X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ba6e6b64033b1f9de49feccb5c9cd438354481f7..0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a:/math/ec.c

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+/* -*-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.
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include "ec.h"
+
+/*----- Trivial wrappers --------------------------------------------------*/
+
+/* --- @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.
+ */
+
+int ec_samep(ec_curve *c, ec_curve *d)
+{
+  return (c == d || (field_samep(c->f, d->f) &&
+		     c->ops == d->ops && EC_SAMEP(c, d)));
+}
+
+/* --- @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).
+ */
+
+ec *ec_create(ec *p) { EC_CREATE(p); return (p); }
+
+/* --- @ec_destroy@ --- *
+ *
+ * Arguments:	@ec *p@ = pointer to an elliptic-curve point
+ *
+ * Returns:	---
+ *
+ * Use:		Destroys a point, making it invalid.
+ */
+
+void ec_destroy(ec *p) { EC_DESTROY(p); }
+
+/* --- @ec_atinf@ --- *
+ *
+ * Arguments:	@const ec *p@ = pointer to a point
+ *
+ * Returns:	Nonzero if %$p = O$% is the point at infinity, zero
+ *		otherwise.
+ */
+
+int ec_atinf(const ec *p) { return (EC_ATINF(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.
+ */
+
+ec *ec_setinf(ec *p) { EC_SETINF(p); return (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.
+ */
+
+ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); }
+
+/* --- @ec_eq@ --- *
+ *
+ * Arguments:	@const ec *p, *q@ = two points
+ *
+ * Returns:	Nonzero if the points are equal.  Compares external-format
+ *		points.
+ */
+
+int ec_eq(const ec *p, const ec *q) { return (EC_EQ(p, q)); }
+
+/*----- 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.
+ */
+
+int ec_stdsamep(ec_curve *c, ec_curve *d)
+  { return (MP_EQ(c->a, d->a) && MP_EQ(c->b, d->b)); }
+
+/* --- @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.)
+ */
+
+ec *ec_idin(ec_curve *c, ec *d, const ec *p)
+{
+  if (EC_ATINF(p))
+    EC_SETINF(d);
+  else {
+    field *f = c->f;
+    d->x = F_IN(f, d->x, p->x);
+    d->y = F_IN(f, d->y, p->y);
+    mp_drop(d->z); d->z = 0;
+  }
+  return (d);
+}
+
+ec *ec_idout(ec_curve *c, ec *d, const ec *p)
+{
+  if (EC_ATINF(p))
+    EC_SETINF(d);
+  else {
+    field *f = c->f;
+    d->x = F_OUT(f, d->x, p->x);
+    d->y = F_OUT(f, d->y, p->y);
+    mp_drop(d->z); d->z = 0;
+  }
+  return (d);
+}
+
+ec *ec_idfix(ec_curve *c, ec *d, const ec *p)
+  { EC_COPY(d, p); return (d); }
+
+/* --- @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.
+ */
+
+ec *ec_projin(ec_curve *c, ec *d, const ec *p)
+{
+  if (EC_ATINF(p))
+    EC_SETINF(d);
+  else {
+    field *f = c->f;
+    d->x = F_IN(f, d->x, p->x);
+    d->y = F_IN(f, d->y, p->y);
+    mp_drop(d->z); d->z = MP_COPY(f->one);
+  }
+  return (d);
+}
+
+ec *ec_projout(ec_curve *c, ec *d, const ec *p)
+{
+  if (EC_ATINF(p))
+    EC_SETINF(d);
+  else {
+    mp *x, *y, *z, *zz;
+    field *f = c->f;
+    if (p->z == f->one) {
+      d->x = F_OUT(f, d->x, p->x);
+      d->y = F_OUT(f, d->y, p->y);
+    } else {
+      z = F_INV(f, MP_NEW, p->z);
+      zz = F_SQR(f, MP_NEW, z);
+      z = F_MUL(f, z, zz, z);
+      x = F_MUL(f, d->x, p->x, zz);
+      y = F_MUL(f, d->y, p->y, z);
+      mp_drop(z);
+      mp_drop(zz);
+      d->x = F_OUT(f, x, x);
+      d->y = F_OUT(f, y, y);
+    }
+    mp_drop(d->z);
+    d->z = 0;
+  }
+  return (d);
+}
+
+ec *ec_projfix(ec_curve *c, ec *d, const ec *p)
+{
+  if (EC_ATINF(p))
+    EC_SETINF(d);
+  else if (p->z == c->f->one)
+    EC_COPY(d, p);
+  else {
+    mp *z, *zz;
+    field *f = c->f;
+    z = F_INV(f, MP_NEW, p->z);
+    zz = F_SQR(f, MP_NEW, z);
+    z = F_MUL(f, z, zz, z);
+    d->x = F_MUL(f, d->x, p->x, zz);
+    d->y = F_MUL(f, d->y, p->y, z);
+    mp_drop(z);
+    mp_drop(zz);
+    mp_drop(d->z);
+    d->z = MP_COPY(f->one);
+  }
+  return (d);
+}
+
+/* --- @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.
