EC_GROUP_NEW(3ossl)

💖 NAME 💖

okay bestie, this is the EC_GROUP_NEW(3ossl) page — yes, that's the manual name — and it's literally the whole squad of functions for creating and destroying EC_GROUP objects. The official tagline is Functions for creating and destroying EC_GROUP objects. The cast: EC_GROUP_get_ecparameters, EC_GROUP_get_ecpkparameters, EC_GROUP_new_from_params, EC_GROUP_to_params, EC_GROUP_new_from_ecparameters, EC_GROUP_new_from_ecpkparameters, 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_ex, EC_GROUP_new_by_curve_name, EC_GROUP_set_curve, EC_GROUP_get_curve, EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, EC_GROUP_set_curve_GF2m, EC_GROUP_get_curve_GF2m, EC_get_builtin_curves, and OSSL_EC_curve_nid2name. Slay. ✨

✨ SYNOPSIS ✨

Bestie, here's the include and the signatures, exactly as they are:

#include <openssl/ec.h>

EC_GROUP *EC_GROUP_new_from_params(const OSSL_PARAM params[],
                                   OSSL_LIB_CTX *libctx, const char *propq);
OSSL_PARAM *EC_GROUP_to_params(const EC_GROUP *group, OSSL_LIB_CTX *libctx,
                               const char *propq, BN_CTX *bnctx);
EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params);
EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params);
void EC_GROUP_free(EC_GROUP *group);

EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a,
                                 const BIGNUM *b, BN_CTX *ctx);
EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a,
                                  const BIGNUM *b, BN_CTX *ctx);
EC_GROUP *EC_GROUP_new_by_curve_name_ex(OSSL_LIB_CTX *libctx, const char *propq,
                                        int nid);
EC_GROUP *EC_GROUP_new_by_curve_name(int nid);

int EC_GROUP_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
                       const BIGNUM *b, BN_CTX *ctx);
int EC_GROUP_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b,
                       BN_CTX *ctx);

ECPARAMETERS *EC_GROUP_get_ecparameters(const EC_GROUP *group,
                                        ECPARAMETERS *params);
ECPKPARAMETERS *EC_GROUP_get_ecpkparameters(const EC_GROUP *group,
                                            ECPKPARAMETERS *params);

size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
const char *OSSL_EC_curve_nid2name(int nid);

The following functions have been deprecated since OpenSSL 3.0, and can be hidden entirely by defining OPENSSL_API_COMPAT with a suitable version value, see openssl_user_macros(7):

EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
void EC_GROUP_clear_free(EC_GROUP *group);

int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p,
                           const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p,
                           BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p,
                            const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p,
                            BIGNUM *a, BIGNUM *b, BN_CTX *ctx);

🌸 DESCRIPTION 🌸

okay so inside the library there are two forms of elliptic curve that matter. Let's vibe-check them.

🧮 the two curve flavors

• The first form is defined over the prime field Fp. The elements of Fp are the integers 0 to p-1, where p is a prime number. The revised elliptic curve equation is: y^2 mod p = x^3 +ax + b mod p
• The second form is defined over a binary field F2^m, where the elements of the field are integers of length at most m bits. The elliptic curve equation is modified to: y^2 + xy = x^3 + ax^2 + b (where b != 0)
• 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. Iconic. 💅

🧸 constructors and curve things

• EC_GROUP_new() — deprecated since OpenSSL 3.0 and should no longer be used, but the page still explains it: it constructs a new curve using the implementation provided by meth (see EC_GFp_simple_method(3)) and associated with the library context ctx (see OSSL_LIB_CTX(3)). The ctx parameter may be NULL, in which case the default library context is used. Then you have to call EC_GROUP_set_curve() to set the curve parameters. Applications should instead use one of the other EC_GROUP_new_* constructors. Not me using deprecated APIs, couldn't be me. 🙈
• EC_GROUP_new_from_params() — creates a group with parameters specified by params. The library context libctx (see OSSL_LIB_CTX(3)) and property query string propq are used to fetch algorithms from providers. params may be either a list of explicit params or a named group, The values for ctx and propq may be NULL. The params that can be used are described in EVP_PKEY-EC(7).
• EC_GROUP_to_params — creates an OSSL_PARAM array with the corresponding parameters describing the given EC_GROUP. The resulting parameters may contain parameters describing a named or explicit curve depending on the EC_GROUP. The library context libctx (see OSSL_LIB_CTX(3)) and property query string propq are used to fetch algorithms from providers. bnctx is an optional preallocated BN_CTX (to save the overhead of allocating and freeing the structure in a loop). The values for libctx, propq and bnctx may be NULL. The caller is responsible for freeing the OSSL_PARAM pointer returned. Free your params, bestie! 🫶
• EC_GROUP_new_from_ecparameters() — creates a group from the specified params. EC_GROUP_new_from_ecpkparameters() — creates a group from the specific PK params. Two constructors, one bullet, periodt. 💖
• EC_GROUP_set_curve() — sets the curve parameters p, a, and b. For a curve over Fp, p is the prime for the field. For a curve over F2^m, 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, a and b represent the coefficients a and b from the relevant equation introduced above. Math girlie moment. 🧚
• EC_group_get_curve() — obtains the previously set curve parameters. (Yes, the page spells it EC_group_get_curve() right there, lowercase g and all — I'm not fixing it, I'm just reporting.) 💀
• EC_GROUP_set_curve_GFp() and EC_GROUP_set_curve_GF2m() — synonyms for EC_GROUP_set_curve(). They are defined for backwards compatibility only and should not be used. Old-school, leave them in the past. 🕰️
• EC_GROUP_get_curve_GFp() and EC_GROUP_get_curve_GF2m() — synonyms for EC_GROUP_get_curve(). They are defined for backwards compatibility only and should not be used. Same vibe. ✨
• EC_GROUP_new_curve_GFp() and EC_GROUP_new_curve_GF2m() — shortcuts for calling EC_GROUP_new() and then the EC_GROUP_set_curve() function. An appropriate default implementation method will be used. Shortcut slay. 🔥

