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Always turn off hyphenation; it makes .\" way too many mistakes in technical documents. .if n .ad l .nh .SH "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_Jprojective_coordinates, 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, EC_POINT_point2oct, EC_POINT_oct2point, EC_POINT_point2bn, EC_POINT_bn2point, EC_POINT_point2hex, EC_POINT_hex2point \- Functions for creating, destroying and manipulating EC_POINT objects. .SH "SYNOPSIS" .IX Header "SYNOPSIS" .Vb 2 \& #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_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_affine_coordinates_GFp(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_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, \& const BIGNUM *x, int y_bit, 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_GF2m(const EC_GROUP *group, \& const EC_POINT *p, BIGNUM *x, BIGNUM *y, 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 *); .Ve .SH "DESCRIPTION" .IX Header "DESCRIPTION" An \s-1EC_POINT\s0 represents a point on a curve. A new point is constructed by calling the function EC_POINT_new and providing the \fBgroup\fR object that the point relates to. .PP EC_POINT_free frees the memory associated with the \s-1EC_POINT.\s0 .PP EC_POINT_clear_free destroys any sensitive data held within the \s-1EC_POINT\s0 and then frees its memory. .PP EC_POINT_copy copies the point \fBsrc\fR into \fBdst\fR. Both \fBsrc\fR and \fBdst\fR must use the same \s-1EC_METHOD.\s0 .PP EC_POINT_dup creates a new \s-1EC_POINT\s0 object and copies the content from \fBsrc\fR to the newly created \&\s-1EC_POINT\s0 object. .PP EC_POINT_method_of obtains the \s-1EC_METHOD\s0 associated with \fBpoint\fR. .PP 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. .PP The affine co-ordinates 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 \fBx\fR and \fBy\fR co-ordinates for the point \&\fBp\fR defined over the curve given in \fBgroup\fR. .PP As well as the affine co-ordinates, a point can alternatively be described in terms of its Jacobian projective co-ordinates (for Fp curves only). Jacobian projective co-ordinates are expressed as three values x, y and z. Working in this co-ordinate system provides more efficient point multiplication operations. A mapping exists between Jacobian projective co-ordinates and affine co-ordinates. A Jacobian projective co-ordinate (x, y, z) can be written as an affine co-ordinate as (x/(z^2), y/(z^3)). Conversion to Jacobian projective to affine co-ordinates is simple. The co-ordinate (x, y) is mapped to (x, y, 1). To set or get the projective co-ordinates use EC_POINT_set_Jprojective_coordinates_GFp and EC_POINT_get_Jprojective_coordinates_GFp respectively. .PP Points can also be described in terms of their compressed co-ordinates. 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 \fBx\fR is the x co-ordinate and \fBy_bit\fR is a value 0 or 1 to identify which of the two possible values for y should be used. .PP In addition EC_POINTs can be converted to and from various external representations. Supported representations are octet strings, BIGNUMs and hexadecimal. Octet strings are stored in a buffer along with an associated buffer length. A point held in a \s-1BIGNUM\s0 is calculated by converting the point to an octet string and then converting that octet string into a \s-1BIGNUM\s0 integer. Points in hexadecimal format are stored in a \s-1NULL\s0 terminated character string where each character is one of the printable values 0\-9 or A\-F (or a\-f). .PP 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, \s-1BIGNUM\s0 and hexadecimal respectively. .PP The function EC_POINT_point2oct must be supplied with a buffer long enough to store the octet string. The return value provides the number of octets stored. Calling the function with a \s-1NULL\s0 buffer will not perform the conversion but will still return the required buffer length. .PP 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 \fBOPENSSL_free()\fR. .SH "RETURN VALUES" .IX Header "RETURN VALUES" EC_POINT_new and EC_POINT_dup return the newly allocated \s-1EC_POINT\s0 or \s-1NULL\s0 on error. .PP 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. .PP EC_POINT_method_of returns the \s-1EC_METHOD\s0 associated with the supplied \s-1EC_POINT.\s0 .PP EC_POINT_point2oct returns the length of the required buffer, or 0 on error. .PP EC_POINT_point2bn returns the pointer to the \s-1BIGNUM\s0 supplied, or \s-1NULL\s0 on error. .PP EC_POINT_bn2point returns the pointer to the \s-1EC_POINT\s0 supplied, or \s-1NULL\s0 on error. .PP EC_POINT_point2hex returns a pointer to the hex string, or \s-1NULL\s0 on error. .PP EC_POINT_hex2point returns the pointer to the \s-1EC_POINT\s0 supplied, or \s-1NULL\s0 on error. .SH "SEE ALSO" .IX Header "SEE ALSO" \&\fBcrypto\fR\|(3), \fBec\fR\|(3), \fBEC_GROUP_new\fR\|(3), \fBEC_GROUP_copy\fR\|(3), \&\fBEC_POINT_add\fR\|(3), \fBEC_KEY_new\fR\|(3), \&\fBEC_GFp_simple_method\fR\|(3), \fBd2i_ECPKParameters\fR\|(3)