experimental crypto: ml2s_lnk_sig_gen implemented
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sowle
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1 changed files with 269 additions and 0 deletions
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@ -78,6 +78,275 @@ bool is_power_of_2(T v)
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return true;
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}
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bool ml2s_lnk_sig_gen(const scalar_t& m, const std::vector<point_t>& B_array, const std::vector<scalar_t>& b_array, const std::vector<size_t>& s_array, ml2s_signature& signature, uint8_t* p_err = nullptr)
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{
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#define CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(cond, err_code) \
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if (!(cond)) { LOG_PRINT_RED("ml2s_lnk_sig_gen: \"" << #cond << "\" is false at " << LOCATION_SS << ENDL << "error code = " << err_code, LOG_LEVEL_3); \
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if (p_err) *p_err = err_code; return false; }
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#ifndef NDEBUG
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# define DBG_CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(cond, err_code) CHECK_AND_ASSERT_MES_CUSTOM(cond, false, if (p_err) *p_err = err_code, "ml2s_lnk_sig_gen check failed: " << #cond)
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#else
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# define DBG_CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(cond, err_code)
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#endif
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// check boundaries
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size_t L = b_array.size();
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size_t N = 2 * B_array.size();
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size_t n = log2sz(N);
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CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(s_array.size() == L, 0);
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CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(1ull << n == N, 1);
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CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(L > 0, 2);
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CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(L <= N / 2, 3);
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// initialize signature
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signature.elements.resize(L);
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for (size_t i = 0; i < L; ++i)
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{
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signature.elements[i].H_array.resize(n);
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signature.elements[i].r_array.resize(n);
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}
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std::vector<scalar_t> b_inv_array;
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b_inv_array.reserve(L);
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for (size_t i = 0; i < L; ++i)
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b_inv_array.emplace_back(b_array[i].reciprocal());
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std::vector<point_t> I_array;
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I_array.reserve(L);
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for (size_t i = 0; i < L; ++i)
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I_array.emplace_back(b_inv_array[i] * hash_helper_t::hp(b_array[i] * c_point_G));
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signature.z = hash_helper_t::hs(m, B_array, I_array);
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const scalar_t& z = signature.z;
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auto hash_point_lambda = [&z](const point_t& point) { return point + z * hash_helper_t::hp(point); };
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std::vector<point_t> A_array; // size == L
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A_array.reserve(L);
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for (size_t i = 0; i < L; ++i)
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A_array.emplace_back(c_point_G + z * I_array[i]);
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std::vector<point_t> P_array; // size == N // 2
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P_array.reserve(B_array.size());
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for (size_t i = 0; i < B_array.size(); ++i)
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P_array.emplace_back(hash_point_lambda(B_array[i]));
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point_t Q_shift = hash_helper_t::hs(A_array, P_array) * c_point_G;
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CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(P_array.size() * 2 == N, 4);
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std::vector<point_t> X_array(N);
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// X_array = { P_array[0], Q_array[0], P_array[1], Q_array[1], etc. }
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for (size_t i = 0; i < N; ++i)
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{
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if (i % 2 == 0)
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X_array[i] = P_array[i / 2];
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else
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X_array[i] = hash_point_lambda(Q_shift + B_array[i / 2]);
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}
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for (size_t i = 0; i < L; ++i)
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{
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size_t s_idx = s_array[i];
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CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(s_idx < B_array.size() && 2 * s_idx + 1 < X_array.size(), 5);
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point_t Ap = b_inv_array[i] * X_array[2 * s_idx];
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CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(Ap == A_array[i], 6);
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}
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///
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struct intermediate_element_t
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{
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scalar_t f;
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scalar_t k0;
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scalar_t q;
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size_t M_cnt;
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size_t z;
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size_t h;
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scalar_t a;
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scalar_t x;
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std::vector<point_t> Y_array;
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};
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std::vector<intermediate_element_t> interms(L);
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// challenge c0
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scalar_t e = hash_helper_t::hs(z);
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hash_helper_t::hs_t hsc;
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hsc.add_scalar(e);
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hsc.add_points_array(X_array);
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for (size_t i = 0; i < L; ++i)
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{
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auto& interm = interms[i];
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auto& sel = signature.elements[i];
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sel.Z0 = A_array[i]; // b_inv_array[i] * X_array[2 * s_array[i]] + 0 * X_array[2 * s + 1], as k1 == 0 always
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interm.f.make_random();
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sel.Z = interm.f * sel.Z0;
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interm.k0 = interm.f * b_inv_array[i];
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interm.q.make_random();
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sel.T0 = interm.q * sel.Z0;
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hsc.add_point(sel.Z0);
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hsc.add_point(sel.T0);
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hsc.add_point(sel.Z);
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}
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scalar_t c0 = hsc.calc_hash();
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// challenges c11, c13
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hsc.add_scalar(c0);
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for (size_t i = 0; i < L; ++i)
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{
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auto& interm = interms[i];
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auto& sel = signature.elements[i];
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sel.t0 = interm.q - interm.f * c0;
