d03ab969 |
1 | /* -*-c-*- |
2 | * |
a69a3efd |
3 | * $Id$ |
d03ab969 |
4 | * |
d3409d5e |
5 | * Simple multiprecision arithmetic |
d03ab969 |
6 | * |
7 | * (c) 1999 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 | |
d9a8ae10 |
30 | #ifndef CATACOMB_MP_H |
31 | #define CATACOMB_MP_H |
d03ab969 |
32 | |
33 | #ifdef __cplusplus |
34 | extern "C" { |
35 | #endif |
36 | |
37 | /*----- Header files ------------------------------------------------------*/ |
38 | |
d3409d5e |
39 | #include <assert.h> |
d03ab969 |
40 | #include <string.h> |
41 | |
d3409d5e |
42 | #include <mLib/sub.h> |
43 | |
d9a8ae10 |
44 | #ifndef CATACOMB_MPW_H |
d3409d5e |
45 | # include "mpw.h" |
d03ab969 |
46 | #endif |
47 | |
d34decd2 |
48 | #ifndef CATACOMB_ARENA_H |
49 | # include "arena.h" |
50 | #endif |
51 | |
52 | #ifndef CATACOMB_MPARENA_H |
53 | # include "mparena.h" |
54 | #endif |
55 | |
d9a8ae10 |
56 | #ifndef CATACOMB_MPX_H |
d03ab969 |
57 | # include "mpx.h" |
58 | #endif |
59 | |
d03ab969 |
60 | /*----- Data structures ---------------------------------------------------*/ |
61 | |
3bc0a0fe |
62 | /* --- A multiprecision integer --- */ |
63 | |
d03ab969 |
64 | typedef struct mp { |
3bc0a0fe |
65 | mpw *v, *vl; /* Vector of digits, current limit */ |
66 | size_t sz; /* Size of digit buffer in words */ |
67 | mparena *a; /* Arena for buffer allocation */ |
68 | unsigned f; /* Flags (see below) */ |
69 | unsigned ref; /* Reference counter */ |
d03ab969 |
70 | } mp; |
71 | |
3bc0a0fe |
72 | #define MP_NEG 1u /* Negative (signed magnitude) */ |
73 | #define MP_BURN 2u /* Secret (viral flag) */ |
74 | #define MP_CONST 4u /* Uses strange memory allocation */ |
75 | #define MP_UNDEF 8u /* Contains nothing interesting */ |
76 | #define MP_DESTROYED 16u /* Has been destroyed */ |
77 | |
78 | /* --- A factor for simultaneous exponentation --- * |
79 | * |
80 | * Used by the Montgomery and Barrett exponentiators. |
81 | */ |
82 | |
83 | typedef struct mp_expfactor { |
84 | mp *base; |
85 | mp *exp; |
86 | } mp_expfactor; |
d03ab969 |
87 | |
d3409d5e |
88 | /*----- Useful constants --------------------------------------------------*/ |
d03ab969 |
89 | |
d3409d5e |
90 | extern mp mp_const[]; |
d03ab969 |
91 | |
d3409d5e |
92 | #define MP_ZERO (&mp_const[0]) |
93 | #define MP_ONE (&mp_const[1]) |
94 | #define MP_TWO (&mp_const[2]) |
95 | #define MP_THREE (&mp_const[3]) |
96 | #define MP_FOUR (&mp_const[4]) |
97 | #define MP_FIVE (&mp_const[5]) |
98 | #define MP_TEN (&mp_const[6]) |
d34decd2 |
99 | #define MP_256 (&mp_const[7]) |
100 | #define MP_MONE (&mp_const[8]) |
d03ab969 |
101 | |
d3409d5e |
102 | #define MP_NEW ((mp *)0) |
d34decd2 |
103 | #define MP_NEWSEC (&mp_const[9]) |
d03ab969 |
104 | |
d34decd2 |
105 | /*----- Trivial macros ----------------------------------------------------*/ |
d03ab969 |
106 | |
d34decd2 |
107 | /* --- @MP_LEN@ --- * |
d03ab969 |
108 | * |
d34decd2 |
109 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
110 | * |
d34decd2 |
111 | * Returns: Length of the integer, in words. |
d03ab969 |
112 | */ |
113 | |
d34decd2 |
114 | #define MP_LEN(m) ((m)->vl - ((m)->v)) |
d03ab969 |
115 | |
d34decd2 |
116 | /*----- Memory management and reference counting --------------------------*/ |
d3409d5e |
117 | |
d34decd2 |
118 | /* --- @mp_new@ --- * |
d03ab969 |
119 | * |
