EC_GROUP_COPY(3ossl)

📦

version 15.1 · 2 versions

15.1 · freebsd 15.1 (latest)
14.5 · freebsd 14.5

✨ NAME ✨

okay so hi bestie 💖 this one is EC_GROUP_COPY(3ossl) — an OpenSSL manual page (that's the 3ossl bit, iykyk) — and it's the whole squad of functions for manipulating EC_GROUP objects. Like, the group-chat of curve-group functions.

Here's everybody in the group chat, in order, no cap:

EC_GROUP_get0_order, EC_GROUP_order_bits, EC_GROUP_get0_cofactor, EC_GROUP_copy, EC_GROUP_dup, EC_GROUP_method_of, EC_GROUP_set_generator, EC_GROUP_get0_generator, EC_GROUP_get_order, EC_GROUP_get_cofactor, EC_GROUP_set_curve_name, EC_GROUP_get_curve_name, EC_GROUP_set_asn1_flag, EC_GROUP_get_asn1_flag, EC_GROUP_set_point_conversion_form, EC_GROUP_get_point_conversion_form, EC_GROUP_get0_seed, EC_GROUP_get_seed_len, EC_GROUP_set_seed, EC_GROUP_get_degree, EC_GROUP_check, EC_GROUP_check_named_curve, EC_GROUP_check_discriminant, EC_GROUP_cmp, EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis, EC_GROUP_get_pentanomial_basis, EC_GROUP_get0_field, EC_GROUP_get_field_type

and the collective vibe of all of them: Functions for manipulating EC_GROUP objects. iconic. 💅

🦋 SYNOPSIS 🦋

first things first, you gotta pull in the header or literally nothing works 🫶

#include <openssl/ec.h>

int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);

int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
                           const BIGNUM *order, const BIGNUM *cofactor);
const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);

int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group);
int EC_GROUP_order_bits(const EC_GROUP *group);
int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group);
const BIGNUM *EC_GROUP_get0_field(const EC_GROUP *group);

void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
int EC_GROUP_get_curve_name(const EC_GROUP *group);

void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
int EC_GROUP_get_asn1_flag(const EC_GROUP *group);

void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *group);

unsigned char *EC_GROUP_get0_seed(const EC_GROUP *group);
size_t EC_GROUP_get_seed_len(const EC_GROUP *group);
size_t EC_GROUP_set_seed(EC_GROUP *group, const unsigned char *, size_t len);

int EC_GROUP_get_degree(const EC_GROUP *group);

int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
int EC_GROUP_check_named_curve(const EC_GROUP *group, int nist_only,
                               BN_CTX *ctx);

int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);

int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);

int EC_GROUP_get_basis_type(const EC_GROUP *group);
int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k);
int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1,
                                   unsigned int *k2, unsigned int *k3);

int EC_GROUP_get_field_type(const EC_GROUP *group);

a little aesthetic note because the way these are written is so telling: the set_* girlies hand back void (they just do the thing and dip), while the get_* ones hand you back an actual value, and the get0_* ones are the ones that just point at what's already there instead of copying it for you. main character energy tbh 🌸

⚠️ okay bestie, READ THIS ONE, it's the only drama on this page: the following function has 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):

const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);

like, she still exists, but she's on the deprecated list now, so don't build new stuff around her, mwah 💋

okay that's the header + NAME + SYNOPSIS portion, the rest is coming next so don't go anywhere 🧚

✨ DESCRIPTION ✨

Okay bestie, buckle up, this is the big one 💅

EC_GROUP_copy() — copies the curve src into dst. Literally both src and dst have to use the same EC_METHOD, no mixing and matching, that's the rule 🚫
EC_GROUP_dup() — makes a brand new EC_GROUP object and copies all the content from src into that shiny new object. Fresh out the box, no cap ✨
EC_GROUP_method_of() — grabs the EC_METHOD of group. Heads up though: this one was deprecated in OpenSSL 3.0, because EC_METHOD is no longer a public concept. It's giving retired icon 💀
EC_GROUP_set_generator() — sets the curve parameters that everybody using the curve has to agree on. These include the generator, the order, and the cofactor. The generator is a well defined point on the curve picked specifically for cryptographic operations. The integers used for point multiplications will be between 0 and n-1, where n is the order. And the order multiplied by the cofactor gives you the number of points on the curve. Math slay 🔥
EC_GROUP_get0_generator() — returns the generator for the identified group.
EC_GROUP_get_order() — retrieves the order of group and copies its value into order. It fails if group isn't fully initialized (meaning its order is not set, or it's set to zero). So like, set it first bestie 😭
EC_GROUP_get_cofactor() — retrieves the cofactor of group and copies its value into cofactor. It fails if group is not fully initialized, or if the cofactor is not set (or set to zero).
EC_GROUP_set_curve_name() / EC_GROUP_get_curve_name() — set and get the NID for the curve, respectively (peep EC_GROUP_new(3)). If a curve doesn't have a NID associated with it, then EC_GROUP_get_curve_name returns NID_undef.

