mphell-jacobi.h File Reference

Declaration of Jacobi ECC functions. More...

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Functions
void	jacobi_quartic_compute_disc (ec_curve E, uint8_t stack)
	Set the discriminant of E: disc = (2^8).(a^2 - 1)^2. More...
bool	jacobi_quartic_verify_random_generation (ec_curve E, const char *seed, uint8_t stack)
	Test if E if generated from the seed "seed". More...
void	jacobi_quartic_curve_random_generation (fe_ptr a, char *seed_res, field_srcptr k, uint8_t stack)
	Generate a 160 bits seed and coefficients a and b defining a Weiestrass elliptic curve. The curve is not tested to be secure !!! More...
void	jacobi_quartic_point_set_neutral (ec_point_ptr dst, ec_curve_srcptr E, uint8_t stack)
	Set dst to the neutral element: (0,1,0,1). More...
void	jacobi_quartic_point_set_aff (ec_point_ptr P, fe_srcptr x, fe_srcptr y, field_srcptr k, uint8_t stack)
	Set dest to the affine point (x,y) More...
void	jacobi_quartic_point_set_aff_str (ec_point_ptr P, const char *str_x, const char *str_y, const bool is_reduced, const uint8_t base, field_srcptr k, uint8_t stack)
	Set dest to the affine point (str_x,str_y) More...
bool	jacobi_quartic_belongs (ec_point_srcptr P, ec_curve_srcptr E, uint8_t stack)
	Test if P belongs to E. More...
void	jacobi_quartic_point_random (ec_point_ptr P, ec_curve_srcptr E, uint8_t stack)
	Create a random point P on the elliptic curve E. More...
void	jacobi_quartic_point_norm (ec_point_ptr P, ec_curve_srcptr E, uint8_t stack)
	Convert a point in extented projective coordinate (X,Y,T,Z) to an affine point (x,y) with x=X/Z, y=Y/Z. More...
void	jacobi_quartic_point_get_x_affine (field_elt x, ec_point_ptr P, ec_curve_srcptr E, uint8_t stack)
	Convert P->x to its affine representation. More...
void	jacobi_quartic_point_get_y_affine (field_elt y, ec_point_ptr P, ec_curve_srcptr E, uint8_t stack)
	Convert P->y to its affine representation. More...
bool	jacobi_quartic_point_is_neutral (ec_point_srcptr P, ec_curve_srcptr E)
	Test if P is the neutral element. More...
bool	jacobi_quartic_point_are_equal (ec_point_srcptr P1, ec_point_srcptr P2, ec_curve_srcptr E, uint8_t stack)
	Test if P1 and P2 are equal on E. More...
void	jacobi_quartic_point_neg (ec_point_ptr P3, ec_point_srcptr P1, ec_curve_srcptr E)
	Set P3 to -P1. More...
void	jacobi_quartic_point_add_unified (ec_point_ptr P3, ec_point_srcptr P1, ec_point_srcptr P2, ec_curve_srcptr E, uint8_t stack)
	Set P3 to P1 + P2 using extended projective coordinate (T=(X^2)/Z), and unified formulae (protection against SPA) More...
void	jacobi_quartic_point_dbl_dedicated (ec_point_ptr P3, ec_point_srcptr P1, ec_curve_srcptr E, uint8_t stack)
	Set P3 to 2*P1, using dedicated formulae (not protected against SPA, but faster) More...

Detailed Description

Declaration of Jacobi ECC functions.

Definition in file mphell-jacobi.h.

Function Documentation

jacobi_quartic_belongs()

bool jacobi_quartic_belongs	(	ec_point_srcptr	P,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Test if P belongs to E.

Parameters

P	Jacobi quartic point
E	Elliptic curve
stack	Temporary memory stack to use

Returns

True if P belongs to E, false otherwise

Definition at line 352 of file mphell-jacobi.c.

jacobi_quartic_compute_disc()

void jacobi_quartic_compute_disc	(	ec_curve	E,
		uint8_t	stack
	)

Set the discriminant of E: disc = (2^8).(a^2 - 1)^2.

Parameters

E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 32 of file mphell-jacobi.c.

jacobi_quartic_curve_random_generation()

void jacobi_quartic_curve_random_generation	(	fe_ptr	a,
		char *	seed_res,
		field_srcptr	k,
		uint8_t	stack
	)

Generate a 160 bits seed and coefficients a and b defining a Weiestrass elliptic curve. The curve is not tested to be secure !!!

Parameters

a	Destination coefficient, generated from a random seed
seed_res	Destination seed (of 160 bits) used to generate an elliptic curve
k	Base field, must be created by the user before use.
stack	Temporary memory stack to use

Definition at line 172 of file mphell-jacobi.c.

jacobi_quartic_point_add_unified()

void jacobi_quartic_point_add_unified	(	ec_point_ptr	P3,
		ec_point_srcptr	P1,
		ec_point_srcptr	P2,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Set P3 to P1 + P2 using extended projective coordinate (T=(X^2)/Z), and unified formulae (protection against SPA)

Parameters

P3	Resulting point
P1	Source point
P2	Source point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 565 of file mphell-jacobi.c.

jacobi_quartic_point_are_equal()

bool jacobi_quartic_point_are_equal	(	ec_point_srcptr	P1,
		ec_point_srcptr	P2,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Test if P1 and P2 are equal on E.

