EC_GROUP_NEW(3) Library Functions Manual EC_GROUP_NEW(3)

EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_new_curve_GFp, 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_get_builtin_curvescreate and destroy EC_GROUP objects

#include <openssl/ec.h>
#include <openssl/bn.h>

EC_GROUP_new(const EC_METHOD *meth);

EC_GROUP_free(EC_GROUP *group);

EC_GROUP_clear_free(EC_GROUP *group);

EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);

EC_GROUP_new_by_curve_name(int nid);

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

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

EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);

EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);

EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);

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:

y^2 = x^3 + ax + b

An EC_GROUP structure is used to represent the definition of an elliptic curve. A new curve can be constructed by calling (), using the implementation provided by meth (see EC_GFp_simple_method(3)). It is then necessary to call EC_GROUP_set_curve() to set the curve parameters.

() sets the curve parameters p, a, and b, where a and b represent the coefficients of the curve equation.

() is a deprecated synonym for EC_GROUP_set_curve().

() obtains the previously set curve parameters.

() is a deprecated synonym for EC_GROUP_get_curve().

The function () is a shortcut for calling EC_GROUP_new() and EC_GROUP_set_curve(). An appropriate default implementation method will be used.

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 (). The parameter r should be an array of EC_builtin_cure structures of size nitems. The function will populate the r array with information about the builtin 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.

In order to construct a builtin curve, use the function () and provide the nid of the curve to be constructed.

() frees the memory associated with the EC_GROUP. If group is a NULL pointer, no action occurs.

() destroys any sensitive data held within the EC_GROUP and then frees its memory. If group is a NULL pointer, no action occurs.

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 builtin curves that are available.

EC_GROUP_set_curve(), EC_GROUP_get_curve(), EC_GROUP_set_curve_GFp(), and EC_GROUP_get_curve_GFp() return 1 on success or 0 on error.

crypto(3), d2i_ECPKParameters(3), EC_GFp_simple_method(3), EC_GROUP_copy(3), EC_KEY_new(3), EC_POINT_add(3), EC_POINT_new(3), ECDH_compute_key(3), ECDSA_SIG_new(3)

EC_GROUP_new(), EC_GROUP_free(), EC_GROUP_clear_free(), EC_GROUP_new_curve_GFp(), EC_GROUP_set_curve_GFp(), and EC_GROUP_get_curve_GFp() first appeared in OpenSSL 0.9.7 and have been available since OpenBSD 3.2.

EC_GROUP_new_by_curve_name(), and EC_get_builtin_curves() first appeared in OpenSSL 0.9.8 and have been available since OpenBSD 4.5. EC_GROUP_set_curve() and EC_GROUP_get_curve() first appeared in OpenSSL 1.1.1 and have been available since OpenBSD 7.0.

April 27, 2023 OpenBSD 7.5