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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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4 | * |
5 | * Elliptic curve definitions |
6 | * |
7 | * (c) 2001 Straylight/Edgeware |
8 | */ |
9 | |
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10 | /*----- Licensing notice --------------------------------------------------* |
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11 | * |
12 | * This file is part of Catacomb. |
13 | * |
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. |
45c0fd36 |
18 | * |
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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. |
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23 | * |
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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, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include "ec.h" |
33 | |
34 | /*----- Trivial wrappers --------------------------------------------------*/ |
35 | |
34e4f738 |
36 | /* --- @ec_samep@ --- * |
37 | * |
38 | * Arguments: @ec_curve *c, *d@ = two elliptic curves |
39 | * |
40 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
41 | * |
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. |
45 | */ |
46 | |
47 | int ec_samep(ec_curve *c, ec_curve *d) |
48 | { |
a02032a3 |
49 | return (c == d || (field_samep(c->f, d->f) && |
50 | c->ops == d->ops && EC_SAMEP(c, d))); |
34e4f738 |
51 | } |
52 | |
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53 | /* --- @ec_create@ --- * |
54 | * |
55 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
56 | * |
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57 | * Returns: The argument @p@. |
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58 | * |
59 | * Use: Initializes a new point. The initial value is the additive |
60 | * identity (which is universal for all curves). |
61 | */ |
62 | |
41cb1beb |
63 | ec *ec_create(ec *p) { EC_CREATE(p); return (p); } |
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64 | |
65 | /* --- @ec_destroy@ --- * |
66 | * |
67 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
68 | * |
69 | * Returns: --- |
70 | * |
71 | * Use: Destroys a point, making it invalid. |
72 | */ |
73 | |
74 | void ec_destroy(ec *p) { EC_DESTROY(p); } |
75 | |
76 | /* --- @ec_atinf@ --- * |
77 | * |
78 | * Arguments: @const ec *p@ = pointer to a point |
79 | * |
80 | * Returns: Nonzero if %$p = O$% is the point at infinity, zero |
81 | * otherwise. |
82 | */ |
83 | |
84 | int ec_atinf(const ec *p) { return (EC_ATINF(p)); } |
85 | |
86 | /* --- @ec_setinf@ --- * |
87 | * |
88 | * Arguments: @ec *p@ = pointer to a point |
89 | * |
41cb1beb |
90 | * Returns: The argument @p@. |
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91 | * |
92 | * Use: Sets the given point to be the point %$O$% at infinity. |
93 | */ |
94 | |
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95 | ec *ec_setinf(ec *p) { EC_SETINF(p); return (p); } |
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96 | |
97 | /* --- @ec_copy@ --- * |
98 | * |
99 | * Arguments: @ec *d@ = pointer to destination point |
100 | * @const ec *p@ = pointer to source point |
101 | * |
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102 | * Returns: The destination @d@. |
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103 | * |
104 | * Use: Creates a copy of an elliptic curve point. |
105 | */ |
106 | |
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107 | ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); } |
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108 | |
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109 | /* --- @ec_eq@ --- * |
110 | * |
111 | * Arguments: @const ec *p, *q@ = two points |
112 | * |
113 | * Returns: Nonzero if the points are equal. Compares external-format |
114 | * points. |
115 | */ |
116 | |
117 | int ec_eq(const ec *p, const ec *q) { return (EC_EQ(p, q)); } |
118 | |
41a324a7 |
119 | /*----- Standard curve operations -----------------------------------------*/ |
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120 | |
34e4f738 |
121 | /* --- @ec_stdsamep@ --- * |
122 | * |
123 | * Arguments: @ec_curve *c, *d@ = two elliptic curves |
124 | * |
125 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
126 | * |
127 | * Use: Simple sameness check on @a@ and @b@ curve members. |
128 | */ |
129 | |
130 | int ec_stdsamep(ec_curve *c, ec_curve *d) |
a02032a3 |
131 | { return (MP_EQ(c->a, d->a) && MP_EQ(c->b, d->b)); } |
34e4f738 |
132 | |
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133 | /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- * |
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134 | * |
135 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
41a324a7 |
136 | * @ec *d@ = pointer to the destination |
137 | * @const ec *p@ = pointer to a source point |
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138 | * |
