/* -*-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.
*
* 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
/*----- 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 -----------------------------------*/
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@ --- *
*
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
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
*
* 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
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
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 -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff