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1 | /* -*-c-*- |
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2 | * |
3 | * Elliptic curve definitions |
4 | * |
5 | * (c) 2001 Straylight/Edgeware |
6 | */ |
7 | |
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8 | /*----- Licensing notice --------------------------------------------------* |
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9 | * |
10 | * This file is part of Catacomb. |
11 | * |
12 | * Catacomb is free software; you can redistribute it and/or modify |
13 | * it under the terms of the GNU Library General Public License as |
14 | * published by the Free Software Foundation; either version 2 of the |
15 | * License, or (at your option) any later version. |
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16 | * |
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17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
20 | * GNU Library General Public License for more details. |
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21 | * |
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22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
25 | * MA 02111-1307, USA. |
26 | */ |
27 | |
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28 | /*----- Header files ------------------------------------------------------*/ |
29 | |
30 | #include "ec.h" |
31 | |
32 | /*----- Trivial wrappers --------------------------------------------------*/ |
33 | |
34e4f738 |
34 | /* --- @ec_samep@ --- * |
35 | * |
36 | * Arguments: @ec_curve *c, *d@ = two elliptic curves |
37 | * |
38 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
39 | * |
40 | * Use: Checks for sameness of curves. This function does the full |
41 | * check, not just the curve-type-specific check done by the |
42 | * @sampep@ field operation. |
43 | */ |
44 | |
45 | int ec_samep(ec_curve *c, ec_curve *d) |
46 | { |
a02032a3 |
47 | return (c == d || (field_samep(c->f, d->f) && |
48 | c->ops == d->ops && EC_SAMEP(c, d))); |
34e4f738 |
49 | } |
50 | |
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51 | /* --- @ec_create@ --- * |
52 | * |
53 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
54 | * |
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55 | * Returns: The argument @p@. |
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56 | * |
57 | * Use: Initializes a new point. The initial value is the additive |
58 | * identity (which is universal for all curves). |
59 | */ |
60 | |
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61 | ec *ec_create(ec *p) { EC_CREATE(p); return (p); } |
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62 | |
63 | /* --- @ec_destroy@ --- * |
64 | * |
65 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
66 | * |
67 | * Returns: --- |
68 | * |
69 | * Use: Destroys a point, making it invalid. |
70 | */ |
71 | |
72 | void ec_destroy(ec *p) { EC_DESTROY(p); } |
73 | |
74 | /* --- @ec_atinf@ --- * |
75 | * |
76 | * Arguments: @const ec *p@ = pointer to a point |
77 | * |
78 | * Returns: Nonzero if %$p = O$% is the point at infinity, zero |
79 | * otherwise. |
80 | */ |
81 | |
82 | int ec_atinf(const ec *p) { return (EC_ATINF(p)); } |
83 | |
84 | /* --- @ec_setinf@ --- * |
85 | * |
86 | * Arguments: @ec *p@ = pointer to a point |
87 | * |
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88 | * Returns: The argument @p@. |
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89 | * |
90 | * Use: Sets the given point to be the point %$O$% at infinity. |
91 | */ |
92 | |
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93 | ec *ec_setinf(ec *p) { EC_SETINF(p); return (p); } |
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94 | |
95 | /* --- @ec_copy@ --- * |
96 | * |
97 | * Arguments: @ec *d@ = pointer to destination point |
98 | * @const ec *p@ = pointer to source point |
99 | * |
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100 | * Returns: The destination @d@. |
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101 | * |
102 | * Use: Creates a copy of an elliptic curve point. |
103 | */ |
104 | |
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105 | ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); } |
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106 | |
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107 | /* --- @ec_eq@ --- * |
108 | * |
109 | * Arguments: @const ec *p, *q@ = two points |
110 | * |
