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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: ec.c,v 1.3 2002/01/13 13:48:44 mdw Exp $ |
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4 | * |
5 | * Elliptic curve definitions |
6 | * |
7 | * (c) 2001 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
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. |
18 | * |
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. |
23 | * |
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 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: ec.c,v $ |
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33 | * Revision 1.3 2002/01/13 13:48:44 mdw |
34 | * Further progress. |
35 | * |
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36 | * Revision 1.2 2001/05/07 17:29:44 mdw |
37 | * Treat projective coordinates as an internal representation. Various |
38 | * minor interface changes. |
39 | * |
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40 | * Revision 1.1 2001/04/29 18:12:33 mdw |
41 | * Prototype version. |
42 | * |
43 | */ |
44 | |
45 | /*----- Header files ------------------------------------------------------*/ |
46 | |
47 | #include "ec.h" |
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48 | #include "ec-exp.h" |
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49 | |
50 | /*----- Trivial wrappers --------------------------------------------------*/ |
51 | |
52 | /* --- @ec_create@ --- * |
53 | * |
54 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
55 | * |
56 | * Returns: --- |
57 | * |
58 | * Use: Initializes a new point. The initial value is the additive |
59 | * identity (which is universal for all curves). |
60 | */ |
61 | |
62 | void ec_create(ec *p) { EC_CREATE(p); } |
63 | |
64 | /* --- @ec_destroy@ --- * |
65 | * |
66 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
67 | * |
68 | * Returns: --- |
69 | * |
70 | * Use: Destroys a point, making it invalid. |
71 | */ |
72 | |
73 | void ec_destroy(ec *p) { EC_DESTROY(p); } |
74 | |
75 | /* --- @ec_atinf@ --- * |
76 | * |
77 | * Arguments: @const ec *p@ = pointer to a point |
78 | * |
79 | * Returns: Nonzero if %$p = O$% is the point at infinity, zero |
80 | * otherwise. |
81 | */ |
82 | |
83 | int ec_atinf(const ec *p) { return (EC_ATINF(p)); } |
84 | |
85 | /* --- @ec_setinf@ --- * |
86 | * |
87 | * Arguments: @ec *p@ = pointer to a point |
88 | * |
89 | * Returns: --- |
90 | * |
91 | * Use: Sets the given point to be the point %$O$% at infinity. |
92 | */ |
93 | |
94 | void ec_setinf(ec *p) { EC_SETINF(p); } |
95 | |
96 | /* --- @ec_copy@ --- * |
97 | * |
98 | * Arguments: @ec *d@ = pointer to destination point |
99 | * @const ec *p@ = pointer to source point |
100 | * |
101 | * Returns: --- |
102 | * |
103 | * Use: Creates a copy of an elliptic curve point. |
104 | */ |
105 | |
106 | void ec_copy(ec *d, const ec *p) { EC_COPY(d, p); } |
107 | |
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108 | /*----- Standard curve operations -----------------------------------------*/ |
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109 | |
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110 | /* --- @ec_idin@, @ec_idout@ --- * |
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111 | * |
112 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
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113 | * @ec *d@ = pointer to the destination |
114 | * @const ec *p@ = pointer to a source point |
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115 | * |
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116 | * Returns: The destination @d@. |
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117 | * |
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118 | * Use: An identity operation if your curve has no internal |
119 | * representation. (The field internal representation is still |
120 | * used.) |
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121 | */ |
122 | |
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123 | ec *ec_idin(ec_curve *c, ec *d, const ec *p) |
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124 | { |
125 | if (EC_ATINF(p)) |
126 | EC_SETINF(d); |
127 | else { |
128 | field *f = c->f; |
129 | d->x = F_IN(f, d->x, p->x); |
130 | d->y = F_IN(f, d->y, p->y); |
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131 | mp_drop(d->z); d->z = 0; |
132 | } |
133 | return (d); |
134 | } |
135 | |
136 | ec *ec_idout(ec_curve *c, ec *d, const ec *p) |
137 | { |
138 | if (EC_ATINF(p)) |
139 | EC_SETINF(d); |
140 | else { |
141 | field *f = c->f; |
142 | d->x = F_OUT(f, d->x, p->x); |
143 | d->y = F_OUT(f, d->y, p->y); |
144 | mp_drop(d->z); d->z = 0; |
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145 | } |
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146 | return (d); |
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147 | } |
148 | |
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149 | /* --- @ec_projin@, @ec_projout@ --- * |
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150 | * |
151 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
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152 | * @ec *d@ = pointer to the destination |
153 | * @const ec *p@ = pointer to a source point |
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154 | * |
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155 | * Returns: The destination @d@. |
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156 | * |
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157 | * Use: Conversion functions if your curve operations use a |
158 | * projective representation. |
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159 | */ |
160 | |
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161 | ec *ec_projin(ec_curve *c, ec *d, const ec *p) |
162 | { |
163 | if (EC_ATINF(p)) |
164 | EC_SETINF(d); |
165 | else { |
166 | field *f = c->f; |
167 | d->x = F_IN(f, d->x, p->x); |
168 | d->y = F_IN(f, d->y, p->y); |
169 | mp_drop(d->z); d->z = MP_COPY(f->one); |
170 | } |
171 | return (d); |
172 | } |
173 | |
174 | ec *ec_projout(ec_curve *c, ec *d, const ec *p) |
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175 | { |
176 | if (EC_ATINF(p)) |
177 | EC_SETINF(d); |
