7765e926 |
1 | /* -*-c-*- |
2 | * |
c3caa2fa |
3 | * $Id: exp.h,v 1.2 2004/03/21 22:52:06 mdw Exp $ |
7765e926 |
4 | * |
5 | * Generalized exponentiation |
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: exp.h,v $ |
c3caa2fa |
33 | * Revision 1.2 2004/03/21 22:52:06 mdw |
34 | * Merge and close elliptic curve branch. |
35 | * |
8823192f |
36 | * Revision 1.1.4.1 2004/03/20 00:13:31 mdw |
37 | * Projective coordinates for prime curves |
38 | * |
7765e926 |
39 | * Revision 1.1 2001/06/16 13:00:59 mdw |
40 | * New generic exponentation code. Includes sliding-window simultaneous |
41 | * exponentiation. |
42 | * |
43 | */ |
44 | |
45 | #ifdef CATACOMB_EXP_H |
46 | # error "Multiple inclusion of <catacomb/exp.h>" |
47 | #endif |
48 | |
49 | #define CATACOMB_EXP_H |
50 | |
51 | #ifdef __cplusplus |
52 | extern "C" { |
53 | #endif |
54 | |
55 | /*----- Header files ------------------------------------------------------*/ |
56 | |
57 | #include <stddef.h> |
58 | |
59 | #include <mLib/alloc.h> |
60 | |
61 | #ifndef CATACOMB_MP_H |
62 | # include "mp.h" |
63 | #endif |
64 | |
65 | /*----- Data structures ---------------------------------------------------*/ |
66 | |
67 | typedef struct exp_simulscan { |
68 | mpw w; |
69 | size_t len; |
70 | const mpw *v; |
71 | } exp_simulscan; |
72 | |
73 | typedef struct exp_simul { |
74 | unsigned b; |
75 | size_t o, n; |
76 | exp_simulscan *s; |
77 | } exp_simul; |
78 | |
79 | /*----- Macros provided ---------------------------------------------------*/ |
80 | |
81 | /* --- Parameters --- */ |
82 | |
83 | #ifndef EXP_WINSZ /* Sliding window size */ |
84 | # define EXP_WINSZ 4 /* Predefine if you need to */ |
85 | #endif |
86 | |
87 | /* --- These are determined from the window size --- */ |
88 | |
89 | #define EXP_TABSZ (1 << EXP_WINSZ) |
90 | #define EXP_THRESH (((MPW_BITS / EXP_WINSZ) << 2) + 1) |
91 | |
92 | /* --- Required operations --- * |
93 | * |
94 | * The macros here are independent of the underlying group elements. You |
95 | * must provide the necessary group operations and other definitions. The |
96 | * group operation is assumed to be written multiplicatively. |
97 | * |
98 | * @EXP_TYPE@ The type of a group element, e.g., @mp *@. |
99 | * |
100 | * @EXP_COPY(d, x)@ Makes @d@ be a copy of @x@. |
101 | * |
102 | * @EXP_DROP(x)@ Discards the element @x@, reclaiming any |
103 | * memory it used. |
104 | * |
105 | * @EXP_MUL(a, x)@ Multiplies @a@ by @x@ (writing the result |
106 | * back to @a@). |
107 | * |
8823192f |
108 | * @EXP_FIX(x)@ Makes @x@ be a canonical representation of |
109 | * its value. All multiplications have the |
110 | * right argument canonical. |
111 | * |
7765e926 |
112 | * @EXP_SQR(a)@ Multiplies @a@ by itself. |
113 | * |
114 | * @EXP_SETMUL(d, x, y)@ Sets @d@ to be the product of @x@ and @y@. |
115 | * The value @d@ has not been initialized. |
116 | * |
117 | * @EXP_SETSQR(d, x)@ Sets @d@ to be the square of @x@. |
118 | * |
119 | * Only @EXP_TYPE@, @EXP_MUL@ and @EXP_SQR@ are required for simple |