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139 | * Returns: The destination @d@. |
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140 | * |
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141 | * Use: An identity operation if your curve has no internal |
142 | * representation. (The field internal representation is still |
143 | * used.) |
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144 | */ |
145 | |
41a324a7 |
146 | ec *ec_idin(ec_curve *c, ec *d, const ec *p) |
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147 | { |
148 | if (EC_ATINF(p)) |
149 | EC_SETINF(d); |
150 | else { |
151 | field *f = c->f; |
152 | d->x = F_IN(f, d->x, p->x); |
153 | d->y = F_IN(f, d->y, p->y); |
41a324a7 |
154 | mp_drop(d->z); d->z = 0; |
155 | } |
156 | return (d); |
157 | } |
158 | |
159 | ec *ec_idout(ec_curve *c, ec *d, const ec *p) |
160 | { |
161 | if (EC_ATINF(p)) |
162 | EC_SETINF(d); |
163 | else { |
164 | field *f = c->f; |
165 | d->x = F_OUT(f, d->x, p->x); |
166 | d->y = F_OUT(f, d->y, p->y); |
167 | mp_drop(d->z); d->z = 0; |
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168 | } |
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169 | return (d); |
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170 | } |
171 | |
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172 | ec *ec_idfix(ec_curve *c, ec *d, const ec *p) |
a02032a3 |
173 | { EC_COPY(d, p); return (d); } |
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174 | |
4edc47b8 |
175 | /* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- * |
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176 | * |
177 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
41a324a7 |
178 | * @ec *d@ = pointer to the destination |
179 | * @const ec *p@ = pointer to a source point |
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180 | * |
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181 | * Returns: The destination @d@. |
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182 | * |
41a324a7 |
183 | * Use: Conversion functions if your curve operations use a |
184 | * projective representation. |
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185 | */ |
186 | |
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187 | ec *ec_projin(ec_curve *c, ec *d, const ec *p) |
188 | { |
189 | if (EC_ATINF(p)) |
190 | EC_SETINF(d); |
191 | else { |
192 | field *f = c->f; |
193 | d->x = F_IN(f, d->x, p->x); |
194 | d->y = F_IN(f, d->y, p->y); |
195 | mp_drop(d->z); d->z = MP_COPY(f->one); |
196 | } |
197 | return (d); |
198 | } |
199 | |
200 | ec *ec_projout(ec_curve *c, ec *d, const ec *p) |
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201 | { |
202 | if (EC_ATINF(p)) |
203 | EC_SETINF(d); |
204 | else { |
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205 | mp *x, *y, *z, *zz; |
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206 | field *f = c->f; |
a02032a3 |
207 | if (p->z == f->one) { |
208 | d->x = F_OUT(f, d->x, p->x); |
209 | d->y = F_OUT(f, d->y, p->y); |
210 | } else { |
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); |
216 | mp_drop(z); |
217 | mp_drop(zz); |
218 | d->x = F_OUT(f, x, x); |
219 | d->y = F_OUT(f, y, y); |
220 | } |
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221 | mp_drop(d->z); |
b0ab12e6 |
222 | d->z = 0; |
223 | } |
41a324a7 |
224 | return (d); |
b0ab12e6 |
225 | } |
226 | |
8823192f |
227 | ec *ec_projfix(ec_curve *c, ec *d, const ec *p) |
228 | { |
229 | if (EC_ATINF(p)) |
230 | EC_SETINF(d); |
a02032a3 |
231 | else if (p->z == c->f->one) |
8823192f |
232 | EC_COPY(d, p); |
233 | else { |
234 | mp *z, *zz; |
235 | field *f = c->f; |
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); |
241 | mp_drop(z); |
242 | mp_drop(zz); |
243 | mp_drop(d->z); |
244 | d->z = MP_COPY(f->one); |
245 | } |
4edc47b8 |
246 | return (d); |
8823192f |
247 | } |
248 | |
b085fd91 |
249 | /* --- @ec_stdsub@ --- * |
250 | * |
251 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
252 | * @ec *d@ = pointer to the destination |
41cb1beb |
253 | * @const ec *p, *q@ = the operand points |
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254 | * |
255 | * Returns: The destination @d@. |
256 | * |
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. |
260 | */ |
261 | |
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262 | ec *ec_stdsub(ec_curve *c, ec *d, const ec *p, const ec *q) |
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263 | { |
264 | ec t = EC_INIT; |
41cb1beb |
265 | EC_NEG(c, &t, q); |
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266 | EC_FIX(c, &t, &t); |
41cb1beb |
267 | EC_ADD(c, d, p, &t); |
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268 | EC_DESTROY(&t); |
269 | return (d); |
270 | } |
271 | |
41cb1beb |
272 | /*----- Creating curves ---------------------------------------------------*/ |
273 | |
274 | /* --- @ec_destroycurve@ --- * |
275 | * |
276 | * Arguments: @ec_curve *c@ = pointer to an ellptic curve |
277 | * |
278 | * Returns: --- |
279 | * |
