Declaration of cubic field (finite field constructed with an irreducible polynomial of degree 3) functions. More...

#include "mphell-fp.h"

Include dependency graph for mphell-fp3.h:

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

Data Structures
struct	fp3_elt_t
	Cubic extension field element structure. More...

struct	fp3_param_t
	Cubic extension field structure. More...

Typedefs
typedef fp3_elt_t	fp3_elt
	Cubic extension field element structure.

typedef fp3_elt_t *	fp3_elt_ptr
	Define fp3_elt_ptr, use in all functions.

typedef const fp3_elt_t *	fp3_elt_srcptr
	Define fp3_elt_srcptr, use in all functions where the parameter is const.

typedef fp3_param_t *	fp3_param
	Address of a cubic extension field structure.

Functions
void	fp3_elt_get_pool_elt (fp3_elt *dst, const fp3_param param, uint8_t stack)
	Allocate and initialise space for a temporary cubic extension field element. More...

void	fp3_elt_relax_pool_elt (fp3_elt *dst, const fp3_param param, uint8_t stack)
	Free space of a temporary cubic extension field element. More...

void	fp3_alloc (fp3_param param, const fp_param base)
	Allocate space for the cubic extension field informations structure. More...

void	fp3_create (fp3_param param, const fp_param base, fp_elt_srcptr non_residue, uint8_t stack)
	Create a cubic extension of the field base. More...

void	fp3_copy (fp3_param param_res, const fp3_param param)
	Copy the cubic extension field structure param into param_res. More...

void	fp3_free (fp3_param param)
	Free the space of the cubic extension field informations structure. More...

void	fp3_get_characteristic (number_ptr c, const fp3_param param)
	Get the characteristic of the cubic extension field "param". More...

void	fp3_get_size (number_ptr c, const fp3_param param)
	Get the size of the cubic extension field "param". More...

void	fp3_elt_alloc (fp3_elt *dst, const fp3_param param)
	Allocate space for a cubic extension field element. More...

void	fp3_elt_init (fp3_elt_ptr dst, const fp3_param param)
	Initialise a cubic extension field element. More...

void	fp3_elt_copy (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param)
	Copy src into dst, src and dst must belong to the same FP3. More...

void	fp3_elt_clear (fp3_elt *src)
	Clear space used by src (remove the action of fp3_elt_init but let the one of fp3_elt_alloc) More...

void	fp3_elt_free (fp3_elt *src)
	Free space used by src. More...

void	fp3_elt_set_one (fp3_elt_ptr dst, const fp3_param param)
	Set dst to one (or its Montgomery form if Montgomery arithmetic is used) More...

void	fp3_elt_set_ui (fp3_elt_ptr dst, const uint64_t src, const bool isreduced, const fp3_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	fp3_elt_set_number (fp3_elt_ptr dst, number_srcptr src, const bool isreduced, const fp3_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	fp3_elt_set_fp_elt (fp3_elt_ptr dst, fp_elt_srcptr src, const fp3_param param)
	Set dst to src. More...

void	fp3_elt_set (fp3_elt_ptr dst, number_srcptr src1, number_srcptr src2, number_srcptr src3, const bool isreduced, const fp3_param param, uint8_t stack)
	Set dst to src1 + src2x + src3x^2, if Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form. More...

void	fp3_elt_set_fp_elts (fp3_elt_ptr dst, fp_elt_srcptr src1, fp_elt_srcptr src2, fp_elt_srcptr src3, const fp3_param param)
	Set dst to src1 + src2x + src3x^2. More...

void	fp3_elt_set_str (fp3_elt_ptr dst, const char *str, const uint8_t base, const bool isreduced, const fp3_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	fp3_elt_random (fp3_elt_ptr dst, const fp3_param param, uint8_t stack)
	Set dst to a random element of FP3, the random process is chosen at the MHELL initialisation. More...

void	fp3_elt_lift (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param, uint8_t stack)
	If Montgomery arithmetic is used, lift src (which is into Montgomery form) to classical FP3. More...

