9#include <botan/internal/polyn_gf2m.h>
11#include <botan/assert.h>
12#include <botan/exceptn.h>
13#include <botan/internal/bit_ops.h>
14#include <botan/internal/code_based_util.h>
20void patch_root_array(
gf2m res_root_arr[],
size_t res_root_arr_len,
size_t root_pos) {
21 volatile gf2m patch_elem = 0x01;
22 volatile gf2m cond_mask = (root_pos == res_root_arr_len);
24 cond_mask = ~cond_mask;
25 patch_elem = patch_elem & cond_mask;
26 for(
size_t i = 0; i < res_root_arr_len; i++) {
27 patch_elem = patch_elem + 1;
28 gf2m masked_patch_elem = patch_elem & cond_mask;
29 res_root_arr[i] ^= masked_patch_elem++;
33class gf2m_decomp_rootfind_state {
35 gf2m_decomp_rootfind_state(
const polyn_gf2m& p_polyn,
size_t code_length);
37 void calc_LiK(
const polyn_gf2m&
sigma);
40 void calc_Ai_zero(
const polyn_gf2m&
sigma);
47 uint32_t m_outer_summands;
51 gf2m m_sigma_3_neq_0_mask;
57uint32_t brootf_decomp_calc_sum_limit(uint32_t t) {
68gf2m_decomp_rootfind_state::gf2m_decomp_rootfind_state(
const polyn_gf2m& polyn,
size_t code_length) :
69 m_code_length(code_length), m_j(0), m_j_gray(0) {
72 std::shared_ptr<GF2m_Field> sp_field = polyn.get_sp_field();
73 int deg_sigma = polyn.get_degree();
75 throw Internal_Error(
"Unexpected degree in gf2m_decomp_rootfind_state");
78 coeff_3 = polyn.get_coef(3);
79 coeff_head = polyn.get_coef(deg_sigma);
81 this->m_sigma_3_l = sp_field->gf_l_from_n(coeff_3);
82 this->m_sigma_3_neq_0_mask = 0xFFFF;
85 this->m_sigma_3_l = sp_field->gf_l_from_n(coeff_head);
86 this->m_sigma_3_neq_0_mask = 0;
89 this->m_outer_summands = 1 + brootf_decomp_calc_sum_limit(deg_sigma);
90 this->m_Lik.resize(this->m_outer_summands * sp_field->get_extension_degree());
91 this->m_Aij.resize(this->m_outer_summands);
94void gf2m_decomp_rootfind_state::calc_Ai_zero(
const polyn_gf2m& sigma) {
99 for(i = 0; i < this->m_outer_summands; i++) {
100 this->m_Aij[i] =
sigma.get_coef(5 * i);
106void gf2m_decomp_rootfind_state::calc_next_Aij() {
113 gf2m diff, new_j_gray;
114 uint32_t Lik_pos_base;
123 }
else if(this->m_j & 2)
125 Lik_pos_base = this->m_outer_summands;
126 }
else if(this->m_j & 4)
128 Lik_pos_base = this->m_outer_summands * 2;
129 }
else if(this->m_j & 8)
131 Lik_pos_base = this->m_outer_summands * 3;
132 }
else if(this->m_j & 16)
134 Lik_pos_base = this->m_outer_summands * 4;
137 diff = this->m_j_gray ^ new_j_gray;
138 while(((
static_cast<gf2m>(1) << delta_offs) & diff) == 0) {
141 Lik_pos_base = delta_offs * this->m_outer_summands;
143 this->m_j_gray = new_j_gray;
146 for(; i < this->m_outer_summands; i++) {
147 this->m_Aij[i] ^= this->m_Lik[Lik_pos_base + i];
151void gf2m_decomp_rootfind_state::calc_LiK(
const polyn_gf2m& sigma) {
152 std::shared_ptr<GF2m_Field> sp_field =