280 | * Use: Destroys a description of an elliptic curve. |
281 | */ |
282 | |
283 | void ec_destroycurve(ec_curve *c) { c->ops->destroy(c); } |
284 | |
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285 | /*----- Real arithmetic ---------------------------------------------------*/ |
286 | |
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287 | /* --- @ec_find@ --- * |
288 | * |
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 |
292 | * |
293 | * Returns: Zero if OK, nonzero if there isn't a point there. |
294 | * |
295 | * Use: Finds a point on an elliptic curve with a given x-coordinate. |
296 | */ |
297 | |
41a324a7 |
298 | ec *ec_find(ec_curve *c, ec *d, mp *x) |
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299 | { |
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300 | x = F_IN(c->f, MP_NEW, x); |
41a324a7 |
301 | if ((d = EC_FIND(c, d, x)) != 0) |
302 | EC_OUT(c, d, d); |
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303 | MP_DROP(x); |
41a324a7 |
304 | return (d); |
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305 | } |
306 | |
dbfee00a |
307 | /* --- @ec_neg@ --- * |
308 | * |
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 |
312 | * |
313 | * Returns: The destination point. |
314 | * |
315 | * Use: Computes the negation of the given point. |
316 | */ |
317 | |
318 | ec *ec_neg(ec_curve *c, ec *d, const ec *p) |
a02032a3 |
319 | { EC_IN(c, d, p); EC_NEG(c, d, d); return (EC_OUT(c, d, d)); } |
dbfee00a |
320 | |
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321 | /* --- @ec_add@ --- * |
322 | * |
323 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
324 | * @ec *d@ = pointer to the destination point |
325 | * @const ec *p, *q@ = pointers to the operand points |
326 | * |
327 | * Returns: --- |
328 | * |
329 | * Use: Adds two points on an elliptic curve. |
330 | */ |
331 | |
41a324a7 |
332 | ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q) |
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333 | { |
334 | ec pp = EC_INIT, qq = EC_INIT; |
41a324a7 |
335 | EC_IN(c, &pp, p); |
336 | EC_IN(c, &qq, q); |
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337 | EC_ADD(c, d, &pp, &qq); |
41a324a7 |
338 | EC_OUT(c, d, d); |
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339 | EC_DESTROY(&pp); |
340 | EC_DESTROY(&qq); |
41a324a7 |
341 | return (d); |
b0ab12e6 |
342 | } |
343 | |
dbfee00a |
344 | /* --- @ec_sub@ --- * |
345 | * |
346 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
347 | * @ec *d@ = pointer to the destination point |
348 | * @const ec *p, *q@ = pointers to the operand points |
349 | * |
350 | * Returns: The destination @d@. |
351 | * |
352 | * Use: Subtracts one point from another on an elliptic curve. |
353 | */ |
354 | |
355 | ec *ec_sub(ec_curve *c, ec *d, const ec *p, const ec *q) |
356 | { |
432c4e18 |
357 | ec pp = EC_INIT, qq = EC_INIT; |
dbfee00a |
358 | EC_IN(c, &pp, p); |
359 | EC_IN(c, &qq, q); |
bc985cef |
360 | EC_SUB(c, d, &pp, &qq); |
dbfee00a |
361 | EC_OUT(c, d, d); |
362 | EC_DESTROY(&pp); |
363 | EC_DESTROY(&qq); |
364 | return (d); |
365 | } |
366 | |
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367 | /* --- @ec_dbl@ --- * |
368 | * |
369 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
370 | * @ec *d@ = pointer to the destination point |
371 | * @const ec *p@ = pointer to the operand point |
372 | * |
373 | * Returns: --- |
374 | * |
375 | * Use: Doubles a point on an elliptic curve. |
376 | */ |
377 | |
41a324a7 |
378 | ec *ec_dbl(ec_curve *c, ec *d, const ec *p) |
a02032a3 |
379 | { EC_IN(c, d, p); EC_DBL(c, d, d); return (EC_OUT(c, d, d)); } |
b0ab12e6 |
380 | |
8823192f |
381 | /* --- @ec_check@ --- * |
382 | * |
383 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
384 | * @const ec *p@ = pointer to the point |
385 | * |
386 | * Returns: Zero if OK, nonzero if this is an invalid point. |
387 | * |
388 | * Use: Checks that a point is actually on an elliptic curve. |
389 | */ |
390 | |
391 | int ec_check(ec_curve *c, const ec *p) |
392 | { |
393 | ec t = EC_INIT; |
394 | int rc; |
395 | |
396 | if (EC_ATINF(p)) |
397 | return (0); |
398 | EC_IN(c, &t, p); |
399 | rc = EC_CHECK(c, &t); |
400 | EC_DESTROY(&t); |
401 | return (rc); |
402 | } |
403 | |
bc985cef |
404 | /* --- @ec_rand@ --- * |
405 | * |
406 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
407 | * @ec *d@ = pointer to the destination point |
408 | * @grand *r@ = random number source |
409 | * |
410 | * Returns: The destination @d@. |
411 | * |
412 | * Use: Finds a random point on the given curve. |
413 | */ |
414 | |
415 | ec *ec_rand(ec_curve *c, ec *d, grand *r) |
416 | { |
417 | mp *x = MP_NEW; |
418 | do x = F_RAND(c->f, x, r); while (!EC_FIND(c, d, x)); |
419 | mp_drop(x); |
420 | if (grand_range(r, 2)) EC_NEG(c, d, d); |
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421 | return (EC_OUT(c, d, d)); |
bc985cef |
422 | } |
423 | |
b0ab12e6 |
424 | /*----- That's all, folks -------------------------------------------------*/ |