+++ /dev/null
-/* -*-c-*-
- *
- * $Id$
- *
- * Elliptic curve definitions
- *
- * (c) 2001 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * 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.
- */
-
-#ifndef CATACOMB_EC_H
-#define CATACOMB_EC_H
-
-#ifdef __cplusplus
- extern "C" {
-#endif
-
-/*----- Header files ------------------------------------------------------*/
-
-#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_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->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 -----------------------------------*/
-
-/* --- @ec_create@ --- *
- *
- * Arguments: @ec *p@ = pointer to an elliptic-curve point
- *
- * Returns: The argument @p@.
- *
- * Use: Initializes a new point. The initial value is the additive
- * identity (which is universal for all curves).
- */
-
-#define EC_INIT { MP_NEW, MP_NEW, MP_NEW }
-
-#define EC_CREATE(p) do { \
- ec *_p = (p); \
- _p->x = _p->y = _p->z = MP_NEW; \
-} while (0)
-
-extern ec *ec_create(ec */*p*/);
-
-/* --- @ec_destroy@ --- *
- *
- * Arguments: @ec *p@ = pointer to an elliptic-curve point
- *
- * Returns: ---
- *
- * Use: Destroys a point, making it invalid.
- */
-
-#define EC_DESTROY(p) do { \
- ec *_p = (p); \
- if (!EC_ATINF(_p)) { \
- MP_DROP(_p->x); \
- MP_DROP(_p->y); \
- if (_p->z) MP_DROP(_p->z); \
- } \
-} while (0)
-
-extern void ec_destroy(ec */*p*/);
-
-/* --- @ec_atinf@ --- *
- *
- * Arguments: @const ec *p@ = pointer to a point
- *
- * Returns: Nonzero if %$p = O$% is the point at infinity, zero
- * otherwise.
- */
-
-#define EC_ATINF(p) ((p)->x == MP_NEW || (p)->x == MP_NEWSEC)
-
-extern int ec_atinf(const ec */*p*/);
-
-/* --- @ec_setinf@ --- *
- *
- * Arguments: @ec *p@ = pointer to a point
- *
- * Returns: The argument @p@.
- *
- * Use: Sets the given point to be the point %$O$% at infinity.
- */
-
-#define EC_SETINF(p) do { \
- ec *_p = (p); \
- if (!EC_ATINF(_p)) { \
- MP_DROP(_p->x); \
- MP_DROP(_p->y); \
- if (_p->z) MP_DROP(_p->z); \
- _p->x = _p->y = _p->z = MP_NEW; \
- _p->y = MP_NEW; \
- _p->z = MP_NEW; \
- } \
-} while (0)
-
-extern ec *ec_setinf(ec */*p*/);
-
-/* --- @ec_copy@ --- *
- *
- * Arguments: @ec *d@ = pointer to destination point
- * @const ec *p@ = pointer to source point
- *
- * Returns: The destination @d@.
- *
- * Use: Creates a copy of an elliptic curve point.
- */
-
-#define EC_COPY(d, p) do { \
- ec *_d = (d); \
- const ec *_p = (p); \
- if (d != p) { \
- EC_DESTROY(d); \
- if (EC_ATINF(p)) \
- _d->x = _d->y = _d->z = MP_NEW; \
- else { \
- _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_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
- * @mp *x@ = a possible x-coordinate
- *
- * Returns: The destination if OK, or null if no point was found.
- *
- * 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 ec *ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/);
-
-/* --- @ec_rand@ --- *
- *
- * Arguments: @ec_curve *c@ = pointer to an elliptic curve
- * @ec *d@ = pointer to the destination point
- * @grand *r@ = random number source
- *
- * Returns: The destination @d@.
- *
- * Use: Finds a random point on the given curve.
- */
-
-extern ec *ec_rand(ec_curve */*c*/, ec */*d*/, grand */*r*/);
-
-/* --- @ec_neg@ --- *
- *
- * Arguments: @ec_curve *c@ = pointer to an elliptic curve
- * @ec *d@ = pointer to the destination point
- * @const ec *p@ = pointer to the operand point
- *
- * Returns: The destination point.
- *
- * Use: Computes the negation of the given point.
- */
-
-extern ec *ec_neg(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
-
-/* --- @ec_add@ --- *
- *
- * 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: Adds two points on an elliptic curve.
- */
-
-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
- * @ec *d@ = pointer to the destination point
- * @const ec *p@ = pointer to the operand point
- *
- * Returns: The destination @d@.
- *
- * Use: Doubles a point on an elliptic curve.
- */
-
-extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
-
-/* --- @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
- * @const ec *p@ = pointer to the generator point
- * @mp *n@ = integer multiplier
- *
- * Returns: The destination @d@.
- *
- * 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_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
- * @const ec *p@ = pointer to a source point
- *
- * Returns: The destination @d@.
- *
- * Use: An identity operation if your curve has no internal
- * representation. (The field internal representation is still
- * used.)
- */
-
-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_projfix@ --- *
- *
- * Arguments: @ec_curve *c@ = pointer to an elliptic curve
- * @ec *d@ = pointer to the destination
- * @const ec *p@ = pointer to a source point
- *
- * Returns: The destination @d@.
- *
- * Use: Conversion functions if your curve operations use a
- * projective representation.
- */
-
-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_destroycurve@ --- *
- *
- * 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, or null.
- *
- * Use: Creates a curve structure for an elliptic curve defined over
- * 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_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, or null.
- *
- * 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 -------------------------------------------------*/
-
-#ifdef __cplusplus
- }
-#endif
-
-#endif
projects / u / mdw / catacomb / blobdiff