X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/41a324a748544b0fb9b0acfc65b1a39b7611550c..6a7dce9165a4a707382e49877334353618fcad9a:/ec.h diff --git a/ec.h b/ec.h index 12ff823..ac0b8fc 100644 --- a/ec.h +++ b/ec.h @@ -1,13 +1,13 @@ /* -*-c-*- * - * $Id: ec.h,v 1.2 2001/05/07 17:29:44 mdw Exp $ + * $Id$ * * Elliptic curve definitions * * (c) 2001 Straylight/Edgeware */ -/*----- Licensing notice --------------------------------------------------* +/*----- Licensing notice --------------------------------------------------* * * This file is part of Catacomb. * @@ -15,30 +15,18 @@ * it under the terms of the GNU Library General Public License as * published by the Free Software Foundation; either version 2 of the * License, or (at your option) any later version. - * + * * Catacomb is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU Library General Public License for more details. - * + * * You should have received a copy of the GNU Library General Public * License along with Catacomb; if not, write to the Free * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, * MA 02111-1307, USA. */ -/*----- Revision history --------------------------------------------------* - * - * $Log: ec.h,v $ - * Revision 1.2 2001/05/07 17:29:44 mdw - * Treat projective coordinates as an internal representation. Various - * minor interface changes. - * - * Revision 1.1 2001/04/29 18:12:33 mdw - * Prototype version. - * - */ - #ifndef CATACOMB_EC_H #define CATACOMB_EC_H @@ -48,38 +36,90 @@ /*----- Header files ------------------------------------------------------*/ -#include "field.h" -#include "mp.h" +#ifndef CATACOMB_FIELD_H +# include "field.h" +#endif + +#ifndef CATACOMB_MP_H +# include "mp.h" +#endif + +#ifndef CATACOMB_QDPARSE_H +# include "qdparse.h" +#endif /*----- Data structures ---------------------------------------------------*/ +/* --- An elliptic curve representation --- */ + typedef struct ec_curve { const struct ec_ops *ops; /* Curve operations */ field *f; /* Underlying field structure */ + mp *a, *b; /* Standard params (internal form) */ } ec_curve; +/* --- An elliptic curve point --- */ + typedef struct ec { mp *x, *y; /* Point coordinates */ mp *z; /* Common denominator (or null) */ } ec; +/* --- A factor for simultaneous multiplication --- */ + +typedef struct ec_mulfactor { + ec base; /* The point */ + mp *exp; /* The exponent */ +} ec_mulfactor; + +/* --- Elliptic curve operations --- * + * + * All operations (apart from @destroy@ and @in@) are guaranteed to be + * performed on internal representations of points. + * + * (Historical note. We used to guarantee that the second to @add@ and @mul@ + * was the output of @in@ or @fix@, but this canonification turned out to + * make the precomputation in @ec_exp@ too slow. Projective implementations + * must therefore cope with a pair of arbitrary points.) + */ + typedef struct ec_ops { + const char *name; void (*destroy)(ec_curve */*c*/); + int (*samep)(ec_curve */*c*/, ec_curve */*d*/); ec *(*in)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); ec *(*out)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); + ec *(*fix)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); ec *(*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/); + ec *(*neg)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); ec *(*add)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); + ec *(*sub)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); ec *(*dbl)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); + int (*check)(ec_curve */*c*/, const ec */*p*/); } ec_ops; -#define EC_DESTROY(c) (c)->ops->destroy((c)) +#define EC_NAME(c) (c)->ops->name +#define EC_SAMEP(c, d) (c)->ops->samep((c), (d)) #define EC_IN(c, d, p) (c)->ops->in((c), (d), (p)) -#define EC_OUT(c, d, p) (c)->ops->in((c), (d), (p)) +#define EC_OUT(c, d, p) (c)->ops->out((c), (d), (p)) +#define EC_FIX(c, d, p) (c)->ops->fix((c), (d), (p)) #define EC_FIND(c, d, x) (c)->ops->find((c), (d), (x)) +#define