Declaration of binary field (finite field constructed with an irreducible polynomial of degree 2) functions. More...

#include "mphell-fp.h"

Include dependency graph for mphell-fp2.h:

This graph shows which files directly or indirectly include this file:

Data Structures
struct	fp2_elt_t
	Quadratic extension field element structure. More...

struct	fp2_param_t
	Quadratic extension field structure. More...

Typedefs
typedef fp2_elt_t	fp2_elt
	Quadratic extension field element structure.

typedef fp2_elt_t *	fp2_elt_ptr
	Define fp2_elt_ptr, use in all functions.

typedef const fp2_elt_t *	fp2_elt_srcptr
	Define fp2_elt_srcptr, use in all functions where the parameter is const.

typedef fp2_param_t *	fp2_param
	Pointer on a quadratic extension field structure.

Functions
void	fp2_elt_get_pool_elt (fp2_elt *dst, const fp2_param param, uint8_t stack)
	Allocate and initialise space for a temporary quadratic extension field element. More...

void	fp2_elt_relax_pool_elt (fp2_elt *dst, const fp2_param param, uint8_t stack)
	Free space of a temporary quadratic extension field element. More...

void	fp2_alloc (fp2_param param, const fp_param base)
	Allocate space for the quadratic extension field informations structure. More...

void	fp2_create (fp2_param param, const fp_param base, fp_elt_srcptr non_residue, uint8_t stack)
	Create a quadratic extension of the field base. More...

void	fp2_copy (fp2_param param_res, const fp2_param param)
	Copy the quadratic extension field structure param into param_res. More...

void	fp2_free (fp2_param param)
	Free the space of the quadratic extension field informations structure. More...

void	fp2_get_characteristic (number_ptr c, const fp2_param param)
	Get the characteristic of the quadratic extension field "param". More...

void	fp2_get_size (number_ptr c, const fp2_param param)
	Get the size of the quadratic extension field "param". More...

void	fp2_elt_alloc (fp2_elt *dst, const fp2_param param)
	Allocate space for a quadratic extension field element. More...

void	fp2_elt_init (fp2_elt_ptr dst, const fp2_param param)
	Initialise a quadratic extension field element. More...

void	fp2_elt_copy (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param)
	Copy src into dst, src and dst must belong to the same FP2. More...

void	fp2_elt_clear (fp2_elt *src)
	Clear space used by src (remove the action of fp2_elt_init but less the one of fp2_elt_alloc) More...

void	fp2_elt_free (fp2_elt *src)
	Free space used by src. More...

void	fp2_elt_set_one (fp2_elt_ptr dst, const fp2_param param)
	Set dst to one (or its Montgomery form if Montgomery arithmetic is used) More...

void	fp2_elt_set_ui (fp2_elt_ptr dst, const uint64_t src, const bool isreduced, const fp2_param param, uint8_t stack)
	Set dst to src, if Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form. More...

void	fp2_elt_set_number (fp2_elt_ptr dst, number_srcptr src, const bool isreduced, const fp2_param param, uint8_t stack)
	Set dst to src, if Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form. More...

void	fp2_elt_set_fp_elt (fp2_elt_ptr dst, fp_elt_srcptr src, const fp2_param param)
	Set dst to src. More...

void	fp2_elt_set (fp2_elt_ptr dst, number_srcptr src1, number_srcptr src2, const bool isreduced, const fp2_param param, uint8_t stack)
	Set dst to src1 + src2*x, if Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form. More...

void	fp2_elt_set_fp_elts (fp2_elt_ptr dst, fp_elt_srcptr src1, fp_elt_srcptr src2, const fp2_param param)
	Set dst to src1 + src2*x. More...

void	fp2_elt_set_str (fp2_elt_ptr dst, const char *str, const uint8_t base, const bool isreduced, const fp2_param param, uint8_t stack)
	Set dst to str, if Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form. More...

void	fp2_elt_random (fp2_elt_ptr dst, const fp2_param param, uint8_t stack)
	Set dst to a random element of FP2, the random process is chosen at the MHELL initialisation. More...

