mphell-weierstrass.h File Reference

Declaration of Weierstrass ECC function. More...

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Functions
void	weierstrass_compute_disc (ec_curve E, uint8_t stack)
	Set the discriminant of E: disc = -16(4a^3 + 27b^2) More...
bool	weierstrass_verify_random_generation (ec_curve E, const char *seed, uint8_t stack)
	Test if E if generated from the seed "seed". More...
void	weierstrass_curve_random_generation (fe_ptr a, fe_ptr b, 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	weierstrass_point_set_neutral (ec_point_ptr dst, ec_curve_srcptr E, uint8_t stack)
	Set dst to the neutral element: (0,1,0) for projective coordinates and (1,1,0) for jacobian coordinates. More...
void	weierstrass_point_set_aff (ec_point_ptr P, fe_srcptr x, fe_srcptr y, field_srcptr k)
	Set dest to the affine point (x, y) More...
void	weierstrass_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	weierstrass_belongs (ec_point_srcptr P, ec_curve_srcptr E, uint8_t stack)
	Test if P belongs to E. More...
void	weierstrass_point_random (ec_point_ptr P, ec_curve_srcptr E, uint8_t stack)
	Set P to a random point on E. More...
void	weierstrass_point_norm (ec_point_ptr P, ec_curve_srcptr E, uint8_t stack)
	Set P in affine coordinates. More...
void	weierstrass_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	weierstrass_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	weierstrass_point_is_neutral (ec_point_srcptr P, ec_curve_srcptr E, uint8_t stack)
	Test if P is the neutral element. More...
bool	weierstrass_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 (BUT do not test if they belong to the curve) More...
void	weierstrass_point_neg (ec_point_ptr P3, ec_point_srcptr P1, ec_curve_srcptr E)
	Set P3 to -P1. More...
void	weierstrass_point_add_ZADDU (ec_point_ptr P3, ec_point_ptr P1, ec_point_srcptr P2, ec_curve_srcptr E, uint8_t stack)
	Co-Z point addition with update: Set P3 = (X3,Y3,Z3) to P1 + P2 using Co-Z addition and update P1 such that Z1 = Z3. More...
void	weierstrass_point_add_ZADDC (ec_point_ptr P3, ec_point_ptr P4, ec_point_srcptr P1, ec_point_srcptr P2, ec_curve_srcptr E, uint8_t stack)
	Conjugate Co-Z point addition: Set P3 to P1 + P2 and P4 to P1 - P2 such that Z3=Z4. More...
void	weierstrass_point_add_ZDAU (ec_point_ptr P3, ec_point_srcptr P1, ec_point_ptr P2, ec_curve_srcptr E, uint8_t stack)
	Co-Z point doubling-addition with update: Set P3 to 2*P1 + P2 and update P2 such that Z2 = Z3. More...
void	weierstrass_point_DBLU (ec_point_ptr P3, ec_point_ptr P4, ec_point_srcptr P1, ec_curve_srcptr E, uint8_t stack)
	Co-Z point doubling with update: Set P3 to 2*P1 and P4 such that P1 = P4 and Z4 = Z3 and assume that P1->z==1. More...
void	weierstrass_point_TPLU (ec_point_ptr P3, ec_point_ptr P4, ec_point_srcptr P1, ec_curve_srcptr E, uint8_t stack)
	Co-Z point tripling with update: Set P3 to 3*P1 and P4 such that P4 = P1 and Z4 = Z3. More...
void	weierstrass_Zmontgomery_Kim (ec_point_ptr P3, number_srcptr n, ec_point_srcptr P1, ec_curve_srcptr E, uint8_t stack)
	Perform the Montgomery ladder, taken from Kim et al's 2017 work, compute P3=[n]P1 it has the drawback to perform an inversion at the end of the computation to have affine coordinates and its formula is not complete and does not work for n = -1 neither 0 see .c for details. More...
void	weierstrass_Zmontgomery_ladder (ec_point_ptr P3, number_srcptr n, ec_point_srcptr P1, ec_curve_srcptr E, uint8_t stack)
	Set P3 to n * P1 using Montgomery ladder with Co-Z addition formula. More...
void	weierstrass_Zjoye_mul (ec_point_ptr P3, number_srcptr n, ec_point_srcptr P1, ec_curve_srcptr E, uint8_t stack)
	Set P3 to n * P1 using Joye’s double-add algorithm with Co-Z addition formula.The formulae are not complete and does not work for n = -1 see .c for details. More...
void	weierstrass_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 unified formulae (protection against SPA) More...
void	weierstrass_point_add_dedicated (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 dedicated formulae (not protected against SPA, but faster) More...
void	weierstrass_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...
void	weierstrass_point_of_order_2 (ec_point_ptr dst, ec_curve_srcptr E, uint8_t stack)
	Set dst to one of the point of order 2 of the curve E assuming that at least one exist. More...
void	weierstrass_points_of_order_2 (ec_point_ptr dst1, ec_point_ptr dst2, ec_point_ptr dst3, ec_curve_srcptr E, uint8_t stack)
	Set dst1, dst2, dst3 to the points of order 2 of the curve E assuming they are different otherwise they are all equal to the unique point of order 2. More...

