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/*
* (C) 2014 cryptosource GmbH
* (C) 2014 Falko Strenzke fstrenzke@cryptosource.de
*
* Botan is released under the Simplified BSD License (see license.txt)
*
*/
#include <botan/polyn_gf2m.h>
#include <botan/internal/bit_ops.h>
#include <botan/internal/code_based_util.h>
#include <botan/exceptn.h>
namespace Botan {
namespace {
void patch_root_array(gf2m res_root_arr[],
size_t res_root_arr_len,
size_t root_pos)
{
volatile gf2m patch_elem = 0x01;
volatile gf2m cond_mask = (root_pos == res_root_arr_len);
cond_mask = expand_mask_16bit(cond_mask);
cond_mask = ~cond_mask; /* now cond = 1 if not enough roots */
patch_elem &= cond_mask;
for(size_t i = 0; i < res_root_arr_len; i++)
{
gf2m masked_patch_elem = (patch_elem++) & cond_mask;
res_root_arr[i] ^= masked_patch_elem++;
}
}
class gf2m_decomp_rootfind_state
{
public:
gf2m_decomp_rootfind_state(const polyn_gf2m & p_polyn, size_t code_length);
void calc_LiK(const polyn_gf2m & sigma);
gf2m calc_Fxj_j_neq_0( const polyn_gf2m & sigma, gf2m j_gray);
void calc_next_Aij();
void calc_Ai_zero(const polyn_gf2m & sigma);
secure_vector<gf2m> find_roots(const polyn_gf2m & sigma);
private:
size_t m_code_length;
secure_vector<gf2m> m_Lik; // size is outer_summands * m
secure_vector<gf2m> m_Aij; // ...
uint32_t m_outer_summands;
gf2m m_j;
gf2m m_j_gray;
gf2m m_sigma_3_l;
gf2m m_sigma_3_neq_0_mask;
};
/*
* !! Attention: assumes gf2m is 16bit !!
*/
#if 0
gf2m brootf_decomp_gray_to_lex(gf2m gray)
{
static_assert(sizeof(gf2m) == 2, "Expected size");
gf2m result = gray ^ (gray>>8);
result ^= (result >> 4);
result ^= (result >> 2);
result ^= (result >> 1);
return result;
}
#endif
/**
* calculates ceil((t-4)/5) = outer_summands - 1
*/
uint32_t brootf_decomp_calc_sum_limit(uint32_t t)
{
uint32_t result;
if(t < 4)
{
return 0;
}
result = t - 4;
result += 4;
result /= 5;
return result;
}
gf2m_decomp_rootfind_state::gf2m_decomp_rootfind_state(const polyn_gf2m & polyn, size_t code_length) :
m_code_length(code_length), m_j(0), m_j_gray(0)
{
gf2m coeff_3;
gf2m coeff_head;
std::shared_ptr<GF2m_Field> sp_field = polyn.get_sp_field();
int deg_sigma = polyn.get_degree();
if(deg_sigma <= 3)
{
throw Internal_Error("Unexpected degree in gf2m_decomp_rootfind_state");
}
coeff_3 = polyn.get_coef( 3);
coeff_head = polyn.get_coef( deg_sigma); /* dummy value for SCA CM */
if(coeff_3 != 0)
{
this->m_sigma_3_l = sp_field->gf_l_from_n(coeff_3);
this->m_sigma_3_neq_0_mask = 0xFFFF;
}
else
{
// dummy value needed for timing countermeasure
this->m_sigma_3_l = sp_field->gf_l_from_n(coeff_head);
this->m_sigma_3_neq_0_mask = 0 ;
}
this->m_outer_summands = 1 + brootf_decomp_calc_sum_limit(deg_sigma);
this->m_Lik.resize(this->m_outer_summands * sp_field->get_extension_degree());
this->m_Aij.resize(this->m_outer_summands);
}
void gf2m_decomp_rootfind_state::calc_Ai_zero(const polyn_gf2m & sigma)
{
uint32_t i;
/*
* this function assumes this the first gray code element is zero
*/
for(i = 0; i < this->m_outer_summands; i++)
{
this->m_Aij[i] = sigma.get_coef(5*i);
}
this->m_j = 0;
this->m_j_gray = 0;
}
void gf2m_decomp_rootfind_state::calc_next_Aij()
{
/*
* upon function entry, we have in the state j, Aij.
* first thing, we declare Aij Aij_minusone and increase j.
* Case j=0 upon function entry also included, then Aij contains A_{i,j=0}.
