--- /dev/null
+/* -*-c-*-
+ *
+ * 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