path: root/src/lib/pubkey/mce/code_based_key_gen.cpp

/**
 * (C) Copyright Projet SECRET, INRIA, Rocquencourt
 * (C) Bhaskar Biswas and  Nicolas Sendrier
 *
 * (C) 2014 cryptosource GmbH
 * (C) 2014 Falko Strenzke fstrenzke@cryptosource.de
 * (C) 2015 Jack Lloyd
 *
 * Botan is released under the Simplified BSD License (see license.txt)
 *
 */

#include <botan/mceliece.h>
#include <botan/internal/mce_internal.h>
#include <botan/internal/code_based_util.h>
#include <botan/loadstor.h>

namespace Botan {

namespace {

struct binary_matrix
   {
   public:
      binary_matrix(u32bit m_rown, u32bit m_coln);

      void row_xor(u32bit a, u32bit b);
      secure_vector<int> row_reduced_echelon_form();

      /**
      * return the coefficient out of F_2
      */
      u32bit coef(u32bit i, u32bit j)
         {
         return (m_elem[(i) * m_rwdcnt + (j) / 32] >> (j % 32)) & 1;
         };

      void set_coef_to_one(u32bit i, u32bit j)
         {
         m_elem[(i) * m_rwdcnt + (j) / 32] |= (static_cast<u32bit>(1) << ((j) % 32)) ;
         };

      void toggle_coeff(u32bit i, u32bit j)
         {
         m_elem[(i) * m_rwdcnt + (j) / 32] ^= (static_cast<u32bit>(1) << ((j) % 32)) ;
         }

      void set_to_zero()
         {
         zeroise(m_elem);
         }

      //private:
      u32bit m_rown;  // number of rows.
      u32bit m_coln; // number of columns.
      u32bit m_rwdcnt; // number of words in a row
      std::vector<u32bit> m_elem;
   };

binary_matrix::binary_matrix (u32bit rown, u32bit coln)
   {
   m_coln = coln;
   m_rown = rown;
   m_rwdcnt = 1 + ((m_coln - 1) / 32);
   m_elem = std::vector<u32bit>(m_rown * m_rwdcnt);
   }

void binary_matrix::row_xor(u32bit a, u32bit b)
   {
   u32bit i;
   for(i=0;i<m_rwdcnt;i++)
      {
      m_elem[a*m_rwdcnt+i]^=m_elem[b*m_rwdcnt+i];
      }
   }

//the matrix is reduced from LSB...(from right)
secure_vector<int> binary_matrix::row_reduced_echelon_form()
   {
   u32bit i, failcnt, findrow, max=m_coln - 1;

   secure_vector<int> perm(m_coln);
   for(i=0;i<m_coln;i++)
      {
      perm[i]=i;//initialize permutation.
      }
   failcnt = 0;

   for(i=0;i<m_rown;i++,max--)
      {
      findrow=0;
      for(u32bit j=i;j<m_rown;j++)
         {
         if(coef(j,max))
            {
            if (i!=j)//not needed as ith row is 0 and jth row is 1.
               row_xor(i,j);//xor to the row.(swap)?
            findrow=1;
            break;
            }//largest value found (end if)
         }

      if(!findrow)//if no row with a 1 found then swap last column and the column with no 1 down.
         {
         perm[m_coln - m_rown - 1 - failcnt] = max;
         failcnt++;
         if (!max)
            {
            //CSEC_FREE_MEM_CHK_SET_NULL(*p_perm);
            //CSEC_THR_RETURN();
            perm.resize(0);
            }
         i--;
         }
      else
         {
         perm[i+m_coln - m_rown] = max;
         for(u32bit j=i+1;j<m_rown;j++)//fill the column downwards with 0's
            {
            if(coef(j,(max)))
               {
               row_xor(j,i);//check the arg. order.
               }
            }

         for(int j=i-1;j>=0;j--)//fill the column with 0's upwards too.
            {
            if(coef(j,(max)))
               {
               row_xor(j,i);
               }
            }
         }
      }//end for(i)
   return perm;
   }

void randomize_support(std::vector<gf2m>& L, RandomNumberGenerator& rng)
   {
   for(u32bit i = 0; i != L.size(); ++i)
      {
      gf2m rnd = random_gf2m(rng);

