scalars[rnd_indecies[i]], &p.m_p3);
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}
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t.stop();
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return HASH_64_VEC(points_p3);
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});
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run("ge_scalarmult_vartime_p3()", 5000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
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helper::make_rnd_indicies(rnd_indecies, rounds);
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scalar_t x;
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x.make_random();
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std::vector<crypto::ec_scalar> scalars(rounds);
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for (size_t i = 0; i < rounds; ++i)
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{
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//scalar_t x = x + x + x;
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scalar_t x;
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x.make_random();
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memcpy(&scalars[i].data, x.data(), 32);
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}
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point_t p = scalar_t::random() * c_point_G;
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//memcpy(&scalars[rnd_indecies[0]], scalar_t(1).data(), 32);
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std::vector<ge_p3> points_p3(rounds);
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t.start();
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for (size_t i = 0; i < rounds; ++i)
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{
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ge_scalarmult_vartime_p3(&points_p3[i], (const unsigned char*)&scalars[rnd_indecies[i]], &p.m_p3);
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}
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t.stop();
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return HASH_64_VEC(points_p3);
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});
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run("ge_scalarmult_vartime_p3_v2()", 5000, [](timer_t& t, size_t rounds) {
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std::vector<size_t> rnd_indecies;
|
|
helper::make_rnd_indicies(rnd_indecies, rounds);
|
|
|
|
scalar_t x;
|
|
x.make_random();
|
|
|
|
std::vector<crypto::ec_scalar> scalars(rounds);
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
//scalar_t x = x + x + x;
|
|
scalar_t x;
|
|
x.make_random();
|
|
memcpy(&scalars[i].data, x.data(), 32);
|
|
}
|
|
|
|
point_t p = scalar_t::random() * c_point_G;
|
|
|
|
std::vector<ge_p3> points_p3(rounds);
|
|
t.start();
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
ge_scalarmult_vartime_p3_v2(&points_p3[i], (const unsigned char*)&scalars[rnd_indecies[i]], &p.m_p3);
|
|
}
|
|
t.stop();
|
|
|
|
return HASH_64_VEC(points_p3);
|
|
});
|
|
|
|
run("ge_scalarmult_base()", 5000, [](timer_t& t, size_t rounds) {
|
|
std::vector<size_t> rnd_indecies;
|
|
helper::make_rnd_indicies(rnd_indecies, rounds);
|
|
|
|
scalar_t x;
|
|
x.make_random();
|
|
|
|
std::vector<crypto::ec_scalar> scalars(rounds);
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
scalar_t x = x + x + x;
|
|
memcpy(&scalars[i].data, x.data(), 32);
|
|
}
|
|
|
|
std::vector<ge_p3> points_p3(rounds);
|
|
t.start();
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
ge_scalarmult_base(&points_p3[i], (const unsigned char*)&scalars[rnd_indecies[i]]);
|
|
}
|
|
t.stop();
|
|
|
|
return HASH_64_VEC(points_p3);
|
|
});
|
|
|
|
run("ge_mul8_p3()", 5000, [](timer_t& t, size_t rounds) {
|
|
std::vector<size_t> rnd_indecies;
|
|
helper::make_rnd_indicies(rnd_indecies, rounds);
|
|
|
|
std::vector<ge_p3> points_p3(rounds);
|
|
ge_scalarmult_base(&points_p3[0], c_scalar_1.data());
|
|
for (size_t i = 1; i < points_p3.size(); ++i)
|
|
ge_bytes_hash_to_ec_32(&points_p3[i], (const unsigned char*)&points_p3[i - 1].X); // P_{i+1} = Hp(P_i.X)
|
|
|
|
std::vector<ge_p3> points_result(rounds);
|
|
t.start();
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
