231 lines
9.0 KiB
Groff
231 lines
9.0 KiB
Groff
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.\" ========================================================================
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.\"
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.IX Title "EC_GROUP_new 3"
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.TH EC_GROUP_new 3 "2015-07-09" "1.0.2d" "OpenSSL"
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.\" For nroff, turn off justification. Always turn off hyphenation; it makes
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.\" way too many mistakes in technical documents.
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.if n .ad l
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.nh
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.SH "NAME"
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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 EC_GROUP objects.
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.SH "SYNOPSIS"
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.IX Header "SYNOPSIS"
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.Vb 2
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\& #include <openssl/ec.h>
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\& #include <openssl/bn.h>
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\&
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\& EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
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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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\&
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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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\&
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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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\&
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\& size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
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.Ve
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.SH "DESCRIPTION"
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.IX Header "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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.PP
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y^2 mod p = x^3 +ax + b mod p
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.PP
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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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.PP
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y^2 + xy = x^3 + ax^2 + b (where b != 0)
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.PP
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Operations in a binary field are performed relative to an \fBirreducible polynomial\fR. All such curves with OpenSSL
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use a trinomial or a pentanomial for this parameter.
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.PP
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A new curve can be constructed by calling EC_GROUP_new, using the implementation provided by \fBmeth\fR (see
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\&\fIEC_GFp_simple_method\fR\|(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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.PP
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EC_GROUP_set_curve_GFp sets the curve parameters \fBp\fR, \fBa\fR and \fBb\fR for a curve over Fp stored in \fBgroup\fR.
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EC_group_get_curve_GFp obtains the previously set curve parameters.
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.PP
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EC_GROUP_set_curve_GF2m sets the equivalent curve parameters for a curve over F2^m. In this case \fBp\fR represents
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the irreducible polybnomial \- each bit represents a term in the polynomial. Therefore there will either be three
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or five bits set dependant 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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.PP
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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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.PP
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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 \fBr\fR should be an array of EC_builtin_curve structures of size \fBnitems\fR. The function
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will populate the \fBr\fR array with information about the builtin curves. If \fBnitems\fR is less than the total number of
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curves available, then the first \fBnitems\fR 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 \fBr\fR or
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not). Passing a \s-1NULL \s0\fBr\fR, or setting \fBnitems\fR 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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.PP
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.Vb 4
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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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.Ve
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.PP
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Each EC_builtin_curve item has a unique integer id (\fBnid\fR), and a human readable comment string describing the curve.
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.PP
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In order to construct a builtin curve use the function EC_GROUP_new_by_curve_name and provide the \fBnid\fR of the curve to
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be constructed.
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.PP
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EC_GROUP_free frees the memory associated with the \s-1EC_GROUP.\s0
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.PP
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EC_GROUP_clear_free destroys any sensitive data held within the \s-1EC_GROUP\s0 and then frees its memory.
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.SH "RETURN VALUES"
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.IX Header "RETURN VALUES"
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All EC_GROUP_new* functions return a pointer to the newly constructed group, or \s-1NULL\s0 on error.
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.PP
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EC_get_builtin_curves returns the number of builtin curves that are available.
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.PP
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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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.SH "SEE ALSO"
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.IX Header "SEE ALSO"
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\&\fIcrypto\fR\|(3), \fIec\fR\|(3), \fIEC_GROUP_copy\fR\|(3),
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\&\fIEC_POINT_new\fR\|(3), \fIEC_POINT_add\fR\|(3), \fIEC_KEY_new\fR\|(3),
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\&\fIEC_GFp_simple_method\fR\|(3), \fId2i_ECPKParameters\fR\|(3)
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