The asn1_flag value is what decides whether the curve encoding uses explicit parameters or a named curve using an ASN1 OID — and a lot of applications only support that latter form, so this matters, fr fr. If asn1_flag is OPENSSL_EC_NAMED_CURVE then the named curve form gets used, and the parameters must have a corresponding named curve NID set. If asn1_flags is OPENSSL_EC_EXPLICIT_CURVE then the parameters are explicitly encoded. EC_GROUP_get_asn1_flag() and EC_GROUP_set_asn1_flag() get and set the status of the asn1_flag for the curve respectively.

📌 Note time, and this one's important: OPENSSL_EC_EXPLICIT_CURVE was added in OpenSSL 1.1.0. For previous versions of OpenSSL the value 0 must be used instead. Before OpenSSL 1.1.0 the default form was to use explicit parameters — meaning apps would have to explicitly set the named curve form — but in OpenSSL 1.1.0 and later, the named curve form is the default. Glow-up era 💅

The point_conversion_form for a curve controls how EC_POINT data is encoded as ASN1, as defined in X9.62 (ECDSA). point_conversion_form_t is an enum defined like this:

typedef enum {
       /** the point is encoded as z||x, where the octet z specifies
        *   which solution of the quadratic equation y is  */
       POINT_CONVERSION_COMPRESSED = 2,
       /** the point is encoded as z||x||y, where z is the octet 0x04  */
       POINT_CONVERSION_UNCOMPRESSED = 4,
       /** the point is encoded as z||x||y, where the octet z specifies
        *  which solution of the quadratic equation y is  */
       POINT_CONVERSION_HYBRID = 6
} point_conversion_form_t;

For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet signifying that the UNCOMPRESSED form has been used, followed by the octets for x, followed by the octets for y. Nice and simple, we love a straightforward encoding 🎀

For any given x coordinate for a point on a curve, it's possible to derive two possible y values. So for POINT_CONVERSION_COMPRESSED the point is encoded as an octet signifying that the COMPRESSED form has been used AND which of the two possible solutions for y has been used, followed by the octets for x. Two-for-one situation, lowkey iconic 🦋

For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying the HYBRID form has been used AND which of the two possible solutions for y has been used, followed by the octets for x, followed by the octets for y.

EC_GROUP_set_point_conversion_form() and EC_GROUP_get_point_conversion_form() set and get the point_conversion_form for the curve respectively.

Now for the seed lore 🌱 ANSI X9.62 (the ECDSA standard) defines a method of generating the curve parameter b from a random number. This is a whole vibe because a parameter obtained this way is highly unlikely to be susceptible to special purpose attacks, or to have any trapdoors hiding in it. Sneaky-proof, we stan 🫶

If the seed is present for a curve, then the b parameter was generated in a verifiable fashion using that seed. The OpenSSL EC library does not use this seed value, but it does let you inspect it using EC_GROUP_get0_seed(). That returns a pointer to a memory block containing the seed that was used. You can get the length of that memory block with EC_GROUP_get_seed_len(). A number of the built-in curves in the library ship with seed values that you can grab. It's also possible to set a custom seed using EC_GROUP_set_seed() by passing a pointer to a memory block along with the length of the seed. Again — the EC library will not use this seed value, though it will be preserved in any ASN1 based communications. Preserved for the memories 💜

EC_GROUP_get_degree() — gets the degree of the field. For Fp fields this is the number of bits in p. For F2^m fields this is the value m.
EC_GROUP_get_field_type() — identifies what type of field the EC_GROUP structure supports, which will be either F2^m or Fp.
EC_GROUP_check_discriminant() — calculates the discriminant for the curve and verifies that it's valid. For a curve defined over Fp the discriminant is given by the formula 4*a^3 + 27*b^2, while for F2^m curves the discriminant is simply b. Either way, for the curve to be valid the discriminant must be non zero. Zero discriminant? Not on our watch 🙈
EC_GROUP_check() — behaves like this: for the OpenSSL default provider it performs a number of checks on a curve to verify that it's valid. Those checks include verifying that the discriminant is non zero; that a generator has been defined; and that the generator is on the curve and has the correct order. For the OpenSSL FIPS provider it uses EC_GROUP_check_named_curve() to conform to SP800-56Ar3. Two paths, one overachiever ✨
EC_GROUP_check_named_curve() — determines if the group's domain parameters match one of the built-in curves supported by the library. The curve name is returned as a NID if it matches. If the group's domain parameters have been modified, then no match will be found. If the curve name of the given group is NID_undef (for example, it was created by using explicit parameters with no curve name), then this method can be used to look up the name of the curve that matches the group domain parameters. The built-in curves contain aliases, so multiple NID's can map to the same domain parameters — and for such curves it is unspecified which of the aliases will be returned if the curve name of the given group is NID_undef. If nist_only is 1 it will only look for NIST approved curves, otherwise it searches all built-in curves. This function may be passed a BN_CTX object in the ctx parameter. The ctx parameter may be NULL. Options, options, we love choices 💅
EC_GROUP_cmp() — compares a and b to determine whether they represent the same curve or not.

