1=pod 2 3=head1 NAME 4 5EC_POINT_set_Jprojective_coordinates_GFp, 6EC_POINT_point2buf, 7EC_POINT_new, 8EC_POINT_free, 9EC_POINT_clear_free, 10EC_POINT_copy, 11EC_POINT_dup, 12EC_POINT_method_of, 13EC_POINT_set_to_infinity, 14EC_POINT_get_Jprojective_coordinates_GFp, 15EC_POINT_set_affine_coordinates, 16EC_POINT_get_affine_coordinates, 17EC_POINT_set_compressed_coordinates, 18EC_POINT_set_affine_coordinates_GFp, 19EC_POINT_get_affine_coordinates_GFp, 20EC_POINT_set_compressed_coordinates_GFp, 21EC_POINT_set_affine_coordinates_GF2m, 22EC_POINT_get_affine_coordinates_GF2m, 23EC_POINT_set_compressed_coordinates_GF2m, 24EC_POINT_point2oct, 25EC_POINT_oct2point, 26EC_POINT_point2bn, 27EC_POINT_bn2point, 28EC_POINT_point2hex, 29EC_POINT_hex2point 30- Functions for creating, destroying and manipulating EC_POINT objects 31 32=head1 SYNOPSIS 33 34 #include <openssl/ec.h> 35 36 EC_POINT *EC_POINT_new(const EC_GROUP *group); 37 void EC_POINT_free(EC_POINT *point); 38 void EC_POINT_clear_free(EC_POINT *point); 39 int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src); 40 EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group); 41 const EC_METHOD *EC_POINT_method_of(const EC_POINT *point); 42 int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point); 43 int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, 44 EC_POINT *p, 45 const BIGNUM *x, const BIGNUM *y, 46 const BIGNUM *z, BN_CTX *ctx); 47 int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group, 48 const EC_POINT *p, 49 BIGNUM *x, BIGNUM *y, BIGNUM *z, 50 BN_CTX *ctx); 51 int EC_POINT_set_affine_coordinates(const EC_GROUP *group, EC_POINT *p, 52 const BIGNUM *x, const BIGNUM *y, 53 BN_CTX *ctx); 54 int EC_POINT_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *p, 55 BIGNUM *x, BIGNUM *y, BN_CTX *ctx); 56 int EC_POINT_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *p, 57 const BIGNUM *x, int y_bit, 58 BN_CTX *ctx); 59 int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, 60 const BIGNUM *x, const BIGNUM *y, 61 BN_CTX *ctx); 62 int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, 63 const EC_POINT *p, 64 BIGNUM *x, BIGNUM *y, BN_CTX *ctx); 65 int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, 66 EC_POINT *p, 67 const BIGNUM *x, int y_bit, 68 BN_CTX *ctx); 69 int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p, 70 const BIGNUM *x, const BIGNUM *y, 71 BN_CTX *ctx); 72 int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, 73 const EC_POINT *p, 74 BIGNUM *x, BIGNUM *y, BN_CTX *ctx); 75 int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, 76 EC_POINT *p, 77 const BIGNUM *x, int y_bit, 78 BN_CTX *ctx); 79 size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p, 80 point_conversion_form_t form, 81 unsigned char *buf, size_t len, BN_CTX *ctx); 82 size_t EC_POINT_point2buf(const EC_GROUP *group, const EC_POINT *point, 83 point_conversion_form_t form, 84 unsigned char **pbuf, BN_CTX *ctx); 85 int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p, 86 const unsigned char *buf, size_t len, BN_CTX *ctx); 87 BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, const EC_POINT *p, 88 point_conversion_form_t form, BIGNUM *bn, 89 BN_CTX *ctx); 90 EC_POINT *EC_POINT_bn2point(const EC_GROUP *group, const BIGNUM *bn, 91 EC_POINT *p, BN_CTX *ctx); 92 char *EC_POINT_point2hex(const EC_GROUP *group, const EC_POINT *p, 93 point_conversion_form_t form, BN_CTX *ctx); 94 EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, const char *hex, 95 EC_POINT *p, BN_CTX *ctx); 96 97 98=head1 DESCRIPTION 99 100An B<EC_POINT> structure represents a point on a curve. A new point is 101constructed by calling the function EC_POINT_new() and providing the 102B<group> object that the point relates to. 103 104EC_POINT_free() frees the memory associated with the B<EC_POINT>. 