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135 .IX Title "EC_GROUP_new 3"
136 .TH EC_GROUP_new 3 "2016-05-03" "1.0.2h" "OpenSSL"
137 .\" For nroff, turn off justification. Always turn off hyphenation; it makes
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142 EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_new_curve_GFp, EC_GROUP_new_curve_GF2m, EC_GROUP_new_by_curve_name, EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, EC_GROUP_set_curve_GF2m, EC_GROUP_get_curve_GF2m, EC_get_builtin_curves \- Functions for creating and destroying EC_GROUP objects.
144 .IX Header "SYNOPSIS"
146 \& #include <openssl/ec.h>
147 \& #include <openssl/bn.h>
149 \& EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
150 \& void EC_GROUP_free(EC_GROUP *group);
151 \& void EC_GROUP_clear_free(EC_GROUP *group);
153 \& EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
154 \& EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
155 \& EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
157 \& int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
158 \& int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
159 \& int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
160 \& int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
162 \& size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
165 .IX Header "DESCRIPTION"
166 Within the library there are two forms of elliptic curve that are of interest. The first form is those defined over the
167 prime field Fp. The elements of Fp are the integers 0 to p\-1, where p is a prime number. This gives us a revised
168 elliptic curve equation as follows:
170 y^2 mod p = x^3 +ax + b mod p
172 The second form is those defined over a binary field F2^m where the elements of the field are integers of length at
173 most m bits. For this form the elliptic curve equation is modified to:
175 y^2 + xy = x^3 + ax^2 + b (where b != 0)
177 Operations in a binary field are performed relative to an \fBirreducible polynomial\fR. All such curves with OpenSSL
178 use a trinomial or a pentanomial for this parameter.
180 A new curve can be constructed by calling EC_GROUP_new, using the implementation provided by \fBmeth\fR (see
181 \&\fIEC_GFp_simple_method\fR\|(3)). It is then necessary to call either EC_GROUP_set_curve_GFp or
182 EC_GROUP_set_curve_GF2m as appropriate to create a curve defined over Fp or over F2^m respectively.
184 EC_GROUP_set_curve_GFp sets the curve parameters \fBp\fR, \fBa\fR and \fBb\fR for a curve over Fp stored in \fBgroup\fR.
185 EC_group_get_curve_GFp obtains the previously set curve parameters.
187 EC_GROUP_set_curve_GF2m sets the equivalent curve parameters for a curve over F2^m. In this case \fBp\fR represents
188 the irreducible polybnomial \- each bit represents a term in the polynomial. Therefore there will either be three
189 or five bits set dependant on whether the polynomial is a trinomial or a pentanomial.
190 EC_group_get_curve_GF2m obtains the previously set curve parameters.
192 The functions EC_GROUP_new_curve_GFp and EC_GROUP_new_curve_GF2m are shortcuts for calling EC_GROUP_new and the
193 appropriate EC_group_set_curve function. An appropriate default implementation method will be used.
195 Whilst the library can be used to create any curve using the functions described above, there are also a number of
196 predefined curves that are available. In order to obtain a list of all of the predefined curves, call the function
197 EC_get_builtin_curves. The parameter \fBr\fR should be an array of EC_builtin_curve structures of size \fBnitems\fR. The function
198 will populate the \fBr\fR array with information about the builtin curves. If \fBnitems\fR is less than the total number of
199 curves available, then the first \fBnitems\fR curves will be returned. Otherwise the total number of curves will be
200 provided. The return value is the total number of curves available (whether that number has been populated in \fBr\fR or
201 not). Passing a \s-1NULL \s0\fBr\fR, or setting \fBnitems\fR to 0 will do nothing other than return the total number of curves available.
202 The EC_builtin_curve structure is defined as follows:
207 \& const char *comment;
208 \& } EC_builtin_curve;
211 Each EC_builtin_curve item has a unique integer id (\fBnid\fR), and a human readable comment string describing the curve.
213 In order to construct a builtin curve use the function EC_GROUP_new_by_curve_name and provide the \fBnid\fR of the curve to
216 EC_GROUP_free frees the memory associated with the \s-1EC_GROUP.\s0
218 EC_GROUP_clear_free destroys any sensitive data held within the \s-1EC_GROUP\s0 and then frees its memory.
220 .IX Header "RETURN VALUES"
221 All EC_GROUP_new* functions return a pointer to the newly constructed group, or \s-1NULL\s0 on error.
223 EC_get_builtin_curves returns the number of builtin curves that are available.
225 EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, EC_GROUP_set_curve_GF2m, EC_GROUP_get_curve_GF2m return 1 on success or 0 on error.
227 .IX Header "SEE ALSO"
228 \&\fIcrypto\fR\|(3), \fIec\fR\|(3), \fIEC_GROUP_copy\fR\|(3),
229 \&\fIEC_POINT_new\fR\|(3), \fIEC_POINT_add\fR\|(3), \fIEC_KEY_new\fR\|(3),
230 \&\fIEC_GFp_simple_method\fR\|(3), \fId2i_ECPKParameters\fR\|(3)