EC_NEG(c, d, x) (c)->ops->neg((c), (d), (x)) #define EC_ADD(c, d, p, q) (c)->ops->add((c), (d), (p), (q)) +#define EC_SUB(c, d, p, q) (c)->ops->sub((c), (d), (p), (q)) #define EC_DBL(c, d, p) (c)->ops->dbl((c), (d), (p)) +#define EC_CHECK(c, p) (c)->ops->check((c), (p)) + +/* --- Elliptic curve parameters --- */ + +typedef struct ec_info { + ec_curve *c; /* The actual curve */ + ec g; /* The common point */ + mp *r; /* Order of %$g$% */ + mp *h; /* Cofactor %$h = \#E/r$% */ +} ec_info; /*----- Simple memory management things -----------------------------------*/ @@ -175,57 +215,87 @@ extern ec *ec_setinf(ec */*p*/); if (EC_ATINF(p)) \ _d->x = _d->y = _d->z = MP_NEW; \ else { \ - _d->x = _p->x; \ - _d->y = _p->y; \ - _d->z = _p->z; \ + _d->x = MP_COPY(_p->x); \ + _d->y = MP_COPY(_p->y); \ + _d->z = _p->z ? MP_COPY(_p->z) : MP_NEW; \ } \ } \ } while (0) extern ec *ec_copy(ec */*d*/, const ec */*p*/); +/* --- @ec_eq@ --- * + * + * Arguments: @const ec *p, *q@ = two points + * + * Returns: Nonzero if the points are equal. Compares external-format + * points. + */ + +#define EC_EQ(p, q) \ + ((EC_ATINF(p) && EC_ATINF(q)) || \ + (!EC_ATINF(p) && !EC_ATINF(q) && \ + MP_EQ((p)->x, (q)->x) && \ + MP_EQ((p)->y, (q)->y))) + +extern int ec_eq(const ec *p, const ec *q); + /*----- Interesting arithmetic --------------------------------------------*/ -/* --- @ec_denorm@ --- * +/* --- @ec_samep@ --- * + * + * Arguments: @ec_curve *c, *d@ = two elliptic curves + * + * Returns: Nonzero if the curves are identical (not just isomorphic). + * + * Use: Checks for sameness of curves. This function does the full + * check, not just the curve-type-specific check done by the + * @sampep@ field operation. + */ + +extern int ec_samep(ec_curve */*c*/, ec_curve */*d*/); + +/* --- @ec_find@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point - * @const ec *p@ = pointer to the source point + * @mp *x@ = a possible x-coordinate * - * Returns: --- + * Returns: The destination if OK, or null if no point was found. * - * Use: Denormalizes the given point, converting to internal - * representations and setting the denominator to 1. + * Use: Finds a point on an elliptic curve with a given + * x-coordinate. If there is no point with the given + * %$x$%-coordinate, a null pointer is returned and the + * destination is left invalid. */ -extern void ec_denorm(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); -/* --- @ec_norm@ --- * +/* --- @ec_rand@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point - * @const ec *p@ = pointer to the source point + * @grand *r@ = random number source * - * Returns: --- + * Returns: The destination @d@. * - * Use: Normalizes the given point, by dividing through by the - * denominator and returning to external representation. + * Use: Finds a random point on the given curve. */ -extern void ec_norm(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_rand(ec_curve */*c*/, ec */*d*/, grand */*r*/); -/* --- @ec_find@ --- * +/* --- @ec_neg@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point - * @mp *x@ = a possible x-coordinate + * @const ec *p@ = pointer to the operand point * - * Returns: Zero if OK, nonzero if there isn't a point there. + * Returns: The destination point. * - * Use: Finds a point on an elliptic curve with a given x-coordinate. + * Use: Computes the negation of the given point. */ -extern void ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); +extern ec *ec_neg(ec_curve */*c*/, ec */*d*/, const ec */*p*/); /* --- @ec_add@ --- * * @@ -241,6 +311,20 @@ extern void ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); extern ec *ec_add(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); +/* --- @ec_sub@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @ec *d@ = pointer to the destination point + * @const ec *p, *q@ = pointers to the operand points + * + * Returns: The destination @d@. + * + * Use: Subtracts one point from another on an elliptic curve. + */ + +extern ec *ec_sub(ec_curve */*c*/, ec */*d*/, + const