1=pod 2 3=head1 NAME 4 5EC_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 B<EC_POINT> objects. 6 7=head1 SYNOPSIS 8 9 #include <openssl/ec.h> 10 #include <openssl/bn.h> 11 12 EC_POINT *EC_POINT_new(const EC_GROUP *group); 13 void EC_POINT_free(EC_POINT *point); 14 void EC_POINT_clear_free(EC_POINT *point); 15 int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src); 16 EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group); 17 const EC_METHOD *EC_POINT_method_of(const EC_POINT *point); 18 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point); 19 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, 20 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx); 21 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group, 22 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx); 23 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, 24 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx); 25 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, 26 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); 27 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, 28 const BIGNUM *x, int y_bit, BN_CTX *ctx); 29 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p, 30 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx); 31 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, 32 const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); 33 int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p, 34 const BIGNUM *x, int y_bit, BN_CTX *ctx); 35 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p, 36 point_conversion_form_t form, 37 unsigned char *buf, size_t len, BN_CTX *ctx); 38 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p, 39 const unsigned char *buf, size_t len, BN_CTX *ctx); 40 BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *, 41 point_conversion_form_t form, BIGNUM *, BN_CTX *); 42 EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *, 43 EC_POINT *, BN_CTX *); 44 char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *, 45 point_conversion_form_t form, BN_CTX *); 46 EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *, 47 EC_POINT *, BN_CTX *); 48 49 50=head1 DESCRIPTION 51 52An EC_POINT represents a point on a curve. A new point is constructed by calling the function EC_POINT_new and providing the B<group> 53object that the point relates to. 54 55EC_POINT_free frees the memory associated with the EC_POINT. 56 57EC_POINT_clear_free destroys any sensitive data held within the EC_POINT and then frees its memory. 58 59EC_POINT_copy copies the point B<src> into B<dst>. Both B<src> and B<dst> must use the same EC_METHOD. 60 61EC_POINT_dup creates a new EC_POINT object and copies the content from B<src> to the newly created 62EC_POINT object. 63 64EC_POINT_method_of obtains the EC_METHOD associated with B<point>. 65 66A 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. 67 68The affine co-ordinates for a point describe a point in terms of its x and y position. The functions 69EC_POINT_set_affine_coordinates_GFp and EC_POINT_set_affine_coordinates_GF2m set the B<x> and B<y> co-ordinates for the point 70B<p> defined over the curve given in B<group>. 71 72As well as the affine co-ordinates, a point can alternatively be described in terms of its Jacobian 73projective co-ordinates (for Fp curves only). Jacobian projective co-ordinates are expressed as three values x, y and z. Working in 74this co-ordinate system provides more efficient point multiplication operations. 75A 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 76mapped to (x, y, 1). To set or get the projective co-ordinates use EC_POINT_set_Jprojective_coordinates_GFp and 77EC_POINT_get_Jprojective_coordinates_GFp respectively. 78 79Points 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 80on 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 81and EC_POINT_set_compressed_coordinates_GF2m functions where B<x> is the x co-ordinate and B<y_bit> is a value 0 or 1 to identify which of 82the two possible values for y should be used. 83 84In addition EC_POINTs can be converted to and from various external 85representations. Supported representations are octet strings, BIGNUMs and 86hexadecimal. Octet strings are stored in a buffer along with an associated 87buffer length. A point held in a BIGNUM is calculated by converting the point to 88an octet string and then converting that octet string into a BIGNUM integer. 89Points in hexadecimal format are stored in a NULL terminated character string 90where each character is one of the printable values 0-9 or A-F (or a-f). 91 92The functions EC_POINT_point2oct, EC_POINT_oct2point, EC_POINT_point2bn, EC_POINT_bn2point, EC_POINT_point2hex and EC_POINT_hex2point convert 93from and to EC_POINTs for the formats: octet string, BIGNUM and hexadecimal respectively. 94 95The function EC_POINT_point2oct must be supplied with a buffer long enough to store the octet string. The return value provides the number of 96octets stored. Calling the function with a NULL buffer will not perform the conversion but will still return the required buffer length. 97 98The function EC_POINT_point2hex will allocate sufficient memory to store the hexadecimal string. It is the caller's responsibility to free 99this memory with a subsequent call to OPENSSL_free(). 100 101=head1 RETURN VALUES 102 103EC_POINT_new and EC_POINT_dup return the newly allocated EC_POINT or NULL on error. 104 105The following functions return 1 on success or 0 on error: EC_POINT_copy, EC_POINT_set_to_infinity, EC_POINT_set_Jprojective_coordinates_GFp, 106EC_POINT_get_Jprojective_coordinates_GFp, EC_POINT_set_affine_coordinates_GFp, EC_POINT_get_affine_coordinates_GFp, 107EC_POINT_set_compressed_coordinates_GFp, EC_POINT_set_affine_coordinates_GF2m, EC_POINT_get_affine_coordinates_GF2m, 108EC_POINT_set_compressed_coordinates_GF2m and EC_POINT_oct2point. 109 110EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT. 111 112EC_POINT_point2oct returns the length of the required buffer, or 0 on error. 113 114EC_POINT_point2bn returns the pointer to the BIGNUM supplied, or NULL on error. 115 116EC_POINT_bn2point returns the pointer to the EC_POINT supplied, or NULL on error. 117 118EC_POINT_point2hex returns a pointer to the hex string, or NULL on error. 119 120EC_POINT_hex2point returns the pointer to the EC_POINT supplied, or NULL on error. 121 122=head1 SEE ALSO 123 124L<crypto(3)|crypto(3)>, L<ec(3)|ec(3)>, L<EC_GROUP_new(3)|EC_GROUP_new(3)>, L<EC_GROUP_copy(3)|EC_GROUP_copy(3)>, 125L<EC_POINT_add(3)|EC_POINT_add(3)>, L<EC_KEY_new(3)|EC_KEY_new(3)>, 126L<EC_GFp_simple_method(3)|EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)|d2i_ECPKParameters(3)> 127 128=cut 129