.\" $OpenBSD: EC_GROUP_new.3,v 1.13 2021/05/11 04:22:32 tb Exp $ .\" OpenSSL 6328d367 Sat Jul 4 21:58:30 2020 +0200 .\" .\" This file was written by Matt Caswell . .\" Copyright (c) 2013 The OpenSSL Project. All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions .\" are met: .\" .\" 1. Redistributions of source code must retain the above copyright .\" notice, this list of conditions and the following disclaimer. .\" .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in .\" the documentation and/or other materials provided with the .\" distribution. .\" .\" 3. All advertising materials mentioning features or use of this .\" software must display the following acknowledgment: .\" "This product includes software developed by the OpenSSL Project .\" for use in the OpenSSL Toolkit. 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IN NO EVENT SHALL THE OpenSSL PROJECT OR .\" ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, .\" SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT .\" NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; .\" LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) .\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, .\" STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) .\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED .\" OF THE POSSIBILITY OF SUCH DAMAGE. .\" .Dd $Mdocdate: May 11 2021 $ .Dt EC_GROUP_NEW 3 .Os .Sh NAME .Nm EC_GROUP_new , .Nm EC_GROUP_free , .Nm EC_GROUP_clear_free , .Nm EC_GROUP_new_curve_GFp , .Nm EC_GROUP_new_curve_GF2m , .Nm EC_GROUP_new_by_curve_name , .Nm EC_GROUP_set_curve , .Nm EC_GROUP_get_curve , .Nm EC_GROUP_set_curve_GFp , .Nm EC_GROUP_get_curve_GFp , .Nm EC_GROUP_set_curve_GF2m , .Nm EC_GROUP_get_curve_GF2m , .Nm EC_get_builtin_curves .Nd create and destroy EC_GROUP objects .Sh SYNOPSIS .In openssl/ec.h .In openssl/bn.h .Ft EC_GROUP * .Fo EC_GROUP_new .Fa "const EC_METHOD *meth" .Fc .Ft void .Fo EC_GROUP_free .Fa "EC_GROUP *group" .Fc .Ft void .Fo EC_GROUP_clear_free .Fa "EC_GROUP *group" .Fc .Ft EC_GROUP * .Fo EC_GROUP_new_curve_GFp .Fa "const BIGNUM *p" .Fa "const BIGNUM *a" .Fa "const BIGNUM *b" .Fa "BN_CTX *ctx" .Fc .Ft EC_GROUP * .Fo EC_GROUP_new_curve_GF2m .Fa "const BIGNUM *p" .Fa "const BIGNUM *a" .Fa "const BIGNUM *b" .Fa "BN_CTX *ctx" .Fc .Ft EC_GROUP * .Fo EC_GROUP_new_by_curve_name .Fa "int nid" .Fc .Ft int .Fo EC_GROUP_set_curve .Fa "EC_GROUP *group" .Fa "const BIGNUM *p" .Fa "const BIGNUM *a" .Fa "const BIGNUM *b" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo EC_GROUP_get_curve .Fa "const EC_GROUP *group" .Fa "BIGNUM *p" .Fa "BIGNUM *a" .Fa "BIGNUM *b" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo EC_GROUP_set_curve_GFp .Fa "EC_GROUP *group" .Fa "const BIGNUM *p" .Fa "const BIGNUM *a" .Fa "const BIGNUM *b" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo EC_GROUP_get_curve_GFp .Fa "const EC_GROUP *group" .Fa "BIGNUM *p" .Fa "BIGNUM *a" .Fa "BIGNUM *b" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo EC_GROUP_set_curve_GF2m .Fa "EC_GROUP *group" .Fa "const BIGNUM *p" .Fa "const BIGNUM *a" .Fa "const BIGNUM *b" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo EC_GROUP_get_curve_GF2m .Fa "const EC_GROUP *group" .Fa "BIGNUM *p" .Fa "BIGNUM *a" .Fa "BIGNUM *b" .Fa "BN_CTX *ctx" .Fc .Ft size_t .Fo EC_get_builtin_curves .Fa "EC_builtin_curve *r" .Fa "size_t nitems" .Fc .Sh DESCRIPTION The EC library provides functions for performing operations on elliptic curves over finite fields. In general, an elliptic curve satisfies an equation of the form: .Pp .Dl y^2 = x^3 + ax + b .Pp Within the library there are two forms of elliptic curves that are of interest. The first form is those defined over the prime field Fp. The elements of Fp are the integers 0 to p-1, where .Fa p is a prime number. This gives us a revised elliptic curve equation as follows: .Pp .Dl y^2 mod p = x^3 + ax + b mod p .Pp The second form is those defined over a binary field F2^m where the elements of the field are integers of length at most m bits. For this form the elliptic curve equation is modified to: .Pp .Dl y^2 + xy = x^3 + ax^2 + b (where b != 0) .Pp Operations in a binary field are performed relative to an