NAME
EC_GROUP_new
,
EC_GROUP_free
,
EC_GROUP_clear_free
,
EC_GROUP_new_curve_GFp
,
EC_GROUP_new_curve_GF2m
,
EC_GROUP_new_by_curve_name
,
EC_GROUP_set_curve_GFp
,
EC_GROUP_get_curve_GFp
,
EC_GROUP_set_curve_GF2m
,
EC_GROUP_get_curve_GF2m
,
EC_get_builtin_curves
—
create and destroy EC_GROUP
objects
SYNOPSIS
#include
<openssl/ec.h>
#include <openssl/bn.h>
EC_GROUP *
EC_GROUP_new
(const EC_METHOD
*meth);
void
EC_GROUP_free
(EC_GROUP
*group);
void
EC_GROUP_clear_free
(EC_GROUP
*group);
EC_GROUP *
EC_GROUP_new_curve_GFp
(const BIGNUM
*p, const BIGNUM *a, const
BIGNUM *b, BN_CTX *ctx);
EC_GROUP *
EC_GROUP_new_curve_GF2m
(const BIGNUM
*p, const BIGNUM *a, const
BIGNUM *b, BN_CTX *ctx);
EC_GROUP *
EC_GROUP_new_by_curve_name
(int
nid);
int
EC_GROUP_set_curve_GFp
(EC_GROUP
*group, const BIGNUM *p, const
BIGNUM *a, const BIGNUM *b,
BN_CTX *ctx);
int
EC_GROUP_get_curve_GFp
(const EC_GROUP
*group, BIGNUM *p, BIGNUM
*a, BIGNUM *b, BN_CTX
*ctx);
int
EC_GROUP_set_curve_GF2m
(EC_GROUP
*group, const BIGNUM *p, const
BIGNUM *a, const BIGNUM *b,
BN_CTX *ctx);
int
EC_GROUP_get_curve_GF2m
(const EC_GROUP
*group, BIGNUM *p, BIGNUM
*a, BIGNUM *b, BN_CTX
*ctx);
size_t
EC_get_builtin_curves
(EC_builtin_curve
*r, size_t nitems);
DESCRIPTION
The EC library provides functions for performing operations on elliptic curves over finite fields. In general, an elliptic curve satisfies an equation of the form:
y^2 = x^3 + ax + b
Within the library there are two forms of elliptic curves that are of interest. The first form is those defined over the prime field Fp. The elements of Fp are the integers 0 to p-1, where p is a prime number. This gives us a revised elliptic curve equation as follows:
y^2 mod p = x^3 + ax + b mod
p
The second form is those defined over a binary field F2^m where the elements of the field are integers of length at most m bits. For this form the elliptic curve equation is modified to:
y^2 + xy = x^3 + ax^2 + b (where b !=
0)
Operations in a binary field are performed relative to an irreducible polynomial. All such curves with OpenSSL use a trinomial or a pentanomial for this parameter.
An EC_GROUP structure is
used to represent the definition of an elliptic curve. A new curve can be
constructed by calling
EC_GROUP_new
(),
using the implementation provided by meth (see
EC_GFp_simple_method(3)). It is then necessary to call either
EC_GROUP_set_curve_GFp
() or
EC_GROUP_set_curve_GF2m
() as appropriate to create a
curve defined over Fp or over F2^m, respectively.
EC_GROUP_set_curve_GFp
()
sets the curve parameters p, a,
and b for a curve over Fp stored in
group.
EC_group_get_curve_GFp
()
obtains the previously set curve parameters.
EC_GROUP_set_curve_GF2m
()
sets the equivalent curve parameters for a curve over F2^m. In this case
p represents the irreducible polynomial - each bit
represents a term in the polynomial. Therefore there will either be three or
five bits set dependent on whether the polynomial is a trinomial or a
pentanomial.
EC_group_get_curve_GF2m
()
obtains the previously set curve parameters.
The functions
EC_GROUP_new_curve_GFp
()
and
EC_GROUP_new_curve_GF2m
()
are shortcuts for calling EC_GROUP_new
() and the
appropriate
EC_GROUP_set_curve_*
()
function. An appropriate default implementation method will be used.
Whilst the library can be used to
create any curve using the functions described above, there are also a
number of predefined curves that are available. In order to obtain a list of
all of the predefined curves, call the function
EC_get_builtin_curves
().
The parameter r should be an array of
EC_builtin_cure structures of size
nitems. The function will populate the
r array with information about the builtin curves. If
nitems is less than the total number of curves
available, then the first nitems curves will be
returned. Otherwise the total number of curves will be provided. The return
value is the total number of curves available (whether that number has been
populated in r or not). Passing a
NULL
r, or setting
nitems to 0, will do nothing other than return the
total number of curves available. The EC_builtin_curve
structure is defined as follows:
typedef struct { int nid; const char *comment; } EC_builtin_curve;
Each EC_builtin_curve item has a unique integer ID (nid) and a human readable comment string describing the curve.
In order to construct a builtin
curve use the function
EC_GROUP_new_by_curve_name
()
and provide the nid of the curve to be
constructed.
EC_GROUP_free
()
frees the memory associated with the EC_GROUP. If
group is a NULL
pointer, no
action occurs.
EC_GROUP_clear_free
()
destroys any sensitive data held within the EC_GROUP
and then frees its memory. If group is a
NULL
pointer, no action occurs.
RETURN VALUES
All EC_GROUP_new*
() functions return a
pointer to the newly constructed group or NULL
on
error.
EC_get_builtin_curves
() returns the number
of builtin curves that are available.
EC_GROUP_set_curve_GFp
(),
EC_GROUP_get_curve_GFp
(),
EC_GROUP_set_curve_GF2m
(), and
EC_GROUP_get_curve_GF2m
() return 1 on success or 0
on error.
SEE ALSO
d2i_ECPKParameters(3), EC_GFp_simple_method(3), EC_GROUP_copy(3), EC_KEY_new(3), EC_POINT_add(3), EC_POINT_new(3), ECDSA_SIG_new(3)