NAME
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
—
manipulate EC_GROUP objects
SYNOPSIS
#include
<openssl/ec.h>
#include <openssl/bn.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);
int
EC_GROUP_get_cofactor
(const EC_GROUP
*group, BIGNUM *cofactor, BN_CTX
*ctx);
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 *);
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
These functions operate on EC_GROUP objects created by the functions described in EC_GROUP_new(3).
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 order - 1.
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.
The functions
EC_GROUP_get_order
()
and
EC_GROUP_get_cofactor
()
populate the provided order and
cofactor parameters with the respective order and
cofactors for the group.
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
0.
The asn1_flag value on a curve is used
to determine whether there is a specific ASN.1 OID to describe the curve or
not. If the asn1_flag is 1 then this is a named curve with an associated
ASN.1 OID. If not then asn1_flag is 0. 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. If set, then the
curve_name must also be set.
The point_conversion_form for a curve controls how EC_POINT data is encoded as ASN.1 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 0x02 */ 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 builtin 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 ASN.1 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.
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
(),
EC_GROUP_get_cofactor
(),
EC_GROUP_get_curve_name
(),
EC_GROUP_get_asn1_flag
(),
EC_GROUP_get_point_conversion_form
(), and
EC_GROUP_get_degree
() return the order, cofactor,
curve name (NID), ASN.1 flag, point_conversion_form and degree for the
specified curve, respectively. If there is no curve name associated with a
curve then EC_GROUP_get_curve_name
() returns 0.
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
d2i_ECPKParameters(3), EC_GFp_simple_method(3), EC_GROUP_new(3), EC_KEY_new(3), EC_POINT_add(3), EC_POINT_new(3)