group.h File Reference

#include "field.h"

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Classes
struct	secp256k1_ge
	A group element in affine coordinates on the secp256k1 curve, or occasionally on an isomorphic curve of the form y^2 = x^3 + 7*t^6. 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)
#define	SECP256K1_GE_X_MAGNITUDE_MAX   4
	Maximum allowed magnitudes for group element coordinates in affine (x, y) and jacobian (x, y, z) representation. More...
#define	SECP256K1_GE_Y_MAGNITUDE_MAX   3
#define	SECP256K1_GEJ_X_MAGNITUDE_MAX   4
#define	SECP256K1_GEJ_Y_MAGNITUDE_MAX   4
#define	SECP256K1_GEJ_Z_MAGNITUDE_MAX   1
#define	SECP256K1_GE_VERIFY(a)   secp256k1_ge_verify(a)
#define	SECP256K1_GEJ_VERIFY(a)   secp256k1_gej_verify(a)

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_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_x_on_curve_var (const secp256k1_fe *x)
	Determine whether x is a valid X coordinate on the curve. More...
static int	secp256k1_ge_x_frac_on_curve_var (const secp256k1_fe *xn, const secp256k1_fe *xd)
	Determine whether fraction xn/xd is a valid X coordinate on the curve (xd != 0). 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_table_set_globalz (size_t len, secp256k1_ge *a, const secp256k1_fe *zr)
	Bring a batch of inputs to the same global z "denominator", based on ratios between (omitted) z coordinates of adjacent elements. More...
static int	secp256k1_ge_eq_var (const secp256k1_ge *a, const secp256k1_ge *b)
	Check two group elements (affine) for equality in variable time. 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_var (const secp256k1_gej *a, const secp256k1_gej *b)
	Check two group elements (jacobian) for equality in variable time. More...
static int	secp256k1_gej_eq_ge_var (const secp256k1_gej *a, const secp256k1_ge *b)
	Check two group elements (jacobian and affine) for equality in variable time. 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 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_gej_cmov (secp256k1_gej *r, const secp256k1_gej *a, int flag)
	If flag is true, set *r equal to *a; otherwise leave it. 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 void	secp256k1_ge_to_bytes (unsigned char *buf, const secp256k1_ge *a)
	Convert a group element that is not infinity to a 64-byte array. More...
static void	secp256k1_ge_from_bytes (secp256k1_ge *r, const unsigned char *buf)
	Convert a 64-byte array into group element. More...
static void	secp256k1_ge_to_bytes_ext (unsigned char *data, const secp256k1_ge *ge)
	Convert a group element (that is allowed to be infinity) to a 64-byte array. More...
static void	secp256k1_ge_from_bytes_ext (secp256k1_ge *ge, const unsigned char *data)
	Convert a 64-byte array into a group element. 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...
static void	secp256k1_ge_verify (const secp256k1_ge *a)
	Check invariants on an affine group element (no-op unless VERIFY is enabled). More...
static void	secp256k1_gej_verify (const secp256k1_gej *a)
	Check invariants on a Jacobian group element (no-op unless VERIFY is enabled). 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 22 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 23 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 43 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 45 of file group.h.

SECP256K1_GE_VERIFY

#define SECP256K1_GE_VERIFY

(

a

)

secp256k1_ge_verify(a)

Definition at line 206 of file group.h.

SECP256K1_GE_X_MAGNITUDE_MAX

#define SECP256K1_GE_X_MAGNITUDE_MAX   4

Maximum allowed magnitudes for group element coordinates in affine (x, y) and jacobian (x, y, z) representation.

Definition at line 49 of file group.h.

SECP256K1_GE_Y_MAGNITUDE_MAX

#define SECP256K1_GE_Y_MAGNITUDE_MAX   3

Definition at line 50 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 35 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 36 of file group.h.

SECP256K1_GEJ_VERIFY

#define SECP256K1_GEJ_VERIFY

(

a

)

secp256k1_gej_verify(a)

Definition at line 210 of file group.h.

SECP256K1_GEJ_X_MAGNITUDE_MAX

#define SECP256K1_GEJ_X_MAGNITUDE_MAX   4

Definition at line 51 of file group.h.

