1 =pod 2 3 =head1 NAME 4 5 EC_GROUP_get_ecparameters, 6 EC_GROUP_get_ecpkparameters, 7 EC_GROUP_new, 8 EC_GROUP_new_from_ecparameters, 9 EC_GROUP_new_from_ecpkparameters, 10 EC_GROUP_free, 11 EC_GROUP_clear_free, 12 EC_GROUP_new_curve_GFp, 13 EC_GROUP_new_curve_GF2m, 14 EC_GROUP_new_by_curve_name, 15 EC_GROUP_set_curve, 16 EC_GROUP_get_curve, 17 EC_GROUP_set_curve_GFp, 18 EC_GROUP_get_curve_GFp, 19 EC_GROUP_set_curve_GF2m, 20 EC_GROUP_get_curve_GF2m, 21 EC_get_builtin_curves - Functions for creating and destroying EC_GROUP 22 objects 23 24 =head1 SYNOPSIS 25 26 #include <openssl/ec.h> 27 28 EC_GROUP *EC_GROUP_new(const EC_METHOD *meth); 29 EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params) 30 EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params) 31 void EC_GROUP_free(EC_GROUP *group); 32 void EC_GROUP_clear_free(EC_GROUP *group); 33 34 EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, 35 const BIGNUM *b, BN_CTX *ctx); 36 EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, 37 const BIGNUM *b, BN_CTX *ctx); 38 EC_GROUP *EC_GROUP_new_by_curve_name(int nid); 39 40 int EC_GROUP_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, 41 const BIGNUM *b, BN_CTX *ctx); 42 int EC_GROUP_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, 43 BN_CTX *ctx); 44 int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, 45 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); 46 int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, 47 BIGNUM *a, BIGNUM *b, BN_CTX *ctx); 48 int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, 49 const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); 50 int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, 51 BIGNUM *a, BIGNUM *b, BN_CTX *ctx); 52 53 ECPARAMETERS *EC_GROUP_get_ecparameters(const EC_GROUP *group, ECPARAMETERS *params) 54 ECPKPARAMETERS *EC_GROUP_get_ecpkparameters(const EC_GROUP *group, ECPKPARAMETERS *params) 55 56 size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems); 57 58 =head1 DESCRIPTION 59 60 Within the library there are two forms of elliptic curve that are of interest. 61 The first form is those defined over the prime field Fp. The elements of Fp are 62 the integers 0 to p-1, where p is a prime number. This gives us a revised 63 elliptic curve equation as follows: 64 65 y^2 mod p = x^3 +ax + b mod p 66 67 The second form is those defined over a binary field F2^m where the elements of 68 the field are integers of length at most m bits. For this form the elliptic 69 curve equation is modified to: 70 71 y^2 + xy = x^3 + ax^2 + b (where b != 0) 72 73 Operations in a binary field are performed relative to an B<irreducible 74 polynomial>. All such curves with OpenSSL use a trinomial or a pentanomial for 75 this parameter. 76 77 A new curve can be constructed by calling EC_GROUP_new(), using the 78 implementation provided by B<meth> (see L<EC_GFp_simple_method(3)>). It is then 79 necessary to call EC_GROUP_set_curve() to set the curve parameters. 80 EC_GROUP_new_from_ecparameters() will create a group from the specified 81 B<params> and EC_GROUP_new_from_ecpkparameters() will create a group from the 82 specific PK B<params>. 83 84 EC_GROUP_set_curve() sets the curve parameters B<p>, B<a> and B<b>. For a curve 85 over Fp B<p> is the prime for the field. For a curve over F2^m B<p> represents 86 the irreducible polynomial - each bit represents a term in the polynomial. 87 Therefore, there will either be three or five bits set dependent on whether the 88 polynomial is a trinomial or a pentanomial. 89 In either case, B<a> and B<b> represents the coefficients a and b from the 90 relevant equation introduced above. 91 92 EC_group_get_curve() obtains the previously set curve parameters. 93 94 EC_GROUP_set_curve_GFp() and EC_GROUP_set_curve_GF2m() are synonyms for 95 EC_GROUP_set_curve(). They are defined for backwards compatibility only and 96 should not be used. 97 98 EC_GROUP_get_curve_GFp() and EC_GROUP_get_curve_GF2m() are synonyms for 99 EC_GROUP_get_curve(). They are defined for backwards compatibility only and 100 should not be used. 101 102 The functions EC_GROUP_new_curve_GFp() and EC_GROUP_new_curve_GF2m() are 103 shortcuts for calling EC_GROUP_new() and then the EC_GROUP_set_curve() function. 104 An appropriate default implementation method will be used. 105 106 Whilst the library can be used to create any curve using the functions described 107 above, there are also a number of predefined curves that are available. In order 108 to obtain a list of all of the predefined curves, call the function 109 EC_get_builtin_curves(). The parameter B<r> should be an array of 110 EC_builtin_curve structures of size B<nitems>. The function will populate the 111 B<r> array with information about the builtin curves. If B<nitems> is less than 112 the total number of curves available, then the first B<nitems> curves will be 113 returned. Otherwise the total number of curves will be provided. The return 114 value is the total number of curves available (whether that number has been 115 populated in B<r> or not). Passing a NULL B<r>, or setting B<nitems> to 0 will 116 do nothing other than return the total number of curves available. 117 The EC_builtin_curve structure is defined as follows: 118 119 typedef struct { 120 int nid; 121 const char *comment; 122 } EC_builtin_curve; 123 124 Each EC_builtin_curve item has a unique integer id (B<nid>), and a human 125 readable comment string describing the curve. 126 127 In order to construct a builtin curve use the function 128 EC_GROUP_new_by_curve_name() and provide the B<nid> of the curve to 129 be constructed. 130 131 EC_GROUP_free() frees the memory associated with the EC_GROUP. 132 If B<group> is NULL nothing is done. 133 134 EC_GROUP_clear_free() destroys any sensitive data held within the EC_GROUP and 135 then frees its memory. If B<group> is NULL nothing is done. 136 137 =head1 RETURN VALUES 138 139 All EC_GROUP_new* functions return a pointer to the newly constructed group, or 140 NULL on error. 141 142 EC_get_builtin_curves() returns the number of builtin curves that are available. 143 144 EC_GROUP_set_curve_GFp(), EC_GROUP_get_curve_GFp(), EC_GROUP_set_curve_GF2m(), 145 EC_GROUP_get_curve_GF2m() return 1 on success or 0 on error. 146 147 =head1 SEE ALSO 148 149 L<crypto(7)>, L<EC_GROUP_copy(3)>, 150 L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>, 151 L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)> 152 153 =head1 COPYRIGHT 154 155 Copyright 2013-2020 The OpenSSL Project Authors. All Rights Reserved. 156 157 Licensed under the OpenSSL license (the "License"). You may not use 158 this file except in compliance with the License. You can obtain a copy 159 in the file LICENSE in the source distribution or at 160 L<https://www.openssl.org/source/license.html>. 161 162 =cut 163