void	fp3_str (char **str, const fp3_param param, const uint8_t base, uint8_t stack)
	Converts fp2_param param to string format in base specified by base. More...

void	fp3_elt_str (char **str, fp3_elt_srcptr src, const uint8_t base, const bool lift, const fp3_param param, uint8_t stack)
	Converts src to string format in base specified by base. More...

int8_t	fp3_elt_cmp_fp_elt (fp3_elt_srcptr src1, fp_elt_srcptr src2, const fp3_param param)
	Compare src1 and src2 in FP3. More...

int8_t	fp3_elt_cmp (fp3_elt_srcptr src1, fp3_elt_srcptr src2, const fp3_param param)
	Compare src1 and src2 in FP3. More...

bool	fp3_elt_isone (fp3_elt_srcptr src, const fp3_param param)
	Test if src is one. More...

bool	fp3_elt_iszero (fp3_elt_srcptr src, const fp3_param param)
	Test if src is zero. More...

void	fp3_elt_inc (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param)
	Set dst <- src + 1. More...

void	fp3_elt_add_fp_elt (fp3_elt_ptr dst, fp3_elt_srcptr src1, fp_elt_srcptr src2, const fp3_param param)
	Set dst <- src1 + src2. More...

void	fp3_elt_add (fp3_elt_ptr dst, fp3_elt_srcptr src1, fp3_elt_srcptr src2, const fp3_param param)
	Set dst <- src1 + src2. More...

void	fp3_elt_dec (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param)
	Set dst <- src - 1. More...

void	fp3_elt_sub_fp_elt (fp3_elt_ptr dst, fp3_elt_srcptr src1, fp_elt_srcptr src2, const fp3_param param)
	Set dst <- src1 - src2. More...

void	fp3_elt_sub (fp3_elt_ptr dst, fp3_elt_srcptr src1, fp3_elt_srcptr src2, const fp3_param param)
	Set dst <- src1 - src2. More...

void	fp3_elt_neg_fp_elt (fp3_elt_ptr dst, fp_elt_srcptr src, const fp3_param param)
	Set dst <- (-src) More...

void	fp3_elt_neg (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param)
	Set dst <- (-src) More...

void	fp3_elt_mul_fp_elt (fp3_elt_ptr dst, fp3_elt_srcptr src1, fp_elt_srcptr src2, const fp3_param param, uint8_t stack)
	Set dst <- src1 * src2, if Montgomery arithmetic is used, the Montgomery multiplication will be used ! More...

void	fp3_elt_mul2 (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param)
	Set dst <- 2 * src. More...

void	fp3_elt_mul4 (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param)
	Set dst <- 4 * src. More...

void	fp3_elt_mul8 (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param)
	Set dst <- 8 * src. More...

void	fp3_elt_mul3 (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param, uint8_t stack)
	Set dst <- 3 * src. More...

void	fp3_elt_mul (fp3_elt_ptr dst, fp3_elt_srcptr src1, fp3_elt_srcptr src2, const fp3_param param, uint8_t stack)
	Set dst <- src1 * src2, if Montgomery arithmetic is used, the Montgomery multiplication will be used ! More...

void	fp3_elt_sqr_fp_elt (fp3_elt_ptr dst, fp_elt_srcptr src, const fp3_param param, uint8_t stack)
	Set dst <- src^2. More...

void	fp3_elt_sqr (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param, uint8_t stack)
	Set dst <- src^2. More...

void	fp3_elt_inv_fp_elt (fp3_elt_ptr dst, fp_elt_srcptr src, const fp3_param param, uint8_t stack)
	Set dst <- src^(-1) More...

void	fp3_elt_inv (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param, uint8_t stack)
	Set dst <- src^(-1) More...

void	fp3_elt_div_fp_elt (fp3_elt_ptr dst, fp3_elt_srcptr src1, fp_elt_srcptr src2, const fp3_param param, uint8_t stack)
	Set dst <- src1 / src2. More...