120 | * exponentation. Sliding window and simultaneous exponentation require all |
121 | * of the operations. |
122 | */ |
123 | |
124 | #ifndef EXP_TYPE |
125 | # error "EXP_TYPE not defined for <catacomb/exp.h>" |
126 | #endif |
127 | |
128 | /* --- @EXP_SIMPLE@ --- * |
129 | * |
130 | * Arguments: @a@ = the result object, initially a multiplicative identity |
131 | * @g@ = the object to exponentiate |
132 | * @x@ = the exponent, as a multiprecision integer |
133 | * |
134 | * Use: Performs a simple left-to-right exponentiation. At the end |
135 | * of the code, the answer is left in @a@; @g@ and @x@ are |
136 | * unchanged. |
137 | */ |
138 | |
139 | #define EXP_SIMPLE(a, g, x) do { \ |
140 | mpscan sc; \ |
141 | unsigned sq = 0; \ |
142 | \ |
143 | /* --- Begin scanning --- */ \ |
144 | \ |
145 | mp_rscan(&sc, x); \ |
146 | if (!MP_RSTEP(&sc)) \ |
147 | goto exp_simple_exit; \ |
148 | while (!MP_RBIT(&sc)) \ |
149 | MP_RSTEP(&sc); \ |
150 | \ |
151 | /* --- Do the main body of the work --- */ \ |
152 | \ |
8823192f |
153 | EXP_FIX(g); \ |
7765e926 |
154 | for (;;) { \ |
155 | EXP_MUL(a, g); \ |
156 | sq = 0; \ |
157 | for (;;) { \ |
158 | if (!MP_RSTEP(&sc)) \ |
159 | goto exp_simple_done; \ |
160 | sq++; \ |
161 | if (MP_RBIT(&sc)) \ |
162 | break; \ |
163 | } \ |
164 | while (sq--) EXP_SQR(a); \ |
165 | } \ |
166 | \ |
167 | /* --- Do a final round of squaring --- */ \ |
168 | \ |
169 | exp_simple_done: \ |
170 | while (sq--) EXP_SQR(a); \ |
171 | exp_simple_exit:; \ |
172 | } while (0) |
173 | |
174 | /* --- @EXP_WINDOW@ --- * |
175 | * |
176 | * Arguments: @a@ = the result object, initially a multiplicative identity |
177 | * @g@ = the object to exponentiate |
178 | * @x@ = the exponent, as a multiprecision integer |
179 | * |
180 | * Use: Performs a sliding-window exponentiation. At the end of the |
181 | * code, the answer is left in @a@; @g@ and @x@ are unchanged. |
182 | */ |
183 | |
184 | #define EXP_WINDOW(a, g, x) do { \ |
185 | EXP_TYPE *v; \ |
186 | EXP_TYPE g2; \ |
187 | unsigned i, sq = 0; \ |
188 | mpscan sc; \ |
189 | \ |
190 | /* --- Get going --- */ \ |
191 | \ |
192 | mp_rscan(&sc, x); \ |
193 | if (!MP_RSTEP(&sc)) \ |
194 | goto exp_window_exit; \ |
195 | \ |
196 | /* --- Do the precomputation --- */ \ |
197 | \ |
8823192f |
198 | EXP_FIX(g); \ |
7765e926 |
199 | EXP_SETSQR(g2, g); \ |
8823192f |
200 | EXP_FIX(g2); \ |
7765e926 |
201 | v = xmalloc(EXP_TABSZ * sizeof(EXP_TYPE)); \ |
202 | EXP_COPY(v[0], g); \ |
8823192f |
203 | for (i = 1; i < EXP_TABSZ; i++) { \ |
7765e926 |
204 | EXP_SETMUL(v[i], v[i - 1], g2); \ |
8823192f |
205 | EXP_FIX(v[i]); \ |
206 | } \ |
7765e926 |
207 | EXP_DROP(g2); \ |
208 | \ |
209 | /* --- Skip top-end zero bits --- * \ |
210 | * \ |
211 | * If the initial step worked, there must be a set bit somewhere, so \ |
212 | * keep stepping until I find it. \ |
213 | */ \ |
214 | \ |
215 | while (!MP_RBIT(&sc)) \ |
216 | MP_RSTEP(&sc); \ |
217 | \ |
218 | /* --- Now for the main work --- */ \ |
219 | \ |
220 | for (;;) { \ |
221 | unsigned l = 1; \ |
222 | unsigned z = 0; \ |
223 | \ |