105if B<point> is NULL nothing is done. 106 107EC_POINT_clear_free() destroys any sensitive data held within the EC_POINT and 108then frees its memory. If B<point> is NULL nothing is done. 109 110EC_POINT_copy() copies the point B<src> into B<dst>. Both B<src> and B<dst> 111must use the same B<EC_METHOD>. 112 113EC_POINT_dup() creates a new B<EC_POINT> object and copies the content from 114B<src> to the newly created B<EC_POINT> object. 115 116EC_POINT_method_of() obtains the B<EC_METHOD> associated with B<point>. 117 118A valid point on a curve is the special point at infinity. A point is set to 119be at infinity by calling EC_POINT_set_to_infinity(). 120 121The affine co-ordinates for a point describe a point in terms of its x and y 122position. The function EC_POINT_set_affine_coordinates() sets the B<x> and B<y> 123co-ordinates for the point B<p> defined over the curve given in B<group>. The 124function EC_POINT_get_affine_coordinates() sets B<x> and B<y>, either of which 125may be NULL, to the corresponding coordinates of B<p>. 126 127The functions EC_POINT_set_affine_coordinates_GFp() and 128EC_POINT_set_affine_coordinates_GF2m() are synonyms for 129EC_POINT_set_affine_coordinates(). They are defined for backwards compatibility 130only and should not be used. 131 132The functions EC_POINT_get_affine_coordinates_GFp() and 133EC_POINT_get_affine_coordinates_GF2m() are synonyms for 134EC_POINT_get_affine_coordinates(). They are defined for backwards compatibility 135only and should not be used. 136 137As well as the affine co-ordinates, a point can alternatively be described in 138terms of its Jacobian projective co-ordinates (for Fp curves only). Jacobian 139projective co-ordinates are expressed as three values x, y and z. Working in 140this co-ordinate system provides more efficient point multiplication 141operations. A mapping exists between Jacobian projective co-ordinates and 142affine co-ordinates. A Jacobian projective co-ordinate (x, y, z) can be written 143as an affine co-ordinate as (x/(z^2), y/(z^3)). Conversion to Jacobian 144projective from affine co-ordinates is simple. The co-ordinate (x, y) is mapped 145to (x, y, 1). To set or get the projective co-ordinates use 146EC_POINT_set_Jprojective_coordinates_GFp() and 147EC_POINT_get_Jprojective_coordinates_GFp() respectively. 148 149Points can also be described in terms of their compressed co-ordinates. For a 150point (x, y), for any given value for x such that the point is on the curve 151there will only ever be two possible values for y. Therefore, a point can be set 152using the EC_POINT_set_compressed_coordinates() function where B<x> is the x 153co-ordinate and B<y_bit> is a value 0 or 1 to identify which of the two 154possible values for y should be used. 155 156The functions EC_POINT_set_compressed_coordinates_GFp() and 157EC_POINT_set_compressed_coordinates_GF2m() are synonyms for 158EC_POINT_set_compressed_coordinates(). They are defined for backwards 159compatibility only and should not be used. 160 161In addition B<EC_POINT> can be converted to and from various external 162representations. The octet form is the binary encoding of the B<ECPoint> 163structure (as defined in RFC5480 and used in certificates and TLS records): 164only the content octets are present, the B<OCTET STRING> tag and length are 165not included. B<BIGNUM> form is the octet form interpreted as a big endian 166integer converted to a B<BIGNUM> structure. Hexadecimal form is the octet 167form converted to a NULL terminated character string where each character 168is one of the printable values 0-9 or A-F (or a-f). 169 170The functions EC_POINT_point2oct(), EC_POINT_oct2point(), EC_POINT_point2bn(), 171EC_POINT_bn2point(), EC_POINT_point2hex() and EC_POINT_hex2point() convert from 172and to EC_POINTs for the formats: octet, BIGNUM and hexadecimal respectively. 