void	fp3_elt_div (fp3_elt_ptr dst, fp3_elt_srcptr src1, fp3_elt_srcptr src2, const fp3_param param, uint8_t stack)
	Set dst <- src1 / src2. More...

void	fp3_elt_pow_ui (fp3_elt_ptr dst, fp3_elt_srcptr src, const block n, const fp3_param param, uint8_t stack)
	Set dst <- src^n. More...

void	fp3_elt_pow_number (fp3_elt_ptr dst, fp3_elt_srcptr src, number_srcptr n, const fp3_param param, uint8_t stack)
	Set dst <- src^n. More...

bool	fp3_elt_issquare (fp3_elt_srcptr src, const fp3_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	fp3_elt_ispower_ui (fp3_elt_srcptr src, const block n, const fp3_param param, uint8_t stack)
	Test if src is a n-power in FP3, using A NOTE ON POWERS IN FINITE FIELDS from ANDREAS AABRANDT AND VAGN LUNDSGAARD HANSEN. More...

int8_t	fp3_elt_ispower_number (fp3_elt_srcptr src, number_srcptr n, const fp3_param param, uint8_t stack)
	Test if src is a n-power in FP3, using A NOTE ON POWERS IN FINITE FIELDS from ANDREAS AABRANDT AND VAGN LUNDSGAARD HANSEN. More...

void	fp3_elt_sqrt (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param, uint8_t stack)
	Set dst <- src^(1/2), using Tonelli–Shanks algorithm. More...

void	fp3_elt_cube_root (fp3_elt_ptr dst, fp3_elt_srcptr src, const fp3_param param, uint8_t stack)
	Set dst <- src^(1/3) More...

void	fp3_elt_unity_nth_root (fp3_elt_ptr dst, const block n, const fp3_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 cubic field (finite field constructed with an irreducible polynomial of degree 3) functions.

Definition in file mphell-fp3.h.

Function Documentation

◆ fp3_alloc()

void fp3_alloc	(	fp3_param	param,
		const fp_param	base
	)

Allocate space for the cubic extension field informations structure.

Parameters

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

Definition at line 69 of file mphell-fp3.c.

◆ fp3_copy()

void fp3_copy	(	fp3_param	param_res,
		const fp3_param	param
	)

Copy the cubic extension field structure param into param_res.

Parameters

param_res	Destination cubic extension field
param	Source cubic extension field

Definition at line 131 of file mphell-fp3.c.

◆ fp3_create()

void fp3_create	(	fp3_param	param,
		const fp_param	base,
		fp_elt_srcptr	non_residue,
		uint8_t	stack
	)

Create a cubic extension of the field base.

Parameters

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

Definition at line 108 of file mphell-fp3.c.

◆ fp3_elt_add()

void fp3_elt_add	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src1,
		fp3_elt_srcptr	src2,
		const fp3_param	param
	)

Set dst <- src1 + src2.

Parameters

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

Definition at line 403 of file mphell-fp3.c.

◆ fp3_elt_add_fp_elt()

void fp3_elt_add_fp_elt	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp3_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 cubic extension field

Definition at line 394 of file mphell-fp3.c.

◆ fp3_elt_alloc()

void fp3_elt_alloc	(	fp3_elt *	dst,
		const fp3_param	param
	)

Allocate space for a cubic extension field element.

Parameters

dst	Cubic extension field element to allocate
param	Information on cubic extension field

Definition at line 174 of file mphell-fp3.c.

◆ fp3_elt_clear()

void fp3_elt_clear ( fp3_elt * src )

Clear space used by src (remove the action of fp3_elt_init but let the one of fp3_elt_alloc)

Parameters

src	cubic extension field element to clear

Definition at line 198 of file mphell-fp3.c.

◆ fp3_elt_cmp()

int8_t fp3_elt_cmp	(	fp3_elt_srcptr	src1,
		fp3_elt_srcptr	src2,
		const fp3_param	param
	)

Compare src1 and src2 in FP3.