void	fp2_elt_lift (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param, uint8_t stack)
	If Montgomery arithmetic is used, lift src (which is into Montgomery form) to classical FP2. More...

void	fp2_str (char **str, const fp2_param param, const uint8_t base, uint8_t stack)
	Converts fp2_param param to string format in base specified by base. More...

void	fp2_elt_str (char **str, fp2_elt_srcptr src, const uint8_t base, const bool lift, const fp2_param param, uint8_t stack)
	Converts src to string format in base specified by base. More...

int8_t	fp2_elt_cmp_fp_elt (fp2_elt_srcptr src1, fp_elt_srcptr src2, const fp2_param param)
	Compare src1 and src2 in FP2. More...

int8_t	fp2_elt_cmp (fp2_elt_srcptr src1, fp2_elt_srcptr src2, const fp2_param param)
	Compare src1 and src2 in FP2. More...

bool	fp2_elt_isone (fp2_elt_srcptr src, const fp2_param param)
	Test if src is one. More...

bool	fp2_elt_iszero (fp2_elt_srcptr src, const fp2_param param)
	Test if src is zero. More...

void	fp2_elt_inc (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param)
	Set dst <- src + 1. More...

void	fp2_elt_add_fp_elt (fp2_elt_ptr dst, fp2_elt_srcptr src1, fp_elt_srcptr src2, const fp2_param param)
	Set dst <- src1 + src2. More...

void	fp2_elt_add (fp2_elt_ptr dst, fp2_elt_srcptr src1, fp2_elt_srcptr src2, const fp2_param param)
	Set dst <- src1 + src2. More...

void	fp2_elt_dec (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param)
	Set dst <- src - 1. More...

void	fp2_elt_sub_fp_elt (fp2_elt_ptr dst, fp2_elt_srcptr src1, fp_elt_srcptr src2, const fp2_param param)
	Set dst <- src1 - src2. More...

void	fp2_elt_sub (fp2_elt_ptr dst, fp2_elt_srcptr src1, fp2_elt_srcptr src2, const fp2_param param)
	Set dst <- src1 - src2. More...

void	fp2_elt_neg_fp_elt (fp2_elt_ptr dst, fp_elt_srcptr src, const fp2_param param)
	Set dst <- (-src) More...

void	fp2_elt_neg (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param)
	Set dst <- (-src) More...

void	fp2_elt_mul_fp_elt (fp2_elt_ptr dst, fp2_elt_srcptr src1, fp_elt_srcptr src2, const fp2_param param, uint8_t stack)
	Set dst <- src1 * src2, if Montgomery arithmetic is used, the Montgomery multiplication will be used ! More...

void	fp2_elt_mul2 (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param)
	Set dst <- 2 * src. More...

void	fp2_elt_mul4 (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param)
	Set dst <- 4 * src. More...

void	fp2_elt_mul8 (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param)
	Set dst <- 8 * src. More...

void	fp2_elt_mul3 (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param, uint8_t stack)
	Set dst <- 3 * src. More...

void	fp2_elt_mul (fp2_elt_ptr dst, fp2_elt_srcptr src1, fp2_elt_srcptr src2, const fp2_param param, uint8_t stack)
	Set dst <- src1 * src2, if Montgomery arithmetic is used, the Montgomery multiplication will be used ! More...

void	fp2_elt_sqr_fp_elt (fp2_elt_ptr dst, fp_elt_srcptr src, const fp2_param param, uint8_t stack)
	Set dst <- src^2. More...

void	fp2_elt_sqr (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param, uint8_t stack)
	Set dst <- src^2. More...

void	fp2_elt_inv_fp_elt (fp2_elt_ptr dst, fp_elt_srcptr src, const fp2_param param, uint8_t stack)
	Set dst <- src^(-1) More...

void	fp2_elt_inv (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param, uint8_t stack)
	Set dst <- src^(-1) More...

