EC_GROUP_COPY(3) OpenSSL EC_GROUP_COPY(3)
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_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
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);
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);
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.
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.
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_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.
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)
COPYRIGHT
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>;.
1.1.1k 2021-03-25 EC_GROUP_COPY(3)
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