NAME
EC_POINT_new,
EC_POINT_free,
EC_POINT_clear_free,
EC_POINT_copy, EC_POINT_dup,
EC_POINT_method_of,
EC_POINT_set_to_infinity,
EC_POINT_set_affine_coordinates_GFp,
EC_POINT_set_affine_coordinates_GF2m,
EC_POINT_get_affine_coordinates_GFp,
EC_POINT_get_affine_coordinates_GF2m,
EC_POINT_set_Jprojective_coordinates_GFp,
EC_POINT_get_Jprojective_coordinates_GFp,
EC_POINT_set_compressed_coordinates_GFp,
EC_POINT_set_compressed_coordinates_GF2m,
EC_POINT_point2oct,
EC_POINT_oct2point,
EC_POINT_point2bn,
EC_POINT_bn2point,
EC_POINT_point2hex,
EC_POINT_hex2point —
create, destroy, and manipulate
EC_POINT objects
SYNOPSIS
#include
<openssl/ec.h>
#include <openssl/bn.h>
EC_POINT *
EC_POINT_new(const EC_GROUP
*group);
void
EC_POINT_free(EC_POINT
*point);
void
EC_POINT_clear_free(EC_POINT
*point);
int
EC_POINT_copy(EC_POINT *dst,
const EC_POINT *src);
EC_POINT *
EC_POINT_dup(const EC_POINT
*src, const EC_GROUP *group);
const EC_METHOD *
EC_POINT_method_of(const EC_POINT
*point);
int
EC_POINT_set_to_infinity(const
EC_GROUP *group, EC_POINT *point);
int
EC_POINT_set_affine_coordinates_GFp(const
EC_GROUP *group, EC_POINT *p,
const BIGNUM *x, const BIGNUM
*y, BN_CTX *ctx);
int
EC_POINT_set_affine_coordinates_GF2m(const
EC_GROUP *group, EC_POINT *p,
const BIGNUM *x, const BIGNUM
*y, BN_CTX *ctx);
int
EC_POINT_get_affine_coordinates_GFp(const
EC_GROUP *group, const EC_POINT *p,
BIGNUM *x, BIGNUM *y,
BN_CTX *ctx);
int
EC_POINT_get_affine_coordinates_GF2m(const
EC_GROUP *group, const EC_POINT *p,
BIGNUM *x, BIGNUM *y,
BN_CTX *ctx);
int
EC_POINT_set_Jprojective_coordinates_GFp(const
EC_GROUP *group, EC_POINT *p,
const BIGNUM *x, const BIGNUM
*y, const BIGNUM *z, BN_CTX
*ctx);
int
EC_POINT_get_Jprojective_coordinates_GFp(const
EC_GROUP *group, const EC_POINT *p,
BIGNUM *x, BIGNUM *y,
BIGNUM *z, BN_CTX *ctx);
int
EC_POINT_set_compressed_coordinates_GFp(const
EC_GROUP *group, EC_POINT *p,
const BIGNUM *x, int y_bit,
BN_CTX *ctx);
int
EC_POINT_set_compressed_coordinates_GF2m(const
EC_GROUP *group, EC_POINT *p,
const BIGNUM *x, int y_bit,
BN_CTX *ctx);
size_t
EC_POINT_point2oct(const EC_GROUP
*group, const EC_POINT *p,
point_conversion_form_t form, unsigned
char *buf, size_t len, BN_CTX
*ctx);
int
EC_POINT_oct2point(const EC_GROUP
*group, EC_POINT *p, const
unsigned char *buf, size_t len,
BN_CTX *ctx);
BIGNUM *
EC_POINT_point2bn(const EC_GROUP
*, const EC_POINT *,
point_conversion_form_t form, BIGNUM
*, BN_CTX *);
EC_POINT *
EC_POINT_bn2point(const EC_GROUP
*, const BIGNUM *, EC_POINT
*, BN_CTX *);
char *
EC_POINT_point2hex(const EC_GROUP
*, const EC_POINT *,
point_conversion_form_t form, BN_CTX
*);
EC_POINT *
EC_POINT_hex2point(const EC_GROUP
*, const char *, EC_POINT
*, BN_CTX *);
DESCRIPTION
An EC_POINT represents a point on a curve. A curve is represented by an EC_GROUP object created by the functions described in EC_GROUP_new(3).
A new point is constructed by calling the
function
EC_POINT_new()
and providing the group object that the point relates
to.
EC_POINT_free()
frees the memory associated with the EC_POINT. If
point is a NULL pointer, no
action occurs.
EC_POINT_clear_free()
destroys any sensitive data held within the EC_POINT
and then frees its memory. If point is a
NULL pointer, no action occurs.
EC_POINT_copy()
copies the point src into dst.
Both src and dst must use the
same EC_METHOD.
EC_POINT_dup()
creates a new EC_POINT object and copies the content
from src to the newly created
EC_POINT object.
EC_POINT_method_of()
obtains the EC_METHOD associated with
point.
A valid point on a curve is the
special point at infinity. A point is set to be at infinity by calling
EC_POINT_set_to_infinity().