void	fp2_elt_div_fp_elt (fp2_elt_ptr dst, fp2_elt_srcptr src1, fp_elt_srcptr src2, const fp2_param param, uint8_t stack)
	Set dst <- src1 / src2. More...

void	fp2_elt_div (fp2_elt_ptr dst, fp2_elt_srcptr src1, fp2_elt_srcptr src2, const fp2_param param, uint8_t stack)
	Set dst <- src1 / src2. More...

void	fp2_elt_pow_ui (fp2_elt_ptr dst, fp2_elt_srcptr src, const block n, const fp2_param param, uint8_t stack)
	Set dst <- src^n. More...

void	fp2_elt_pow_number (fp2_elt_ptr dst, fp2_elt_srcptr src, number_srcptr n, const fp2_param param, uint8_t stack)
	Set dst <- src^n. More...

bool	fp2_elt_issquare (fp2_elt_srcptr src, const fp2_param param, uint8_t stack)
	Test if src is a square, using A NOTE ON POWERS IN FINITE FIELDS from ANDREAS AABRANDT AND VAGN LUNDSGAARD HANSEN. More...

int8_t	fp2_elt_ispower_ui (fp2_elt_srcptr src, const block n, const fp2_param param, uint8_t stack)
	Test if src is a n-power in FP2, using A NOTE ON POWERS IN FINITE FIELDS from ANDREAS AABRANDT AND VAGN LUNDSGAARD HANSEN. More...

int8_t	fp2_elt_ispower_number (fp2_elt_srcptr src, number_srcptr n, const fp2_param param, uint8_t stack)
	Test if src is a n-power in FP2, using A NOTE ON POWERS IN FINITE FIELDS from ANDREAS AABRANDT AND VAGN LUNDSGAARD HANSEN. More...

void	fp2_elt_sqrt (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param, uint8_t stack)
	Set dst <- src^(1/2), using Tonelli–Shanks algorithm. More...

void	fp2_elt_cube_root (fp2_elt_ptr dst, fp2_elt_srcptr src, const fp2_param param, uint8_t stack)
	Set dst <- src^(1/3) More...

void	fp2_elt_unity_nth_root (fp2_elt_ptr dst, const block n, const fp2_param param, uint8_t stack)
	Set dst to a non trivial n-th root of unity if it exists (ie n divides q-1), 1 otherwise. More...

Detailed Description

Declaration of binary field (finite field constructed with an irreducible polynomial of degree 2) functions.

Definition in file mphell-fp2.h.

Function Documentation

◆ fp2_alloc()

void fp2_alloc	(	fp2_param	param,
		const fp_param	base
	)

Allocate space for the quadratic extension field informations structure.

Parameters

param	Structure for the quadratic extension field informations to allocate
base	Base prime field

Definition at line 67 of file mphell-fp2.c.

◆ fp2_copy()

void fp2_copy	(	fp2_param	param_res,
		const fp2_param	param
	)

Copy the quadratic extension field structure param into param_res.

Parameters

param_res	Destination quadratic extension field
param	Source quadratic extension field

Definition at line 125 of file mphell-fp2.c.

◆ fp2_create()

void fp2_create	(	fp2_param	param,
		const fp_param	base,
		fp_elt_srcptr	non_residue,
		uint8_t	stack
	)

Create a quadratic extension of the field base.

Parameters

param	Informations structure on quadratic extension field to fill (must be allocated)
base	Base prime field
non_residue	Non quadratic residue
stack	Temporary memory stack to use

Definition at line 106 of file mphell-fp2.c.

◆ fp2_elt_add()

void fp2_elt_add	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src1,
		fp2_elt_srcptr	src2,
		const fp2_param	param
	)

Set dst <- src1 + src2.

Parameters

dst	To store the result
src1	Source field element
src2	Source field element
param	Information on the quadratic extension field

Definition at line 364 of file mphell-fp2.c.

◆ fp2_elt_add_fp_elt()

void fp2_elt_add_fp_elt	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp2_param	param
	)

Set dst <- src1 + src2.

