3 * $Id: ec.c,v 1.10 2004/04/08 01:36:15 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 /*----- Header files ------------------------------------------------------*/
34 /*----- Trivial wrappers --------------------------------------------------*/
36 /* --- @ec_samep@ --- *
38 * Arguments: @ec_curve *c, *d@ = two elliptic curves
40 * Returns: Nonzero if the curves are identical (not just isomorphic).
42 * Use: Checks for sameness of curves. This function does the full
43 * check, not just the curve-type-specific check done by the
44 * @sampep@ field operation.
47 int ec_samep(ec_curve *c, ec_curve *d)
49 return (field_samep(c->f, d->f) && c->ops == d->ops && EC_SAMEP(c, d));
52 /* --- @ec_create@ --- *
54 * Arguments: @ec *p@ = pointer to an elliptic-curve point
56 * Returns: The argument @p@.
58 * Use: Initializes a new point. The initial value is the additive
59 * identity (which is universal for all curves).
62 ec *ec_create(ec *p) { EC_CREATE(p); return (p); }
64 /* --- @ec_destroy@ --- *
66 * Arguments: @ec *p@ = pointer to an elliptic-curve point
70 * Use: Destroys a point, making it invalid.
73 void ec_destroy(ec *p) { EC_DESTROY(p); }
75 /* --- @ec_atinf@ --- *
77 * Arguments: @const ec *p@ = pointer to a point
79 * Returns: Nonzero if %$p = O$% is the point at infinity, zero
83 int ec_atinf(const ec *p) { return (EC_ATINF(p)); }
85 /* --- @ec_setinf@ --- *
87 * Arguments: @ec *p@ = pointer to a point
89 * Returns: The argument @p@.
91 * Use: Sets the given point to be the point %$O$% at infinity.
94 ec *ec_setinf(ec *p) { EC_SETINF(p); return (p); }
96 /* --- @ec_copy@ --- *
98 * Arguments: @ec *d@ = pointer to destination point
99 * @const ec *p@ = pointer to source point
101 * Returns: The destination @d@.
103 * Use: Creates a copy of an elliptic curve point.
106 ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); }
110 * Arguments: @const ec *p, *q@ = two points
112 * Returns: Nonzero if the points are equal. Compares external-format
116 int ec_eq(const ec *p, const ec *q) { return (EC_EQ(p, q)); }
118 /*----- Standard curve operations -----------------------------------------*/
120 /* --- @ec_stdsamep@ --- *
122 * Arguments: @ec_curve *c, *d@ = two elliptic curves
124 * Returns: Nonzero if the curves are identical (not just isomorphic).
126 * Use: Simple sameness check on @a@ and @b@ curve members.
129 int ec_stdsamep(ec_curve *c, ec_curve *d)
131 return (MP_EQ(c->a, d->a) && MP_EQ(c->b, d->b));
134 /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- *
136 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
137 * @ec *d@ = pointer to the destination
138 * @const ec *p@ = pointer to a source point
140 * Returns: The destination @d@.
142 * Use: An identity operation if your curve has no internal
143 * representation. (The field internal representation is still
147 ec *ec_idin(ec_curve *c, ec *d, const ec *p)
153 d->x = F_IN(f, d->x, p->x);
154 d->y = F_IN(f, d->y, p->y);
155 mp_drop(d->z); d->z = 0;
160 ec *ec_idout(ec_curve *c, ec *d, const ec *p)
166 d->x = F_OUT(f, d->x, p->x);
167 d->y = F_OUT(f, d->y, p->y);
168 mp_drop(d->z); d->z = 0;
173 ec *ec_idfix(ec_curve *c, ec *d, const ec *p)
179 /* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- *
181 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
182 * @ec *d@ = pointer to the destination
183 * @const ec *p@ = pointer to a source point
185 * Returns: The destination @d@.
187 * Use: Conversion functions if your curve operations use a
188 * projective representation.