224 | /* --- The next bit is set, so read a window index --- * \ |
225 | * \ |
226 | * Reset @i@ to zero and increment @sq@. Then, until either I read \ |
227 | * @WINSZ@ bits or I run out of bits, scan in a bit: if it's clear, \ |
228 | * bump the @z@ counter; if it's set, push a set bit into @i@, \ |
229 | * shift it over by @z@ bits, bump @sq@ by @z + 1@ and clear @z@. \ |
230 | * By the end of this palaver, @i@ is an index to the precomputed \ |
231 | * value in @v@. \ |
232 | */ \ |
233 | \ |
234 | i = 0; \ |
235 | sq++; \ |
236 | while (l < EXP_WINSZ && MP_RSTEP(&sc)) { \ |
237 | l++; \ |
238 | if (!MP_RBIT(&sc)) \ |
239 | z++; \ |
240 | else { \ |
241 | i = ((i << 1) | 1) << z; \ |
242 | sq += z + 1; \ |
243 | z = 0; \ |
244 | } \ |
245 | } \ |
246 | \ |
247 | /* --- Do the squaring --- * \ |
248 | * \ |
249 | * Remember that @sq@ carries over from the zero-skipping stuff \ |
250 | * below. \ |
251 | */ \ |
252 | \ |
253 | while (sq--) EXP_SQR(a); \ |
254 | \ |
255 | /* --- Do the multiply --- */ \ |
256 | \ |
257 | EXP_MUL(a, v[i]); \ |
258 | \ |
259 | /* --- Now grind along through the rest of the bits --- */ \ |
260 | \ |
261 | sq = z; \ |
262 | for (;;) { \ |
263 | if (!MP_RSTEP(&sc)) \ |
264 | goto exp_window_done; \ |
265 | if (MP_RBIT(&sc)) \ |
266 | break; \ |
267 | sq++; \ |
268 | } \ |
269 | } \ |
270 | \ |
271 | /* --- Do a final round of squaring --- */ \ |
272 | \ |
273 | exp_window_done: \ |
274 | while (sq--) EXP_SQR(a); \ |
275 | for (i = 0; i < EXP_TABSZ; i++) \ |
276 | EXP_DROP(v[i]); \ |
277 | xfree(v); \ |
278 | exp_window_exit:; \ |
279 | } while (0) |
280 | |
281 | /* --- @EXP_SIMUL@ --- * |
282 | * |
283 | * Arguments: @a@ = the result object, initially a multiplicative identity |
284 | * @f@ = pointer to a vector of base/exp pairs |
285 | * @n@ = the number of base/exp pairs |
286 | * |
287 | * Use: Performs a simultaneous sliding-window exponentiation. The |
288 | * @f@ table is an array of structures containing members @base@ |
289 | * of type @EXP_TYPE@, and @exp@ of type @mp *@. |
290 | */ |
291 | |
292 | #define EXP_SIMUL(a, f, n) do { \ |
293 | size_t i, j, jj, k; \ |
294 | size_t vn = 1 << (EXP_WINSZ * n), m = (1 << n) - 1; \ |
295 | EXP_TYPE *v = xmalloc(vn * sizeof(EXP_TYPE)); \ |
296 | exp_simul e; \ |
297 | unsigned sq = 0; \ |
298 | \ |
299 | /* --- Fill in the precomputed table --- */ \ |
300 | \ |
301 | j = 1; \ |
302 | for (i = 0; i < n; i++) { \ |
303 | EXP_COPY(v[j], f[n - 1 - i].base); \ |
8823192f |
304 | EXP_FIX(v[j]); \ |
7765e926 |
305 | j <<= 1; \ |
306 | } \ |
307 | k = n * EXP_WINSZ; \ |
308 | jj = 1; \ |
309 | for (; i < k; i++) { \ |
310 | EXP_SETSQR(v[j], v[jj]); \ |
8823192f |
311 | EXP_FIX(v[j]); \ |
7765e926 |
312 | j <<= 1; jj <<= 1; \ |
313 | } \ |
314 | for (i = 1; i < vn; i <<= 1) { \ |
8823192f |
315 | for (j = 1; j < i; j++) { \ |
7765e926 |
316 | EXP_SETMUL(v[j + i], v[j], v[i]); \ |
8823192f |
317 | EXP_FIX(v[j + i]); \ |
318 | } \ |
7765e926 |
319 | } \ |
320 | \ |
321 | /* --- Set up the bitscanners --- * \ |
322 | * \ |
