group.h File Reference

#include "field.h"

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Classes
struct	secp256k1_ge
	A group element of the secp256k1 curve, in affine coordinates. More...
struct	secp256k1_gej
	A group element of the secp256k1 curve, in jacobian coordinates. More...
struct	secp256k1_ge_storage

Macros
#define	SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p)   {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
#define	SECP256K1_GE_CONST_INFINITY   {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
#define	SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p)   {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
#define	SECP256K1_GEJ_CONST_INFINITY   {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
#define	SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p)   {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
#define	SECP256K1_GE_STORAGE_CONST_GET(t)   SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y)

Functions
static void	secp256k1_ge_set_xy (secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y)
	Set a group element equal to the point with given X and Y coordinates. More...
static int	secp256k1_ge_set_xquad (secp256k1_ge *r, const secp256k1_fe *x)
	Set a group element (affine) equal to the point with the given X coordinate and a Y coordinate that is a quadratic residue modulo p. More...
static int	secp256k1_ge_set_xo_var (secp256k1_ge *r, const secp256k1_fe *x, int odd)
	Set a group element (affine) equal to the point with the given X coordinate, and given oddness for Y. More...
static int	secp256k1_ge_is_infinity (const secp256k1_ge *a)
	Check whether a group element is the point at infinity. More...
static int	secp256k1_ge_is_valid_var (const secp256k1_ge *a)
	Check whether a group element is valid (i.e., on the curve). More...
static void	secp256k1_ge_neg (secp256k1_ge *r, const secp256k1_ge *a)
	Set r equal to the inverse of a (i.e., mirrored around the X axis) More...
static void	secp256k1_ge_set_gej (secp256k1_ge *r, secp256k1_gej *a)
	Set a group element equal to another which is given in jacobian coordinates. More...
static void	secp256k1_ge_set_gej_var (secp256k1_ge *r, secp256k1_gej *a)
	Set a group element equal to another which is given in jacobian coordinates. More...
static void	secp256k1_ge_set_all_gej_var (secp256k1_ge *r, const secp256k1_gej *a, size_t len)
	Set a batch of group elements equal to the inputs given in jacobian coordinates. More...
static void	secp256k1_ge_globalz_set_table_gej (size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr)
	Bring a batch inputs given in jacobian coordinates (with known z-ratios) to the same global z "denominator". More...
static void	secp256k1_ge_set_infinity (secp256k1_ge *r)
	Set a group element (affine) equal to the point at infinity. More...
static void	secp256k1_gej_set_infinity (secp256k1_gej *r)
	Set a group element (jacobian) equal to the point at infinity. More...
static void	secp256k1_gej_set_ge (secp256k1_gej *r, const secp256k1_ge *a)
	Set a group element (jacobian) equal to another which is given in affine coordinates. More...
static int	secp256k1_gej_eq_x_var (const secp256k1_fe *x, const secp256k1_gej *a)
	Compare the X coordinate of a group element (jacobian). More...
static void	secp256k1_gej_neg (secp256k1_gej *r, const secp256k1_gej *a)
	Set r equal to the inverse of a (i.e., mirrored around the X axis) More...
static int	secp256k1_gej_is_infinity (const secp256k1_gej *a)
	Check whether a group element is the point at infinity. More...
static int	secp256k1_gej_has_quad_y_var (const secp256k1_gej *a)
	Check whether a group element's y coordinate is a quadratic residue. More...
static void	secp256k1_gej_double (secp256k1_gej *r, const secp256k1_gej *a)
	Set r equal to the double of a. More...
static void	secp256k1_gej_double_var (secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr)
	Set r equal to the double of a. More...
static void	secp256k1_gej_add_var (secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr)
	Set r equal to the sum of a and b. More...
static void	secp256k1_gej_add_ge (secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b)
	Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). More...
static void	secp256k1_gej_add_ge_var (secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr)
	Set r equal to the sum of a and b (with b given in affine coordinates). More...
static void	secp256k1_gej_add_zinv_var (secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv)
	Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). More...
static void	secp256k1_ge_mul_lambda (secp256k1_ge *r, const secp256k1_ge *a)
	Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. More...
static void	secp256k1_gej_clear (secp256k1_gej *r)
	Clear a secp256k1_gej to prevent leaking sensitive information. More...
static void	secp256k1_ge_clear (secp256k1_ge *r)
	Clear a secp256k1_ge to prevent leaking sensitive information. More...
static void	secp256k1_ge_to_storage (secp256k1_ge_storage *r, const secp256k1_ge *a)
	Convert a group element to the storage type. More...
static void	secp256k1_ge_from_storage (secp256k1_ge *r, const secp256k1_ge_storage *a)
	Convert a group element back from the storage type. More...
static void	secp256k1_ge_storage_cmov (secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag)
	If flag is true, set *r equal to *a; otherwise leave it. More...
static void	secp256k1_gej_rescale (secp256k1_gej *r, const secp256k1_fe *b)
	Rescale a jacobian point by b which must be non-zero. More...
static int	secp256k1_ge_is_in_correct_subgroup (const secp256k1_ge *ge)
	Determine if a point (which is assumed to be on the curve) is in the correct (sub)group of the curve. More...

