operations on polynomials More...

#include "ntru_err.h"
#include "ntru_mem.h"
#include "ntru_params.h"
#include "ntru_poly.h"
#include <stdarg.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/types.h>
#include <fmpz_poly.h>
#include <fmpz.h>

Include dependency graph for ntru_poly.c:

Go to the source code of this file.

Functions
static void	poly_mod2_to_modq (const fmpz_poly_t a, fmpz_poly_t Fq, const ntru_params *params)

int	fmpz_cmp_si_n (const fmpz_t f, slong g)

void	poly_new (fmpz_poly_t new_poly, int const *const c, const size_t len)

void	poly_delete (fmpz_poly_t poly)

void	poly_delete_array (fmpz_poly_t **poly_array)

void	poly_delete_all (fmpz_poly_t poly,...)

void	fmpz_poly_mod_unsigned (fmpz_poly_t a, const uint32_t mod)

void	fmpz_poly_mod (fmpz_poly_t a, const uint32_t mod)

void	fmpz_poly_set_coeff_fmpz_n (fmpz_poly_t poly, slong n, const fmpz_t x)

int	fmpz_invmod_ui (fmpz_t f, const fmpz_t g, const uint32_t mod)

void	fmpz_add_n (fmpz_t f, const fmpz_t g, const fmpz_t h)

void	poly_starmultiply (const fmpz_poly_t a, const fmpz_poly_t b, fmpz_poly_t c, const ntru_params *params, uint32_t modulus)

bool	poly_inverse_poly_q (const fmpz_poly_t a, fmpz_poly_t Fq, const ntru_params *params)

bool	poly_inverse_poly_p (const fmpz_poly_t a, fmpz_poly_t Fp, const ntru_params *params)

void	poly_draw (const fmpz_poly_t poly)

void	poly_draw_pretty (const fmpz_poly_t poly)

Detailed Description

operations on polynomials

This files purpose is to handle polynomials in general, allowing modification, arithmetic and common algorithms like inverting them.

Definition in file ntru_poly.c.

Function Documentation

void fmpz_add_n	(	fmpz_t	f,
		const fmpz_t	g,
		const fmpz_t	h
	)

The same as fmpz_add() except that it handles NULL pointer for g and h.

Definition at line 222 of file ntru_poly.c.

int fmpz_cmp_si_n	(	const fmpz_t	f,
		slong	g
	)

The same as fmpz_cmp_si except that it will interpret f as a 0-coefficient if it is a NULL pointer.

Parameters

f	the fmpz value to use for comparison
g	the signed long integer to use for comparison

Returns: negative value if f < g, positiv evalue if g < f, otherwise 0

Definition at line 93 of file ntru_poly.c.

int fmpz_invmod_ui	(	fmpz_t	f,
		const fmpz_t	g,
		const uint32_t	mod
	)

Wrapper around fmpz_invmod() where we convert mod to an fmpz_t implicitly.

Parameters

f	result [out]
g	the inverse
mod	the modulo

Definition at line 210 of file ntru_poly.c.

void fmpz_poly_mod	(	fmpz_poly_t	a,
		const uint32_t	mod
	)

Calls fmpz_poly_get_nmod_poly() and fmpz_poly_set_nmod_poly() in a row, so we don't have to deal with the intermediate nmod_poly_t type if we don't need it.

This also normalises the coefficients to the interval -m/2 <= r < m/2.

Parameters

a	the polynom to apply the modulus to
mod	the modulus

Definition at line 182 of file ntru_poly.c.

void fmpz_poly_mod_unsigned	(	fmpz_poly_t	a,
		const uint32_t	mod
	)

Calls fmpz_poly_get_nmod_poly() and fmpz_poly_set_nmod_poly_unsigned() in a row, so we don't have to deal with the intermediate nmod_poly_t type if we don't need it.

This also normalises the coefficients to the interval 0 <= r < m.

Parameters

a	the polynom to apply the modulus to
mod	the modulus

Definition at line 166 of file ntru_poly.c.

void fmpz_poly_set_coeff_fmpz_n	(	fmpz_poly_t	poly,
		slong	n,
		const fmpz_t	x
	)

The same as fmpz_poly_set_coeff_fmpz() except that it will take care of null-pointer coefficients and use fmpz_poly_set_coeff_si() in that case.

