3 * $Id: ec.c,v 1.2 2001/05/07 17:29:44 mdw Exp $
5 * Elliptic curve definitions
7 * (c) 2001 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
30 /*----- Revision history --------------------------------------------------*
33 * Revision 1.2 2001/05/07 17:29:44 mdw
34 * Treat projective coordinates as an internal representation. Various
35 * minor interface changes.
37 * Revision 1.1 2001/04/29 18:12:33 mdw
42 /*----- Header files ------------------------------------------------------*/
46 /*----- Trivial wrappers --------------------------------------------------*/
48 /* --- @ec_create@ --- *
50 * Arguments: @ec *p@ = pointer to an elliptic-curve point
54 * Use: Initializes a new point. The initial value is the additive
55 * identity (which is universal for all curves).
58 void ec_create(ec *p) { EC_CREATE(p); }
60 /* --- @ec_destroy@ --- *
62 * Arguments: @ec *p@ = pointer to an elliptic-curve point
66 * Use: Destroys a point, making it invalid.
69 void ec_destroy(ec *p) { EC_DESTROY(p); }
71 /* --- @ec_atinf@ --- *
73 * Arguments: @const ec *p@ = pointer to a point
75 * Returns: Nonzero if %$p = O$% is the point at infinity, zero
79 int ec_atinf(const ec *p) { return (EC_ATINF(p)); }
81 /* --- @ec_setinf@ --- *
83 * Arguments: @ec *p@ = pointer to a point
87 * Use: Sets the given point to be the point %$O$% at infinity.
90 void ec_setinf(ec *p) { EC_SETINF(p); }
92 /* --- @ec_copy@ --- *
94 * Arguments: @ec *d@ = pointer to destination point
95 * @const ec *p@ = pointer to source point
99 * Use: Creates a copy of an elliptic curve point.
102 void ec_copy(ec *d, const ec *p) { EC_COPY(d, p); }
104 /*----- Standard curve operations -----------------------------------------*/
106 /* --- @ec_idin@, @ec_idout@ --- *
108 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
109 * @ec *d@ = pointer to the destination
110 * @const ec *p@ = pointer to a source point
112 * Returns: The destination @d@.
114 * Use: An identity operation if your curve has no internal
115 * representation. (The field internal representation is still
119 ec *ec_idin(ec_curve *c, ec *d, const ec *p)
125 d->x = F_IN(f, d->x, p->x);
126 d->y = F_IN(f, d->y, p->y);
127 mp_drop(d->z); d->z = 0;
132 ec *ec_idout(ec_curve *c, ec *d, const ec *p)
138 d->x = F_OUT(f, d->x, p->x);
139 d->y = F_OUT(f, d->y, p->y);
140 mp_drop(d->z); d->z = 0;
145 /* --- @ec_projin@, @ec_projout@ --- *
147 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
148 * @ec *d@ = pointer to the destination
149 * @const ec *p@ = pointer to a source point
151 * Returns: The destination @d@.
153 * Use: Conversion functions if your curve operations use a
154 * projective representation.
157 ec *ec_projin(ec_curve *c, ec *d, const ec *p)
163 d->x = F_IN(f, d->x, p->x);
164 d->y = F_IN(f, d->y, p->y);
165 mp_drop(d->z); d->z = MP_COPY(f->one);
170 ec *ec_projout(ec_curve *c, ec *d, const ec *p)
177 z = F_INV(f, MP_NEW, p->z);
178 x = F_MUL(f, d->x, p->x, z);
179 y = F_MUL(f, d->y, p->y, z);
182 d->x = F_OUT(f, x, x);
183 d->y = F_OUT(f, y, y);
189 /*----- Real arithmetic ---------------------------------------------------*/
191 /* --- @ec_find@ --- *
193 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
194 * @ec *d@ = pointer to the destination point
195 * @mp *x@ = a possible x-coordinate
197 * Returns: Zero if OK, nonzero if there isn't a point there.
199 * Use: Finds a point on an elliptic curve with a given x-coordinate.
202 ec *ec_find(ec_curve *c, ec *d, mp *x)
204 x = F_IN(c->f, MP_NEW, x);
205 if ((d = EC_FIND(c, d, x)) != 0)
211 /* --- @ec_add@ --- *
213 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
214 * @ec *d@ = pointer to the destination point
215 * @const ec *p, *q@ = pointers to the operand points
219 * Use: Adds two points on an elliptic curve.
222 ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
224 ec pp = EC_INIT, qq = EC_INIT;
227 EC_ADD(c, d, &pp, &qq);
234 /* --- @ec_dbl@ --- *
236 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
237 * @ec *d@ = pointer to the destination point
238 * @const ec *p@ = pointer to the operand point
242 * Use: Doubles a point on an elliptic curve.
245 ec *ec_dbl(ec_curve *c, ec *d, const ec *p)
249 return (EC_OUT(c, d, d));
252 /* --- @ec_mul@ --- *
254 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
255 * @ec *d@ = pointer to the destination point
256 * @const ec *p@ = pointer to the generator point
257 * @mp *n@ = integer multiplier
261 * Use: Multiplies a point by a scalar, returning %$n p$%.
264 ec *ec_mul(ec_curve *c, ec *d, const ec *p, mp *n)
277 while (!MP_RBIT(&sc))
281 if ((n->f & MP_BURN) && !(g.x->f & MP_BURN))
282 MP_DEST(g.x, 0, MP_BURN);
283 if ((n->f & MP_BURN) && !(g.y->f & MP_BURN))
284 MP_DEST(g.y, 0, MP_BURN);
311 return (EC_OUT(c, d, d));
314 /*----- That's all, folks -------------------------------------------------*/