+ */
+
+ec *ec_stdsub(ec_curve *c, ec *d, const ec *p, const ec *q)
+{
+  ec t = EC_INIT;
+  EC_NEG(c, &t, q);
+  EC_FIX(c, &t, &t);
+  EC_ADD(c, d, p, &t);
+  EC_DESTROY(&t);
+  return (d);
+}
+
+/*----- Creating curves ---------------------------------------------------*/
+
+/* --- @ec_destroycurve@ --- *
+ *
+ * Arguments:	@ec_curve *c@ = pointer to an ellptic curve
+ *
+ * Returns:	---
+ *
+ * Use:		Destroys a description of an elliptic curve.
+ */
+
+void ec_destroycurve(ec_curve *c) { c->ops->destroy(c); }
+
+/*----- Real arithmetic ---------------------------------------------------*/
+
+/* --- @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:	Zero if OK, nonzero if there isn't a point there.
+ *
+ * Use:		Finds a point on an elliptic curve with a given x-coordinate.
+ */
+
+ec *ec_find(ec_curve *c, ec *d, mp *x)
+{
+  x = F_IN(c->f, MP_NEW, x);
+  if ((d = EC_FIND(c, d, x)) != 0)
+    EC_OUT(c, d, d);
+  MP_DROP(x);
+  return (d);
+}
+
+/* --- @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.
+ */
+
+ec *ec_neg(ec_curve *c, ec *d, const ec *p)
+  { EC_IN(c, d, p); EC_NEG(c, d, d); return (EC_OUT(c, d, d)); }
+
+/* --- @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:	---
+ *
+ * Use:		Adds two points on an elliptic curve.
+ */
+
+ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
+{
+  ec pp = EC_INIT, qq = EC_INIT;
+  EC_IN(c, &pp, p);
+  EC_IN(c, &qq, q);
+  EC_ADD(c, d, &pp, &qq);
+  EC_OUT(c, d, d);
+  EC_DESTROY(&pp);
+  EC_DESTROY(&qq);
+  return (d);
+}
+
+/* --- @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.
+ */
+
+ec *ec_sub(ec_curve *c, ec *d, const ec *p, const ec *q)
+{
+  ec pp = EC_INIT, qq = EC_INIT;
+  EC_IN(c, &pp, p);
+  EC_IN(c, &qq, q);
+  EC_SUB(c, d, &pp, &qq);
+  EC_OUT(c, d, d);
+  EC_DESTROY(&pp);
+  EC_DESTROY(&qq);
+  return (d);
+}
+
+/* --- @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:	---
+ *
+ * Use:		Doubles a point on an elliptic curve.
+ */
+
+ec *ec_dbl(ec_curve *c, ec *d, const ec *p)
+  { EC_IN(c, d, p); EC_DBL(c, d, d); return (EC_OUT(c, d, d)); }
+
+/* --- @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.
+ */
+
+int ec_check(ec_curve *c, const ec *p)
+{
+  ec t = EC_INIT;
+  int rc;
+
+  if (EC_ATINF(p))
+    return (0);
+  EC_IN(c, &t, p);
+  rc = EC_CHECK(c, &t);
+  EC_DESTROY(&t);
+  return (rc);
+}
+
+/* --- @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.
+ */
+
+ec *ec_rand(ec_curve *c, ec *d, grand *r)
+{
+  mp *x = MP_NEW;
+  do x = F_RAND(c->f, x, r); while (!EC_FIND(c, d, x));
+  mp_drop(x);
+  if (grand_range(r, 2)) EC_NEG(c, d, d);
+  return (EC_OUT(c, d, d));
+}
+
+/*----- That's all, folks -------------------------------------------------*/