Parameters

dst	To store the result
src1	Source field element
src2	Source field element in the prime field
param	Information on the quadratic extension field

Definition at line 356 of file mphell-fp2.c.

◆ fp2_elt_alloc()

void fp2_elt_alloc	(	fp2_elt *	dst,
		const fp2_param	param
	)

Allocate space for a quadratic extension field element.

Parameters

dst	Quadratic extension field element to allocate
param	Information on quadratic extension field

Definition at line 162 of file mphell-fp2.c.

◆ fp2_elt_clear()

void fp2_elt_clear ( fp2_elt * src )

Clear space used by src (remove the action of fp2_elt_init but less the one of fp2_elt_alloc)

Parameters

src	Quadratic extension field element to clear

Definition at line 183 of file mphell-fp2.c.

◆ fp2_elt_cmp()

int8_t fp2_elt_cmp	(	fp2_elt_srcptr	src1,
		fp2_elt_srcptr	src2,
		const fp2_param	param
	)

Compare src1 and src2 in FP2.

Parameters

src1	Source field element in FP2
src2	Source field element in FP2
param	Information on the quadratic extension field

Returns: -1 if src1 < src2; 0 if src1 == src2; 1 if src1 > src2

Definition at line 321 of file mphell-fp2.c.

◆ fp2_elt_cmp_fp_elt()

int8_t fp2_elt_cmp_fp_elt	(	fp2_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp2_param	param
	)

Compare src1 and src2 in FP2.

Parameters

src1	Source field element in FP2
src2	Source number_ptr in FP
param	Information on the quadratic extension field

Returns: -1 if src1 < src2; 0 if src1 == src2; 1 if src1 > src2

Definition at line 311 of file mphell-fp2.c.

◆ fp2_elt_copy()

void fp2_elt_copy	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param
	)

Copy src into dst, src and dst must belong to the same FP2.

Parameters

dst	Destination quadratic extension field element
src	Source quadratic extension field element
param	Information on quadratic extension field

Definition at line 176 of file mphell-fp2.c.

◆ fp2_elt_cube_root()

void fp2_elt_cube_root	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src^(1/3)

Parameters

dst	To store the result
src	Source field element
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 819 of file mphell-fp2.c.

◆ fp2_elt_dec()

void fp2_elt_dec	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param
	)

Set dst <- src - 1.

Parameters

dst	To store the result
src	Source field element
param	Information on the quadratic extension field

Definition at line 372 of file mphell-fp2.c.

◆ fp2_elt_div()

void fp2_elt_div	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src1,
		fp2_elt_srcptr	src2,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src1 / src2.

Parameters

dst	To store the result
src1	Source field element
src2	Source field element
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 543 of file mphell-fp2.c.

◆ fp2_elt_div_fp_elt()

void fp2_elt_div_fp_elt	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src1 / src2.

Parameters

dst	To store the result
src1	Source field element
src2	Source field element in the prime field
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 532 of file mphell-fp2.c.

◆ fp2_elt_free()

void fp2_elt_free ( fp2_elt * src )

Free space used by src.

Parameters

src	Quadratic extension field element to free

Definition at line 190 of file mphell-fp2.c.

◆ fp2_elt_get_pool_elt()

void fp2_elt_get_pool_elt	(	fp2_elt *	dst,
		const fp2_param	param,
		uint8_t	stack
	)

Allocate and initialise space for a temporary quadratic extension field element.

Parameters

dst	Temporary element to allocate
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 51 of file mphell-fp2.c.

◆ fp2_elt_inc()

void fp2_elt_inc	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param
	)

Set dst <- src + 1.

Parameters

dst	To store the result
src	Source field element
param	Information on the quadratic extension field

Definition at line 349 of file mphell-fp2.c.

◆ fp2_elt_init()

void fp2_elt_init	(	fp2_elt_ptr	dst,
		const fp2_param	param
	)

Initialise a quadratic extension field element.