irreducible polynomial. All such curves with OpenSSL use a trinomial or a pentanomial for this parameter. .Pp An .Vt EC_GROUP structure is used to represent the definition of an elliptic curve. A new curve can be constructed by calling .Fn EC_GROUP_new , using the implementation provided by .Fa meth (see .Xr EC_GFp_simple_method 3 ) . It is then necessary to call .Fn EC_GROUP_set_curve to set the curve parameters. .Pp .Fn EC_GROUP_set_curve sets the curve parameters .Fa p , .Fa a , and .Fa b . For a curve over Fp, .Fa p is the prime for the field. For a curve over F2^m .Fa p represents the irreducible polynomial - each bit represents a term in the polynomial. Therefore, there will either be three or five bits set dependent on whether the polynomial is a trinomial or a pentanomial. In either case, .Fa a and .Fa b represent the coefficients of the curve equation. .Pp .Fn EC_GROUP_set_curve_GFp and .Fn EC_GROUP_set_curve_GF2m are deprecated synonyms for .Fn EC_GROUP_set_curve . .Pp .Fn EC_GROUP_get_curve obtains the previously set curve parameters. .Pp .Fn EC_GROUP_get_curve_GFp and .Fn EC_GROUP_get_curve_GF2m are deprecated synonyms for .Fn EC_GROUP_get_curve . .Pp The functions .Fn EC_GROUP_new_curve_GFp and .Fn EC_GROUP_new_curve_GF2m are shortcuts for calling .Fn EC_GROUP_new and the appropriate .Fn EC_GROUP_set_curve_* function. An appropriate default implementation method will be used. .Pp Whilst the library can be used to create any curve using the functions described above, there are also a number of predefined curves that are available. In order to obtain a list of all of the predefined curves, call the function .Fn EC_get_builtin_curves . The parameter .Fa r should be an array of .Vt EC_builtin_cure structures of size .Fa nitems . The function will populate the .Fa r array with information about the builtin curves. If .Fa nitems is less than the total number of curves available, then the first .Fa nitems curves will be returned. Otherwise the total number of curves will be provided. The return value is the total number of curves available (whether that number has been populated in .Fa r or not). Passing a .Dv NULL .Fa r , or setting .Fa nitems to 0, will do nothing other than return the total number of curves available. The .Vt EC_builtin_curve structure is defined as follows: .Bd -literal typedef struct { int nid; const char *comment; } EC_builtin_curve; .Ed .Pp Each .Vt EC_builtin_curve item has a unique integer ID .Pq Fa nid and a human readable comment string describing the curve. .Pp In order to construct a builtin curve use the function .Fn EC_GROUP_new_by_curve_name and provide the .Fa nid of the curve to be constructed. .Pp .Fn EC_GROUP_free frees the memory associated with the .Vt EC_GROUP . If .Fa group is a .Dv NULL pointer, no action occurs. .Pp .Fn EC_GROUP_clear_free destroys any sensitive data held within the .Vt EC_GROUP and then frees its memory. If .Fa group is a .Dv NULL pointer, no action occurs. .Sh RETURN VALUES All .Fn EC_GROUP_new* functions return a pointer to the newly constructed group or .Dv NULL on error. .Pp .Fn EC_get_builtin_curves returns the number of builtin curves that are available. .Pp .Fn EC_GROUP_set_curve , .Fn EC_GROUP_get_curve , .Fn EC_GROUP_set_curve_GFp , .Fn EC_GROUP_get_curve_GFp , .Fn EC_GROUP_set_curve_GF2m , and .Fn EC_GROUP_get_curve_GF2m return 1 on success or 0 on error. .Sh SEE ALSO .Xr crypto 3 , .Xr d2i_ECPKParameters 3 , .Xr EC_GFp_simple_method 3 , .Xr EC_GROUP_copy 3 , .Xr EC_KEY_new 3 , .Xr EC_POINT_add 3 , .Xr EC_POINT_new 3 , .Xr ECDH_compute_key 3 , .Xr ECDSA_SIG_new 3 .Sh HISTORY .Fn EC_GROUP_new , .Fn EC_GROUP_free , .Fn EC_GROUP_clear_free , .Fn EC_GROUP_new_curve_GFp , .Fn EC_GROUP_set_curve_GFp , and .Fn EC_GROUP_get_curve_GFp first appeared in OpenSSL 0.9.7 and have been available since .Ox 3.2 . .Pp .Fn EC_GROUP_new_curve_GF2m , .Fn EC_GROUP_new_by_curve_name , .Fn EC_GROUP_set_curve_GF2m , .Fn EC_GROUP_get_curve_GF2m , and .Fn EC_get_builtin_curves first appeared in OpenSSL 0.9.8 and have been available since .Ox 4.5 . .Fn EC_GROUP_set_curve and .Fn EC_GROUP_get_curve first appeared in OpenSSL 1.1.1 and have been available since .Ox 7.0 .