The library can be used to create any curve using the functions above, but there are also a number of predefined curves available. To get a list of all the predefined curves, call EC_get_builtin_curves(). The parameter r should be an array of EC_builtin_curve structures of size nitems. The function will populate the r array with information about the built-in curves. If nitems is less than the total number of curves available, then the first 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 r or not). Passing a NULL r, or setting nitems to 0 will do nothing other than return the total number of curves available. The EC_builtin_curve structure is defined as follows:

typedef struct {
       int nid;
       const char *comment;
       } EC_builtin_curve;

Each EC_builtin_curve item has a unique integer id (nid), and a human readable comment string describing the curve. Cute. 🎀

• To construct a built-in curve use EC_GROUP_new_by_curve_name_ex() and provide the nid of the curve to be constructed, the associated library context to be used in ctx (see OSSL_LIB_CTX(3)) and any property query string in propq. The ctx value may be NULL, in which case the default library context is used. The propq value may also be NULL.
• EC_GROUP_new_by_curve_name() is the same as EC_GROUP_new_by_curve_name_ex() except that the default library context is always used along with a NULL property query string. Defaults, but make it cute. 🌈
• EC_GROUP_free() — frees the memory associated with the EC_GROUP. If group is NULL nothing is done. Free your group, bestie. 🫶
• EC_GROUP_clear_free() — deprecated: it was meant to destroy any sensitive data held within the EC_GROUP and then free its memory, but since all the data stored in the EC_GROUP is public anyway, this function is unnecessary. Its use can be safely replaced with EC_GROUP_free(). If group is NULL nothing is done. Not the sensitive-data cleanup you thought, bestie. 💀
• OSSL_EC_curve_nid2name() — converts a curve nid into the corresponding name. Name reveal! 👑

💅 RETURN VALUES 💅

• All EC_GROUP_new* functions return a pointer to the newly constructed group, or NULL on error.
• EC_get_builtin_curves() returns the number of built-in curves that are available.
• 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.
• OSSL_EC_curve_nid2name() returns a character string constant, or NULL on error.

🦋 SEE ALSO 🦋

• crypto(7)
• EC_GROUP_copy(3)
• EC_POINT_new(3)
• EC_POINT_add(3)
• EC_KEY_new(3)
• EC_GFp_simple_method(3)
• d2i_ECPKParameters(3)
• OSSL_LIB_CTX(3)
• EVP_PKEY-EC(7)

🌟 HISTORY 🌟

• EC_GROUP_to_params() was added in OpenSSL 3.2.
• EC_GROUP_new() was deprecated in OpenSSL 3.0.
• EC_GROUP_new_by_curve_name_ex() and EC_GROUP_new_from_params() were added in OpenSSL 3.0.
• EC_GROUP_clear_free() was deprecated in OpenSSL 3.0; use EC_GROUP_free() instead.
• EC_GROUP_set_curve_GFp(), EC_GROUP_get_curve_GFp(), EC_GROUP_set_curve_GF2m() and EC_GROUP_get_curve_GF2m() were deprecated in OpenSSL 3.0; use EC_GROUP_set_curve() and EC_GROUP_get_curve() instead.

👑 COPYRIGHT 👑

Copyright 2013-2024 The OpenSSL Project Authors. All Rights Reserved.

Licensed under the Apache License 2.0 (the "License"). You may not use this file except in compliance with the License. You can obtain a copy in the file LICENSE in the source distribution or at <https://www.openssl.org/source/license.html>.

---

and that's the tea, bestie. This page is from OpenSSL 3.5.6, dated 2026-04-07 💖✨