Detailed Description

Declaration of Weierstrass ECC function.

Definition in file mphell-weierstrass.h.

Function Documentation

weierstrass_belongs()

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

Test if P belongs to E.

Parameters

P	Point
E	Elliptic curve
stack	Temporary memory stack to use

Returns

true if P belongs to E

false otherwise

Definition at line 442 of file mphell-weierstrass.c.

weierstrass_compute_disc()

void weierstrass_compute_disc	(	ec_curve	E,
		uint8_t	stack
	)

Set the discriminant of E: disc = -16(4a^3 + 27b^2)

Parameters

E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 70 of file mphell-weierstrass.c.

weierstrass_curve_random_generation()

void weierstrass_curve_random_generation	(	fe_ptr	a,
		fe_ptr	b,
		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
b	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 227 of file mphell-weierstrass.c.

weierstrass_point_add_dedicated()

void weierstrass_point_add_dedicated	(	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 dedicated formulae (not protected against SPA, but faster)

--> Interface

Parameters

P3	Destination point
P1	Point
P2	Point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 1921 of file mphell-weierstrass.c.

weierstrass_point_add_unified()

void weierstrass_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 unified formulae (protection against SPA)

Parameters

P3	Destination point
P1	Point
P2	Point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 1951 of file mphell-weierstrass.c.

weierstrass_point_add_ZADDC()

void weierstrass_point_add_ZADDC	(	ec_point_ptr	P3,
		ec_point_ptr	P4,
		ec_point_srcptr	P1,
		ec_point_srcptr	P2,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Conjugate Co-Z point addition: Set P3 to P1 + P2 and P4 to P1 - P2 such that Z3=Z4.

Parameters

P3	Destination point
P4	Destination point
P1	Point (X1, Y1, Z)
P2	Point (X2, Y2, Z)
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 815 of file mphell-weierstrass.c.

weierstrass_point_add_ZADDU()

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

Co-Z point addition with update: Set P3 = (X3,Y3,Z3) to P1 + P2 using Co-Z addition and update P1 such that Z1 = Z3.

--> COZ

Parameters

P3	Destination point
P1	Point (X1, Y1, Z)
P2	Point (X2, Y2, Z)
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 775 of file mphell-weierstrass.c.

weierstrass_point_add_ZDAU()

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

Co-Z point doubling-addition with update: Set P3 to 2*P1 + P2 and update P2 such that Z2 = Z3.

Parameters

P3	Destination point
P1	Point (X1, Y1, Z2)
P2	Point (X2, Y2, Z2)
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 866 of file mphell-weierstrass.c.

weierstrass_point_are_equal()

bool weierstrass_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 (BUT do not test if they belong to the curve)

Parameters

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

Returns

True if P1 == P2, False otherwise

Definition at line 677 of file mphell-weierstrass.c.

weierstrass_point_dbl_dedicated()

void weierstrass_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	Destination point
P1	Point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 1981 of file mphell-weierstrass.c.

weierstrass_point_DBLU()

void weierstrass_point_DBLU	(	ec_point_ptr	P3,
		ec_point_ptr	P4,
		ec_point_srcptr	P1,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Co-Z point doubling with update: Set P3 to 2*P1 and P4 such that P1 = P4 and Z4 = Z3 and assume that P1->z==1.

Parameters

P3	Destination point
P4	Destination point
P1	Point with P1->z==1
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 940 of file mphell-weierstrass.c.

weierstrass_point_get_x_affine()

void weierstrass_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 578 of file mphell-weierstrass.c.

weierstrass_point_get_y_affine()

void weierstrass_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 604 of file mphell-weierstrass.c.

weierstrass_point_is_neutral()

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

Test if P is the neutral element.

