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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: ec.h,v 1.2 2001/05/07 17:29:44 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.h,v $ |
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33 | * Revision 1.2 2001/05/07 17:29:44 mdw |
34 | * Treat projective coordinates as an internal representation. Various |
35 | * minor interface changes. |
36 | * |
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37 | * Revision 1.1 2001/04/29 18:12:33 mdw |
38 | * Prototype version. |
39 | * |
40 | */ |
41 | |
42 | #ifndef CATACOMB_EC_H |
43 | #define CATACOMB_EC_H |
44 | |
45 | #ifdef __cplusplus |
46 | extern "C" { |
47 | #endif |
48 | |
49 | /*----- Header files ------------------------------------------------------*/ |
50 | |
51 | #include "field.h" |
52 | #include "mp.h" |
53 | |
54 | /*----- Data structures ---------------------------------------------------*/ |
55 | |
56 | typedef struct ec_curve { |
57 | const struct ec_ops *ops; /* Curve operations */ |
58 | field *f; /* Underlying field structure */ |
59 | } ec_curve; |
60 | |
61 | typedef struct ec { |
62 | mp *x, *y; /* Point coordinates */ |
63 | mp *z; /* Common denominator (or null) */ |
64 | } ec; |
65 | |
66 | typedef struct ec_ops { |
67 | void (*destroy)(ec_curve */*c*/); |
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68 | ec *(*in)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
69 | ec *(*out)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
70 | ec *(*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/); |
71 | ec *(*add)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); |
72 | ec *(*dbl)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
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73 | } ec_ops; |
74 | |
75 | #define EC_DESTROY(c) (c)->ops->destroy((c)) |
76 | |
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77 | #define EC_IN(c, d, p) (c)->ops->in((c), (d), (p)) |
78 | #define EC_OUT(c, d, p) (c)->ops->in((c), (d), (p)) |
79 | |
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80 | #define EC_FIND(c, d, x) (c)->ops->find((c), (d), (x)) |
81 | #define EC_ADD(c, d, p, q) (c)->ops->add((c), (d), (p), (q)) |
82 | #define EC_DBL(c, d, p) (c)->ops->dbl((c), (d), (p)) |
83 | |
84 | /*----- Simple memory management things -----------------------------------*/ |
85 | |
86 | /* --- @ec_create@ --- * |
87 | * |
88 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
89 | * |
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90 | * Returns: The argument @p@. |
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91 | * |
92 | * Use: Initializes a new point. The initial value is the additive |
93 | * identity (which is universal for all curves). |
94 | */ |
95 | |
96 | #define EC_INIT { MP_NEW, MP_NEW, MP_NEW } |
97 | |
98 | #define EC_CREATE(p) do { \ |
99 | ec *_p = (p); \ |
100 | _p->x = _p->y = _p->z = MP_NEW; \ |
101 | } while (0) |
102 | |
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103 | extern ec *ec_create(ec */*p*/); |
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104 | |
105 | /* --- @ec_destroy@ --- * |
106 | * |
107 | * Arguments: @ec *p@ = pointer to an elliptic-curve point |
108 | * |
109 | * Returns: --- |
110 | * |
111 | * Use: Destroys a point, making it invalid. |
112 | */ |
113 | |
114 | #define EC_DESTROY(p) do { \ |
115 | ec *_p = (p); \ |
116 | if (!EC_ATINF(_p)) { \ |
117 | MP_DROP(_p->x); \ |
118 | MP_DROP(_p->y); \ |
119 | if (_p->z) MP_DROP(_p->z); \ |
120 | } \ |
121 | } while (0) |
122 | |
123 | extern void ec_destroy(ec */*p*/); |
124 | |
125 | /* --- @ec_atinf@ --- * |
126 | * |
127 | * Arguments: @const ec *p@ = pointer to a point |
128 | * |
129 | * Returns: Nonzero if %$p = O$% is the point at infinity, zero |
130 | * otherwise. |
131 | */ |
132 | |
133 | #define EC_ATINF(p) ((p)->x == MP_NEW || (p)->x == MP_NEWSEC) |
134 | |
135 | extern int ec_atinf(const ec */*p*/); |
136 | |
137 | /* --- @ec_setinf@ --- * |
138 | * |
139 | * Arguments: @ec *p@ = pointer to a point |
140 | * |
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141 | * Returns: The argument @p@. |
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142 | * |
143 | * Use: Sets the given point to be the point %$O$% at infinity. |
144 | */ |
145 | |
146 | #define EC_SETINF(p) do { \ |
147 | ec *_p = (p); \ |
148 | if (!EC_ATINF(_p)) { \ |
149 | MP_DROP(_p->x); \ |
150 | MP_DROP(_p->y); \ |
151 | if (_p->z) MP_DROP(_p->z); \ |
152 | _p->x = _p->y = _p->z = MP_NEW; \ |
153 | _p->y = MP_NEW; \ |
154 | _p->z = MP_NEW; \ |
155 | } \ |
156 | } while (0) |
157 | |
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158 | extern ec *ec_setinf(ec */*p*/); |
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159 | |
160 | /* --- @ec_copy@ --- * |
161 | * |
162 | * Arguments: @ec *d@ = pointer to destination point |
163 | * @const ec *p@ = pointer to source point |
164 | * |
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165 | * Returns: The destination @d@. |
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166 | * |
167 | * Use: Creates a copy of an elliptic curve point. |
168 | */ |
169 | |
170 | #define EC_COPY(d, p) do { \ |
171 | ec *_d = (d); \ |
172 | const ec *_p = (p); \ |
173 | if (d != p) { \ |
174 | EC_DESTROY(d); \ |
175 | if (EC_ATINF(p)) \ |
176 | _d->x = _d->y = _d->z = MP_NEW; \ |
177 | else { \ |
178 | _d->x = _p->x; \ |
179 | _d->y = _p->y; \ |
180 | _d->z = _p->z; \ |
181 | } \ |
182 | } \ |
183 | } while (0) |
184 | |
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185 | extern ec *ec_copy(ec */*d*/, const ec */*p*/); |