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interm.M_cnt = N;
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interm.z = 2 * s_array[i];
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interm.h = 2 * s_array[i] + 1; // we already checked s_array elements against X_array.size() above
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interm.a = 1;
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interm.q.make_random(); // new q
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interm.Y_array = X_array;
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sel.H_array[0] = interm.k0 / interm.q * X_array[interm.h]; // H1
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hsc.add_scalar(sel.t0);
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hsc.add_point(sel.H_array[0]);
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}
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// challenges c11, c13
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#ifndef NDEBUG
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// these vectors are only needed for self-check in the end
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std::vector<scalar_t> c1_array(n); // counting from 0, so c11 is c1_array[0], will have n elements
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std::vector<scalar_t> c3_array(n-1); // the same, will have n - 1 elements
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#endif
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scalar_t ci1 = hsc.calc_hash();
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scalar_t ci3 = hash_helper_t::hs(ci1);
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// ci1, ci3 for i in [2; n] -- corresponds c1_array for i in [1; n - 1], c3_array for i in [1; n - 2]
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for (size_t idx_n = 0; idx_n < n - 1; ++idx_n)
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{
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#ifndef NDEBUG
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c1_array[idx_n] = ci1;
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c3_array[idx_n] = ci3;
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#endif
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std::vector<const scalar_t*> c_array = { &c_scalar_1, &ci1, &c_scalar_1, &ci3 };
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hsc.add_scalar(ci1);
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for (size_t idx_L = 0; idx_L < L; ++idx_L)
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{
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auto& interm = interms[idx_L];
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auto& sel = signature.elements[idx_L];
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const scalar_t& e_local = *c_array[interm.z % 4];
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const scalar_t& g_local = *c_array[interm.h % 4];
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sel.r_array[idx_n] = interm.q * g_local / e_local; // r_i
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interm.a *= e_local;
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DBG_CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(is_power_of_2(interm.M_cnt), 200);
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interm.M_cnt = interm.M_cnt / 2;
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// TODO: check M_scalar is power of 2
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for (size_t j = 0; j < interm.M_cnt; ++j)
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interm.Y_array[j] = (interm.Y_array[2 * j] + *c_array[(2 * j + 1) % 4] * interm.Y_array[2 * j + 1]) / e_local;
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interm.z /= 2;
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interm.h = invert_last_bit(interm.z);
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interm.q.make_random();
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sel.H_array[idx_n + 1] = interm.k0 / interm.q * interm.Y_array[interm.h]; // H_{i+1}
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hsc.add_scalar(sel.r_array[idx_n]);
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hsc.add_point(sel.H_array[idx_n + 1]);
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}
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ci1 = hsc.calc_hash();
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ci3 = hash_helper_t::hs(ci1);
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}
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// challenge cn
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#ifndef NDEBUG
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c1_array[n - 1] = ci1;
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#endif
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// challenge c
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hsc.add_scalar(ci1);
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for (size_t i = 0; i < L; ++i)
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{
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auto& interm = interms[i];
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auto& sel = signature.elements[i];
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CHECK_AND_FAIL_WITH_ERROR_IF_FALSE((interm.z == 0 && interm.h == 1) || (interm.z == 1 && interm.h == 0), 7);
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const scalar_t& e_local = interm.z == 0 ? c_scalar_1 : ci1;
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const scalar_t& g_local = interm.z == 0 ? ci1 : c_scalar_1;
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sel.r_array[n - 1] = interm.q * g_local / e_local; // r_n
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interm.a *= e_local;
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interm.x = interm.a / interm.k0;
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interm.q.make_random(); // qn
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DBG_CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(interm.k0 * X_array[2 * s_array[i]] == sel.Z, 201);
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point_t W = sel.Z;
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for (size_t j = 0; j < n; ++j)
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W = W + sel.r_array[j] * sel.H_array[j];
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sel.T = interm.q * W;
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hsc.add_scalar(sel.r_array[n - 1]);
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hsc.add_point(sel.T);
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}
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scalar_t c = hsc.calc_hash();
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for (size_t i = 0; i < L; ++i)
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{
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auto& interm = interms[i];
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auto& sel = signature.elements[i];
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sel.t = interm.q - interm.x * c;
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}
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// L2S signature is complete
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#ifndef NDEBUG
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// self-check
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for (size_t i = 0; i < L; ++i)
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{
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auto& interm = interms[i];
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auto& sel = signature.elements[i];
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point_t W = sel.Z;
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for (size_t j = 0; j < n; ++j)
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W = W + sel.r_array[j] * sel.H_array[j];
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DBG_CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(sel.T == interm.q * W, 230);
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point_t R;
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R.zero();
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bool r = ml2s_rsum(n, X_array, c1_array, c3_array, R);
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DBG_CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(r, 231);
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DBG_CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(R == interm.x * W, 232);
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DBG_CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(sel.t == interm.q - interm.x * c, 233);
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DBG_CHECK_AND_FAIL_WITH_ERROR_IF_FALSE(sel.t * W + c * R == sel.T, 234);
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}
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#endif // #ifndef NDEBUG
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return true;
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#undef DBG_CHECK_AND_FAIL_WITH_ERROR_IF_FALSE
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#undef CHECK_AND_FAIL_WITH_ERROR_IF_FALSE
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} // ml2s_lnk_sig_gen
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bool ml2s_lnk_sig_verif(const scalar_t& m, const std::vector<point_t>& B_array, const ml2s_signature& signature, uint8_t* p_err = nullptr,
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std::vector<point_t>* p_I_array = nullptr)
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