Parameters

P	Point to test
E	Elliptic curve
stack	Temporary memory stack to use

Returns

True if P is neutral, False otherwise

Definition at line 633 of file mphell-weierstrass.c.

weierstrass_point_neg()

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

Set P3 to -P1.

Parameters

P3	Destination point
P1	Point
E	Elliptic curve

Definition at line 2007 of file mphell-weierstrass.c.

weierstrass_point_norm()

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

Set P in affine coordinates.

Parameters

P	Point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 537 of file mphell-weierstrass.c.

weierstrass_point_of_order_2()

void weierstrass_point_of_order_2	(	ec_point_ptr	dst,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Set dst to one of the point of order 2 of the curve E assuming that at least one exist.

--> Miscellaneaous

Parameters

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

Definition at line 2019 of file mphell-weierstrass.c.

weierstrass_point_random()

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

Set P to a random point on E.

Parameters

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

Definition at line 511 of file mphell-weierstrass.c.

weierstrass_point_set_aff()

void weierstrass_point_set_aff	(	ec_point_ptr	P,
		fe_srcptr	x,
		fe_srcptr	y,
		field_srcptr	k
	)

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

Definition at line 423 of file mphell-weierstrass.c.

weierstrass_point_set_aff_str()

void weierstrass_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 432 of file mphell-weierstrass.c.

weierstrass_point_set_neutral()

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

Set dst to the neutral element: (0,1,0) for projective coordinates and (1,1,0) for jacobian coordinates.

Parameters

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

Definition at line 397 of file mphell-weierstrass.c.

weierstrass_point_TPLU()

void weierstrass_point_TPLU	(	ec_point_ptr	P3,
		ec_point_ptr	P4,
		ec_point_srcptr	P1,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Co-Z point tripling with update: Set P3 to 3*P1 and P4 such that P4 = P1 and Z4 = Z3.

Parameters

P3	Destination point
P4	Destination point
P1	Point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 1001 of file mphell-weierstrass.c.

weierstrass_points_of_order_2()

void weierstrass_points_of_order_2	(	ec_point_ptr	dst1,
		ec_point_ptr	dst2,
		ec_point_ptr	dst3,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Set dst1, dst2, dst3 to the points of order 2 of the curve E assuming they are different otherwise they are all equal to the unique point of order 2.

Parameters

dst1	Destination point
dst2	Destination point
dst3	Destination point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 2166 of file mphell-weierstrass.c.

weierstrass_verify_random_generation()

bool weierstrass_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
stack	Temporary memory stack to use

Returns

true if E is generated from seed

false otherwise

Definition at line 100 of file mphell-weierstrass.c.

weierstrass_Zjoye_mul()

void weierstrass_Zjoye_mul	(	ec_point_ptr	P3,
		number_srcptr	n,
		ec_point_srcptr	P1,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Set P3 to n * P1 using Joye’s double-add algorithm with Co-Z addition formula.The formulae are not complete and does not work for n = -1 see .c for details.

Parameters

P3	Destination point
P1	Point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 1843 of file mphell-weierstrass.c.

weierstrass_Zmontgomery_Kim()

void weierstrass_Zmontgomery_Kim	(	ec_point_ptr	P3,
		number_srcptr	n,
		ec_point_srcptr	P1,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Perform the Montgomery ladder, taken from Kim et al's 2017 work, compute P3=[n]P1 it has the drawback to perform an inversion at the end of the computation to have affine coordinates and its formula is not complete and does not work for n = -1 neither 0 see .c for details.

Parameters

P3	Destination point
n	Number element for the scalar multiplication (different from -1 mod #E)
P1	Input point
E	Elliptic curve on which the points belong
stack	Temporary memory stack to use

Definition at line 1757 of file mphell-weierstrass.c.

weierstrass_Zmontgomery_ladder()

void weierstrass_Zmontgomery_ladder	(	ec_point_ptr	P3,
		number_srcptr	n,
		ec_point_srcptr	P1,
		ec_curve_srcptr	E,
		uint8_t	stack
	)

Set P3 to n * P1 using Montgomery ladder with Co-Z addition formula.

--> COZ multiplication

Parameters

P3	Destination point
P1	Point
E	Elliptic curve
stack	Temporary memory stack to use

Definition at line 1496 of file mphell-weierstrass.c.