ge_mul8_p3(&points_result[i], &points_p3[rnd_indecies[i]]);
|
|
}
|
|
t.stop();
|
|
|
|
return HASH_64_VEC(points_result);
|
|
});
|
|
|
|
run("ge_mul8()", 5000, [](timer_t& t, size_t rounds) {
|
|
std::vector<size_t> rnd_indecies;
|
|
helper::make_rnd_indicies(rnd_indecies, rounds);
|
|
|
|
point_t p = scalar_t::random() * c_point_G;
|
|
|
|
std::vector<ge_p2> points_p2(rounds);
|
|
ge_p3_to_p2(&points_p2[0], &p.m_p3);
|
|
ge_p1p1 p1;
|
|
for (size_t i = 0; i < points_p2.size() - 1; ++i)
|
|
{
|
|
ge_p2_dbl(&p1, &points_p2[i]);
|
|
ge_p1p1_to_p2(&points_p2[i + 1], &p1);
|
|
}
|
|
|
|
std::vector<ge_p1p1> points_result(rounds);
|
|
t.start();
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
ge_mul8(&points_result[i], &points_p2[rnd_indecies[i]]);
|
|
}
|
|
t.stop();
|
|
|
|
return HASH_64_VEC(points_result);
|
|
});
|
|
|
|
|
|
|
|
|
|
LOG_PRINT_L0(ENDL << "new primitives:");
|
|
|
|
run("point_t + point_t", 50000, [](timer_t& t, size_t rounds) {
|
|
std::vector<size_t> rnd_indecies;
|
|
helper::make_rnd_indicies(rnd_indecies, rounds);
|
|
|
|
std::vector<point_t> points(rounds);
|
|
point_t p = c_point_G;
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
points[i] = p;
|
|
p = p + p;
|
|
}
|
|
|
|
std::vector<point_t> result(rounds);
|
|
t.start();
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
result[i] = points[rnd_indecies[i]] + p;
|
|
}
|
|
t.stop();
|
|
|
|
return HASH_64_VEC(result);
|
|
});
|
|
|
|
run("sclar_t * point_t", 5000, [](timer_t& t, size_t rounds) {
|
|
std::vector<size_t> rnd_indecies;
|
|
helper::make_rnd_indicies(rnd_indecies, rounds);
|
|
|
|
std::vector<scalar_t> scalars(rounds);
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
scalars[i].make_random();
|
|
|
|
point_t p = scalar_t::random() * c_point_G;
|
|
|
|
std::vector<point_t> result(rounds);
|
|
t.start();
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
result[i] = scalars[rnd_indecies[i]] * p;
|
|
}
|
|
t.stop();
|
|
|
|
return HASH_64_VEC(result);
|
|
});
|
|
|
|
run("sclar_t * point_g_t", 5000, [](timer_t& t, size_t rounds) {
|
|
std::vector<size_t> rnd_indecies;
|
|
helper::make_rnd_indicies(rnd_indecies, rounds);
|
|
|
|
std::vector<scalar_t> scalars(rounds);
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
scalars[i].make_random();
|
|
|
|
std::vector<point_t> result(rounds);
|
|
t.start();
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
result[i] = scalars[rnd_indecies[i]] * c_point_G;
|
|
}
|
|
t.stop();
|
|
|
|
return HASH_64_VEC(result);
|
|
});
|
|
|
|
run("sclar_t * scalar_t", 50000, [](timer_t& t, size_t rounds) {
|
|
std::vector<size_t> rnd_indecies;
|
|
helper::make_rnd_indicies(rnd_indecies, rounds);
|
|
|
|
std::vector<scalar_t> scalars(rounds);
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
scalars[i].make_random();
|
|
|
|
scalar_t s = scalar_t::random();
|
|
|
|
std::vector<scalar_t> result(rounds);
|
|
t.start(4);
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
result[i] = scalars[rnd_indecies[i]] * s * s * s * s;
|
|
}
|
|
t.stop();
|
|
|
|
return HASH_64_VEC(result);
|
|
});
|
|
|
|
run("sclar_t / scalar_t", 10000, [](timer_t& t, size_t rounds) {
|
|
std::vector<size_t> rnd_indecies;
|
|
helper::make_rnd_indicies(rnd_indecies, rounds);
|
|
|
|
std::vector<scalar_t> scalars(rounds);
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
scalars[i].make_random();
|
|
|
|
scalar_t s = scalar_t::random();
|
|
|
|
std::vector<scalar_t> result(rounds);
|
|
t.start(2);
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
result[i] = scalars[rnd_indecies[i]] / s / s;
|
|
}
|
|
t.stop();
|
|
|
|
return HASH_64_VEC(result);
|
|
});
|
|
|
|
run("mul_plus_G", 2000, [](timer_t& t, size_t rounds) {
|
|
std::vector<size_t> rnd_indecies;
|
|
helper::make_rnd_indicies(rnd_indecies, rounds);
|
|
|
|
std::vector<point_t> points(rounds);
|
|
point_t p = c_point_G;
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
points[i] = p;
|
|
p = p + p;
|
|
}
|
|
|
|
scalar_t a, b;
|
|
a.make_random();
|
|
b.make_random();
|
|
|
|
std::vector<point_t> result(rounds);
|
|
t.start(2);
|
|
for (size_t i = 0; i < rounds; ++i)
|
|
{
|
|
result[i] = points[rnd_indecies[i]].mul_plus_G(a, b).mul_plus_G(a, b);
|
|
}
|
|
t.stop();
|
|
|
|
return HASH_64_VEC(result);
|
|
});
|
|
|
|
return true;
|
|
}
|