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186 | |
187 | /*----- Interesting arithmetic --------------------------------------------*/ |
188 | |
189 | /* --- @ec_denorm@ --- * |
190 | * |
191 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
192 | * @ec *d@ = pointer to the destination point |
193 | * @const ec *p@ = pointer to the source point |
194 | * |
195 | * Returns: --- |
196 | * |
197 | * Use: Denormalizes the given point, converting to internal |
198 | * representations and setting the denominator to 1. |
199 | */ |
200 | |
201 | extern void ec_denorm(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
202 | |
203 | /* --- @ec_norm@ --- * |
204 | * |
205 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
206 | * @ec *d@ = pointer to the destination point |
207 | * @const ec *p@ = pointer to the source point |
208 | * |
209 | * Returns: --- |
210 | * |
211 | * Use: Normalizes the given point, by dividing through by the |
212 | * denominator and returning to external representation. |
213 | */ |
214 | |
215 | extern void ec_norm(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
216 | |
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 | |
228 | extern void ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); |
229 | |
230 | /* --- @ec_add@ --- * |
231 | * |
232 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
233 | * @ec *d@ = pointer to the destination point |
234 | * @const ec *p, *q@ = pointers to the operand points |
235 | * |
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236 | * Returns: The destination @d@. |
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237 | * |
238 | * Use: Adds two points on an elliptic curve. |
239 | */ |
240 | |
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241 | extern ec *ec_add(ec_curve */*c*/, ec */*d*/, |
242 | const ec */*p*/, const ec */*q*/); |
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243 | |
244 | /* --- @ec_dbl@ --- * |
245 | * |
246 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
247 | * @ec *d@ = pointer to the destination point |
248 | * @const ec *p@ = pointer to the operand point |
249 | * |
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250 | * Returns: The destination @d@. |
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251 | * |
252 | * Use: Doubles a point on an elliptic curve. |
253 | */ |
254 | |
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255 | extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
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256 | |
257 | /* --- @ec_mul@ --- * |
258 | * |
259 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
260 | * @ec *d@ = pointer to the destination point |
261 | * @const ec *p@ = pointer to the generator point |
262 | * @mp *n@ = integer multiplier |
263 | * |
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264 | * Returns: The destination @d@. |
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265 | * |
266 | * Use: Multiplies a point by a scalar, returning %$n p$%. |
267 | */ |
268 | |
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269 | extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); |
270 | |
271 | /*----- Standard curve operations -----------------------------------------*/ |
272 | |
273 | /* --- @ec_idin@, @ec_idout@ --- * |
274 | * |
275 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
276 | * @ec *d@ = pointer to the destination |
277 | * @const ec *p@ = pointer to a source point |
278 | * |
279 | * Returns: The destination @d@. |
280 | * |
281 | * Use: An identity operation if your curve has no internal |
282 | * representation. (The field internal representation is still |
283 | * used.) |
284 | */ |
285 | |
286 | extern ec *ec_idin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
287 | extern ec *ec_idout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
288 | |
289 | /* --- @ec_projin@, @ec_projout@ --- * |
290 | * |
291 | * Arguments: @ec_curve *c@ = pointer to an elliptic curve |
292 | * @ec *d@ = pointer to the destination |
293 | * @const ec *p@ = pointer to a source point |
294 | * |
295 | * Returns: The destination @d@. |
296 | * |
297 | * Use: Conversion functions if your curve operations use a |
298 | * projective representation. |
299 | */ |
300 | |
301 | extern ec *ec_projin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
302 | extern ec *ec_projout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); |
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303 | |
304 | /*----- Creating curves ---------------------------------------------------*/ |
305 | |
306 | /* --- @ec_prime@ --- * |
307 | * |
308 | * Arguments: @field *f@ = the underyling field for this elliptic curve |
309 | * @mp *a, *b@ = the coefficients for this curve |
310 | * |
311 | * Returns: A pointer to the curve. |
312 | * |
313 | * Use: Creates a curve structure for an elliptic curve defined over |
314 | * a prime field. |
315 | */ |
316 | |
317 | extern ec_curve *ec_prime(field */*f*/, mp */*a*/, mp */*b*/); |
318 | |
319 | /* --- @ec_bin@ --- * |
320 | * |
321 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
322 | * @mp *a, *b@ = the coefficients for this curve |
323 | * |
324 | * Returns: A pointer to the curve. |
325 | * |
326 | * Use: Creates a curve structure for a non-supersingular elliptic |
327 | * curve defined over a binary field. |
328 | */ |
329 | |
330 | extern ec_curve *ec_bin(field */*f*/, mp */*a*/, mp */*b*/); |
331 | |
332 | /*----- That's all, folks -------------------------------------------------*/ |
333 | |
334 | #ifdef __cplusplus |
335 | } |
336 | #endif |
337 | |
338 | #endif |