gf2e.h File Reference

\(\mathbb{F}_{2^e}\) More...

#include <m4ri/m4ri.h>
#include <m4rie/gf2x.h>

Go to the source code of this file.

Data Structures
struct	gf2e_struct
	\(\mathbb{F}_{2^e}\) More...

Macros
#define	M4RIE_MAX_DEGREE   16
	maximal supported degree

Typedefs
typedef struct gf2e_struct	gf2e
	\(\mathbb{F}_{2^e}\)

Functions
gf2e *	gf2e_init (const word minpoly)
void	gf2e_free (gf2e *ff)
static word	gf2e_inv (const gf2e *ff, word a)
	a^(-1) % minpoly
static word	_gf2e_mul_table (const gf2e *ff, const word a, const word b)
	a*b in \(\mathbb{F}_{2^e}\) using a table lookups.
static word	_gf2e_mul_arith (const gf2e *ff, const word a, const word b)
	a*b in \(\mathbb{F}_{2^e}\) using a gf2x_mul() lookups.
static word	gf2e_mul (const gf2e *ff, const word a, const word b)
	a*b in \(\mathbb{F}_{2^e}\).
static size_t	gf2e_degree_to_w (const gf2e *ff)
static word *	gf2e_t16_init (const gf2e *ff, const word a)
static void	gf2e_t16_free (word *mul)
	Free multiplication table. More...

Variables
const word *	irreducible_polynomials [17]
	all Irreducible polynomials over GF(2) up to degree 16.

Detailed Description

\(\mathbb{F}_{2^e}\)

Author

Martin Albrecht marti.nosp@m.nral.nosp@m.brech.nosp@m.t@go.nosp@m.oglem.nosp@m.ail..nosp@m.com

Function Documentation

static size_t gf2e_degree_to_w ( const gf2e *  ff )

inlinestatic

Return the width used for storing elements of ff

Parameters

ff	Finite field.

void gf2e_free

(

gf2e *

ff

)

Free ff

Parameters

ff	Finite field.

Examples:

tests/test_multiplication.c.

gf2e* gf2e_init

(

const word

minpoly

)

Create finite field from minimal polynomial

Parameters

minpoly

Polynomial represented as series of bits.

red

pow_gen: X^i

mul tables

Examples:

tests/test_multiplication.c.

static void gf2e_t16_free ( word *  mul )

inlinestatic

Free multiplication table.

Parameters

mul	Multiplication table

static word* gf2e_t16_init ( const gf2e *  ff, const word  a  )

inlinestatic

Compute all multiples by a of vectors fitting into 16 bits.

Parameters

ff	Finite field.
a	Finite field element.

Todo:

: this is a bit of overkill, we could do better