Parameters

poly	the polynom we want to change a coefficient of
n	the coefficient we want to set
x	the value to assign to the coefficient

Definition at line 198 of file ntru_poly.c.

void poly_delete ( fmpz_poly_t poly )

This deletes the internal structure of a polynomial, and frees the pointer.

Parameters

poly	the polynomial to delete

Definition at line 123 of file ntru_poly.c.

void poly_delete_all	(	fmpz_poly_t	poly,
			...
	)

This deletes the internal structure of all polynomials, and frees the pointers. You must call this with NULL as last argument!

Parameters

poly	the polynomial to delete
...	follow up polynomials

Definition at line 149 of file ntru_poly.c.

void poly_delete_array ( fmpz_poly_t ** poly_array )

Delete the internal structure of a polynomial array which must be NULL terminated. It is expected that poly_array is not on the stack and was obtained by a function like ascii_to_poly().

Parameters

poly_array the polynomial array

Definition at line 131 of file ntru_poly.c.

void poly_draw ( const fmpz_poly_t poly )

Draws a polynomial to stdout.

Parameters

poly draw this

Definition at line 574 of file ntru_poly.c.

void poly_draw_pretty ( const fmpz_poly_t poly )

Draws a polynomial to stdout, in pretty format.

Parameters

poly draw this

Definition at line 583 of file ntru_poly.c.

bool poly_inverse_poly_p	(	const fmpz_poly_t	a,
		fmpz_poly_t	Fp,
		const ntru_params *	params
	)

Compute the inverse of a polynomial in (Z/pZ)[X]/(X^N - 1). See NTRU Cryptosystems Tech Report #014 "Almost Inverses and Fast NTRU Key Creation."

Parameters

a	polynomial to invert
Fp	polynomial [out]
params	NTRU parameters

Returns: true if invertible, false if not

Definition at line 409 of file ntru_poly.c.

bool poly_inverse_poly_q	(	const fmpz_poly_t	a,
		fmpz_poly_t	Fq,
		const ntru_params *	params
	)

Compute the inverse of a polynomial in modulo a power of 2, which is q. This is based off the pseudo-code for "Inversion in (Z/2Z)[X](X^N - 1)" and "Inversion in (Z/p^r Z)[X](X^N - 1)". See NTRU Cryptosystems Tech Report #014 "Almost Inverses and Fast NTRU Key Creation."

Parameters

a	polynomial to invert (is allowed to be the same as param Fq)
Fq	polynomial [out]
params	NTRU parameters

Returns: true if invertible, false if not

Definition at line 297 of file ntru_poly.c.

static void poly_mod2_to_modq	(	const fmpz_poly_t	a,
		fmpz_poly_t	Fq,
		const ntru_params *	params
	)

static

Find the inverse polynomial modulo a power of 2, which is q.

Parameters

a	polynomial to invert
Fq	polynomial [out]
params	NTRU parameters

Definition at line 63 of file ntru_poly.c.

void poly_new	(	fmpz_poly_t	new_poly,
		int const *const	c,
		const size_t	len
	)

Initializes and builds a polynomial with the coefficient values of c[] of size len within NTRU parameters and returns a newly allocated polynomial. For an empty polynom, both c and len can be NULL/0.

Parameters

new_poly	the polynomial to initialize and fill with coefficients [out]
c	array of polynomial coefficients, can be NULL
len	size of the coefficient array, can be 0

Returns: newly allocated polynomial pointer, must be freed with fmpz_poly_clear()

Definition at line 110 of file ntru_poly.c.

void poly_starmultiply	(	const fmpz_poly_t	a,
		const fmpz_poly_t	b,
		fmpz_poly_t	c,
		const ntru_params *	params,
		uint32_t	modulus
	)

Starmultiplication, as follows: c = a * b mod (x^N − 1)

Parameters

a	polynom to multiply (can be the same as c)
b	polynom to multiply
c	polynom [out]
params	NTRU parameters
modulus	whether we use p or q

Definition at line 239 of file ntru_poly.c.

Functions

Detailed Description

Function Documentation