ec */*p*/, const ec */*q*/); + /* --- @ec_dbl@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve @@ -254,7 +338,19 @@ extern ec *ec_add(ec_curve */*c*/, ec */*d*/, extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); -/* --- @ec_mul@ --- * +/* --- @ec_check@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @const ec *p@ = pointer to the point + * + * Returns: Zero if OK, nonzero if this is an invalid point. + * + * Use: Checks that a point is actually on an elliptic curve. + */ + +extern int ec_check(ec_curve */*c*/, const ec */*p*/); + +/* --- @ec_mul@, @ec_imul@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point @@ -263,14 +359,46 @@ extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); * * Returns: The destination @d@. * - * Use: Multiplies a point by a scalar, returning %$n p$%. + * Use: Multiplies a point by a scalar, returning %$n p$%. The + * @imul@ variant uses internal representations for argument + * and result. */ extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); +extern ec *ec_imul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); + +/* --- @ec_mmul@, @ec_immul@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @ec *d@ = pointer to the destination point + * @const ec_mulfactor *f@ = pointer to vector of factors + * @size_t n@ = number of factors + * + * Returns: The destination @d@. + * + * Use: Does simultaneous point multiplication. The @immul@ variant + * uses internal representations for arguments and result. + */ + +extern ec *ec_mmul(ec_curve */*c*/, ec */*d*/, + const ec_mulfactor */*f*/, size_t /*n*/); +extern ec *ec_immul(ec_curve */*c*/, ec */*d*/, + const ec_mulfactor */*f*/, size_t /*n*/); /*----- Standard curve operations -----------------------------------------*/ -/* --- @ec_idin@, @ec_idout@ --- * +/* --- @ec_stdsamep@ --- * + * + * Arguments: @ec_curve *c, *d@ = two elliptic curves + * + * Returns: Nonzero if the curves are identical (not just isomorphic). + * + * Use: Simple sameness check on @a@ and @b@ curve members. + */ + +extern int ec_stdsamep(ec_curve */*c*/, ec_curve */*d*/); + +/* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination @@ -285,8 +413,9 @@ extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); extern ec *ec_idin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); extern ec *ec_idout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_idfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/); -/* --- @ec_projin@, @ec_projout@ --- * +/* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination @@ -300,34 +429,185 @@ extern ec *ec_idout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); extern ec *ec_projin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); extern ec *ec_projout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_projfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/); + +/* --- @ec_stdsub@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @ec *d@ = pointer to the destination + * @const ec *p, *q@ = the operand points + * + * Returns: The destination @d@. + * + * Use: Standard point subtraction operation, in terms of negation + * and addition. This isn't as efficient as a ready-made + * subtraction operator. + */ + +extern ec *ec_stdsub(ec_curve */*c*/, ec */*d*/, + const ec */*p*/, const ec */*q*/); /*----- Creating curves ---------------------------------------------------*/ -/* --- @ec_prime@ --- * +/* --- @ec_destroycurve@ --- * * - * Arguments: @field *f@ = the underyling field for this elliptic curve + * Arguments: @ec_curve *c@ = pointer to an ellptic curve + * + * Returns: --- + * + * Use: Destroys a description of an elliptic curve. + */ + +extern void ec_destroycurve(ec_curve */*c*/); + +/* --- @ec_prime@, @ec_primeproj@ --- * + * + * Arguments: @field *f@ = the underlying field for this elliptic curve * @mp *a, *b@ = the coefficients for this curve * - * Returns: A pointer to the curve. + * Returns: A pointer to the curve, or null. * * Use: Creates a curve structure for an elliptic curve