Parameters

src1	Source field element in FP3
src2	Source field element in FP3
param	Information on the cubic extension field

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

Definition at line 348 of file mphell-fp3.c.

◆ fp3_elt_cmp_fp_elt()

int8_t fp3_elt_cmp_fp_elt	(	fp3_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp3_param	param
	)

Compare src1 and src2 in FP3.

Parameters

src1	Source field element in FP3
src2	Source number in FP
param	Information on the cubic extension field

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

Definition at line 338 of file mphell-fp3.c.

◆ fp3_elt_copy()

void fp3_elt_copy	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param
	)

Copy src into dst, src and dst must belong to the same FP3.

Parameters

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

Definition at line 190 of file mphell-fp3.c.

◆ fp3_elt_cube_root()

void fp3_elt_cube_root	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param,
		uint8_t	stack
	)

Set dst <- src^(1/3)

Parameters

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

Definition at line 910 of file mphell-fp3.c.

◆ fp3_elt_dec()

void fp3_elt_dec	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param
	)

Set dst <- src - 1.

Parameters

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

Definition at line 412 of file mphell-fp3.c.

◆ fp3_elt_div()

void fp3_elt_div	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src1,
		fp3_elt_srcptr	src2,
		const fp3_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 cubic extension field
stack	Temporary memory stack to use

Definition at line 635 of file mphell-fp3.c.

◆ fp3_elt_div_fp_elt()

void fp3_elt_div_fp_elt	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp3_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 cubic extension field
stack	Temporary memory stack to use

Definition at line 624 of file mphell-fp3.c.

◆ fp3_elt_free()

void fp3_elt_free ( fp3_elt * src )

Free space used by src.

Parameters

src	cubic extension field element to free

Definition at line 206 of file mphell-fp3.c.

◆ fp3_elt_get_pool_elt()

void fp3_elt_get_pool_elt	(	fp3_elt *	dst,
		const fp3_param	param,
		uint8_t	stack
	)

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

Parameters

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

Definition at line 51 of file mphell-fp3.c.

◆ fp3_elt_inc()

void fp3_elt_inc	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param
	)

Set dst <- src + 1.

Parameters

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

Definition at line 386 of file mphell-fp3.c.

◆ fp3_elt_init()

void fp3_elt_init	(	fp3_elt_ptr	dst,
		const fp3_param	param
	)

Initialise a cubic extension field element.

Parameters

dst	Cubic extension field element to initialise
param	Information on cubic extension field

Definition at line 182 of file mphell-fp3.c.

◆ fp3_elt_inv()

void fp3_elt_inv	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param,
		uint8_t	stack
	)

Set dst <- src^(-1)

Parameters

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

Definition at line 580 of file mphell-fp3.c.

◆ fp3_elt_inv_fp_elt()

void fp3_elt_inv_fp_elt	(	fp3_elt_ptr	dst,
		fp_elt_srcptr	src,
		const fp3_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 cubic extension field

Definition at line 572 of file mphell-fp3.c.

◆ fp3_elt_isone()

bool fp3_elt_isone	(	fp3_elt_srcptr	src,
		const fp3_param	param
	)

Test if src is one.

Parameters

src	Source field element
param	Information on the cubic extension field

Returns: true if scr is one, false otherwise

Definition at line 370 of file mphell-fp3.c.

◆ fp3_elt_ispower_number()

int8_t fp3_elt_ispower_number	(	fp3_elt_srcptr	src,
		number_srcptr	n,
		const fp3_param	param,
		uint8_t	stack
	)

Test if src is a n-power in FP3, 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 cubic extension field
stack	Temporary memory stack to use

Returns: 2 if all element in FP3 are some n-power; 1 if src is a n-power in FP3; false otherwise

Definition at line 767 of file mphell-fp3.c.