111 | * Returns: Nonzero if the points are equal. Compares external-format |
112 | * points. |
113 | */ |
114 | |
115 | int ec_eq(const ec *p, const ec *q) { return (EC_EQ(p, q)); } |
116 | |
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117 | /*----- Standard curve operations -----------------------------------------*/ |
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118 | |
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119 | /* --- @ec_stdsamep@ --- * |
120 | * |
121 | * Arguments: @ec_curve *c, *d@ = two elliptic curves |
122 | * |
123 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
124 | * |
125 | * Use: Simple sameness check on @a@ and @b@ curve members. |
126 | */ |
127 | |
128 | int ec_stdsamep(ec_curve *c, ec_curve *d) |
a02032a3 |
129 | { return (MP_EQ(c->a, d->a) && MP_EQ(c->b, d->b)); } |
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130 | |
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131 | /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- * |
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132 | * |
133 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
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134 | * @ec *d@ = pointer to the destination |
135 | * @const ec *p@ = pointer to a source point |
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136 | * |
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137 | * Returns: The destination @d@. |
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138 | * |
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139 | * Use: An identity operation if your curve has no internal |
140 | * representation. (The field internal representation is still |
141 | * used.) |
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142 | */ |
143 | |
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144 | ec *ec_idin(ec_curve *c, ec *d, const ec *p) |
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145 | { |
146 | if (EC_ATINF(p)) |
147 | EC_SETINF(d); |
148 | else { |
149 | field *f = c->f; |
150 | d->x = F_IN(f, d->x, p->x); |
151 | d->y = F_IN(f, d->y, p->y); |
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152 | mp_drop(d->z); d->z = 0; |
153 | } |
154 | return (d); |
155 | } |
156 | |
157 | ec *ec_idout(ec_curve *c, ec *d, const ec *p) |
158 | { |
159 | if (EC_ATINF(p)) |
160 | EC_SETINF(d); |
161 | else { |
162 | field *f = c->f; |
163 | d->x = F_OUT(f, d->x, p->x); |
164 | d->y = F_OUT(f, d->y, p->y); |
165 | mp_drop(d->z); d->z = 0; |
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166 | } |
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167 | return (d); |
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168 | } |
169 | |
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170 | ec *ec_idfix(ec_curve *c, ec *d, const ec *p) |
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171 | { EC_COPY(d, p); return (d); } |
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172 | |
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173 | /* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- * |
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174 | * |
175 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
41a324a7 |
176 | * @ec *d@ = pointer to the destination |
177 | * @const ec *p@ = pointer to a source point |
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178 | * |
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179 | * Returns: The destination @d@. |
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180 | * |
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181 | * Use: Conversion functions if your curve operations use a |
182 | * projective representation. |
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183 | */ |
184 | |
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185 | ec *ec_projin(ec_curve *c, ec *d, const ec *p) |
186 | { |
187 | if (EC_ATINF(p)) |
188 | EC_SETINF(d); |
189 | else { |
190 | field *f = c->f; |
191 | d->x = F_IN(f, d->x, p->x); |
192 | d->y = F_IN(f, d->y, p->y); |
193 | mp_drop(d->z); d->z = MP_COPY(f->one); |
194 | } |
195 | return (d); |
196 | } |
197 | |
198 | ec *ec_projout(ec_curve *c, ec *d, const ec *p) |
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199 | { |
200 | if (EC_ATINF(p)) |
201 | EC_SETINF(d); |
202 | else { |
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203 | mp *x, *y, *z, *zz; |
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204 | field *f = c->f; |