Parameters

dst	Quadratic extension field element to initialise
param	Information on quadratic extension field

Definition at line 169 of file mphell-fp2.c.

◆ fp2_elt_inv()

void fp2_elt_inv	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src^(-1)

Parameters

dst	To store the result
src	Source field element
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 508 of file mphell-fp2.c.

◆ fp2_elt_inv_fp_elt()

void fp2_elt_inv_fp_elt	(	fp2_elt_ptr	dst,
		fp_elt_srcptr	src,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src^(-1)

Parameters

dst	To store the result
src	Source field element in the prime field
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 501 of file mphell-fp2.c.

◆ fp2_elt_isone()

bool fp2_elt_isone	(	fp2_elt_srcptr	src,
		const fp2_param	param
	)

Test if src is one.

Parameters

src	Source field element
param	Information on the quadratic extension field

Returns: true if scr is one, false otherwise

Definition at line 335 of file mphell-fp2.c.

◆ fp2_elt_ispower_number()

int8_t fp2_elt_ispower_number	(	fp2_elt_srcptr	src,
		number_srcptr	n,
		const fp2_param	param,
		uint8_t	stack
	)

Test if src is a n-power in FP2, using A NOTE ON POWERS IN FINITE FIELDS from ANDREAS AABRANDT AND VAGN LUNDSGAARD HANSEN.

Parameters

src	Source field element
n	Source number
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Returns: 2 if all element in FP2 are some n-power; 1 if src is a n-power in FP2; false otherwise

Definition at line 675 of file mphell-fp2.c.

◆ fp2_elt_ispower_ui()

int8_t fp2_elt_ispower_ui	(	fp2_elt_srcptr	src,
		const block	n,
		const fp2_param	param,
		uint8_t	stack
	)

Test if src is a n-power in FP2, using A NOTE ON POWERS IN FINITE FIELDS from ANDREAS AABRANDT AND VAGN LUNDSGAARD HANSEN.

Parameters

src	Source field element
n	Source block
stack	Temporary memory stack to use
param	Information on the quadratic extension field

Returns: 2 if all element in FP2 are some n-power; 1 if src is a n-power in FP2; false otherwise

Definition at line 634 of file mphell-fp2.c.

◆ fp2_elt_issquare()

bool fp2_elt_issquare	(	fp2_elt_srcptr	src,
		const fp2_param	param,
		uint8_t	stack
	)

Test if src is a square, using A NOTE ON POWERS IN FINITE FIELDS from ANDREAS AABRANDT AND VAGN LUNDSGAARD HANSEN.

Parameters

src	Source field element
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Returns: true if src is a square in Fp2, false otherwise

Definition at line 616 of file mphell-fp2.c.

◆ fp2_elt_iszero()

bool fp2_elt_iszero	(	fp2_elt_srcptr	src,
		const fp2_param	param
	)

Test if src is zero.

Parameters

src	Source field element
param	Information on the quadratic extension field

Returns: true if scr is zero, false otherwise

Definition at line 341 of file mphell-fp2.c.

◆ fp2_elt_lift()

void fp2_elt_lift	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param,
		uint8_t	stack
	)

If Montgomery arithmetic is used, lift src (which is into Montgomery form) to classical FP2.

Parameters

dst	Destination primary field element (in FP)
src	Source quadratic extension field element (under Montgomery form)
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 267 of file mphell-fp2.c.

◆ fp2_elt_mul()

void fp2_elt_mul	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src1,
		fp2_elt_srcptr	src2,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src1 * src2, if Montgomery arithmetic is used, the Montgomery multiplication will be used !

Parameters

dst	To store the result
src1	Source field element
src2	Source field element
param	Information the quadratic extension prime field
stack	Temporary memory stack to use

Definition at line 451 of file mphell-fp2.c.

◆ fp2_elt_mul2()

void fp2_elt_mul2	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param
	)

Set dst <- 2 * src.

Parameters

dst	To store the result
src	Source field element
param	Information the quadratic extension prime field

Definition at line 419 of file mphell-fp2.c.

