112 lines
5.4 KiB
Plaintext
112 lines
5.4 KiB
Plaintext
=pod
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=head1 NAME
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EC_GROUP_new, EC_GROUP_new_from_ecparameters,
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EC_GROUP_new_from_ecpkparameters,
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EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_new_curve_GFp,
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EC_GROUP_new_curve_GF2m, EC_GROUP_new_by_curve_name, EC_GROUP_set_curve_GFp,
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EC_GROUP_get_curve_GFp, EC_GROUP_set_curve_GF2m, EC_GROUP_get_curve_GF2m,
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EC_get_builtin_curves - Functions for creating and destroying B<EC_GROUP>
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objects.
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=head1 SYNOPSIS
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#include <openssl/ec.h>
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#include <openssl/bn.h>
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EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
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EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params)
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EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params)
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void EC_GROUP_free(EC_GROUP *group);
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void EC_GROUP_clear_free(EC_GROUP *group);
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EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
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int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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ECPARAMETERS *EC_GROUP_get_ecparameters(const EC_GROUP *group, ECPARAMETERS *params)
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ECPKPARAMETERS *EC_GROUP_get_ecpkparameters(const EC_GROUP *group, ECPKPARAMETERS *params)
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size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
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=head1 DESCRIPTION
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Within the library there are two forms of elliptic curve that are of interest. The first form is those defined over the
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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
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elliptic curve equation as follows:
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y^2 mod p = x^3 +ax + b mod p
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The second form is those defined over a binary field F2^m where the elements of the field are integers of length at
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most m bits. For this form the elliptic curve equation is modified to:
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y^2 + xy = x^3 + ax^2 + b (where b != 0)
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Operations in a binary field are performed relative to an B<irreducible polynomial>. All such curves with OpenSSL
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use a trinomial or a pentanomial for this parameter.
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A new curve can be constructed by calling EC_GROUP_new, using the implementation provided by B<meth> (see
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L<EC_GFp_simple_method(3)>). It is then necessary to call either EC_GROUP_set_curve_GFp or
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EC_GROUP_set_curve_GF2m as appropriate to create a curve defined over Fp or over F2^m respectively.
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EC_GROUP_new_from_ecparameters() will create a group from the
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specified B<params> and
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EC_GROUP_new_from_ecpkparameters() will create a group from the specific PK B<params>.
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EC_GROUP_set_curve_GFp sets the curve parameters B<p>, B<a> and B<b> for a curve over Fp stored in B<group>.
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EC_group_get_curve_GFp obtains the previously set curve parameters.
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EC_GROUP_set_curve_GF2m sets the equivalent curve parameters for a curve over F2^m. In this case B<p> represents
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the irreducible polynomial - each bit represents a term in the polynomial. Therefore there will either be three
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or five bits set dependent on whether the polynomial is a trinomial or a pentanomial.
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EC_group_get_curve_GF2m obtains the previously set curve parameters.
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The functions EC_GROUP_new_curve_GFp and EC_GROUP_new_curve_GF2m are shortcuts for calling EC_GROUP_new and the
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appropriate EC_group_set_curve function. An appropriate default implementation method will be used.
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Whilst the library can be used to create any curve using the functions described above, there are also a number of
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predefined curves that are available. In order to obtain a list of all of the predefined curves, call the function
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EC_get_builtin_curves. The parameter B<r> should be an array of EC_builtin_curve structures of size B<nitems>. The function
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will populate the B<r> array with information about the builtin curves. If B<nitems> is less than the total number of
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curves available, then the first B<nitems> curves will be returned. Otherwise the total number of curves will be
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provided. The return value is the total number of curves available (whether that number has been populated in B<r> or
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not). Passing a NULL B<r>, or setting B<nitems> to 0 will do nothing other than return the total number of curves available.
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The EC_builtin_curve structure is defined as follows:
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typedef struct {
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int nid;
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const char *comment;
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} EC_builtin_curve;
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Each EC_builtin_curve item has a unique integer id (B<nid>), and a human readable comment string describing the curve.
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In order to construct a builtin curve use the function EC_GROUP_new_by_curve_name and provide the B<nid> of the curve to
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be constructed.
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EC_GROUP_free frees the memory associated with the EC_GROUP.
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If B<group> is NULL nothing is done.
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EC_GROUP_clear_free destroys any sensitive data held within the EC_GROUP and then frees its memory.
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If B<group> is NULL nothing is done.
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=head1 RETURN VALUES
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All EC_GROUP_new* functions return a pointer to the newly constructed group, or NULL on error.
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EC_get_builtin_curves returns the number of builtin curves that are available.
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EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, EC_GROUP_set_curve_GF2m, EC_GROUP_get_curve_GF2m return 1 on success or 0 on error.
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=head1 SEE ALSO
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L<crypto(3)>, L<ec(3)>, L<EC_GROUP_copy(3)>,
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L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>,
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L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)>
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=cut
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