       // no rejection sampling, but for useful code-based parameters with n <= 13 this seem tolerable
      std::swap(L[i], L[rnd % L.size()]);
      }
   }

std::unique_ptr<binary_matrix> generate_R(std::vector<gf2m> &L, polyn_gf2m* g, std::shared_ptr<GF2m_Field> sp_field, u32bit code_length, u32bit t )
   {
   //L- Support
   //t- Number of errors
   //n- Length of the Goppa code
   //m- The extension degree of the GF
   //g- The generator polynomial.
   gf2m x,y;
   u32bit i,j,k,r,n;
   std::vector<int> Laux(code_length);
   n=code_length;
   r=t*sp_field->get_extension_degree();

   binary_matrix H(r, n) ;

   for(i=0;i< n;i++)
      {
      x = g->eval(lex_to_gray(L[i]));//evaluate the polynomial at the point L[i].
      x = sp_field->gf_inv(x);
      y = x;
      for(j=0;j<t;j++)
         {
         for(k=0;k<sp_field->get_extension_degree();k++)
            {
            if(y & (1<<k))
               {
               //the co-eff. are set in 2^0,...,2^11 ; 2^0,...,2^11 format along the rows/cols?
               H.set_coef_to_one(j*sp_field->get_extension_degree()+ k,i);
               }
            }
         y = sp_field->gf_mul(y,lex_to_gray(L[i]));
         }
      }//The H matrix is fed.

   secure_vector<int> perm = H.row_reduced_echelon_form();
   if (perm.size() == 0)
      {
      // result still is NULL
      throw Invalid_State("could not bring matrix in row reduced echelon form");
      }

   std::unique_ptr<binary_matrix> result(new binary_matrix(n-r,r)) ;
   for (i = 0; i < (*result).m_rown; ++i)
      {
      for (j = 0; j < (*result).m_coln; ++j)
         {
         if (H.coef(j,perm[i]))
            {
            result->toggle_coeff(i,j);
            }
         }
      }
   for (i = 0; i < code_length; ++i)
      {
      Laux[i] = L[perm[i]];
      }
   for (i = 0; i < code_length; ++i)
      {
      L[i] = Laux[i];
      }
   return result;
   }
}

McEliece_PrivateKey generate_mceliece_key( RandomNumberGenerator & rng, u32bit ext_deg, u32bit code_length, u32bit t)
   {
   u32bit i, j, k, l;
   std::unique_ptr<binary_matrix> R;

   u32bit codimension = t * ext_deg;
   if(code_length <= codimension)
      {
      throw Invalid_Argument("invalid McEliece parameters");
      }
   std::shared_ptr<GF2m_Field> sp_field ( new GF2m_Field(ext_deg ));

   //pick the support.........
   std::vector<gf2m> L(code_length);

   for(i=0;i<code_length;i++)
      {
      L[i]=i;
      }
   randomize_support(L, rng);
   polyn_gf2m g(sp_field); // create as zero
   bool success = false;
   do
      {
      // create a random irreducible polynomial
      g = polyn_gf2m (t, rng, sp_field);

      try{
      R = generate_R(L,&g, sp_field, code_length, t);
      success = true;
      }
      catch(const Invalid_State &)
         {
         }
      } while (!success);

   std::vector<polyn_gf2m> sqrtmod = polyn_gf2m::sqrt_mod_init( g);
   std::vector<polyn_gf2m> F = syndrome_init(g, L, code_length);

   // Each F[i] is the (precomputed) syndrome of the error vector with
   // a single '1' in i-th position.
   // We do not store the F[i] as polynomials of degree t , but
   // as binary vectors of length ext_deg * t (this will
   // speed up the syndrome computation)
   //
   //
   std::vector<u32bit> H(bit_size_to_32bit_size(codimension) * code_length );
   u32bit* sk = H.data();
   for (i = 0; i < code_length; ++i)
      {
      for (l = 0; l < t; ++l)
         {
         k = (l * ext_deg) / 32;
         j = (l * ext_deg) % 32;
         sk[k] ^= static_cast<u32bit>(F[i].get_coef(l)) << j;
         if (j + ext_deg > 32)
            {
            sk[k + 1] ^= F[i].get_coef( l) >> (32 - j);
            }
         }
      sk += bit_size_to_32bit_size(codimension);
      }

   // We need the support L for decoding (decryption). In fact the
   // inverse is needed

   std::vector<gf2m> Linv(code_length) ;
   for (i = 0; i < code_length; ++i)
      {
      Linv[L[i]] = i;
      }
   std::vector<byte> pubmat (R->m_elem.size() * 4);
   for(i = 0; i < R->m_elem.size(); i++)
      {
      store_le(R->m_elem[i], &pubmat[i*4]);
      }

   return McEliece_PrivateKey(g, H, sqrtmod, Linv, pubmat);
   }

}