3 * $Id: ec.c,v 1.7 2004/03/27 17:54:11 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 1.7 2004/03/27 17:54:11 mdw
34 * Standard curves and curve checking.
36 * Revision 1.6 2004/03/23 15:19:32 mdw
37 * Test elliptic curves more thoroughly.
39 * Revision 1.5 2004/03/21 22:52:06 mdw
40 * Merge and close elliptic curve branch.
42 * Revision 1.4.4.2 2004/03/20 00:13:31 mdw
43 * Projective coordinates for prime curves
45 * Revision 1.4.4.1 2003/06/10 13:43:53 mdw
46 * Simple (non-projective) curves over prime fields now seem to work.
48 * Revision 1.4 2003/05/15 23:25:59 mdw
49 * Make elliptic curve stuff build.
51 * Revision 1.3 2002/01/13 13:48:44 mdw
54 * Revision 1.2 2001/05/07 17:29:44 mdw
55 * Treat projective coordinates as an internal representation. Various
56 * minor interface changes.
58 * Revision 1.1 2001/04/29 18:12:33 mdw
63 /*----- Header files ------------------------------------------------------*/
68 /*----- Trivial wrappers --------------------------------------------------*/
70 /* --- @ec_create@ --- *
72 * Arguments: @ec *p@ = pointer to an elliptic-curve point
74 * Returns: The argument @p@.
76 * Use: Initializes a new point. The initial value is the additive
77 * identity (which is universal for all curves).
80 ec
*ec_create(ec
*p
) { EC_CREATE(p
); return (p
); }
82 /* --- @ec_destroy@ --- *
84 * Arguments: @ec *p@ = pointer to an elliptic-curve point
88 * Use: Destroys a point, making it invalid.
91 void ec_destroy(ec
*p
) { EC_DESTROY(p
); }
93 /* --- @ec_atinf@ --- *
95 * Arguments: @const ec *p@ = pointer to a point
97 * Returns: Nonzero if %$p = O$% is the point at infinity, zero
101 int ec_atinf(const ec
*p
) { return (EC_ATINF(p
)); }
103 /* --- @ec_setinf@ --- *
105 * Arguments: @ec *p@ = pointer to a point
107 * Returns: The argument @p@.
109 * Use: Sets the given point to be the point %$O$% at infinity.
112 ec
*ec_setinf(ec
*p
) { EC_SETINF(p
); return (p
); }
114 /* --- @ec_copy@ --- *
116 * Arguments: @ec *d@ = pointer to destination point
117 * @const ec *p@ = pointer to source point
119 * Returns: The destination @d@.
121 * Use: Creates a copy of an elliptic curve point.
124 ec
*ec_copy(ec
*d
, const ec
*p
) { EC_COPY(d
, p
); return (d
); }
128 * Arguments: @const ec *p, *q@ = two points
130 * Returns: Nonzero if the points are equal. Compares external-format
134 int ec_eq(const ec
*p
, const ec
*q
) { return (EC_EQ(p
, q
)); }
136 /*----- Standard curve operations -----------------------------------------*/
138 /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- *
140 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
141 * @ec *d@ = pointer to the destination
142 * @const ec *p@ = pointer to a source point
144 * Returns: The destination @d@.
146 * Use: An identity operation if your curve has no internal
147 * representation. (The field internal representation is still
151 ec
*ec_idin(ec_curve
*c
, ec
*d
, const ec
*p
)
157 d
->x
= F_IN(f
, d
->x
, p
->x
);
158 d
->y
= F_IN(f
, d
->y
, p
->y
);
159 mp_drop(d
->z
); d
->z
= 0;
164 ec
*ec_idout(ec_curve
*c
, ec
*d
, const ec
*p
)
170 d
->x
= F_OUT(f
, d
->x
, p
->x
);
171 d
->y
= F_OUT(f
, d
->y
, p
->y
);
172 mp_drop(d
->z
); d
->z
= 0;
177 ec
*ec_idfix(ec_curve
*c
, ec
*d
, const ec
*p
)
183 /* --- @ec_projin@, @ec_projout@ --- *
185 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
186 * @ec *d@ = pointer to the destination
187 * @const ec *p@ = pointer to a source point
189 * Returns: The destination @d@.
191 * Use: Conversion functions if your curve operations use a
192 * projective representation.
195 ec
*ec_projin(ec_curve
*c
, ec
*d
, const ec
*p
)
201 d
->x
= F_IN(f
, d
->x
, p
->x
);
202 d
->y
= F_IN(f
, d
->y
, p
->y
);
203 mp_drop(d
->z
); d
->z
= MP_COPY(f
->one
);
208 ec
*ec_projout(ec_curve
*c
, ec
*d
, const ec
*p
)
215 z
= F_INV(f
, MP_NEW
, p
->z
);
216 zz
= F_SQR(f
, MP_NEW
, z
);
217 z
= F_MUL(f
, z
, zz
, z
);
218 x
= F_MUL(f
, d
->x
, p
->x
, zz
);
219 y
= F_MUL(f
, d
->y
, p
->y
, z
);
223 d
->x
= F_OUT(f
, x
, x
);
224 d
->y
= F_OUT(f
, y
, y
);
230 ec
*ec_projfix(ec_curve
*c
, ec
*d
, const ec
*p
)
234 else if (d
->z
== c
->f
->one
)
239 z
= F_INV(f
, MP_NEW
, p
->z
);
240 zz
= F_SQR(f
, MP_NEW
, z
);
241 z
= F_MUL(f
, z
, zz
, z
);
242 d
->x
= F_MUL(f
, d
->x
, p
->x
, zz
);
243 d
->y
= F_MUL(f
, d
->y
, p
->y
, z
);
247 d
->z
= MP_COPY(f
->one
);
252 /* --- @ec_stdsub@ --- *
254 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
255 * @ec *d@ = pointer to the destination
256 * @const ec *p, *q@ = the operand points
258 * Returns: The destination @d@.