323 | * Got to use custom scanners, to keep them all in sync. \ |
324 | */ \ |
325 | \ |
326 | e.n = n; \ |
327 | e.b = 0; \ |
328 | e.s = xmalloc(n * sizeof(*e.s)); \ |
329 | e.o = 0; \ |
330 | for (i = 0; i < n; i++) { \ |
331 | MP_SHRINK(f[i].exp); \ |
332 | e.s[i].len = MP_LEN(f[i].exp); \ |
333 | e.s[i].v = f[i].exp->v; \ |
334 | if (e.s[i].len > e.o) \ |
335 | e.o = e.s[i].len; \ |
336 | } \ |
337 | \ |
338 | /* --- Skip as far as a nonzero column in the exponent matrix --- */ \ |
339 | \ |
340 | do { \ |
341 | if (!e.o && !e.b) \ |
342 | goto exp_simul_done; \ |
343 | i = exp_simulnext(&e, 0); \ |
344 | } while (!(i & m)); \ |
345 | \ |
346 | /* --- Now for the main work --- */ \ |
347 | \ |
348 | for (;;) { \ |
349 | unsigned l = 1; \ |
350 | unsigned z = 0; \ |
351 | \ |
352 | /* --- Just read a nonzero column, so read a window index --- * \ |
353 | * \ |
354 | * Clear high bits of @i@ and increment @sq@. Then, until either I \ |
355 | * read @WINSZ@ columns or I run out, scan in a column and append \ |
356 | * it to @i@. If it's zero, bump the @z@ counter; if it's nonzero, \ |
357 | * bump @sq@ by @z + 1@ and clear @z@. By the end of this palaver, \ |
358 | * @i@ is an index to the precomputed value in @v@, followed by \ |
359 | * @n * z@ zero bits. \ |
360 | */ \ |
361 | \ |
362 | sq++; \ |
363 | while (l < EXP_WINSZ && (e.o || e.b)) { \ |
364 | l++; \ |
365 | i = exp_simulnext(&e, i); \ |
366 | if (!(i & m)) \ |
367 | z++; \ |
368 | else { \ |
369 | sq += z + 1; \ |
370 | z = 0; \ |
371 | } \ |
372 | } \ |
373 | \ |
374 | /* --- Do the squaring --- * \ |
375 | * \ |
376 | * Remember that @sq@ carries over from the zero-skipping stuff \ |
377 | * below. \ |
378 | */ \ |
379 | \ |
380 | while (sq--) EXP_SQR(a); \ |
381 | \ |
382 | /* --- Do the multiply --- */ \ |
383 | \ |
384 | i >>= (z * n); \ |
385 | EXP_MUL(a, v[i]); \ |
386 | \ |
387 | /* --- Now grind along through the rest of the bits --- */ \ |
388 | \ |
389 | sq = z; \ |
390 | for (;;) { \ |
391 | if (!e.o && !e.b) \ |
392 | goto exp_simul_done; \ |
393 | if ((i = exp_simulnext(&e, 0)) != 0) \ |
394 | break; \ |
395 | sq++; \ |
396 | } \ |
397 | } \ |
398 | \ |
399 | /* --- Do a final round of squaring --- */ \ |
400 | \ |
401 | exp_simul_done: \ |
402 | while (sq--) EXP_SQR(a); \ |
8823192f |
403 | for (i = 1; i < vn; i++) \ |
7765e926 |
404 | EXP_DROP(v[i]); \ |
405 | xfree(v); \ |
406 | } while (0) |
407 | |
408 | /*----- Functions provided ------------------------------------------------*/ |
409 | |
410 | /* --- @exp_simulnext@ --- * |
411 | * |
412 | * Arguments: @exp_simul *e@ = pointer to state structure |
413 | * @size_t x@ = a current accumulator |
414 | * |
415 | * Returns: The next column of bits. |
416 | * |
417 | * Use: Scans the next column of bits for a simultaneous |
418 | * exponentiation. |
419 | */ |
420 | |
421 | extern size_t exp_simulnext(exp_simul */*e*/, size_t /*x*/); |
422 | |
423 | /*----- That's all, folks -------------------------------------------------*/ |
424 | |
425 | #ifdef __cplusplus |
426 | } |
427 | #endif |