text: /*
   * (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 {
  
  uint32_t patch_root_array(gf2m* res_root_arr,
                          uint32_t res_root_arr_len,
                          uint32_t root_pos)
     {
     volatile uint32_t i;
     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(i = 0; i < res_root_arr_len; i++)
        {
  
        gf2m masked_patch_elem = (patch_elem++) & cond_mask;
        res_root_arr[i] ^= masked_patch_elem++;
        }
     return res_root_arr_len;
     }
  
  class gf2m_decomp_rootfind_state
     {
     public:
        gf2m_decomp_rootfind_state(const polyn_gf2m & p_polyn, uint32_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);
        uint32_t get_code_length() const { return code_length; }
        uint32_t 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, uint32_t the_code_length) :
     code_length(the_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);
     do
        {
        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) == this->get_code_length())
           {
           break;
           }
        this->calc_next_Aij();
        }while(1);
  
     // side channel / fault attack countermeasure:
     root_pos = patch_root_array(result.data(), result.size(), root_pos);
     result.resize(root_pos);
     return result;
     }
  
  } // end anonymous namespace
  
  secure_vector<gf2m> find_roots_gf2m_decomp(const polyn_gf2m & polyn, uint32_t code_length)
     {
     gf2m_decomp_rootfind_state state(polyn, code_length);
     return state.find_roots(polyn);
     }
  
  } // end namespace Botan
  