*/
uint32_t i;
gf2m diff, new_j_gray;
uint32_t Lik_pos_base;
this->m_j++;
new_j_gray = lex_to_gray(this->m_j);
if(this->m_j & 1) /* half of the times */
{
Lik_pos_base = 0;
}
else if(this->m_j & 2) /* one quarter of the times */
{
Lik_pos_base = this->m_outer_summands;
}
else if( this->m_j & 4) /* one eighth of the times */
{
Lik_pos_base = this->m_outer_summands * 2;
}
else if( this->m_j & 8) /* one sixteenth of the times */
{
Lik_pos_base = this->m_outer_summands * 3;
}
else if( this->m_j & 16) /* ... */
{
Lik_pos_base = this->m_outer_summands * 4;
}
else
{
gf2m delta_offs = 5;
diff = this->m_j_gray ^ new_j_gray;
while(((static_cast<gf2m>(1) << delta_offs) & diff) == 0)
{
delta_offs++;
}
Lik_pos_base = delta_offs * this->m_outer_summands;
}
this->m_j_gray = new_j_gray;
i = 0;
for(; i < this->m_outer_summands; i++)
{
this->m_Aij[i] ^= this->m_Lik[Lik_pos_base + i];
}
}
void gf2m_decomp_rootfind_state::calc_LiK(const polyn_gf2m & sigma)
{
std::shared_ptr<GF2m_Field> sp_field = sigma.get_sp_field();
uint32_t i, k, d;
d = sigma.get_degree();
for(k = 0; k < sp_field->get_extension_degree(); k++)
{
uint32_t Lik_pos_base = k * this->m_outer_summands;
gf2m alpha_l_k_tt2_ttj[4];
alpha_l_k_tt2_ttj[0] = sp_field->gf_l_from_n(static_cast<gf2m>(1) << k);
alpha_l_k_tt2_ttj[1] = sp_field->gf_mul_rrr(alpha_l_k_tt2_ttj[0], alpha_l_k_tt2_ttj[0]);
alpha_l_k_tt2_ttj[2] = sp_field->gf_mul_rrr(alpha_l_k_tt2_ttj[1],alpha_l_k_tt2_ttj[1] );
alpha_l_k_tt2_ttj[3] = sp_field->gf_mul_rrr(alpha_l_k_tt2_ttj[2], alpha_l_k_tt2_ttj[2]);
for(i = 0; i < this->m_outer_summands; i++)
{
uint32_t j;
uint32_t five_i = 5*i;
uint32_t Lik_pos = Lik_pos_base + i;
this->m_Lik[Lik_pos] = 0;
for(j = 0; j <= 3; j++)
{
gf2m f, x;
uint32_t f_ind = five_i + (static_cast<uint32_t>(1) << j);
if(f_ind > d)
{
break;
}
f = sigma.get_coef( f_ind);
x = sp_field->gf_mul_zrz(alpha_l_k_tt2_ttj[j], f);
this->m_Lik[Lik_pos] ^= x;
}
}
}
}
gf2m gf2m_decomp_rootfind_state::calc_Fxj_j_neq_0( const polyn_gf2m & sigma, gf2m j_gray)
{
//needs the A_{ij} to compute F(x)_j
gf2m sum = 0;
uint32_t i;
std::shared_ptr<GF2m_Field> sp_field = sigma.get_sp_field();
const gf2m jl_gray = sp_field->gf_l_from_n(j_gray);
gf2m xl_j_tt_5 = sp_field->gf_square_rr(jl_gray);
gf2m xl_gray_tt_3 = sp_field->gf_mul_rrr(xl_j_tt_5, jl_gray);
xl_j_tt_5 = sp_field->gf_mul_rrr(xl_j_tt_5, xl_gray_tt_3);
sum = sp_field->gf_mul_nrr(xl_gray_tt_3, this->m_sigma_3_l);
sum &= this->m_sigma_3_neq_0_mask;
/* here, we rely on compiler to be unable to optimize
* for the state->sigma_3_neq_0_mask value
*/
/* treat i = 0 special: */
sum ^= this->m_Aij[0];
/* treat i = 1 special also */
if(this->m_outer_summands > 1)
{
gf2m x;
x = sp_field->gf_mul_zrz(xl_j_tt_5, this->m_Aij[1]); /* x_j^{5i} A_i^j */
sum ^= x;
}
gf2m xl_j_tt_5i = xl_j_tt_5;
for(i = 2; i < this->m_outer_summands; i++)
{
gf2m x;
xl_j_tt_5i = sp_field->gf_mul_rrr(xl_j_tt_5i, xl_j_tt_5);
// now x_j_tt_5i lives up to its name
x = sp_field->gf_mul_zrz(xl_j_tt_5i, this->m_Aij[i]); /* x_j^{5i} A_i^(j) */
sum ^= x;
}
return sum;
}
secure_vector<gf2m> gf2m_decomp_rootfind_state::find_roots(const polyn_gf2m & sigma)
{
const int sigma_degree = sigma.get_degree();
BOTAN_ASSERT(sigma_degree > 0, "Valid sigma");
secure_vector<gf2m> result(sigma_degree);
uint32_t root_pos = 0;
this->calc_Ai_zero(sigma);
this->calc_LiK(sigma);
for(;;)
{
gf2m eval_result;
if(this->m_j_gray == 0)
{
eval_result = sigma.get_coef(0);
}
else
{
eval_result = this->calc_Fxj_j_neq_0(sigma, this->m_j_gray);
}
if(eval_result == 0)
{
result[root_pos] = this->m_j_gray;
root_pos++;
}
if(this->m_j + static_cast<uint32_t>(1) == m_code_length)
{
break;
}
this->calc_next_Aij();
}
// side channel / fault attack countermeasure:
patch_root_array(result.data(), result.size(), root_pos);
return result;
}
} // end anonymous namespace
secure_vector<gf2m> find_roots_gf2m_decomp(const polyn_gf2m & polyn, size_t code_length)
{
gf2m_decomp_rootfind_state state(polyn, code_length);
return state.find_roots(polyn);
}
} // end namespace Botan