260 * Use: Standard point subtraction operation, in terms of negation
261 * and addition. This isn't as efficient as a ready-made
262 * subtraction operator.
265 ec
*ec_stdsub(ec_curve
*c
, ec
*d
, const ec
*p
, const ec
*q
)
275 /*----- Creating curves ---------------------------------------------------*/
277 /* --- @ec_destroycurve@ --- *
279 * Arguments: @ec_curve *c@ = pointer to an ellptic curve
283 * Use: Destroys a description of an elliptic curve.
286 void ec_destroycurve(ec_curve
*c
) { c
->ops
->destroy(c
); }
288 /*----- Real arithmetic ---------------------------------------------------*/
290 /* --- @ec_find@ --- *
292 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
293 * @ec *d@ = pointer to the destination point
294 * @mp *x@ = a possible x-coordinate
296 * Returns: Zero if OK, nonzero if there isn't a point there.
298 * Use: Finds a point on an elliptic curve with a given x-coordinate.
301 ec
*ec_find(ec_curve
*c
, ec
*d
, mp
*x
)
303 x
= F_IN(c
->f
, MP_NEW
, x
);
304 if ((d
= EC_FIND(c
, d
, x
)) != 0)
310 /* --- @ec_neg@ --- *
312 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
313 * @ec *d@ = pointer to the destination point
314 * @const ec *p@ = pointer to the operand point
316 * Returns: The destination point.
318 * Use: Computes the negation of the given point.
321 ec
*ec_neg(ec_curve
*c
, ec
*d
, const ec
*p
)
325 return (EC_OUT(c
, d
, d
));
328 /* --- @ec_add@ --- *
330 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
331 * @ec *d@ = pointer to the destination point
332 * @const ec *p, *q@ = pointers to the operand points
336 * Use: Adds two points on an elliptic curve.
339 ec
*ec_add(ec_curve
*c
, ec
*d
, const ec
*p
, const ec
*q
)
341 ec pp
= EC_INIT
, qq
= EC_INIT
;
344 EC_ADD(c
, d
, &pp
, &qq
);
351 /* --- @ec_sub@ --- *
353 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
354 * @ec *d@ = pointer to the destination point
355 * @const ec *p, *q@ = pointers to the operand points
357 * Returns: The destination @d@.
359 * Use: Subtracts one point from another on an elliptic curve.
362 ec
*ec_sub(ec_curve
*c
, ec
*d
, const ec
*p
, const ec
*q
)
364 ec pp
= EC_INIT
, qq
= EC_INIT
;
367 EC_SUB(c
, d
, &pp
, &qq
);
374 /* --- @ec_dbl@ --- *
376 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
377 * @ec *d@ = pointer to the destination point
378 * @const ec *p@ = pointer to the operand point
382 * Use: Doubles a point on an elliptic curve.
385 ec
*ec_dbl(ec_curve
*c
, ec
*d
, const ec
*p
)
389 return (EC_OUT(c
, d
, d
));
392 /* --- @ec_check@ --- *
394 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
395 * @const ec *p@ = pointer to the point
397 * Returns: Zero if OK, nonzero if this is an invalid point.
399 * Use: Checks that a point is actually on an elliptic curve.
402 int ec_check(ec_curve
*c
, const ec
*p
)
410 rc
= EC_CHECK(c
, &t
);
415 /* --- @ec_rand@ --- *
417 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
418 * @ec *d@ = pointer to the destination point
419 * @grand *r@ = random number source
421 * Returns: The destination @d@.
423 * Use: Finds a random point on the given curve.
426 ec
*ec_rand(ec_curve
*c
, ec
*d
, grand
*r
)
429 do x
= F_RAND(c
->f
, x
, r
); while (!EC_FIND(c
, d
, x
));
431 if (grand_range(r
, 2)) EC_NEG(c
, d
, d
);
432 return (EC_OUT(c
, d
, d
));
435 /* --- @ec_imul@, @ec_mul@ --- *
437 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
438 * @ec *d@ = pointer to the destination point
439 * @const ec *p@ = pointer to the generator point
440 * @mp *n@ = integer multiplier
442 * Returns: The destination @d@.
444 * Use: Multiplies a point by a scalar, returning %$n p$%. The
445 * @imul@ variant uses internal representations for argument
449 ec
*ec_imul(ec_curve
*c
, ec
*d
, const ec
*p
, mp
*n
)
454 if (t
.x
&& (n
->f
& MP_BURN
))
463 if (MP_LEN(n
) < EXP_THRESH
)
464 EXP_SIMPLE(*d
, t
, n
);
466 EXP_WINDOW(*d
, t
, n
);
472 ec
*ec_mul(ec_curve
*c
, ec
*d
, const ec
*p
, mp
*n
)
476 return (EC_OUT(c
, d
, d
));
479 /*----- That's all, folks -------------------------------------------------*/