a02032a3 |
205 | if (p->z == f->one) { |
206 | d->x = F_OUT(f, d->x, p->x); |
207 | d->y = F_OUT(f, d->y, p->y); |
208 | } else { |
209 | z = F_INV(f, MP_NEW, p->z); |
210 | zz = F_SQR(f, MP_NEW, z); |
211 | z = F_MUL(f, z, zz, z); |
212 | x = F_MUL(f, d->x, p->x, zz); |
213 | y = F_MUL(f, d->y, p->y, z); |
214 | mp_drop(z); |
215 | mp_drop(zz); |
216 | d->x = F_OUT(f, x, x); |
217 | d->y = F_OUT(f, y, y); |
218 | } |
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219 | mp_drop(d->z); |
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220 | d->z = 0; |
221 | } |
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222 | return (d); |
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223 | } |
224 | |
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225 | ec *ec_projfix(ec_curve *c, ec *d, const ec *p) |
226 | { |
227 | if (EC_ATINF(p)) |
228 | EC_SETINF(d); |
a02032a3 |
229 | else if (p->z == c->f->one) |
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230 | EC_COPY(d, p); |
231 | else { |
232 | mp *z, *zz; |
233 | field *f = c->f; |
234 | z = F_INV(f, MP_NEW, p->z); |
235 | zz = F_SQR(f, MP_NEW, z); |
236 | z = F_MUL(f, z, zz, z); |
237 | d->x = F_MUL(f, d->x, p->x, zz); |
238 | d->y = F_MUL(f, d->y, p->y, z); |
239 | mp_drop(z); |
240 | mp_drop(zz); |
241 | mp_drop(d->z); |
242 | d->z = MP_COPY(f->one); |
243 | } |
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244 | return (d); |
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245 | } |
246 | |
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247 | /* --- @ec_stdsub@ --- * |
248 | * |
249 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
250 | * @ec *d@ = pointer to the destination |
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251 | * @const ec *p, *q@ = the operand points |
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252 | * |
253 | * Returns: The destination @d@. |
254 | * |
255 | * Use: Standard point subtraction operation, in terms of negation |
256 | * and addition. This isn't as efficient as a ready-made |
257 | * subtraction operator. |
258 | */ |
259 | |
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260 | ec *ec_stdsub(ec_curve *c, ec *d, const ec *p, const ec *q) |
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261 | { |
262 | ec t = EC_INIT; |
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263 | EC_NEG(c, &t, q); |
264 | EC_ADD(c, d, p, &t); |
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265 | EC_DESTROY(&t); |
266 | return (d); |
267 | } |
268 | |
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269 | /*----- Creating curves ---------------------------------------------------*/ |
270 | |
271 | /* --- @ec_destroycurve@ --- * |
272 | * |
273 | * Arguments: @ec_curve *c@ = pointer to an ellptic curve |
274 | * |
275 | * Returns: --- |
276 | * |
277 | * Use: Destroys a description of an elliptic curve. |
278 | */ |
279 | |
280 | void ec_destroycurve(ec_curve *c) { c->ops->destroy(c); } |
281 | |
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282 | /*----- Real arithmetic ---------------------------------------------------*/ |
283 | |
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284 | /* --- @ec_find@ --- * |
285 | * |
286 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
287 | * @ec *d@ = pointer to the destination point |
288 | * @mp *x@ = a possible x-coordinate |
289 | * |
290 | * Returns: Zero if OK, nonzero if there isn't a point there. |
291 | * |
292 | * Use: Finds a point on an elliptic curve with a given x-coordinate. |
293 | */ |
294 | |
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295 | ec *ec_find(ec_curve *c, ec *d, mp *x) |
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296 | { |
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297 | x = F_IN(c->f, MP_NEW, x); |
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298 | if ((d = EC_FIND(c, d, x)) != 0) |
299 | EC_OUT(c, d, d); |
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300 | MP_DROP(x); |
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301 | return (d); |
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302 | } |
303 | |
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304 | /* --- @ec_neg@ --- * |
305 | * |
306 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
307 | * @ec *d@ = pointer to the destination point |
308 | * @const ec *p@ = pointer to the operand point |
309 | * |