The affine coordinates
for a point describe a point in terms of its x and
y position. The functions
EC_POINT_set_affine_coordinates_GFp()
and
EC_POINT_set_affine_coordinates_GF2m()
set the x and y coordinates for
the point p defined over the curve given in
group. The functions
EC_POINT_get_affine_coordinates_GFp()
and
EC_POINT_get_affine_coordinates_GF2m()
set x and y, either of which may
be NULL, to the corresponding coordinates of
p.
As well as the affine coordinates, a point can alternatively be described in terms of its Jacobian projective coordinates (for Fp curves only). Jacobian projective coordinates are expressed as three values x, y, and z. Working in this coordinate system provides more efficient point multiplication operations. A mapping exists between Jacobian projective coordinates and affine coordinates. A Jacobian projective coordinate (x, y, z) can be written as an affine coordinate as
(x/(z^2), y/(z^3))Conversion to
Jacobian projective from affine coordinates is simple. The coordinate
(x, y) is mapped to
(x, y,
1). To set or get the projective coordinates use
EC_POINT_set_Jprojective_coordinates_GFp()
and
EC_POINT_get_Jprojective_coordinates_GFp(),
respectively.
Points can also be
described in terms of their compressed coordinates. For a point
(x, y), for any given value for
x such that the point is on the curve, there will only
ever be two possible values for y. Therefore a point
can be set using the
EC_POINT_set_compressed_coordinates_GFp()
and
EC_POINT_set_compressed_coordinates_GF2m()
functions where x is the x coordinate and
y_bit is a value 0 or 1 to identify which of the two
possible values for y should be used.
In addition EC_POINTs can be converted to and from various external representations. Supported representations are octet strings, BIGNUMs, and hexadecimal. The format of the external representation is described by the point_conversion_form. See EC_GROUP_copy(3) for a description of point_conversion_form. Octet strings are stored in a buffer along with an associated buffer length. A point held in a BIGNUM is calculated by converting the point to an octet string and then converting that octet string into a BIGNUM integer. Points in hexadecimal format are stored in a NUL terminated character string where each character is one of the printable values 0-9 or A-F (or a-f).
The functions
EC_POINT_point2oct(),
EC_POINT_oct2point(),
EC_POINT_point2bn(),
EC_POINT_bn2point(),
EC_POINT_point2hex(), and
EC_POINT_hex2point()
convert from and to EC_POINTs for the formats octet
string, BIGNUM, and hexadecimal, respectively.
The function
EC_POINT_point2oct()
must be supplied with a buf long enough to store the
octet string. The return value provides the number of octets stored. Calling
the function with a NULL buf
will not perform the conversion but will still return the required buffer
length.
The function
EC_POINT_point2hex()
will allocate sufficient memory to store the hexadecimal string. It is the
caller's responsibility to free this memory with a subsequent call to
free(3).
RETURN VALUES
EC_POINT_new() and
EC_POINT_dup() return the newly allocated
EC_POINT or NULL on error.
The following functions return 1 on success or 0 on error:
EC_POINT_copy(),
EC_POINT_set_to_infinity(),
EC_POINT_set_Jprojective_coordinates_GFp(),
EC_POINT_get_Jprojective_coordinates_GFp(),
EC_POINT_set_affine_coordinates_GFp(),
EC_POINT_get_affine_coordinates_GFp(),
EC_POINT_set_compressed_coordinates_GFp(),
EC_POINT_set_affine_coordinates_GF2m(),
EC_POINT_get_affine_coordinates_GF2m(),
EC_POINT_set_compressed_coordinates_GF2m(), and
EC_POINT_oct2point().
EC_POINT_method_of() returns the
EC_METHOD associated with the supplied
EC_POINT.
EC_POINT_point2oct() returns the length of
the required buffer, or 0 on error.
EC_POINT_point2bn() returns the pointer to
the BIGNUM supplied or NULL on
error.
EC_POINT_bn2point() returns the pointer to
the EC_POINT supplied or NULL
on error.
EC_POINT_point2hex() returns a pointer to
the hex string or NULL on error.
EC_POINT_hex2point() returns the pointer
to the EC_POINT supplied or
NULL on error.
SEE ALSO
d2i_ECPKParameters(3), EC_GFp_simple_method(3), EC_GROUP_copy(3), EC_GROUP_new(3), EC_KEY_new(3), EC_POINT_add(3)
HISTORY
EC_POINT_new(),
EC_POINT_free(),
EC_POINT_clear_free(),
EC_POINT_copy(),
EC_POINT_method_of(),
EC_POINT_set_to_infinity(),
EC_POINT_set_affine_coordinates_GFp(),
EC_POINT_get_affine_coordinates_GFp(),
EC_POINT_set_Jprojective_coordinates_GFp(),
EC_POINT_get_Jprojective_coordinates_GFp(),
EC_POINT_set_compressed_coordinates_GFp(),
EC_POINT_point2oct(), and
EC_POINT_oct2point() first appeared in OpenSSL 0.9.7
and have been available since OpenBSD 3.2.
EC_POINT_dup(),
EC_POINT_set_affine_coordinates_GF2m(),
EC_POINT_get_affine_coordinates_GF2m(),
EC_POINT_set_compressed_coordinates_GF2m(),
EC_POINT_point2bn(),
EC_POINT_bn2point(),
EC_POINT_point2hex(), and
EC_POINT_hex2point() first appeared in OpenSSL 0.9.8
and have been available since OpenBSD 4.5.