◆ fp2_elt_mul3()

void fp2_elt_mul3	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- 3 * src.

Parameters

dst	To store the result
src	Source field element
param	Information the quadratic extension prime field
stack	Temporary memory stack to use

Definition at line 443 of file mphell-fp2.c.

◆ fp2_elt_mul4()

void fp2_elt_mul4	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param
	)

Set dst <- 4 * src.

Parameters

dst	To store the result
src	Source field element
param	Information the quadratic extension prime field

Definition at line 427 of file mphell-fp2.c.

◆ fp2_elt_mul8()

void fp2_elt_mul8	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param
	)

Set dst <- 8 * src.

Parameters

dst	To store the result
src	Source field element
param	Information the quadratic extension prime field

Definition at line 435 of file mphell-fp2.c.

◆ fp2_elt_mul_fp_elt()

void fp2_elt_mul_fp_elt	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src1 * src2, if Montgomery arithmetic is used, the Montgomery multiplication will be used !

Parameters

dst	To store the result
src1	Source field element
src2	Source field element in the prime field
param	Information the quadratic extension prime field
stack	Temporary memory stack to use

Definition at line 411 of file mphell-fp2.c.

◆ fp2_elt_neg()

void fp2_elt_neg	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param
	)

Set dst <- (-src)

Parameters

dst	To store the result
src	Source field element
param	Information on the quadratic extension field

Definition at line 402 of file mphell-fp2.c.

◆ fp2_elt_neg_fp_elt()

void fp2_elt_neg_fp_elt	(	fp2_elt_ptr	dst,
		fp_elt_srcptr	src,
		const fp2_param	param
	)

Set dst <- (-src)

Parameters

dst	To store the result
src	Source field element in the prime field
param	Information on the quadratic extension field

Definition at line 395 of file mphell-fp2.c.

◆ fp2_elt_pow_number()

void fp2_elt_pow_number	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		number_srcptr	n,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src^n.

Parameters

dst	To store the result
src	Source field element
n	Source number
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 577 of file mphell-fp2.c.

◆ fp2_elt_pow_ui()

void fp2_elt_pow_ui	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const block	n,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src^n.

Parameters

dst	To store the result
src	Source field element
n	Source block
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 554 of file mphell-fp2.c.

◆ fp2_elt_random()

void fp2_elt_random	(	fp2_elt_ptr	dst,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst to a random element of FP2, the random process is chosen at the MHELL initialisation.

Parameters

dst	Destination quadratic extension field element
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 260 of file mphell-fp2.c.

◆ fp2_elt_relax_pool_elt()

void fp2_elt_relax_pool_elt	(	fp2_elt *	dst,
		const fp2_param	param,
		uint8_t	stack
	)

Free space of a temporary quadratic extension field element.

Parameters

dst	Temporary element to free
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 58 of file mphell-fp2.c.

◆ fp2_elt_set()

void fp2_elt_set	(	fp2_elt_ptr	dst,
		number_srcptr	src1,
		number_srcptr	src2,
		const bool	isreduced,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst to src1 + src2*x, if Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form.

Parameters

dst	Destination quadratic extension field element
src1	Source number
src2	Source number
isreduced	If Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form, is_reduced == true -> simple copy
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 227 of file mphell-fp2.c.

◆ fp2_elt_set_fp_elt()

void fp2_elt_set_fp_elt	(	fp2_elt_ptr	dst,
		fp_elt_srcptr	src,
		const fp2_param	param
	)

Set dst to src.

Parameters

dst	Destination quadratic extension field element
src	Source fp_elt
param	Information on the quadratic extension field

Definition at line 220 of file mphell-fp2.c.

◆ fp2_elt_set_fp_elts()

void fp2_elt_set_fp_elts	(	fp2_elt_ptr	dst,
		fp_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp2_param	param
	)

Set dst to src1 + src2*x.

Parameters

dst	Destination quadratic extension field element
src1	Source fp_elt
src2	Source fp_elt
param	Information on the quadratic extension field

Definition at line 235 of file mphell-fp2.c.

