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| 1 | =pod | ||
| 2 | |||
| 3 | =head1 NAME | ||
| 4 | |||
| 5 | 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 - Functions for creating and destroying B<EC_GROUP> objects. | ||
| 6 | |||
| 7 | =head1 SYNOPSIS | ||
| 8 | |||
| 9 | #include <openssl/ec.h> | ||
| 10 | #include <openssl/bn.h> | ||
| 11 | |||
| 12 | EC_GROUP *EC_GROUP_new(const EC_METHOD *meth); | ||
| 13 | void EC_GROUP_free(EC_GROUP *group); | ||
| 14 | void EC_GROUP_clear_free(EC_GROUP *group); | ||
| 15 | |||
| 16 | EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); | ||
| 17 | EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); | ||
| 18 | EC_GROUP *EC_GROUP_new_by_curve_name(int nid); | ||
| 19 | |||
| 20 | int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); | ||
| 21 | int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); | ||
| 22 | int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); | ||
| 23 | int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); | ||
| 24 | |||
| 25 | size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems); | ||
| 26 | |||
| 27 | =head1 DESCRIPTION | ||
| 28 | |||
| 29 | Within the library there are two forms of elliptic curve that are of interest. The first form is those defined over the | ||
| 30 | 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 | ||
| 31 | elliptic curve equation as follows: | ||
| 32 | |||
| 33 | y^2 mod p = x^3 +ax + b mod p | ||
| 34 | |||
| 35 | The second form is those defined over a binary field F2^m where the elements of the field are integers of length at | ||
| 36 | most m bits. For this form the elliptic curve equation is modified to: | ||
| 37 | |||
| 38 | y^2 + xy = x^3 + ax^2 + b (where b != 0) | ||
| 39 | |||
| 40 | Operations in a binary field are performed relative to an B<irreducible polynomial>. All such curves with OpenSSL | ||
| 41 | use a trinomial or a pentanomial for this parameter. | ||
| 42 | |||
| 43 | A new curve can be constructed by calling EC_GROUP_new, using the implementation provided by B<meth> (see | ||
| 44 | L<EC_GFp_simple_method(3)|EC_GFp_simple_method(3)>). It is then necessary to call either EC_GROUP_set_curve_GFp or | ||
| 45 | EC_GROUP_set_curve_GF2m as appropriate to create a curve defined over Fp or over F2^m respectively. | ||
| 46 | |||
| 47 | 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>. | ||
| 48 | EC_group_get_curve_GFp obtains the previously set curve parameters. | ||
| 49 | |||
| 50 | EC_GROUP_set_curve_GF2m sets the equivalent curve parameters for a curve over F2^m. In this case B<p> represents | ||
| 51 | the irreducible polybnomial - each bit represents a term in the polynomial. Therefore there will either be three | ||
| 52 | or five bits set dependant on whether the polynomial is a trinomial or a pentanomial. | ||
| 53 | EC_group_get_curve_GF2m obtains the previously set curve parameters. | ||
| 54 | |||
| 55 | The functions EC_GROUP_new_curve_GFp and EC_GROUP_new_curve_GF2m are shortcuts for calling EC_GROUP_new and the | ||
| 56 | appropriate EC_group_set_curve function. An appropriate default implementation method will be used. | ||
| 57 | |||
| 58 | Whilst the library can be used to create any curve using the functions described above, there are also a number of | ||
| 59 | predefined curves that are available. In order to obtain a list of all of the predefined curves, call the function | ||
| 60 | EC_get_builtin_curves. The parameter B<r> should be an array of EC_builtin_curve structures of size B<nitems>. The function | ||
| 61 | will populate the B<r> array with information about the builtin curves. If B<nitems> is less than the total number of | ||
| 62 | curves available, then the first B<nitems> curves will be returned. Otherwise the total number of curves will be | ||
| 63 | provided. The return value is the total number of curves available (whether that number has been populated in B<r> or | ||
| 64 | not). Passing a NULL B<r>, or setting B<nitems> to 0 will do nothing other than return the total number of curves available. | ||
| 65 | The EC_builtin_curve structure is defined as follows: | ||
| 66 | |||
| 67 | typedef struct { | ||
| 68 | int nid; | ||
| 69 | const char *comment; | ||
| 70 | } EC_builtin_curve; | ||
| 71 | |||
| 72 | Each EC_builtin_curve item has a unique integer id (B<nid>), and a human readable comment string describing the curve. | ||
| 73 | |||
| 74 | 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 | ||
| 75 | be constructed. | ||
| 76 | |||
| 77 | EC_GROUP_free frees the memory associated with the EC_GROUP. | ||
| 78 | |||
| 79 | EC_GROUP_clear_free destroys any sensitive data held within the EC_GROUP and then frees its memory. | ||
| 80 | |||
| 81 | =head1 RETURN VALUES | ||
| 82 | |||
| 83 | All EC_GROUP_new* functions return a pointer to the newly constructed group, or NULL on error. | ||
| 84 | |||
| 85 | EC_get_builtin_curves returns the number of builtin curves that are available. | ||
| 86 | |||
| 87 | 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. | ||
| 88 | |||
| 89 | =head1 SEE ALSO | ||
| 90 | |||
| 91 | L<crypto(3)|crypto(3)>, L<ec(3)|ec(3)>, L<EC_GROUP_copy(3)|EC_GROUP_copy(3)>, | ||
| 92 | L<EC_POINT_new(3)|EC_POINT_new(3)>, L<EC_POINT_add(3)|EC_POINT_add(3)>, L<EC_KEY_new(3)|EC_KEY_new(3)>, | ||
| 93 | L<EC_GFp_simple_method(3)|EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)|d2i_ECPKParameters(3)> | ||
| 94 | |||
| 95 | =cut | ||