◆ fp3_elt_ispower_ui()

int8_t fp3_elt_ispower_ui	(	fp3_elt_srcptr	src,
		const block	n,
		const fp3_param	param,
		uint8_t	stack
	)

Test if src is a n-power in FP3, using A NOTE ON POWERS IN FINITE FIELDS from ANDREAS AABRANDT AND VAGN LUNDSGAARD HANSEN.

Parameters

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

Returns: 2 if all element in FP3 are some n-power; 1 if src is a n-power in FP3; false otherwise

Definition at line 726 of file mphell-fp3.c.

◆ fp3_elt_issquare()

bool fp3_elt_issquare	(	fp3_elt_srcptr	src,
		const fp3_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 cubic extension field
stack	Temporary memory stack to use

Returns: true if src is a square in FP3, false otherwise

Definition at line 708 of file mphell-fp3.c.

◆ fp3_elt_iszero()

bool fp3_elt_iszero	(	fp3_elt_srcptr	src,
		const fp3_param	param
	)

Test if src is zero.

Parameters

src	Source field element
param	Information on the cubic extension field

Returns: true if scr is zero, false otherwise

Definition at line 377 of file mphell-fp3.c.

◆ fp3_elt_lift()

void fp3_elt_lift	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param,
		uint8_t	stack
	)

If Montgomery arithmetic is used, lift src (which is into Montgomery form) to classical FP3.

Parameters

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

Definition at line 293 of file mphell-fp3.c.

◆ fp3_elt_mul()

void fp3_elt_mul	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src1,
		fp3_elt_srcptr	src2,
		const fp3_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 cubic extension prime field
stack	Temporary memory stack to use

Definition at line 501 of file mphell-fp3.c.

◆ fp3_elt_mul2()

void fp3_elt_mul2	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param
	)

Set dst <- 2 * src.

Parameters

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

Definition at line 465 of file mphell-fp3.c.

◆ fp3_elt_mul3()

void fp3_elt_mul3	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param,
		uint8_t	stack
	)

Set dst <- 3 * src.

Parameters

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

Definition at line 492 of file mphell-fp3.c.

◆ fp3_elt_mul4()

void fp3_elt_mul4	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param
	)

Set dst <- 4 * src.

Parameters

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

Definition at line 474 of file mphell-fp3.c.

◆ fp3_elt_mul8()

void fp3_elt_mul8	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param
	)

Set dst <- 8 * src.

Parameters

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

Definition at line 483 of file mphell-fp3.c.

◆ fp3_elt_mul_fp_elt()

void fp3_elt_mul_fp_elt	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp3_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 cubic extension prime field
stack	Temporary memory stack to use

Definition at line 456 of file mphell-fp3.c.

◆ fp3_elt_neg()

void fp3_elt_neg	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param
	)

Set dst <- (-src)

Parameters

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

Definition at line 446 of file mphell-fp3.c.

◆ fp3_elt_neg_fp_elt()

void fp3_elt_neg_fp_elt	(	fp3_elt_ptr	dst,
		fp_elt_srcptr	src,
		const fp3_param	param
	)

Set dst <- (-src)

Parameters

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

Definition at line 438 of file mphell-fp3.c.

◆ fp3_elt_pow_number()

void fp3_elt_pow_number	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		number_srcptr	n,
		const fp3_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 cubic extension field
stack	Temporary memory stack to use

Definition at line 669 of file mphell-fp3.c.

◆ fp3_elt_pow_ui()

void fp3_elt_pow_ui	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const block	n,
		const fp3_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 cubic extension field
stack	Temporary memory stack to use

Definition at line 646 of file mphell-fp3.c.

◆ fp3_elt_random()

void fp3_elt_random	(	fp3_elt_ptr	dst,
		const fp3_param	param,
		uint8_t	stack
	)

Set dst to a random element of FP3, the random process is chosen at the MHELL initialisation.

Parameters

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

Definition at line 285 of file mphell-fp3.c.

◆ fp3_elt_relax_pool_elt()

void fp3_elt_relax_pool_elt	(	fp3_elt *	dst,
		const fp3_param	param,
		uint8_t	stack
	)

Free space of a temporary cubic extension field element.