Parameters

P1	Point
P2	Point
E	Elliptic curve
stack	Temporary memory stack to use

Returns

True if P1 == P2, False otherwise

Definition at line 488 of file mphell-jacobi.c.

jacobi_quartic_point_dbl_dedicated()

void jacobi_quartic_point_dbl_dedicated	(	ec_point_ptr	P3,
		ec_point_srcptr	P1,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Set P3 to 2*P1, using dedicated formulae (not protected against SPA, but faster)

Parameters

P3	Resulting point
P1	Source point
E	Elliptic curve (Jacobi quartic)
stack	Temporary memory stack to use

Definition at line 659 of file mphell-jacobi.c.

jacobi_quartic_point_get_x_affine()

void jacobi_quartic_point_get_x_affine	(	field_elt	x,
		ec_point_ptr	P,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Convert P->x to its affine representation.

Parameters

x	P->x in affine coordinates
P	Point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 452 of file mphell-jacobi.c.

jacobi_quartic_point_get_y_affine()

void jacobi_quartic_point_get_y_affine	(	field_elt	y,
		ec_point_ptr	P,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Convert P->y to its affine representation.

Parameters

x	P->y in affine coordinates
P	Point
E	Elliptic curve
stack	Temporary memory stack to use

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

jacobi_quartic_point_is_neutral()

bool jacobi_quartic_point_is_neutral	(	ec_point_srcptr	P,
		ec_curve_srcptr	E
	)

Test if P is the neutral element.

Parameters

P	Point to test
E	Elliptic curve

Returns

True if P is neutral, False otherwise

Definition at line 480 of file mphell-jacobi.c.

jacobi_quartic_point_neg()

void jacobi_quartic_point_neg	(	ec_point_ptr	P3,
		ec_point_srcptr	P1,
		ec_curve_srcptr	E
	)

Set P3 to -P1.

Parameters

P3	Resulting point
P1	Source point
E	Elliptic curve (Jacobi quartic)

Definition at line 553 of file mphell-jacobi.c.

jacobi_quartic_point_norm()

void jacobi_quartic_point_norm	(	ec_point_ptr	P,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Convert a point in extented projective coordinate (X,Y,T,Z) to an affine point (x,y) with x=X/Z, y=Y/Z.

Parameters

P	Point in extented projective coordinate (X,Y,T,Z) with T=(X^2)/Z
E	Jacobi quartic elliptic curve
stack	Temporary memory stack to use

Definition at line 436 of file mphell-jacobi.c.

jacobi_quartic_point_random()

void jacobi_quartic_point_random	(	ec_point_ptr	P,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Create a random point P on the elliptic curve E.

Parameters

P	Destination point in extented projective coordinate (X,Y,T,Z) with T=(X^2)/Z
E	Jacobi quartic elliptic curve
stack	Temporary memory stack to use

Definition at line 407 of file mphell-jacobi.c.

jacobi_quartic_point_set_aff()

void jacobi_quartic_point_set_aff	(	ec_point_ptr	P,
		fe_srcptr	x,
		fe_srcptr	y,
		field_srcptr	k,
		uint8_t	stack
	)

Set dest to the affine point (x,y)

Parameters

P	Destination point
x	x-coordinate of the affine point (x,y)
y	y-coordinate of the affine point (x,y)
k	Base field
stack	Temporary memory stack to use

Definition at line 333 of file mphell-jacobi.c.

jacobi_quartic_point_set_aff_str()

void jacobi_quartic_point_set_aff_str	(	ec_point_ptr	P,
		const char *	str_x,
		const char *	str_y,
		const bool	is_reduced,
		const uint8_t	base,
		field_srcptr	k,
		uint8_t	stack
	)

Set dest to the affine point (str_x,str_y)

Parameters

P	Destination point
str_x	x-coordinate of the affine point (x,y) under string form
str_y	y-coordinate of the affine point (x,y) under string form
is_reduced	Set true if str_x and str_y are already reduced in k, false otherwise
base	Base (either 10 or 16) used for str_x and str_y
k	Base field
stack	Temporary memory stack to use

Definition at line 342 of file mphell-jacobi.c.

jacobi_quartic_point_set_neutral()

void jacobi_quartic_point_set_neutral	(	ec_point_ptr	dst,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Set dst to the neutral element: (0,1,0,1).

Parameters

dst	Destination point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 323 of file mphell-jacobi.c.

jacobi_quartic_verify_random_generation()

bool jacobi_quartic_verify_random_generation	(	ec_curve	E,
		const char *	seed,
		uint8_t	stack
	)

Test if E if generated from the seed "seed".

Parameters

E	Elliptic curve to test
seed	Seed (of 160 bits) used to generate an elliptic curve

Returns

true if E is generated from seed

false otherwise

Definition at line 54 of file mphell-jacobi.c.