3 * $Id: ec.c,v 1.6 2004/03/23 15:19:32 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 1.6 2004/03/23 15:19:32 mdw
34 * Test elliptic curves more thoroughly.
36 * Revision 1.5 2004/03/21 22:52:06 mdw
37 * Merge and close elliptic curve branch.
39 * Revision 1.4.4.2 2004/03/20 00:13:31 mdw
40 * Projective coordinates for prime curves
42 * Revision 1.4.4.1 2003/06/10 13:43:53 mdw
43 * Simple (non-projective) curves over prime fields now seem to work.
45 * Revision 1.4 2003/05/15 23:25:59 mdw
46 * Make elliptic curve stuff build.
48 * Revision 1.3 2002/01/13 13:48:44 mdw
51 * Revision 1.2 2001/05/07 17:29:44 mdw
52 * Treat projective coordinates as an internal representation. Various
53 * minor interface changes.
55 * Revision 1.1 2001/04/29 18:12:33 mdw
60 /*----- Header files ------------------------------------------------------*/
65 /*----- Trivial wrappers --------------------------------------------------*/
67 /* --- @ec_create@ --- *
69 * Arguments: @ec *p@ = pointer to an elliptic-curve point
71 * Returns: The argument @p@.
73 * Use: Initializes a new point. The initial value is the additive
74 * identity (which is universal for all curves).
77 ec *ec_create(ec *p) { EC_CREATE(p); return (p); }
79 /* --- @ec_destroy@ --- *
81 * Arguments: @ec *p@ = pointer to an elliptic-curve point
85 * Use: Destroys a point, making it invalid.
88 void ec_destroy(ec *p) { EC_DESTROY(p); }
90 /* --- @ec_atinf@ --- *
92 * Arguments: @const ec *p@ = pointer to a point
94 * Returns: Nonzero if %$p = O$% is the point at infinity, zero
98 int ec_atinf(const ec *p) { return (EC_ATINF(p)); }
100 /* --- @ec_setinf@ --- *
102 * Arguments: @ec *p@ = pointer to a point
104 * Returns: The argument @p@.
106 * Use: Sets the given point to be the point %$O$% at infinity.
109 ec *ec_setinf(ec *p) { EC_SETINF(p); return (p); }
111 /* --- @ec_copy@ --- *
113 * Arguments: @ec *d@ = pointer to destination point
114 * @const ec *p@ = pointer to source point
116 * Returns: The destination @d@.
118 * Use: Creates a copy of an elliptic curve point.
121 ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); }
125 * Arguments: @const ec *p, *q@ = two points
127 * Returns: Nonzero if the points are equal. Compares external-format
131 int ec_eq(const ec *p, const ec *q) { return (EC_EQ(p, q)); }
133 /*----- Standard curve operations -----------------------------------------*/
135 /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- *
137 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
138 * @ec *d@ = pointer to the destination
139 * @const ec *p@ = pointer to a source point
141 * Returns: The destination @d@.
143 * Use: An identity operation if your curve has no internal
144 * representation. (The field internal representation is still
148 ec *ec_idin(ec_curve *c, ec *d, const ec *p)
154 d->x = F_IN(f, d->x, p->x);
155 d->y = F_IN(f, d->y, p->y);
156 mp_drop(d->z); d->z = 0;
161 ec *ec_idout(ec_curve *c, ec *d, const ec *p)
167 d->x = F_OUT(f, d->x, p->x);
168 d->y = F_OUT(f, d->y, p->y);
169 mp_drop(d->z); d->z = 0;
174 ec *ec_idfix(ec_curve *c, ec *d, const ec *p)
180 /* --- @ec_projin@, @ec_projout@ --- *
182 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
183 * @ec *d@ = pointer to the destination
184 * @const ec *p@ = pointer to a source point
186 * Returns: The destination @d@.
188 * Use: Conversion functions if your curve operations use a
189 * projective representation.
192 ec *ec_projin(ec_curve *c, ec *d, const ec *p)
198 d->x = F_IN(f, d->x, p->x);
199 d->y = F_IN(f, d->y, p->y);
200 mp_drop(d->z); d->z = MP_COPY(f->one);
205 ec *ec_projout(ec_curve *c, ec *d, const ec *p)
212 z = F_INV(f, MP_NEW, p->z);
213 zz = F_SQR(f, MP_NEW, z);
214 z = F_MUL(f, z, zz, z);
215 x = F_MUL(f, d->x, p->x, zz);
216 y = F_MUL(f, d->y, p->y, z);
220 d->x = F_OUT(f, x, x);
221 d->y = F_OUT(f, y, y);
227 ec *ec_projfix(ec_curve *c, ec *d, const ec *p)
231 else if (d->z == c->f->one)
236 z = F_INV(f, MP_NEW, p->z);
237 zz = F_SQR(f, MP_NEW, z);
238 z = F_MUL(f, z, zz, z);
239 d->x = F_MUL(f, d->x, p->x, zz);
240 d->y = F_MUL(f, d->y, p->y, z);
244 d->z = MP_COPY(f->one);
249 /* --- @ec_stdsub@ --- *
251 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
252 * @ec *d@ = pointer to the destination
253 * @const ec *p, *q@ = the operand points
255 * Returns: The destination @d@.