Parameters

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

Definition at line 59 of file mphell-fp3.c.

◆ fp3_elt_set()

void fp3_elt_set	(	fp3_elt_ptr	dst,
		number_srcptr	src1,
		number_srcptr	src2,
		number_srcptr	src3,
		const bool	isreduced,
		const fp3_param	param,
		uint8_t	stack
	)

Set dst to src1 + src2*x + src3*x^2, if Montgomery arithmetic is used, is_reduced == false -> transform dst into its Montgomery form.

Parameters

dst	Destination cubic extension field element
src1	Source number
src2	Source number
src3	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 cubic extension field
stack	Temporary memory stack to use

Definition at line 248 of file mphell-fp3.c.

◆ fp3_elt_set_fp_elt()

void fp3_elt_set_fp_elt	(	fp3_elt_ptr	dst,
		fp_elt_srcptr	src,
		const fp3_param	param
	)

Set dst to src.

Parameters

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

Definition at line 240 of file mphell-fp3.c.

◆ fp3_elt_set_fp_elts()

void fp3_elt_set_fp_elts	(	fp3_elt_ptr	dst,
		fp_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		fp_elt_srcptr	src3,
		const fp3_param	param
	)

Set dst to src1 + src2*x + src3*x^2.

Parameters

dst	Destination cubic extension field element
src1	Source fp_elt
src2	Source fp_elt
src3	Source fp_elt
param	Information on the cubic extension field

Definition at line 257 of file mphell-fp3.c.

◆ fp3_elt_set_number()

void fp3_elt_set_number	(	fp3_elt_ptr	dst,
		number_srcptr	src,
		const bool	isreduced,
		const fp3_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 cubic 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 cubic extension field
stack	Temporary memory stack to use

Definition at line 231 of file mphell-fp3.c.

◆ fp3_elt_set_one()

void fp3_elt_set_one	(	fp3_elt_ptr	dst,
		const fp3_param	param
	)

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

Parameters

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

Definition at line 214 of file mphell-fp3.c.

◆ fp3_elt_set_str()

void fp3_elt_set_str	(	fp3_elt_ptr	dst,
		const char *	str,
		const uint8_t	base,
		const bool	isreduced,
		const fp3_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 cubic extension field element
str	Source polynomial coefficient under string format in base "base", separated by a "," without space. ex: "123,456,789" will create the polynomial 123 + 456.X + 789.X^2
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 cubic extension field
stack	Temporary memory stack to use

Definition at line 265 of file mphell-fp3.c.

◆ fp3_elt_set_ui()

void fp3_elt_set_ui	(	fp3_elt_ptr	dst,
		const uint64_t	src,
		const bool	isreduced,
		const fp3_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 cubic 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 cubic extension field
stack	Temporary memory stack to use

Definition at line 222 of file mphell-fp3.c.

◆ fp3_elt_sqr()

void fp3_elt_sqr	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_param	param,
		uint8_t	stack
	)

Set dst <- src^2.

Parameters

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

Definition at line 566 of file mphell-fp3.c.

◆ fp3_elt_sqr_fp_elt()

void fp3_elt_sqr_fp_elt	(	fp3_elt_ptr	dst,
		fp_elt_srcptr	src,
		const fp3_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 cubic extension field
stack	Temporary memory stack to use

Definition at line 558 of file mphell-fp3.c.

◆ fp3_elt_sqrt()

void fp3_elt_sqrt	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src,
		const fp3_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 cubic extension field
stack	Temporary memory stack to use

Definition at line 833 of file mphell-fp3.c.

◆ fp3_elt_str()

void fp3_elt_str	(	char **	str,
		fp3_elt_srcptr	src,
		const uint8_t	base,
		const bool	lift,
		const fp3_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 + 789.X^2 will be written as "123,456,789"
src	Source cubic 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 cubic extension field
stack	Temporary memory stack to use

Definition at line 321 of file mphell-fp3.c.