◆ fp2_elt_set_number()

void fp2_elt_set_number	(	fp2_elt_ptr	dst,
		number_srcptr	src,
		const bool	isreduced,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst to src, if Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form.

Parameters

dst	Destination quadratic extension field element
src	Source number
isreduced	If Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form, is_reduced == true -> simple copy
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 212 of file mphell-fp2.c.

◆ fp2_elt_set_one()

void fp2_elt_set_one	(	fp2_elt_ptr	dst,
		const fp2_param	param
	)

Set dst to one (or its Montgomery form if Montgomery arithmetic is used)

Parameters

dst	Destination quadratic extension field element (must be allocated)
param	Information on the quadratic extension field

Definition at line 197 of file mphell-fp2.c.

◆ fp2_elt_set_str()

void fp2_elt_set_str	(	fp2_elt_ptr	dst,
		const char *	str,
		const uint8_t	base,
		const bool	isreduced,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst to str, if Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form.

Parameters

dst	Destination quadratic extension field element
str	Source polynomial coefficient under string format in base "base", separated by a "," without space. ex: "123,456" will create the polynomial 123 + 456.X
base	Base used to write str, can be 2, 10 or 16
isreduced	If Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form, is_reduced == true -> simple copy
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 242 of file mphell-fp2.c.

◆ fp2_elt_set_ui()

void fp2_elt_set_ui	(	fp2_elt_ptr	dst,
		const uint64_t	src,
		const bool	isreduced,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst to src, if Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form.

Parameters

dst	Destination quadratic extension field element
src	Source block
isreduced	If Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form, is_reduced == true -> simple copy
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 204 of file mphell-fp2.c.

◆ fp2_elt_sqr()

void fp2_elt_sqr	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src^2.

Parameters

dst	To store the result
src	Source field element
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 495 of file mphell-fp2.c.

◆ fp2_elt_sqr_fp_elt()

void fp2_elt_sqr_fp_elt	(	fp2_elt_ptr	dst,
		fp_elt_srcptr	src,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src^2.

Parameters

dst	To store the result
src	Source field element in the prime field
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 483 of file mphell-fp2.c.

◆ fp2_elt_sqrt()

void fp2_elt_sqrt	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst <- src^(1/2), using Tonelli–Shanks algorithm.

Parameters

dst	To store the result
src	Source field element
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 742 of file mphell-fp2.c.

◆ fp2_elt_str()

void fp2_elt_str	(	char **	str,
		fp2_elt_srcptr	src,
		const uint8_t	base,
		const bool	lift,
		const fp2_param	param,
		uint8_t	stack
	)

Converts src to string format in base specified by base.

Parameters

str	Destination string, allocated by the function, must be free by the user. Polynomial coefficient are written separated by ",". ex: 123 + 456.X will be written as "123,456"
src	Source quadratic extension field element (under Montgomery form if Montgomery arithmetic is used)
base	Base to use to write str, can be 2, 10 or 16
lift	If Montgomery arithmetic is used, lift == true -> lift src into FP2 before conversion
param	Information on the quadratic extension field
stack	Temporary memory stack to use

Definition at line 294 of file mphell-fp2.c.

◆ fp2_elt_sub()

void fp2_elt_sub	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src1,
		fp2_elt_srcptr	src2,
		const fp2_param	param
	)

Set dst <- src1 - src2.

Parameters

dst	To store the result
src1	Source field element
src2	Source field element
param	Information on the quadratic extension field

Definition at line 387 of file mphell-fp2.c.

◆ fp2_elt_sub_fp_elt()

void fp2_elt_sub_fp_elt	(	fp2_elt_ptr	dst,
		fp2_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp2_param	param
	)

Set dst <- src1 - src2.

Parameters

dst	To store the result
src1	Source field element
src2	Source field element in the prime field
param	Information on the quadratic extension field

Definition at line 379 of file mphell-fp2.c.

