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_discriminant, EC_GROUP_cmp, EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis, EC_GROUP_get_pentanomial_basis − Functions for manipulating EC_GROUP objects

#include
<openssl/ec.h>

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

EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);

const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);

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);

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 *x);

size_t EC_GROUP_get_seed_len(const EC_GROUP *);

size_t EC_GROUP_set_seed(EC_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_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 *);

int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned
int *k);

int EC_GROUP_get_pentanomial_basis(const EC_GROUP *,
unsigned int *k1,

unsigned int *k2, unsigned int *k3);

**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**.

**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 co-ordinate 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.

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()** 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.

**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.

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_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_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.

**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)

Copyright 2013−2017 The OpenSSL Project Authors. All Rights Reserved.

Licensed under the OpenSSL license (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>.