◆ fp3_elt_sub()

void fp3_elt_sub	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src1,
		fp3_elt_srcptr	src2,
		const fp3_param	param
	)

Set dst <- src1 - src2.

Parameters

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

Definition at line 429 of file mphell-fp3.c.

◆ fp3_elt_sub_fp_elt()

void fp3_elt_sub_fp_elt	(	fp3_elt_ptr	dst,
		fp3_elt_srcptr	src1,
		fp_elt_srcptr	src2,
		const fp3_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 cubic extension field

Definition at line 420 of file mphell-fp3.c.

◆ fp3_elt_unity_nth_root()

void fp3_elt_unity_nth_root	(	fp3_elt_ptr	dst,
		const block	n,
		const fp3_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 1099 of file mphell-fp3.c.

◆ fp3_free()

void fp3_free ( fp3_param param )

Free the space of the cubic extension field informations structure.

Parameters

param cubic extension field informations structure

Definition at line 143 of file mphell-fp3.c.

◆ fp3_get_characteristic()

void fp3_get_characteristic	(	number_ptr	c,
		const fp3_param	param
	)

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

Parameters

c	Destination number (to store the characteristic)
param	Information on cubic extension field

Definition at line 156 of file mphell-fp3.c.

◆ fp3_get_size()

void fp3_get_size	(	number_ptr	c,
		const fp3_param	param
	)

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

Parameters

c	Destination number (to store the characteristic)
param	Information on cubic extension field

Definition at line 162 of file mphell-fp3.c.

◆ fp3_str()

void fp3_str	(	char **	str,
		const fp3_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 cubic extension field
base	Base to use to write str, can be 2, 10 or 16
stack	Temporary memory stack to use

Definition at line 301 of file mphell-fp3.c.

Data Structures

Typedefs

Functions

Detailed Description

Function Documentation

◆ fp3_alloc()

◆ fp3_copy()

◆ fp3_create()

◆ fp3_elt_add()

◆ fp3_elt_add_fp_elt()

◆ fp3_elt_alloc()

◆ fp3_elt_clear()

◆ fp3_elt_cmp()

◆ fp3_elt_cmp_fp_elt()

◆ fp3_elt_copy()

◆ fp3_elt_cube_root()

◆ fp3_elt_dec()

◆ fp3_elt_div()

◆ fp3_elt_div_fp_elt()

◆ fp3_elt_free()

◆ fp3_elt_get_pool_elt()

◆ fp3_elt_inc()

◆ fp3_elt_init()

◆ fp3_elt_inv()

◆ fp3_elt_inv_fp_elt()

◆ fp3_elt_isone()

◆ fp3_elt_ispower_number()

◆ fp3_elt_ispower_ui()

◆ fp3_elt_issquare()

◆ fp3_elt_iszero()

◆ fp3_elt_lift()

◆ fp3_elt_mul()

◆ fp3_elt_mul2()

◆ fp3_elt_mul3()

◆ fp3_elt_mul4()

◆ fp3_elt_mul8()

◆ fp3_elt_mul_fp_elt()

◆ fp3_elt_neg()

◆ fp3_elt_neg_fp_elt()

◆ fp3_elt_pow_number()

◆ fp3_elt_pow_ui()

◆ fp3_elt_random()

◆ fp3_elt_relax_pool_elt()

◆ fp3_elt_set()

◆ fp3_elt_set_fp_elt()

◆ fp3_elt_set_fp_elts()

◆ fp3_elt_set_number()

◆ fp3_elt_set_one()

◆ fp3_elt_set_str()

◆ fp3_elt_set_ui()

◆ fp3_elt_sqr()

◆ fp3_elt_sqr_fp_elt()

◆ fp3_elt_sqrt()

◆ fp3_elt_str()

◆ fp3_elt_sub()

◆ fp3_elt_sub_fp_elt()

◆ fp3_elt_unity_nth_root()

◆ fp3_free()

◆ fp3_get_characteristic()

◆ fp3_get_size()

◆ fp3_str()