gf2m_small_m.cpp

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/*
* (C) Copyright Projet SECRET, INRIA, Rocquencourt
* (C) Bhaskar Biswas and  Nicolas Sendrier
*
* (C) 2014 cryptosource GmbH
* (C) 2014 Falko Strenzke fstrenzke@cryptosource.de
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
 
#include <botan/internal/gf2m_small_m.h>
#include <botan/exceptn.h>
#include <string>
 
namespace Botan {
 
const size_t MAX_EXT_DEG = 16;
 
namespace {
 
const gf2m prim_poly[MAX_EXT_DEG + 1] = {
   01,       /* extension degree 0 (!) never used */
   03,       /* extension degree 1 (!) never used */
   07,       /* extension degree 2 */
   013,      /* extension degree 3 */
   023,      /* extension degree 4 */
   045,      /* extension degree 5 */
   0103,     /* extension degree 6 */
   0203,     /* extension degree 7 */
   0435,     /* extension degree 8 */
   01041,    /* extension degree 9 */
   02011,    /* extension degree 10 */
   04005,    /* extension degree 11 */
   010123,   /* extension degree 12 */
   020033,   /* extension degree 13 */
   042103,   /* extension degree 14 */
   0100003,  /* extension degree 15 */
};
 
std::vector<gf2m> gf_exp_table(size_t deg, gf2m prime_poly)
   {
   // construct the table gf_exp[i]=alpha^i
 
   std::vector<gf2m> tab((static_cast<size_t>(1) << deg) + 1);
 
   tab[0] = 1;
   for(size_t i = 1; i < tab.size(); ++i)
      {
      const gf2m overflow = tab[i-1] >> (deg - 1);
      tab[i] = (tab[i-1] << 1) ^ (overflow * prime_poly);
      }
 
   return tab;
   }
 
const std::vector<gf2m>& exp_table(size_t deg)
   {
   static std::vector<gf2m> tabs[MAX_EXT_DEG + 1];
 
   if(deg < 2 || deg > MAX_EXT_DEG)
      throw Invalid_Argument("GF2m_Field does not support degree " + std::to_string(deg));
 
   if(tabs[deg].empty())
      tabs[deg] = gf_exp_table(deg, prim_poly[deg]);
 
   return tabs[deg];
   }
 
std::vector<gf2m> gf_log_table(size_t deg, const std::vector<gf2m>& exp)
   {
   std::vector<gf2m> tab(static_cast<size_t>(1) << deg);
 
   tab[0] = static_cast<gf2m>((static_cast<gf2m>(1) << deg) - 1); // log of 0 is the order by convention
   for(size_t i = 0; i < tab.size(); ++i)
      {
      tab[exp[i]] = static_cast<gf2m>(i);
      }
   return tab;
   }
 
const std::vector<gf2m>& log_table(size_t deg)
   {
   static std::vector<gf2m> tabs[MAX_EXT_DEG + 1];
 
   if(deg < 2 || deg > MAX_EXT_DEG)
      throw Invalid_Argument("GF2m_Field does not support degree " + std::to_string(deg));
 
   if(tabs[deg].empty())
      tabs[deg] = gf_log_table(deg, exp_table(deg));
 
   return tabs[deg];
   }
 
}
 
uint32_t encode_gf2m(gf2m to_enc, uint8_t* mem)
   {
   mem[0] = to_enc >> 8;
   mem[1] = to_enc & 0xFF;
   return sizeof(to_enc);
   }
 
gf2m decode_gf2m(const uint8_t* mem)
   {
   gf2m result;
   result = mem[0] << 8;
   result |= mem[1];
   return result;
   }
 
GF2m_Field::GF2m_Field(size_t extdeg) : m_gf_extension_degree(extdeg),
                                        m_gf_multiplicative_order((1 << extdeg) - 1),
                                        m_gf_log_table(log_table(m_gf_extension_degree)),
                                        m_gf_exp_table(exp_table(m_gf_extension_degree))
   {
   }
 
gf2m GF2m_Field::gf_div(gf2m x, gf2m y) const
   {
   const int32_t sub_res = static_cast<int32_t>(gf_log(x) - static_cast<int32_t>(gf_log(y)));
   const gf2m modq_res = _gf_modq_1(sub_res);
   const int32_t div_res = static_cast<int32_t>(x) ? static_cast<int32_t>(gf_exp(modq_res)) : 0;
   return static_cast<gf2m>(div_res);
   }
 
}