forked from cory/tildefriends
280 lines
11 KiB
Groff
280 lines
11 KiB
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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 "2020-04-21" "1.1.1g" "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_get_ecparameters, EC_GROUP_get_ecpkparameters, EC_GROUP_new, EC_GROUP_new_from_ecparameters, EC_GROUP_new_from_ecpkparameters, 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, EC_GROUP_get_curve, 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 1
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\& #include <openssl/ec.h>
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\&
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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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\&
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\& EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a,
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\& const BIGNUM *b, BN_CTX *ctx);
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\& EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a,
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\& 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(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
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\& const BIGNUM *b, BN_CTX *ctx);
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\& int EC_GROUP_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b,
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\& BN_CTX *ctx);
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\& int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p,
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\& 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,
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\& BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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\& int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p,
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\& 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,
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\& BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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\&
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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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\&
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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.
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The first form is those defined over the prime field Fp. The elements of Fp are
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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
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the field are integers of length at most m bits. For this form the elliptic
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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
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polynomial\fR. All such curves with OpenSSL use a trinomial or a pentanomial for
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this parameter.
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.PP
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A new curve can be constructed by calling \fBEC_GROUP_new()\fR, using the
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implementation provided by \fBmeth\fR (see \fBEC_GFp_simple_method\fR\|(3)). It is then
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necessary to call \fBEC_GROUP_set_curve()\fR to set the curve parameters.
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\&\fBEC_GROUP_new_from_ecparameters()\fR will create a group from the specified
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\&\fBparams\fR and \fBEC_GROUP_new_from_ecpkparameters()\fR will create a group from the
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specific \s-1PK\s0 \fBparams\fR.
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.PP
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\&\fBEC_GROUP_set_curve()\fR sets the curve parameters \fBp\fR, \fBa\fR and \fBb\fR. For a curve
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over Fp \fBp\fR is the prime for the field. For a curve over F2^m \fBp\fR represents
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the irreducible polynomial \- each bit represents a term in the polynomial.
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Therefore there will either be three or five bits set dependent on whether the
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polynomial is a trinomial or a pentanomial.
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In either case, \fBa\fR and \fBb\fR represents the coefficients a and b from the
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relevant equation introduced above.
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.PP
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\&\fBEC_group_get_curve()\fR obtains the previously set curve parameters.
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.PP
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\&\fBEC_GROUP_set_curve_GFp()\fR and \fBEC_GROUP_set_curve_GF2m()\fR are synonyms for
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\&\fBEC_GROUP_set_curve()\fR. They are defined for backwards compatibility only and
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should not be used.
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.PP
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\&\fBEC_GROUP_get_curve_GFp()\fR and \fBEC_GROUP_get_curve_GF2m()\fR are synonyms for
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\&\fBEC_GROUP_get_curve()\fR. They are defined for backwards compatibility only and
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should not be used.
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.PP
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The functions \fBEC_GROUP_new_curve_GFp()\fR and \fBEC_GROUP_new_curve_GF2m()\fR are
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shortcuts for calling \fBEC_GROUP_new()\fR and then the \fBEC_GROUP_set_curve()\fR function.
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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
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above, there are also a number of predefined curves that are available. In order
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to obtain a list of all of the predefined curves, call the function
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\&\fBEC_get_builtin_curves()\fR. The parameter \fBr\fR should be an array of
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EC_builtin_curve structures of size \fBnitems\fR. The function will populate the
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\&\fBr\fR array with information about the builtin curves. If \fBnitems\fR is less than
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the total number of curves available, then the first \fBnitems\fR curves will be
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returned. Otherwise the total number of curves will be provided. The return
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value is the total number of curves available (whether that number has been
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populated in \fBr\fR or not). Passing a \s-1NULL\s0 \fBr\fR, or setting \fBnitems\fR to 0 will
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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
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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
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\&\fBEC_GROUP_new_by_curve_name()\fR and provide the \fBnid\fR of the curve to
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be constructed.
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.PP
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\&\fBEC_GROUP_free()\fR frees the memory associated with the \s-1EC_GROUP.\s0
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If \fBgroup\fR is \s-1NULL\s0 nothing is done.
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.PP
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\&\fBEC_GROUP_clear_free()\fR destroys any sensitive data held within the \s-1EC_GROUP\s0 and
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then frees its memory. If \fBgroup\fR is \s-1NULL\s0 nothing is done.
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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
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\&\s-1NULL\s0 on error.
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.PP
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\&\fBEC_get_builtin_curves()\fR returns the number of builtin curves that are available.
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.PP
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\&\fBEC_GROUP_set_curve_GFp()\fR, \fBEC_GROUP_get_curve_GFp()\fR, \fBEC_GROUP_set_curve_GF2m()\fR,
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\&\fBEC_GROUP_get_curve_GF2m()\fR 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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\&\fBcrypto\fR\|(7), \fBEC_GROUP_copy\fR\|(3),
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\&\fBEC_POINT_new\fR\|(3), \fBEC_POINT_add\fR\|(3), \fBEC_KEY_new\fR\|(3),
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\&\fBEC_GFp_simple_method\fR\|(3), \fBd2i_ECPKParameters\fR\|(3)
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.SH "COPYRIGHT"
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.IX Header "COPYRIGHT"
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Copyright 2013\-2019 The OpenSSL Project Authors. All Rights Reserved.
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.PP
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Licensed under the OpenSSL license (the \*(L"License\*(R"). You may not use
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this file except in compliance with the License. You can obtain a copy
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in the file \s-1LICENSE\s0 in the source distribution or at
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<https://www.openssl.org/source/license.html>.
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