257 * Use: Standard point subtraction operation, in terms of negation
258 * and addition. This isn't as efficient as a ready-made
259 * subtraction operator.
262 ec *ec_stdsub(ec_curve *c, ec *d, const ec *p, const ec *q)
272 /*----- Creating curves ---------------------------------------------------*/
274 /* --- @ec_destroycurve@ --- *
276 * Arguments: @ec_curve *c@ = pointer to an ellptic curve
280 * Use: Destroys a description of an elliptic curve.
283 void ec_destroycurve(ec_curve *c) { c->ops->destroy(c); }
285 /*----- Real arithmetic ---------------------------------------------------*/
287 /* --- @ec_find@ --- *
289 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
290 * @ec *d@ = pointer to the destination point
291 * @mp *x@ = a possible x-coordinate
293 * Returns: Zero if OK, nonzero if there isn't a point there.
295 * Use: Finds a point on an elliptic curve with a given x-coordinate.
298 ec *ec_find(ec_curve *c, ec *d, mp *x)
300 x = F_IN(c->f, MP_NEW, x);
301 if ((d = EC_FIND(c, d, x)) != 0)
307 /* --- @ec_neg@ --- *
309 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
310 * @ec *d@ = pointer to the destination point
311 * @const ec *p@ = pointer to the operand point
313 * Returns: The destination point.
315 * Use: Computes the negation of the given point.
318 ec *ec_neg(ec_curve *c, ec *d, const ec *p)
322 return (EC_OUT(c, d, d));
325 /* --- @ec_add@ --- *
327 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
328 * @ec *d@ = pointer to the destination point
329 * @const ec *p, *q@ = pointers to the operand points
333 * Use: Adds two points on an elliptic curve.
336 ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
338 ec pp = EC_INIT, qq = EC_INIT;
341 EC_ADD(c, d, &pp, &qq);
348 /* --- @ec_sub@ --- *
350 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
351 * @ec *d@ = pointer to the destination point
352 * @const ec *p, *q@ = pointers to the operand points
354 * Returns: The destination @d@.
356 * Use: Subtracts one point from another on an elliptic curve.
359 ec *ec_sub(ec_curve *c, ec *d, const ec *p, const ec *q)
364 EC_SUB(c, d, &pp, &qq);
371 /* --- @ec_dbl@ --- *
373 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
374 * @ec *d@ = pointer to the destination point
375 * @const ec *p@ = pointer to the operand point
379 * Use: Doubles a point on an elliptic curve.
382 ec *ec_dbl(ec_curve *c, ec *d, const ec *p)
386 return (EC_OUT(c, d, d));
389 /* --- @ec_check@ --- *
391 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
392 * @const ec *p@ = pointer to the point
394 * Returns: Zero if OK, nonzero if this is an invalid point.
396 * Use: Checks that a point is actually on an elliptic curve.
399 int ec_check(ec_curve *c, const ec *p)
407 rc = EC_CHECK(c, &t);
412 /* --- @ec_rand@ --- *
414 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
415 * @ec *d@ = pointer to the destination point
416 * @grand *r@ = random number source
418 * Returns: The destination @d@.
420 * Use: Finds a random point on the given curve.
423 ec *ec_rand(ec_curve *c, ec *d, grand *r)
426 do x = F_RAND(c->f, x, r); while (!EC_FIND(c, d, x));
428 if (grand_range(r, 2)) EC_NEG(c, d, d);
429 return (EC_OUT(c, d, d));
432 /* --- @ec_imul@, @ec_mul@ --- *
434 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
435 * @ec *d@ = pointer to the destination point
436 * @const ec *p@ = pointer to the generator point
437 * @mp *n@ = integer multiplier
439 * Returns: The destination @d@.
441 * Use: Multiplies a point by a scalar, returning %$n p$%. The
442 * @imul@ variant uses internal representations for argument
446 ec *ec_imul(ec_curve *c, ec *d, const ec *p, mp *n)
451 if (t.x && (n->f & MP_BURN))
460 if (MP_LEN(n) < EXP_THRESH)
461 EXP_SIMPLE(*d, t, n);
463 EXP_WINDOW(*d, t, n);
469 ec *ec_mul(ec_curve *c, ec *d, const ec *p, mp *n)
473 return (EC_OUT(c, d, d));
476 /*----- That's all, folks -------------------------------------------------*/