178 | else { |
179 | mp *x, *y, *z; |
180 | field *f = c->f; |
181 | z = F_INV(f, MP_NEW, p->z); |
182 | x = F_MUL(f, d->x, p->x, z); |
183 | y = F_MUL(f, d->y, p->y, z); |
184 | mp_drop(z); |
185 | mp_drop(d->z); |
186 | d->x = F_OUT(f, x, x); |
187 | d->y = F_OUT(f, y, y); |
188 | d->z = 0; |
189 | } |
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190 | return (d); |
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191 | } |
192 | |
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193 | /* --- @ec_stdsub@ --- * |
194 | * |
195 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
196 | * @ec *d@ = pointer to the destination |
197 | * @const ec *a, *b@ = the operand points |
198 | * |
199 | * Returns: The destination @d@. |
200 | * |
201 | * Use: Standard point subtraction operation, in terms of negation |
202 | * and addition. This isn't as efficient as a ready-made |
203 | * subtraction operator. |
204 | */ |
205 | |
206 | ec *ec_stdsub(ec_curve *c, ec *d, const ec *a, const ec *b) |
207 | { |
208 | ec t = EC_INIT; |
209 | EC_NEG(c, &t, b); |
210 | EC_SUB(c, d, a, &t); |
211 | EC_DESTROY(&t); |
212 | return (d); |
213 | } |
214 | |
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215 | /*----- Real arithmetic ---------------------------------------------------*/ |
216 | |
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217 | /* --- @ec_find@ --- * |
218 | * |
219 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
220 | * @ec *d@ = pointer to the destination point |
221 | * @mp *x@ = a possible x-coordinate |
222 | * |
223 | * Returns: Zero if OK, nonzero if there isn't a point there. |
224 | * |
225 | * Use: Finds a point on an elliptic curve with a given x-coordinate. |
226 | */ |
227 | |
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228 | ec *ec_find(ec_curve *c, ec *d, mp *x) |
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229 | { |
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230 | x = F_IN(c->f, MP_NEW, x); |
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231 | if ((d = EC_FIND(c, d, x)) != 0) |
232 | EC_OUT(c, d, d); |
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233 | mp_drop(x); |
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234 | return (d); |
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235 | } |
236 | |
237 | /* --- @ec_add@ --- * |
238 | * |
239 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
240 | * @ec *d@ = pointer to the destination point |
241 | * @const ec *p, *q@ = pointers to the operand points |
242 | * |
243 | * Returns: --- |
244 | * |
245 | * Use: Adds two points on an elliptic curve. |
246 | */ |
247 | |
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248 | ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q) |
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249 | { |
250 | ec pp = EC_INIT, qq = EC_INIT; |
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251 | EC_IN(c, &pp, p); |
252 | EC_IN(c, &qq, q); |
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253 | EC_ADD(c, d, &pp, &qq); |
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254 | EC_OUT(c, d, d); |
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255 | EC_DESTROY(&pp); |
256 | EC_DESTROY(&qq); |
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257 | return (d); |
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258 | } |
259 | |
260 | /* --- @ec_dbl@ --- * |
261 | * |
262 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
263 | * @ec *d@ = pointer to the destination point |
264 | * @const ec *p@ = pointer to the operand point |
265 | * |
266 | * Returns: --- |
267 | * |
268 | * Use: Doubles a point on an elliptic curve. |
269 | */ |
270 | |
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271 | ec *ec_dbl(ec_curve *c, ec *d, const ec *p) |
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272 | { |
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273 | EC_IN(c, d, p); |
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274 | EC_DBL(c, d, d); |
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275 | return (EC_OUT(c, d, d)); |
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276 | } |
277 | |
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278 | /* --- @ec_imul@, @ec_mul@ --- * |
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279 | * |
280 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
281 | * @ec *d@ = pointer to the destination point |
282 | * @const ec *p@ = pointer to the generator point |
283 | * @mp *n@ = integer multiplier |
284 | * |
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285 | * Returns: The destination @d@. |
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286 | * |
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287 | * Use: Multiplies a point by a scalar, returning %$n p$%. The |
288 | * @imul@ variant uses internal representations for argument |
289 | * and result. |
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290 | */ |
291 | |
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292 | ec *ec_imul(ec_curve *c, ec *d, const ec *p, mp *n) |
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293 | { |
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294 | ec t = EC_INIT; |
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295 | |
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296 | EC_COPY(&t, p); |
297 | if (t.x && (n->f & MP_BURN)) |
298 | t.x->f |= MP_BURN; |
299 | MP_SHRINK(n); |
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300 | EC_SETINF(d); |
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301 | if (MP_LEN(n) == 0) |
302 | ; |
303 | else if (MP_LEN(n) < EXP_THRESH) |
304 | EXP_SIMPLE(&d, t, n); |
305 | else |
306 | EXP_WINDOW(&d, t, n); |
307 | return (d); |
308 | } |
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309 | |
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310 | ec *ec_mul(ec_curve *c, ec *d, const ec *p, mp *n) |
311 | { |
312 | EC_IN(c, d, p); |
313 | ec_imul(c, d, d, n); |
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314 | return (EC_OUT(c, d, d)); |
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315 | } |
316 | |
317 | /*----- That's all, folks -------------------------------------------------*/ |