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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_GF2M_SMALL_M_H__
#define BOTAN_GF2M_SMALL_M_H__
#include <vector>
#include <botan/types.h>
namespace Botan {
typedef u16bit gf2m;
/**
* GF(2^m) field for m = [2...16]
*/
class BOTAN_DLL GF2m_Field
{
public:
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_pow(gf2m x, int i) 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;
}
gf2m 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(s32bit 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 (((d) & gf_ord()) + ((d) >> get_extension_degree()));
}
gf2m m_gf_extension_degree, m_gf_multiplicative_order;
const std::vector<gf2m>& m_gf_log_table;
const std::vector<gf2m>& m_gf_exp_table;
};
u32bit encode_gf2m(gf2m to_enc, byte* mem);
gf2m decode_gf2m(const byte* mem);
}
#endif
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