EC_GROUP_COPY(3ssl) | OpenSSL | EC_GROUP_COPY(3ssl) |

# NAME

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 - Functions for manipulating EC_GROUP objects

# SYNOPSIS

#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);

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);

# DESCRIPTION

**EC_GROUP_copy()** copies the curve **src** into
**dst**. Both **src** and **dst** must use the same EC_METHOD.

**EC_GROUP_dup()** creates a new EC_GROUP object and copies the
content from **src** to the newly created EC_GROUP object.

**EC_GROUP_method_of()** obtains the EC_METHOD of **group**.
This function was deprecated in OpenSSL 3.0, since EC_METHOD is no longer a
public concept.

**EC_GROUP_set_generator()** sets curve parameters that must be
agreed by all participants using the curve. These parameters include the
**generator**, the **order** and the **cofactor**. The
**generator** is a well defined point on the curve chosen for
cryptographic operations. Integers used for point multiplications will be
between 0 and n-1 where n is the **order**. The **order** multiplied
by the **cofactor** gives the number of points on the curve.

**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 in case **group** is not
fully initialized (i.e., its order is not set or set to zero).

**EC_GROUP_get_cofactor()** retrieves the cofactor of
**group** and copies its value into **cofactor**. It fails in case
**group** is not fully initialized or if the cofactor is not set (or set
to zero).

The functions **EC_GROUP_set_curve_name()** and
**EC_GROUP_get_curve_name()**, set and get the NID for the curve
respectively (see EC_GROUP_new(3)). If a curve does not have a NID
associated with it, then EC_GROUP_get_curve_name will return NID_undef.

The asn1_flag value is used to determine whether the curve
encoding uses explicit parameters or a named curve using an ASN1 OID: many
applications only support the latter form. If asn1_flag is
**OPENSSL_EC_NAMED_CURVE** then the named curve form is used and the
parameters must have a corresponding named curve NID set. If asn1_flags is
**OPENSSL_EC_EXPLICIT_CURVE** the parameters are explicitly encoded. The
functions **EC_GROUP_get_asn1_flag()** and
**EC_GROUP_set_asn1_flag()** get and set the status of the asn1_flag for
the curve. Note: **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 that applications would have to explicitly set the named curve
form) in OpenSSL 1.1.0 and later the named curve form is the default.

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 as follows:

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 the UNCOMPRESSED form has been used followed by the octets for x, followed by the octets for y.

For any given x coordinate for a point on a curve it is possible to derive two possible y values. 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.

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.

The functions **EC_GROUP_set_point_conversion_form()** and
**EC_GROUP_get_point_conversion_form()**, set and get the
point_conversion_form for the curve respectively.

ANSI X9.62 (ECDSA standard) defines a method of generating the
curve parameter b from a random number. This provides advantages in that a
parameter obtained in this way is highly unlikely to be susceptible to
special purpose attacks, or have any trapdoors in it. 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 does
enable you to inspect it using **EC_GROUP_get0_seed()**. This returns a
pointer to a memory block containing the seed that was used. The length of
the memory block can be obtained using **EC_GROUP_get_seed_len()**. A
number of the built-in curves within the library provide seed values that
can be obtained. It is also possible to set a custom seed using
**EC_GROUP_set_seed()** and passing a pointer to a memory block, along
with the length of the seed. Again, the EC library will not use this seed
value, although it will be preserved in any ASN1 based communications.

**EC_GROUP_get_degree()** gets the degree of the field. For Fp
fields this will be the number of bits in p. For F2^m fields this will be
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.

The function **EC_GROUP_check_discriminant()** calculates the
discriminant for the curve and verifies that it is valid. For a curve
defined over Fp the discriminant is given by the formula 4*a^3 + 27*b^2
whilst for F2^m curves the discriminant is simply b. In either case for the
curve to be valid the discriminant must be non zero.

The function **EC_GROUP_check()** behaves in the following way:
For the OpenSSL default provider it performs a number of checks on a curve
to verify that it is valid. Checks performed include verifying that the
discriminant is non zero; that a generator has been defined; 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.

The function **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** (e.g. it has been
created by using explicit parameters with no curve name), then this method
can be used to lookup the name of the curve that matches the group domain
parameters. The built-in curves contain aliases, so that multiple NID's can
map to the same domain parameters. 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.

**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. 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

The function **EC_GROUP_get_basis_type()** returns a NID
identifying whether a trinomial or pentanomial is in use for the field. The
function **EC_GROUP_get_trinomial_basis()** must only be called where
f(x) is of the trinomial form, and returns the value of **k**. Similarly
the function **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.

# 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()**.

**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, 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, 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.

**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.

**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.

# SEE ALSO

crypto(7), EC_GROUP_new(3), EC_POINT_new(3), EC_POINT_add(3), EC_KEY_new(3), EC_GFp_simple_method(3), d2i_ECPKParameters(3)

# HISTORY

**EC_GROUP_method_of()** was deprecated in OpenSSL 3.0.
**EC_GROUP_get0_field()**, **EC_GROUP_check_named_curve()** and
**EC_GROUP_get_field_type()** were added in OpenSSL 3.0.
**EC_GROUP_get0_order()**, **EC_GROUP_order_bits()** and
**EC_GROUP_get0_cofactor()** were added in OpenSSL 1.1.0.

# COPYRIGHT

Copyright 2013-2023 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.

2024-09-03 | 3.3.2 |