The functions EC_GROUP_get_basis_type(), EC_GROUP_get_trinomial_basis() and EC_GROUP_get_pentanomial_basis() should only be called for curves defined over an F2^m field — like, do not come for them otherwise, they will not serve you 😭

Addition and multiplication operations within an F2^m field are performed using an irreducible polynomial function f(x). This function is either a trinomial of the form:

f(x) = x^m + x^k + 1 with m > k >= 1

or a pentanomial of the form:

f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1

EC_GROUP_get_basis_type() returns a NID identifying whether a trinomial or pentanomial is in use for the field. EC_GROUP_get_trinomial_basis() must only be called where f(x) is of the trinomial form, and returns the value of k. Similarly, EC_GROUP_get_pentanomial_basis() must only be called where f(x) is of the pentanomial form, and returns the values of k1, k2 and k3 respectively. Three ks, one function, she's efficient 🌸

🎀 RETURN VALUES 🎀

The following functions return 1 on success or 0 on error: EC_GROUP_copy(), EC_GROUP_set_generator(), EC_GROUP_check(), EC_GROUP_check_discriminant(), EC_GROUP_get_trinomial_basis() and EC_GROUP_get_pentanomial_basis(). Classic binary queen behavior 👑

EC_GROUP_dup() — returns a pointer to the duplicated curve, or NULL on error.
EC_GROUP_method_of() — returns the EC_METHOD implementation in use for the given curve, or NULL on error.
EC_GROUP_get0_generator() — returns the generator for the given curve, or NULL on error.
EC_GROUP_get_order() — returns 0 if the order is not set (or set to zero) for group, or if copying into order fails; returns 1 otherwise.
EC_GROUP_get_cofactor() — returns 0 if the cofactor is not set (or is set to zero) for group, or if copying into cofactor fails; returns 1 otherwise.
EC_GROUP_get_curve_name() — returns the curve name (NID) for group, or will return NID_undef if no curve name is associated.
EC_GROUP_get_asn1_flag() — returns the ASN1 flag for the specified group.
EC_GROUP_get_point_conversion_form() — returns the point_conversion_form for group.
EC_GROUP_get_degree() — returns the degree for group, or 0 if the operation is not supported by the underlying group implementation.
EC_GROUP_get_field_type() — returns either NID_X9_62_prime_field for prime curves or NID_X9_62_characteristic_two_field for binary curves; these values are defined in the <openssl/obj_mac.h> header file. Header file lore, go check it 🦋
EC_GROUP_check_named_curve() — returns the nid of the matching named curve, otherwise it returns 0 for no match, or -1 on error.
EC_GROUP_get0_order() — returns an internal pointer to the group order.
EC_GROUP_order_bits() — returns the number of bits in the group order.
EC_GROUP_get0_cofactor() — returns an internal pointer to the group cofactor.
EC_GROUP_get0_field() — returns an internal pointer to the group field. For curves over GF(p), this is the modulus; for curves over GF(2^m), this is the irreducible polynomial defining the field.
EC_GROUP_get0_seed() — returns a pointer to the seed that was used to generate the parameter b, or NULL if the seed is not specified.
EC_GROUP_get_seed_len() — returns the length of the seed, or 0 if the seed is not specified.
EC_GROUP_set_seed() — returns the length of the seed that has been set. If the supplied seed is NULL, or the supplied seed length is 0, the return value will be 1. On error, 0 is returned.
EC_GROUP_cmp() — returns 0 if the curves are equal, 1 if they are not equal, or -1 on error. (Yes, zero means equal here, it's giving chaotic but we respect it 💀)
EC_GROUP_get_basis_type() — returns the values NID_X9_62_tpBasis or NID_X9_62_ppBasis (as defined in <openssl/obj_mac.h>) for a trinomial or pentanomial respectively. Alternatively, in the event of an error, a 0 is returned.

Go read those too, you'll be so smart, iykyk 💖

✨ HISTORY ✨

okay so here's the lore of how we got here, bestie 📜

EC_GROUP_method_of() — was deprecated in OpenSSL 3.0. it's giving retired icon, we don't really use it anymore 💅
EC_GROUP_get0_field(), EC_GROUP_check_named_curve() and EC_GROUP_get_field_type() — these three were added in OpenSSL 3.0. brand new, main character energy, they ate ✨
EC_GROUP_get0_order(), EC_GROUP_order_bits() and EC_GROUP_get0_cofactor() — and these legends have been around since OpenSSL 1.1.0, so they're lowkey veterans at this point 👑

🌸 COPYRIGHT 🌸

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 whole page, bestie, you made it to the end!! 🎉 this was version 3.5.6, dated 2026-04-07, from the EC_GROUP_COPY(3ossl) fam — go forth and copy those groups, ily, byeeee 💖🦋

📦 where this page comes from

freebsd 15.1: base 15.1
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms