3 * $Id: ec.c,v 1.4.4.1 2003/06/10 13:43:53 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 1.4.4.1 2003/06/10 13:43:53 mdw
34 * Simple (non-projective) curves over prime fields now seem to work.
36 * Revision 1.4 2003/05/15 23:25:59 mdw
37 * Make elliptic curve stuff build.
39 * Revision 1.3 2002/01/13 13:48:44 mdw
42 * Revision 1.2 2001/05/07 17:29:44 mdw
43 * Treat projective coordinates as an internal representation. Various
44 * minor interface changes.
46 * Revision 1.1 2001/04/29 18:12:33 mdw
51 /*----- Header files ------------------------------------------------------*/
56 /*----- Trivial wrappers --------------------------------------------------*/
58 /* --- @ec_create@ --- *
60 * Arguments: @ec *p@ = pointer to an elliptic-curve point
62 * Returns: The argument @p@.
64 * Use: Initializes a new point. The initial value is the additive
65 * identity (which is universal for all curves).
68 ec *ec_create(ec *p) { EC_CREATE(p); return (p); }
70 /* --- @ec_destroy@ --- *
72 * Arguments: @ec *p@ = pointer to an elliptic-curve point
76 * Use: Destroys a point, making it invalid.
79 void ec_destroy(ec *p) { EC_DESTROY(p); }
81 /* --- @ec_atinf@ --- *
83 * Arguments: @const ec *p@ = pointer to a point
85 * Returns: Nonzero if %$p = O$% is the point at infinity, zero
89 int ec_atinf(const ec *p) { return (EC_ATINF(p)); }
91 /* --- @ec_setinf@ --- *
93 * Arguments: @ec *p@ = pointer to a point
95 * Returns: The argument @p@.
97 * Use: Sets the given point to be the point %$O$% at infinity.
100 ec *ec_setinf(ec *p) { EC_SETINF(p); return (p); }
102 /* --- @ec_copy@ --- *
104 * Arguments: @ec *d@ = pointer to destination point
105 * @const ec *p@ = pointer to source point
107 * Returns: The destination @d@.
109 * Use: Creates a copy of an elliptic curve point.
112 ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); }
114 /*----- Standard curve operations -----------------------------------------*/
116 /* --- @ec_idin@, @ec_idout@ --- *
118 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
119 * @ec *d@ = pointer to the destination
120 * @const ec *p@ = pointer to a source point
122 * Returns: The destination @d@.
124 * Use: An identity operation if your curve has no internal
125 * representation. (The field internal representation is still
129 ec *ec_idin(ec_curve *c, ec *d, const ec *p)
135 d->x = F_IN(f, d->x, p->x);
136 d->y = F_IN(f, d->y, p->y);
137 mp_drop(d->z); d->z = 0;
142 ec *ec_idout(ec_curve *c, ec *d, const ec *p)
148 d->x = F_OUT(f, d->x, p->x);
149 d->y = F_OUT(f, d->y, p->y);
150 mp_drop(d->z); d->z = 0;
155 /* --- @ec_projin@, @ec_projout@ --- *
157 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
158 * @ec *d@ = pointer to the destination
159 * @const ec *p@ = pointer to a source point
161 * Returns: The destination @d@.
163 * Use: Conversion functions if your curve operations use a
164 * projective representation.
167 ec *ec_projin(ec_curve *c, ec *d, const ec *p)
173 d->x = F_IN(f, d->x, p->x);
174 d->y = F_IN(f, d->y, p->y);
175 mp_drop(d->z); d->z = MP_COPY(f->one);
180 ec *ec_projout(ec_curve *c, ec *d, const ec *p)
187 z = F_INV(f, MP_NEW, p->z);
188 x = F_MUL(f, d->x, p->x, z);
189 y = F_MUL(f, d->y, p->y, z);
192 d->x = F_OUT(f, x, x);
193 d->y = F_OUT(f, y, y);
199 /* --- @ec_stdsub@ --- *
201 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
202 * @ec *d@ = pointer to the destination
203 * @const ec *p, *q@ = the operand points
205 * Returns: The destination @d@.
207 * Use: Standard point subtraction operation, in terms of negation
208 * and addition. This isn't as efficient as a ready-made
209 * subtraction operator.
212 ec *ec_stdsub(ec_curve *c, ec *d, const ec *p, const ec *q)
221 /*----- Creating curves ---------------------------------------------------*/
223 /* --- @ec_destroycurve@ --- *
225 * Arguments: @ec_curve *c@ = pointer to an ellptic curve
229 * Use: Destroys a description of an elliptic curve.
232 void ec_destroycurve(ec_curve *c) { c->ops->destroy(c); }
234 /*----- Real arithmetic ---------------------------------------------------*/
236 /* --- @ec_find@ --- *
238 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
239 * @ec *d@ = pointer to the destination point
240 * @mp *x@ = a possible x-coordinate
242 * Returns: Zero if OK, nonzero if there isn't a point there.
244 * Use: Finds a point on an elliptic curve with a given x-coordinate.
247 ec *ec_find(ec_curve *c, ec *d, mp *x)
249 x = F_IN(c->f, MP_NEW, x);
250 if ((d = EC_FIND(c, d, x)) != 0)
256 /* --- @ec_neg@ --- *
258 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
259 * @ec *d@ = pointer to the destination point
260 * @const ec *p@ = pointer to the operand point
262 * Returns: The destination point.
264 * Use: Computes the negation of the given point.
267 ec *ec_neg(ec_curve *c, ec *d, const ec *p)
271 return (EC_OUT(c, d, d));
274 /* --- @ec_add@ --- *
276 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
277 * @ec *d@ = pointer to the destination point
278 * @const ec *p, *q@ = pointers to the operand points
282 * Use: Adds two points on an elliptic curve.
285 ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
287 ec pp = EC_INIT, qq = EC_INIT;
290 EC_ADD(c, d, &pp, &qq);
297 /* --- @ec_sub@ --- *
299 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
300 * @ec *d@ = pointer to the destination point
301 * @const ec *p, *q@ = pointers to the operand points
303 * Returns: The destination @d@.
305 * Use: Subtracts one point from another on an elliptic curve.
308 ec *ec_sub(ec_curve *c, ec *d, const ec *p, const ec *q)
313 EC_SUB(c, d, &qq, &qq);
320 /* --- @ec_dbl@ --- *
322 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
323 * @ec *d@ = pointer to the destination point
324 * @const ec *p@ = pointer to the operand point
328 * Use: Doubles a point on an elliptic curve.
331 ec *ec_dbl(ec_curve *c, ec *d, const ec *p)
335 return (EC_OUT(c, d, d));
338 /* --- @ec_imul@, @ec_mul@ --- *
340 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
341 * @ec *d@ = pointer to the destination point
342 * @const ec *p@ = pointer to the generator point
343 * @mp *n@ = integer multiplier
345 * Returns: The destination @d@.
347 * Use: Multiplies a point by a scalar, returning %$n p$%. The
348 * @imul@ variant uses internal representations for argument
352 ec *ec_imul(ec_curve *c, ec *d, const ec *p, mp *n)
357 if (t.x && (n->f & MP_BURN))
363 else if (MP_LEN(n) < EXP_THRESH)
364 EXP_SIMPLE(*d, t, n);
366 EXP_WINDOW(*d, t, n);
371 ec *ec_mul(ec_curve *c, ec *d, const ec *p, mp *n)
375 return (EC_OUT(c, d, d));
378 /*----- That's all, folks -------------------------------------------------*/