sigma.get_sp_field();
154 d =
sigma.get_degree();
155 for(k = 0; k < sp_field->get_extension_degree(); k++) {
156 uint32_t Lik_pos_base = k * this->m_outer_summands;
157 gf2m alpha_l_k_tt2_ttj[4];
158 alpha_l_k_tt2_ttj[0] = sp_field->gf_l_from_n(
static_cast<gf2m>(1) << k);
159 alpha_l_k_tt2_ttj[1] = sp_field->gf_mul_rrr(alpha_l_k_tt2_ttj[0], alpha_l_k_tt2_ttj[0]);
160 alpha_l_k_tt2_ttj[2] = sp_field->gf_mul_rrr(alpha_l_k_tt2_ttj[1], alpha_l_k_tt2_ttj[1]);
162 alpha_l_k_tt2_ttj[3] = sp_field->gf_mul_rrr(alpha_l_k_tt2_ttj[2], alpha_l_k_tt2_ttj[2]);
163 for(i = 0; i < this->m_outer_summands; i++) {
165 uint32_t five_i = 5 * i;
166 uint32_t Lik_pos = Lik_pos_base + i;
167 this->m_Lik[Lik_pos] = 0;
168 for(j = 0; j <= 3; j++) {
170 uint32_t f_ind = five_i + (
static_cast<uint32_t
>(1) << j);
174 f =
sigma.get_coef(f_ind);
176 x = sp_field->gf_mul_zrz(alpha_l_k_tt2_ttj[j], f);
177 this->m_Lik[Lik_pos] ^= x;
183gf2m gf2m_decomp_rootfind_state::calc_Fxj_j_neq_0(
const polyn_gf2m& sigma, gf2m j_gray) {
187 std::shared_ptr<GF2m_Field> sp_field =
sigma.get_sp_field();
188 const gf2m jl_gray = sp_field->gf_l_from_n(j_gray);
189 gf2m xl_j_tt_5 = sp_field->gf_square_rr(jl_gray);
190 gf2m xl_gray_tt_3 = sp_field->gf_mul_rrr(xl_j_tt_5, jl_gray);
191 xl_j_tt_5 = sp_field->gf_mul_rrr(xl_j_tt_5, xl_gray_tt_3);
193 sum = sp_field->gf_mul_nrr(xl_gray_tt_3, this->m_sigma_3_l);
194 sum &= this->m_sigma_3_neq_0_mask;
199 sum ^= this->m_Aij[0];
202 if(this->m_outer_summands > 1) {
204 x = sp_field->gf_mul_zrz(xl_j_tt_5, this->m_Aij[1]);
208 gf2m xl_j_tt_5i = xl_j_tt_5;
210 for(i = 2; i < this->m_outer_summands; i++) {
212 xl_j_tt_5i = sp_field->gf_mul_rrr(xl_j_tt_5i, xl_j_tt_5);
214 x = sp_field->gf_mul_zrz(xl_j_tt_5i, this->m_Aij[i]);
220secure_vector<gf2m> gf2m_decomp_rootfind_state::find_roots(
const polyn_gf2m& sigma) {
221 const int sigma_degree =
sigma.get_degree();
223 secure_vector<gf2m> result(sigma_degree);
224 uint32_t root_pos = 0;
226 this->calc_Ai_zero(sigma);
227 this->calc_LiK(sigma);
231 if(this->m_j_gray == 0) {
232 eval_result =
sigma.get_coef(0);
234 eval_result = this->calc_Fxj_j_neq_0(sigma, this->m_j_gray);
237 if(eval_result == 0) {
238 result[root_pos] = this->m_j_gray;
242 if(this->m_j +
static_cast<uint32_t
>(1) == m_code_length) {
245 this->calc_next_Aij();
249 patch_root_array(result.data(), result.size(), root_pos);
256 gf2m_decomp_rootfind_state state(polyn, code_length);
257 return state.find_roots(polyn);
#define BOTAN_ASSERT(expr, assertion_made)
gf2m lex_to_gray(gf2m lex)
uint16_t expand_mask_16bit(T tst)
std::vector< T, secure_allocator< T > > secure_vector
secure_vector< gf2m > find_roots_gf2m_decomp(const polyn_gf2m &polyn, size_t code_length)