Macro Definition Documentation

SECP256K1_GE_CONST

#define SECP256K1_GE_CONST	(		a,
			b,
			c,
			d,
			e,
			f,
			g,
			h,
			i,
			j,
			k,
			l,
			m,
			n,
			o,
			p
	)		{SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}

Definition at line 19 of file group.h.

SECP256K1_GE_CONST_INFINITY

#define SECP256K1_GE_CONST_INFINITY   {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}

Definition at line 20 of file group.h.

SECP256K1_GE_STORAGE_CONST

#define SECP256K1_GE_STORAGE_CONST	(		a,
			b,
			c,
			d,
			e,
			f,
			g,
			h,
			i,
			j,
			k,
			l,
			m,
			n,
			o,
			p
	)		{SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}

Definition at line 38 of file group.h.

SECP256K1_GE_STORAGE_CONST_GET

#define SECP256K1_GE_STORAGE_CONST_GET

(

t

)

SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y)

Definition at line 40 of file group.h.

SECP256K1_GEJ_CONST

#define SECP256K1_GEJ_CONST	(		a,
			b,
			c,
			d,
			e,
			f,
			g,
			h,
			i,
			j,
			k,
			l,
			m,
			n,
			o,
			p
	)		{SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}

Definition at line 30 of file group.h.

SECP256K1_GEJ_CONST_INFINITY

#define SECP256K1_GEJ_CONST_INFINITY   {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}

Definition at line 31 of file group.h.

Function Documentation

secp256k1_ge_clear()

static void secp256k1_ge_clear ( secp256k1_ge *  r )

static

Clear a secp256k1_ge to prevent leaking sensitive information.

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secp256k1_ge_from_storage()

static void secp256k1_ge_from_storage ( secp256k1_ge *  r, const secp256k1_ge_storage *  a  )

static

Convert a group element back from the storage type.

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secp256k1_ge_globalz_set_table_gej()

static void secp256k1_ge_globalz_set_table_gej ( size_t  len, secp256k1_ge *  r, secp256k1_fe *  globalz, const secp256k1_gej *  a, const secp256k1_fe *  zr  )

static

Bring a batch inputs given in jacobian coordinates (with known z-ratios) to the same global z "denominator".

zr must contain the known z-ratios such that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. The x and y coordinates of the result are stored in r, the common z coordinate is stored in globalz.

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secp256k1_ge_is_in_correct_subgroup()

static int secp256k1_ge_is_in_correct_subgroup ( const secp256k1_ge *  ge )

static

Determine if a point (which is assumed to be on the curve) is in the correct (sub)group of the curve.

In normal mode, the used group is secp256k1, which has cofactor=1 meaning that every point on the curve is in the group, and this function returns always true.

When compiling in exhaustive test mode, a slightly different curve equation is used, leading to a group with a (very) small subgroup, and that subgroup is what is used for all cryptographic operations. In that mode, this function checks whether a point that is on the curve is in fact also in that subgroup.

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secp256k1_ge_is_infinity()

static int secp256k1_ge_is_infinity ( const secp256k1_ge *  a )

static

Check whether a group element is the point at infinity.

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secp256k1_ge_is_valid_var()

static int secp256k1_ge_is_valid_var ( const secp256k1_ge *  a )

static

Check whether a group element is valid (i.e., on the curve).

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secp256k1_ge_mul_lambda()

static void secp256k1_ge_mul_lambda ( secp256k1_ge *  r, const secp256k1_ge *  a  )

static

Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast.

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secp256k1_ge_neg()

static void secp256k1_ge_neg ( secp256k1_ge *  r, const secp256k1_ge *  a  )

static

Set r equal to the inverse of a (i.e., mirrored around the X axis)

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secp256k1_ge_set_all_gej_var()

static void secp256k1_ge_set_all_gej_var ( secp256k1_ge *  r, const secp256k1_gej *  a, size_t  len  )

static

Set a batch of group elements equal to the inputs given in jacobian coordinates.

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secp256k1_ge_set_gej()

static void secp256k1_ge_set_gej ( secp256k1_ge *  r, secp256k1_gej *  a  )

static

Set a group element equal to another which is given in jacobian coordinates.

Constant time.

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secp256k1_ge_set_gej_var()

static void secp256k1_ge_set_gej_var ( secp256k1_ge *  r, secp256k1_gej *  a  )

static

Set a group element equal to another which is given in jacobian coordinates.

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secp256k1_ge_set_infinity()

static void secp256k1_ge_set_infinity ( secp256k1_ge *  r )

static

Set a group element (affine) equal to the point at infinity.