173 174The function EC_POINT_point2oct() encodes the given curve point B<p> as an 175octet string into the buffer B<buf> of size B<len>, using the specified 176conversion form B<form>. 177The encoding conforms with Sec. 2.3.3 of the SECG SEC 1 ("Elliptic Curve 178Cryptography") standard. 179Similarly the function EC_POINT_oct2point() decodes a curve point into B<p> from 180the octet string contained in the given buffer B<buf> of size B<len>, conforming 181to Sec. 2.3.4 of the SECG SEC 1 ("Elliptic Curve Cryptography") standard. 182 183The functions EC_POINT_point2hex() and EC_POINT_point2bn() convert a point B<p>, 184respectively, to the hexadecimal or BIGNUM representation of the same 185encoding of the function EC_POINT_point2oct(). 186Vice versa, similarly to the function EC_POINT_oct2point(), the functions 187EC_POINT_hex2point() and EC_POINT_point2bn() decode the hexadecimal or 188BIGNUM representation into the EC_POINT B<p>. 189 190Notice that, according to the standard, the octet string encoding of the point 191at infinity for a given curve is fixed to a single octet of value zero and that, 192vice versa, a single octet of size zero is decoded as the point at infinity. 193 194The function EC_POINT_point2oct() must be supplied with a buffer long enough to 195store the octet form. The return value provides the number of octets stored. 196Calling the function with a NULL buffer will not perform the conversion but 197will still return the required buffer length. 198 199The function EC_POINT_point2buf() allocates a buffer of suitable length and 200writes an EC_POINT to it in octet format. The allocated buffer is written to 201B<*pbuf> and its length is returned. The caller must free up the allocated 202buffer with a call to OPENSSL_free(). Since the allocated buffer value is 203written to B<*pbuf> the B<pbuf> parameter B<MUST NOT> be B<NULL>. 204 205The function EC_POINT_point2hex() will allocate sufficient memory to store the 206hexadecimal string. It is the caller's responsibility to free this memory with 207a subsequent call to OPENSSL_free(). 208 209=head1 RETURN VALUES 210 211EC_POINT_new() and EC_POINT_dup() return the newly allocated EC_POINT or NULL 212on error. 213 214The following functions return 1 on success or 0 on error: EC_POINT_copy(), 215EC_POINT_set_to_infinity(), EC_POINT_set_Jprojective_coordinates_GFp(), 216EC_POINT_get_Jprojective_coordinates_GFp(), 217EC_POINT_set_affine_coordinates_GFp(), EC_POINT_get_affine_coordinates_GFp(), 218EC_POINT_set_compressed_coordinates_GFp(), 219EC_POINT_set_affine_coordinates_GF2m(), EC_POINT_get_affine_coordinates_GF2m(), 220EC_POINT_set_compressed_coordinates_GF2m() and EC_POINT_oct2point(). 221 222EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT. 223 224EC_POINT_point2oct() and EC_POINT_point2buf() return the length of the required 225buffer or 0 on error. 226 227EC_POINT_point2bn() returns the pointer to the BIGNUM supplied, or NULL on 228error. 229 230EC_POINT_bn2point() returns the pointer to the EC_POINT supplied, or NULL on 231error. 232 233EC_POINT_point2hex() returns a pointer to the hex string, or NULL on error. 234 235EC_POINT_hex2point() returns the pointer to the EC_POINT supplied, or NULL on 236error. 237 238=head1 SEE ALSO 239 240L<crypto(7)>, L<EC_GROUP_new(3)>, L<EC_GROUP_copy(3)>, 241L<EC_POINT_add(3)>, L<EC_KEY_new(3)>, 242L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)> 243 244=head1 COPYRIGHT 245 246Copyright 2013-2020 The OpenSSL Project Authors. All Rights Reserved. 247 248Licensed under the OpenSSL license (the "License"). You may not use 249this file except in compliance with the License. You can obtain a copy 250in the file LICENSE in the source distribution or at 251L<https://www.openssl.org/source/license.html>. 252 253=cut 254