191 ec *ec_projin(ec_curve *c, ec *d, const ec *p)
197 d->x = F_IN(f, d->x, p->x);
198 d->y = F_IN(f, d->y, p->y);
199 mp_drop(d->z); d->z = MP_COPY(f->one);
204 ec *ec_projout(ec_curve *c, ec *d, const ec *p)
211 z = F_INV(f, MP_NEW, p->z);
212 zz = F_SQR(f, MP_NEW, z);
213 z = F_MUL(f, z, zz, z);
214 x = F_MUL(f, d->x, p->x, zz);
215 y = F_MUL(f, d->y, p->y, z);
219 d->x = F_OUT(f, x, x);
220 d->y = F_OUT(f, y, y);
226 ec *ec_projfix(ec_curve *c, ec *d, const ec *p)
230 else if (d->z == c->f->one)
235 z = F_INV(f, MP_NEW, p->z);
236 zz = F_SQR(f, MP_NEW, z);
237 z = F_MUL(f, z, zz, z);
238 d->x = F_MUL(f, d->x, p->x, zz);
239 d->y = F_MUL(f, d->y, p->y, z);
243 d->z = MP_COPY(f->one);
248 /* --- @ec_stdsub@ --- *
250 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
251 * @ec *d@ = pointer to the destination
252 * @const ec *p, *q@ = the operand points
254 * Returns: The destination @d@.
256 * Use: Standard point subtraction operation, in terms of negation
257 * and addition. This isn't as efficient as a ready-made
258 * subtraction operator.
261 ec *ec_stdsub(ec_curve *c, ec *d, const ec *p, const ec *q)
271 /*----- Creating curves ---------------------------------------------------*/
273 /* --- @ec_destroycurve@ --- *
275 * Arguments: @ec_curve *c@ = pointer to an ellptic curve
279 * Use: Destroys a description of an elliptic curve.
282 void ec_destroycurve(ec_curve *c) { c->ops->destroy(c); }
284 /*----- Real arithmetic ---------------------------------------------------*/
286 /* --- @ec_find@ --- *
288 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
289 * @ec *d@ = pointer to the destination point
290 * @mp *x@ = a possible x-coordinate
292 * Returns: Zero if OK, nonzero if there isn't a point there.
294 * Use: Finds a point on an elliptic curve with a given x-coordinate.
297 ec *ec_find(ec_curve *c, ec *d, mp *x)
299 x = F_IN(c->f, MP_NEW, x);
300 if ((d = EC_FIND(c, d, x)) != 0)
306 /* --- @ec_neg@ --- *
308 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
309 * @ec *d@ = pointer to the destination point
310 * @const ec *p@ = pointer to the operand point
312 * Returns: The destination point.
314 * Use: Computes the negation of the given point.
317 ec *ec_neg(ec_curve *c, ec *d, const ec *p)
321 return (EC_OUT(c, d, d));
324 /* --- @ec_add@ --- *
326 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
327 * @ec *d@ = pointer to the destination point
328 * @const ec *p, *q@ = pointers to the operand points
332 * Use: Adds two points on an elliptic curve.
335 ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
337 ec pp = EC_INIT, qq = EC_INIT;
340 EC_ADD(c, d, &pp, &qq);
347 /* --- @ec_sub@ --- *
349 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
350 * @ec *d@ = pointer to the destination point
351 * @const ec *p, *q@ = pointers to the operand points
353 * Returns: The destination @d@.
355 * Use: Subtracts one point from another on an elliptic curve.
358 ec *ec_sub(ec_curve *c, ec *d, const ec *p, const ec *q)
360 ec pp = EC_INIT, qq = EC_INIT;
363 EC_SUB(c, d, &pp, &qq);
370 /* --- @ec_dbl@ --- *
372 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
373 * @ec *d@ = pointer to the destination point
374 * @const ec *p@ = pointer to the operand point
378 * Use: Doubles a point on an elliptic curve.
381 ec *ec_dbl(ec_curve *c, ec *d, const ec *p)
385 return (EC_OUT(c, d, d));
388 /* --- @ec_check@ --- *
390 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
391 * @const ec *p@ = pointer to the point
393 * Returns: Zero if OK, nonzero if this is an invalid point.
395 * Use: Checks that a point is actually on an elliptic curve.
398 int ec_check(ec_curve *c, const ec *p)
406 rc = EC_CHECK(c, &t);
411 /* --- @ec_rand@ --- *
413 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
414 * @ec *d@ = pointer to the destination point
415 * @grand *r@ = random number source
417 * Returns: The destination @d@.
419 * Use: Finds a random point on the given curve.
422 ec *ec_rand(ec_curve *c, ec *d, grand *r)
425 do x = F_RAND(c->f, x, r); while (!EC_FIND(c, d, x));
427 if (grand_range(r, 2)) EC_NEG(c, d, d);
428 return (EC_OUT(c, d, d));
431 /*----- That's all, folks -------------------------------------------------*/