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secp256k1_ge_set_xo_var()

static int secp256k1_ge_set_xo_var ( secp256k1_ge *  r, const secp256k1_fe *  x, int  odd  )

static

Set a group element (affine) equal to the point with the given X coordinate, and given oddness for Y.

Return value indicates whether the result is valid.

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secp256k1_ge_set_xquad()

static int secp256k1_ge_set_xquad ( secp256k1_ge *  r, const secp256k1_fe *  x  )

static

Set a group element (affine) equal to the point with the given X coordinate and a Y coordinate that is a quadratic residue modulo p.

The return value is true iff a coordinate with the given X coordinate exists.

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secp256k1_ge_set_xy()

static void secp256k1_ge_set_xy ( secp256k1_ge *  r, const secp256k1_fe *  x, const secp256k1_fe *  y  )

static

Set a group element equal to the point with given X and Y coordinates.

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secp256k1_ge_storage_cmov()

static void secp256k1_ge_storage_cmov ( secp256k1_ge_storage *  r, const secp256k1_ge_storage *  a, int  flag  )

static

If flag is true, set *r equal to *a; otherwise leave it.

Constant-time. Both *r and *a must be initialized.

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secp256k1_ge_to_storage()

static void secp256k1_ge_to_storage ( secp256k1_ge_storage *  r, const secp256k1_ge *  a  )

static

Convert a group element to the storage type.

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secp256k1_gej_add_ge()

static void secp256k1_gej_add_ge ( secp256k1_gej *  r, const secp256k1_gej *  a, const secp256k1_ge *  b  )

static

Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity).

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secp256k1_gej_add_ge_var()

static void secp256k1_gej_add_ge_var ( secp256k1_gej *  r, const secp256k1_gej *  a, const secp256k1_ge *  b, secp256k1_fe *  rzr  )

static

Set r equal to the sum of a and b (with b given in affine coordinates).

This is more efficient than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time guarantee, and b is allowed to be infinity. If rzr is non-NULL this sets *rzr such that r->z == a->z * *rzr (a cannot be infinity in that case).

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secp256k1_gej_add_var()

static void secp256k1_gej_add_var ( secp256k1_gej *  r, const secp256k1_gej *  a, const secp256k1_gej *  b, secp256k1_fe *  rzr  )

static

Set r equal to the sum of a and b.

If rzr is non-NULL this sets *rzr such that r->z == a->z * *rzr (a cannot be infinity in that case).

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secp256k1_gej_add_zinv_var()

static void secp256k1_gej_add_zinv_var ( secp256k1_gej *  r, const secp256k1_gej *  a, const secp256k1_ge *  b, const secp256k1_fe *  bzinv  )

static

Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv).

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secp256k1_gej_clear()

static void secp256k1_gej_clear ( secp256k1_gej *  r )

static

Clear a secp256k1_gej to prevent leaking sensitive information.

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secp256k1_gej_double()

static void secp256k1_gej_double ( secp256k1_gej *  r, const secp256k1_gej *  a  )

static

Set r equal to the double of a.

Constant time.

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secp256k1_gej_double_var()

static void secp256k1_gej_double_var ( secp256k1_gej *  r, const secp256k1_gej *  a, secp256k1_fe *  rzr  )

static

Set r equal to the double of a.

If rzr is not-NULL this sets *rzr such that r->z == a->z * *rzr (where infinity means an implicit z = 0).

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secp256k1_gej_eq_x_var()

static int secp256k1_gej_eq_x_var ( const secp256k1_fe *  x, const secp256k1_gej *  a  )

static

Compare the X coordinate of a group element (jacobian).

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secp256k1_gej_has_quad_y_var()

static int secp256k1_gej_has_quad_y_var ( const secp256k1_gej *  a )

static

Check whether a group element's y coordinate is a quadratic residue.

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secp256k1_gej_is_infinity()

static int secp256k1_gej_is_infinity ( const secp256k1_gej *  a )

static

Check whether a group element is the point at infinity.

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secp256k1_gej_neg()

static void secp256k1_gej_neg ( secp256k1_gej *  r, const secp256k1_gej *  a  )

static

Set r equal to the inverse of a (i.e., mirrored around the X axis)

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secp256k1_gej_rescale()

static void secp256k1_gej_rescale ( secp256k1_gej *  r, const secp256k1_fe *  b  )

static

Rescale a jacobian point by b which must be non-zero.

Constant-time.

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secp256k1_gej_set_ge()

static void secp256k1_gej_set_ge ( secp256k1_gej *  r, const secp256k1_ge *  a  )

static

Set a group element (jacobian) equal to another which is given in affine coordinates.

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secp256k1_gej_set_infinity()

static void secp256k1_gej_set_infinity ( secp256k1_gej *  r )

static

Set a group element (jacobian) equal to the point at infinity.

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