◆ fp2_elt_unity_nth_root()

void fp2_elt_unity_nth_root	(	fp2_elt_ptr	dst,
		const block	n,
		const fp2_param	param,
		uint8_t	stack
	)

Set dst to a non trivial n-th root of unity if it exists (ie n divides q-1), 1 otherwise.

Parameters

dst	To store the result
n	Source block
param	Information on prime field
stack	Temporary memory stack to use

Definition at line 1007 of file mphell-fp2.c.

◆ fp2_free()

void fp2_free ( fp2_param param )

Free the space of the quadratic extension field informations structure.

Parameters

param Quadratic extension field informations structure

Definition at line 133 of file mphell-fp2.c.

◆ fp2_get_characteristic()

void fp2_get_characteristic	(	number_ptr	c,
		const fp2_param	param
	)

Get the characteristic of the quadratic extension field "param".

Parameters

c	Destination number_ptr (to store the characteristic)
param	Information on quadratic extension field

Definition at line 144 of file mphell-fp2.c.

◆ fp2_get_size()

void fp2_get_size	(	number_ptr	c,
		const fp2_param	param
	)

Get the size of the quadratic extension field "param".

Parameters

c	Destination number_ptr (to store the characteristic)
param	Information on quadratic extension field

Definition at line 150 of file mphell-fp2.c.

◆ fp2_str()

void fp2_str	(	char **	str,
		const fp2_param	param,
		const uint8_t	base,
		uint8_t	stack
	)

Converts fp2_param param to string format in base specified by base.

Parameters

str	Destination string, allocated by the function, must be free by the user.
param	Information on the quadratic extension field
base	Base to use to write str, can be 2, 10 or 16
stack	Temporary memory stack to use

Definition at line 274 of file mphell-fp2.c.

Data Structures

Typedefs

Functions

Detailed Description

Function Documentation

◆ fp2_alloc()

◆ fp2_copy()

◆ fp2_create()

◆ fp2_elt_add()

◆ fp2_elt_add_fp_elt()

◆ fp2_elt_alloc()

◆ fp2_elt_clear()

◆ fp2_elt_cmp()

◆ fp2_elt_cmp_fp_elt()

◆ fp2_elt_copy()

◆ fp2_elt_cube_root()

◆ fp2_elt_dec()

◆ fp2_elt_div()

◆ fp2_elt_div_fp_elt()

◆ fp2_elt_free()

◆ fp2_elt_get_pool_elt()

◆ fp2_elt_inc()

◆ fp2_elt_init()

◆ fp2_elt_inv()

◆ fp2_elt_inv_fp_elt()

◆ fp2_elt_isone()

◆ fp2_elt_ispower_number()

◆ fp2_elt_ispower_ui()

◆ fp2_elt_issquare()

◆ fp2_elt_iszero()

◆ fp2_elt_lift()

◆ fp2_elt_mul()

◆ fp2_elt_mul2()

◆ fp2_elt_mul3()

◆ fp2_elt_mul4()

◆ fp2_elt_mul8()

◆ fp2_elt_mul_fp_elt()

◆ fp2_elt_neg()

◆ fp2_elt_neg_fp_elt()

◆ fp2_elt_pow_number()

◆ fp2_elt_pow_ui()

◆ fp2_elt_random()

◆ fp2_elt_relax_pool_elt()

◆ fp2_elt_set()

◆ fp2_elt_set_fp_elt()

◆ fp2_elt_set_fp_elts()

◆ fp2_elt_set_number()

◆ fp2_elt_set_one()

◆ fp2_elt_set_str()

◆ fp2_elt_set_ui()

◆ fp2_elt_sqr()

◆ fp2_elt_sqr_fp_elt()

◆ fp2_elt_sqrt()

◆ fp2_elt_str()

◆ fp2_elt_sub()

◆ fp2_elt_sub_fp_elt()

◆ fp2_elt_unity_nth_root()

◆ fp2_free()

◆ fp2_get_characteristic()

◆ fp2_get_size()

◆ fp2_str()