defined over - * a prime field. + * a prime field. The @primeproj@ variant uses projective + * coordinates, which can be a win. */ extern ec_curve *ec_prime(field */*f*/, mp */*a*/, mp */*b*/); +extern ec_curve *ec_primeproj(field */*f*/, mp */*a*/, mp */*b*/); -/* --- @ec_bin@ --- * +/* --- @ec_bin@, @ec_binproj@ --- * * * Arguments: @field *f@ = the underlying field for this elliptic curve * @mp *a, *b@ = the coefficients for this curve * - * Returns: A pointer to the curve. + * Returns: A pointer to the curve, or null. * - * Use: Creates a curve structure for a non-supersingular elliptic - * curve defined over a binary field. + * Use: Creates a curve structure for an elliptic curve defined over + * a binary field. The @binproj@ variant uses projective + * coordinates, which can be a win. */ extern ec_curve *ec_bin(field */*f*/, mp */*a*/, mp */*b*/); +extern ec_curve *ec_binproj(field */*f*/, mp */*a*/, mp */*b*/); + +/*----- Curve parameter sets ----------------------------------------------*/ + +/* --- @ec_curveparse@ --- * + * + * Arguments: @qd_parse *qd@ = parser context + * + * Returns: Elliptic curve pointer if OK, or null. + * + * Use: Parses an elliptic curve description, which has the form + * + * * a field description + * * an optional `;' + * * `prime', `primeproj', `bin', or `binproj' + * * an optional `:' + * * the %$a$% parameter + * * an optional `,' + * * the %$b$% parameter + */ + +extern ec_curve *ec_curveparse(qd_parse */*qd*/); + +/* --- @ec_ptparse@ --- * + * + * Arguments: @qd_parse *qd@ = parser context + * @ec *p@ = where to put the point + * + * Returns: The point address, or null. + * + * Use: Parses an elliptic curve point. This has the form + * + * * %$x$%-coordinate + * * optional `,' + * * %$y$%-coordinate + */ + +extern ec *ec_ptparse(qd_parse */*qd*/, ec */*p*/); + +/* --- @ec_infoparse@ --- * + * + * Arguments: @qd_parse *qd@ = parser context + * @ec_info *ei@ = curve information block, currently + * uninitialized + * + * Returns: Zero on success, nonzero on failure. + * + * Use: Parses an elliptic curve information string, and stores the + * information in @ei@. This has the form + * + * * elliptic curve description + * * optional `;' + * * common point + * * optional `:' + * * group order + * * optional `*' + * * cofactor + */ + +extern int ec_infoparse(qd_parse */*qd*/, ec_info */*ei*/); + +/* --- @ec_infofromdata@ --- * + * + * Arguments: @ec_info *ei@ = where to write the information + * @ecdata *ed@ = raw data + * + * Returns: --- + * + * Use: Loads elliptic curve information about one of the standard + * curves. + */ + +struct ecdata; +extern void ec_infofromdata(ec_info */*ei*/, struct ecdata */*ed*/); + +/* --- @ec_getinfo@ --- * + * + * Arguments: @ec_info *ei@ = where to write the information + * @const char *p@ = string describing a curve + * + * Returns: Null on success, or a pointer to an error message. + * + * Use: Parses out information about a curve. The string is either a + * standard curve name, or a curve info string. + */ + +extern const char *ec_getinfo(ec_info */*ei*/, const char */*p*/); + +/* --- @ec_sameinfop@ --- * + * + * Arguments: @ec_info *ei, *ej@ = two elliptic curve parameter sets + * + * Returns: Nonzero if the curves are identical (not just isomorphic). + * + * Use: Checks for sameness of curve parameters. + */ + +extern int ec_sameinfop(ec_info */*ei*/, ec_info */*ej*/); + +/* --- @ec_freeinfo@ --- * + * + * Arguments: @ec_info *ei@ = elliptic curve information block to free + * + * Returns: --- + * + * Use: Frees the information block. + */ + +extern void ec_freeinfo(ec_info */*ei*/); + +/* --- @ec_checkinfo@ --- * + * + * Arguments: @const ec_info *ei@ = elliptic curve information block + * + * Returns: Null if OK, or pointer to error message. + * + * Use: Checks an elliptic curve according to the rules in SEC1. + */ + +extern const char *ec_checkinfo(const ec_info */*ei*/, grand */*gr*/); /*----- That's all, folks -------------------------------------------------*/