polyn_gf2m.h

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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)
 *
 */

#ifndef BOTAN_POLYN_GF2M_H_
#define BOTAN_POLYN_GF2M_H_

#include <botan/secmem.h>
#include <botan/gf2m_small_m.h>
#include <utility>

namespace Botan {

class RandomNumberGenerator;

class polyn_gf2m
   {
   public:
      /**
      * create a zero polynomial:
      */
      explicit polyn_gf2m( std::shared_ptr<GF2m_Field> sp_field );

      polyn_gf2m()
         :m_deg(-1) {}

      polyn_gf2m(const secure_vector<uint8_t>& encoded, std::shared_ptr<GF2m_Field> sp_field );

      polyn_gf2m& operator=(const polyn_gf2m&) = default;

      bool operator==(const polyn_gf2m & other) const ;

      bool operator!=(const polyn_gf2m & other) const { return !(*this == other); }

      polyn_gf2m(polyn_gf2m&& other)
         {
         this->swap(other);
         }

      polyn_gf2m & operator=(polyn_gf2m&& other)
         {
         if(this != &other)
            {
            this->swap(other);
            }
         return *this;
         }

      void swap(polyn_gf2m& other);

      secure_vector<uint8_t> encode() const;
      /**
      * create zero polynomial with reservation of space for a degree d polynomial
      */
      polyn_gf2m(int d, std::shared_ptr<GF2m_Field> sp_field);

      polyn_gf2m(polyn_gf2m const& other);
      /**
      * create zero polynomial with allocated size determined by specified degree d:
      */

      /**
      * random irreducible polynomial of degree t
      */
      polyn_gf2m(int t, RandomNumberGenerator& rng, std::shared_ptr<GF2m_Field> sp_field);

      std::shared_ptr<GF2m_Field> get_sp_field() const
         { return msp_field; }

      gf2m& operator[](size_t i) { return coeff[i]; }

      gf2m operator[](size_t i) const { return coeff[i]; }

      gf2m get_lead_coef() const { return coeff[m_deg]; }

      gf2m get_coef(uint32_t i) const { return coeff[i]; }

      inline void set_coef(uint32_t i, gf2m v)
         {
         coeff[i] = v;
         }

      inline void add_to_coef(uint32_t i, gf2m v)
         {
         coeff[i] = coeff[i] ^ v;
         }

      std::string to_string() const;

      /** decode a polynomial from memory: **/
      polyn_gf2m(const uint8_t* mem, uint32_t mem_len, std::shared_ptr<GF2m_Field> sp_field);
      // remove one! ^v!
      /**
      *  create a polynomial from memory area (encoded)
      */
      polyn_gf2m(int degree, const unsigned  char* mem, uint32_t mem_byte_len, std::shared_ptr<GF2m_Field> sp_field);

      void encode(uint32_t min_numo_coeffs, uint8_t* mem, uint32_t mem_len) const;

      int get_degree() const;

      /**
      * determine the degree in a timing secure manner. the timing of this function
      * only depends on the number of allocated coefficients, not on the actual
      * degree
      */
      int calc_degree_secure() const;

      void degppf(const polyn_gf2m & g, int* p_result);

      static std::vector<polyn_gf2m> sqmod_init(const polyn_gf2m & g);

      static std::vector<polyn_gf2m> sqrt_mod_init(const polyn_gf2m & g);


      polyn_gf2m sqmod(const std::vector<polyn_gf2m> & sq, int d);
      void set_to_zero();
      gf2m eval(gf2m a);

      static std::pair<polyn_gf2m, polyn_gf2m> eea_with_coefficients(const polyn_gf2m & p,
                                                                     const polyn_gf2m & g,
                                                                     int break_deg);

      void patchup_deg_secure( uint32_t trgt_deg, volatile gf2m patch_elem);

   private:

      void set_degree(int d) { m_deg = d; }

      void poly_shiftmod( const polyn_gf2m & g);
      void realloc(uint32_t new_size);
      static polyn_gf2m gcd(polyn_gf2m const& p1, polyn_gf2m const& p2);

      /**
      * destructive:
      */
      static void remainder(polyn_gf2m & p, const polyn_gf2m & g);

      static polyn_gf2m gcd_aux(polyn_gf2m& p1, polyn_gf2m& p2);
   public:
      // public member variable:
      int m_deg;

      // public member variable:
      secure_vector<gf2m> coeff;

      // public member variable:
      std::shared_ptr<GF2m_Field> msp_field;
   };

gf2m random_gf2m(RandomNumberGenerator& rng);
gf2m random_code_element(unsigned code_length, RandomNumberGenerator& rng);

std::vector<polyn_gf2m> syndrome_init(polyn_gf2m const& generator, std::vector<gf2m> const& support, int n);

/**
* Find the roots of a polynomial over GF(2^m) using the method by Federenko
* et al.
*/
secure_vector<gf2m> find_roots_gf2m_decomp(const polyn_gf2m & polyn, uint32_t code_length);

}

#endif