/*

 * (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)

 *

 */

#ifndef BOTAN_GF2M_SMALL_M_H_

#define BOTAN_GF2M_SMALL_M_H_

#include <botan/types.h>

#include <vector>

namespace Botan {

typedef uint16_t gf2m;

/**

* GF(2^m) field for m = [2...16]

*/

class BOTAN_TEST_API GF2m_Field

   {

   public:

      explicit GF2m_Field(size_t extdeg);

      gf2m gf_mul(gf2m x, gf2m y) const

         {

         return ((x) ? gf_mul_fast(x, y) : 0);

         }

      gf2m gf_square(gf2m x) const

         {

         return ((x) ? gf_exp(_gf_modq_1(gf_log(x) << 1)) : 0);

         }

      gf2m square_rr(gf2m x) const

         {

         return _gf_modq_1(x << 1);

         }

      gf2m gf_mul_fast(gf2m x, gf2m y) const

         {

         return ((y) ? gf_exp(_gf_modq_1(gf_log(x) + gf_log(y))) : 0);

         }

      /*

      naming convention of GF(2^m) field operations:

        l logarithmic, unreduced

        r logarithmic, reduced

        n normal, non-zero

        z normal, might be zero

      */

      gf2m gf_mul_lll(gf2m a, gf2m b) const

         {

         return (a + b);

         }

      gf2m gf_mul_rrr(gf2m a, gf2m b) const

         {

         return (_gf_modq_1(gf_mul_lll(a, b)));

         }

      gf2m gf_mul_nrr(gf2m a, gf2m b) const

         {

         return (gf_exp(gf_mul_rrr(a, b)));

         }

      gf2m gf_mul_rrn(gf2m a, gf2m y) const

         {

         return _gf_modq_1(gf_mul_lll(a, gf_log(y)));

         }

      gf2m gf_mul_rnr(gf2m y, gf2m a) const

         {

         return gf_mul_rrn(a, y);

         }

      gf2m gf_mul_lnn(gf2m x, gf2m y) const

         {

         return (gf_log(x) + gf_log(y));

         }

      gf2m gf_mul_rnn(gf2m x, gf2m y) const

         {

         return _gf_modq_1(gf_mul_lnn(x, y));

         }

      gf2m gf_mul_nrn(gf2m a, gf2m y) const

         {

         return gf_exp(_gf_modq_1((a) + gf_log(y)));

         }

      /**

      * zero operand allowed

      */

      gf2m gf_mul_zrz(gf2m a, gf2m y) const

         {

         return ( (y == 0) ? 0 : gf_mul_nrn(a, y) );

         }

      gf2m gf_mul_zzr(gf2m a, gf2m y) const

         {

         return gf_mul_zrz(y, a);

         }

      /**

      * non-zero operand

      */

      gf2m gf_mul_nnr(gf2m y, gf2m a) const

         {

         return gf_mul_nrn(a, y);

         }

      gf2m gf_sqrt(gf2m x) const

         {

         return ((x) ? gf_exp(_gf_modq_1(gf_log(x) << (get_extension_degree()-1))) : 0);

         }

      gf2m gf_div_rnn(gf2m x, gf2m y) const

         {

         return _gf_modq_1(gf_log(x) - gf_log(y));

         }

      gf2m gf_div_rnr(gf2m x, gf2m b) const

         {

         return _gf_modq_1(gf_log(x) - b);

         }

      gf2m gf_div_nrr(gf2m a, gf2m b) const

         {

         return gf_exp(_gf_modq_1(a - b));

         }

      gf2m gf_div_zzr(gf2m x, gf2m b) const

         {

         return ((x) ? gf_exp(_gf_modq_1(gf_log(x) - b)) : 0);

         }

      gf2m gf_inv(gf2m x) const

         {

         return gf_exp(gf_ord() - gf_log(x));

         }

      gf2m gf_inv_rn(gf2m x) const

         {

         return (gf_ord() - gf_log(x));

         }

      gf2m gf_square_ln(gf2m x) const

         {

         return gf_log(x) << 1;

         }

      gf2m gf_square_rr(gf2m a) const

         {

         return a << 1;

         }

      gf2m gf_l_from_n(gf2m x) const

         {

         return gf_log(x);

         }

      gf2m gf_div(gf2m x, gf2m y) const;

      gf2m gf_exp(gf2m i) const

         {

         return m_gf_exp_table.at(i); /* alpha^i */

         }

      gf2m gf_log(gf2m i) const

         {

         return m_gf_log_table.at(i); /* return i when x=alpha^i */

         }

      gf2m gf_ord() const

         {

         return m_gf_multiplicative_order;

         }

      size_t get_extension_degree() const

         {

         return m_gf_extension_degree;

         }

      gf2m get_cardinality() const

         {

         return static_cast<gf2m>(1 << get_extension_degree());

         }

   private:

      gf2m _gf_modq_1(int32_t d) const

         {

         /* residual modulo q-1

         when -q < d < 0, we get (q-1+d)

         when 0 <= d < q, we get (d)

         when q <= d < 2q-1, we get (d-q+1)

         */

         return static_cast<gf2m>(((d) & gf_ord()) + ((d) >> get_extension_degree()));

         }

      const size_t m_gf_extension_degree;

      const gf2m m_gf_multiplicative_order;

      const std::vector<gf2m>& m_gf_log_table;

      const std::vector<gf2m>& m_gf_exp_table;

   };

uint32_t encode_gf2m(gf2m to_enc, uint8_t* mem);

gf2m decode_gf2m(const uint8_t* mem);

}

#endif