libecc/polynomial.h File Reference

Field of Polynomials with binairy coefficents and fixed reduction polynomial. More...

#include <stdexcept>
#include <libecc/bitset.h>
#include <libecc/debug.h>
#include <libecc/square.hcc>

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Classes
class	libecc::polynomial< m, k, k1, k2 >
	Polynomial representation of the Galois field F2m. More...
Namespaces
namespace	libecc
	Namespace for libecc.
Functions
template<unsigned int m, unsigned int k, unsigned int k1, unsigned int k2>
polynomial< m, k, k1, k2 >	libecc::operator* (polynomial< m, k, k1, k2 > const &, polynomial< m, k, k1, k2 > const &)
template<unsigned int m, unsigned int k, unsigned int k1, unsigned int k2>
polynomial< m, k, k1, k2 >	libecc::operator/ (polynomial< m, k, k1, k2 > const &, polynomial< m, k, k1, k2 > const &)
template<unsigned int m, unsigned int k, unsigned int k1, unsigned int k2>
bool	libecc::operator== (polynomial< m, k, k1, k2 > const &, polynomial< m, k, k1, k2 > const &)
template<unsigned int m, unsigned int k, unsigned int k1, unsigned int k2>
bool	libecc::operator!= (polynomial< m, k, k1, k2 > const &, polynomial< m, k, k1, k2 > const &)
template<unsigned int m, unsigned int k, unsigned int k1, unsigned int k2>
std::ostream &	libecc::operator<< (std::ostream &, polynomial< m, k, k1, k2 > const &)
template<unsigned int m, unsigned int k, unsigned int k1, unsigned int k2>
polynomial< m, k, k1, k2 > ::xor_type	libecc::operator+ (polynomial< m, k, k1, k2 > const &, polynomial< m, k, k1, k2 > const &)
template<unsigned int m, unsigned int k, unsigned int k1, unsigned int k2>
polynomial< m, k, k1, k2 > ::xor_type	libecc::operator- (polynomial< m, k, k1, k2 > const &, polynomial< m, k, k1, k2 > const &)

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Detailed Description

Field of Polynomials with binairy coefficents and fixed reduction polynomial.

This header file declares the type libecc::polynomial<m, k, k1, k2>, representing the polynomials with binary coefficients, of a finite extension field with fixed degree m and reduction pentanomial tm + tk + tk1 + tk2 + 1 = 0 or, when k1 == 0, trinomial tm + tk + 1 = 0.