310 | * Returns: The destination point. |
311 | * |
312 | * Use: Computes the negation of the given point. |
313 | */ |
314 | |
315 | ec *ec_neg(ec_curve *c, ec *d, const ec *p) |
a02032a3 |
316 | { EC_IN(c, d, p); EC_NEG(c, d, d); return (EC_OUT(c, d, d)); } |
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317 | |
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318 | /* --- @ec_add@ --- * |
319 | * |
320 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
321 | * @ec *d@ = pointer to the destination point |
322 | * @const ec *p, *q@ = pointers to the operand points |
323 | * |
324 | * Returns: --- |
325 | * |
326 | * Use: Adds two points on an elliptic curve. |
327 | */ |
328 | |
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329 | ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q) |
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330 | { |
331 | ec pp = EC_INIT, qq = EC_INIT; |
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332 | EC_IN(c, &pp, p); |
333 | EC_IN(c, &qq, q); |
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334 | EC_ADD(c, d, &pp, &qq); |
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335 | EC_OUT(c, d, d); |
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336 | EC_DESTROY(&pp); |
337 | EC_DESTROY(&qq); |
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338 | return (d); |
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339 | } |
340 | |
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341 | /* --- @ec_sub@ --- * |
342 | * |
343 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
344 | * @ec *d@ = pointer to the destination point |
345 | * @const ec *p, *q@ = pointers to the operand points |
346 | * |
347 | * Returns: The destination @d@. |
348 | * |
349 | * Use: Subtracts one point from another on an elliptic curve. |
350 | */ |
351 | |
352 | ec *ec_sub(ec_curve *c, ec *d, const ec *p, const ec *q) |
353 | { |
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354 | ec pp = EC_INIT, qq = EC_INIT; |
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355 | EC_IN(c, &pp, p); |
356 | EC_IN(c, &qq, q); |
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357 | EC_SUB(c, d, &pp, &qq); |
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358 | EC_OUT(c, d, d); |
359 | EC_DESTROY(&pp); |
360 | EC_DESTROY(&qq); |
361 | return (d); |
362 | } |
363 | |
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364 | /* --- @ec_dbl@ --- * |
365 | * |
366 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
367 | * @ec *d@ = pointer to the destination point |
368 | * @const ec *p@ = pointer to the operand point |
369 | * |
370 | * Returns: --- |
371 | * |
372 | * Use: Doubles a point on an elliptic curve. |
373 | */ |
374 | |
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375 | ec *ec_dbl(ec_curve *c, ec *d, const ec *p) |
a02032a3 |
376 | { EC_IN(c, d, p); EC_DBL(c, d, d); return (EC_OUT(c, d, d)); } |
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377 | |
8823192f |
378 | /* --- @ec_check@ --- * |
379 | * |
380 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
381 | * @const ec *p@ = pointer to the point |
382 | * |
383 | * Returns: Zero if OK, nonzero if this is an invalid point. |
384 | * |
385 | * Use: Checks that a point is actually on an elliptic curve. |
386 | */ |
387 | |
388 | int ec_check(ec_curve *c, const ec *p) |
389 | { |
390 | ec t = EC_INIT; |
391 | int rc; |
392 | |
393 | if (EC_ATINF(p)) |
394 | return (0); |
395 | EC_IN(c, &t, p); |
396 | rc = EC_CHECK(c, &t); |
397 | EC_DESTROY(&t); |
398 | return (rc); |
399 | } |
400 | |
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401 | /* --- @ec_rand@ --- * |
402 | * |
403 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
404 | * @ec *d@ = pointer to the destination point |
405 | * @grand *r@ = random number source |
406 | * |
407 | * Returns: The destination @d@. |
408 | * |
409 | * Use: Finds a random point on the given curve. |
410 | */ |
411 | |
412 | ec *ec_rand(ec_curve *c, ec *d, grand *r) |
413 | { |
414 | mp *x = MP_NEW; |
415 | do x = F_RAND(c->f, x, r); while (!EC_FIND(c, d, x)); |
416 | mp_drop(x); |
417 | if (grand_range(r, 2)) EC_NEG(c, d, d); |
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418 | return (EC_OUT(c, d, d)); |
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419 | } |
420 | |
b0ab12e6 |
421 | /*----- That's all, folks -------------------------------------------------*/ |