SECP256K1_GEJ_Y_MAGNITUDE_MAX

#define SECP256K1_GEJ_Y_MAGNITUDE_MAX   4

Definition at line 52 of file group.h.

SECP256K1_GEJ_Z_MAGNITUDE_MAX

#define SECP256K1_GEJ_Z_MAGNITUDE_MAX   1

Definition at line 53 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_eq_var()

static int secp256k1_ge_eq_var ( const secp256k1_ge *  a, const secp256k1_ge *  b  )

static

Check two group elements (affine) for equality in variable time.

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secp256k1_ge_from_bytes()

static void secp256k1_ge_from_bytes ( secp256k1_ge *  r, const unsigned char *  buf  )

static

Convert a 64-byte array into group element.

This function assumes that the provided buffer correctly encodes a group element.

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secp256k1_ge_from_bytes_ext()

static void secp256k1_ge_from_bytes_ext ( secp256k1_ge *  ge, const unsigned char *  data  )

static

Convert a 64-byte array into a group element.

This function assumes that the provided buffer is the output of secp256k1_ge_to_bytes_ext.

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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_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_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_table_set_globalz()

static void secp256k1_ge_table_set_globalz ( size_t  len, secp256k1_ge *  a, const secp256k1_fe *  zr  )

static

Bring a batch of inputs to the same global z "denominator", based on ratios between (omitted) z coordinates of adjacent elements.

Although the elements a[i] are _ge rather than _gej, they actually represent elements in Jacobian coordinates with their z coordinates omitted.

Using the notation z(b) to represent the omitted z coordinate of b, the array zr of z coordinate ratios must satisfy zr[i] == z(a[i]) / z(a[i-1]) for 0 < 'i' < len. The zr[0] value is unused.

This function adjusts the coordinates of 'a' in place so that for all 'i', z(a[i]) == z(a[len-1]). In other words, the initial value of z(a[len-1]) becomes the global z "denominator". Only the a[i].x and a[i].y coordinates are explicitly modified; the adjustment of the omitted z coordinate is implicit.

The coordinates of the final element a[len-1] are not changed.

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secp256k1_ge_to_bytes()

static void secp256k1_ge_to_bytes ( unsigned char *  buf, const secp256k1_ge *  a  )

static

Convert a group element that is not infinity to a 64-byte array.

The output array is platform-dependent.

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secp256k1_ge_to_bytes_ext()

static void secp256k1_ge_to_bytes_ext ( unsigned char *  data, const secp256k1_ge *  ge  )

static

Convert a group element (that is allowed to be infinity) to a 64-byte array.

The output array is platform-dependent.

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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_ge_verify()

static void secp256k1_ge_verify ( const secp256k1_ge *  a )

static

Check invariants on an affine group element (no-op unless VERIFY is enabled).

secp256k1_ge_x_frac_on_curve_var()

static int secp256k1_ge_x_frac_on_curve_var ( const secp256k1_fe *  xn, const secp256k1_fe *  xd  )

static

Determine whether fraction xn/xd is a valid X coordinate on the curve (xd != 0).

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secp256k1_ge_x_on_curve_var()

static int secp256k1_ge_x_on_curve_var ( const secp256k1_fe *  x )

static

Determine whether x is a valid X coordinate on the curve.

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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_cmov()

static void secp256k1_gej_cmov ( secp256k1_gej *  r, const secp256k1_gej *  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_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_ge_var()

static int secp256k1_gej_eq_ge_var ( const secp256k1_gej *  a, const secp256k1_ge *  b  )

static

Check two group elements (jacobian and affine) for equality in variable time.

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secp256k1_gej_eq_var()

static int secp256k1_gej_eq_var ( const secp256k1_gej *  a, const secp256k1_gej *  b  )

static

Check two group elements (jacobian) for equality in variable time.

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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).

The magnitude of the group element's X coordinate must not exceed 31.

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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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secp256k1_gej_verify()

static void secp256k1_gej_verify ( const secp256k1_gej *  a )

static

Check invariants on a Jacobian group element (no-op unless VERIFY is enabled).