d34decd2 |
120 | * Arguments: @size_t sz@ = size of vector required |
121 | * @unsigned f@ = flags to set |
d03ab969 |
122 | * |
d34decd2 |
123 | * Returns: Pointer to a new MP structure. |
d03ab969 |
124 | * |
d34decd2 |
125 | * Use: Allocates a new multiprecision integer. The data space is |
126 | * allocated from either the standard global or secret arena, |
127 | * depending on the initial flags requested. |
d03ab969 |
128 | */ |
129 | |
d34decd2 |
130 | extern mp *mp_new(size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
131 | |
d34decd2 |
132 | /* --- @mp_create@ --- * |
d03ab969 |
133 | * |
d34decd2 |
134 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
135 | * |
d34decd2 |
136 | * Returns: Pointer to pristine new MP structure with enough memory |
137 | * bolted onto it. |
138 | * |
139 | * Use: Creates a new multiprecision integer with indeterminate |
140 | * contents. The integer has a single reference. |
d03ab969 |
141 | */ |
142 | |
d34decd2 |
143 | extern mp *mp_create(size_t /*sz*/); |
d3409d5e |
144 | |
d34decd2 |
145 | /* --- @mp_createsecure@ --- * |
d03ab969 |
146 | * |
d3409d5e |
147 | * Arguments: @size_t sz@ = size of vector required |
d03ab969 |
148 | * |
d3409d5e |
149 | * Returns: Pointer to pristine new MP structure with enough memory |
150 | * bolted onto it. |
d03ab969 |
151 | * |
d3409d5e |
152 | * Use: Creates a new multiprecision integer with indeterminate |
d34decd2 |
153 | * contents. The integer has a single reference. The integer's |
154 | * data space is allocated from the secure arena. Its burn flag |
155 | * is set. |
d03ab969 |
156 | */ |
157 | |
d34decd2 |
158 | extern mp *mp_createsecure(size_t /*sz*/); |
d03ab969 |
159 | |
d3409d5e |
160 | /* --- @mp_build@ --- * |
d03ab969 |
161 | * |
d3409d5e |
162 | * Arguments: @mp *m@ = pointer to an MP block to fill in |
163 | * @mpw *v@ = pointer to a word array |
164 | * @mpw *vl@ = pointer just past end of array |
d03ab969 |
165 | * |
166 | * Returns: --- |
167 | * |
d3409d5e |
168 | * Use: Creates a multiprecision integer representing some smallish |
169 | * number. You must provide storage for the number and dispose |
170 | * of it when you've finished with it. The number is marked as |
171 | * constant while it exists. |
d03ab969 |
172 | */ |
173 | |
d3409d5e |
174 | extern void mp_build(mp */*m*/, mpw */*v*/, mpw */*vl*/); |
d03ab969 |
175 | |
d3409d5e |
176 | /* --- @mp_destroy@ --- * |
d03ab969 |
177 | * |
d3409d5e |
178 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
179 | * |
180 | * Returns: --- |
181 | * |
d3409d5e |
182 | * Use: Destroys a multiprecision integer. The reference count isn't |
183 | * checked. Don't use this function if you don't know what |
184 | * you're doing: use @mp_drop@ instead. |
d03ab969 |
185 | */ |
186 | |
d3409d5e |
187 | extern void mp_destroy(mp */*m*/); |
d03ab969 |
188 | |
d3409d5e |
189 | /* --- @mp_copy@ --- * |
d03ab969 |
190 | * |
d3409d5e |
191 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
192 | * |
d3409d5e |
193 | * Returns: A copy of the given multiprecision integer. |
194 | * |
195 | * Use: Copies the given integer. In fact you just get another |
196 | * reference to the same old one again. |
d03ab969 |
197 | */ |
198 | |
d3409d5e |
199 | extern mp *mp_copy(mp */*m*/); |
d03ab969 |
200 | |
d3409d5e |
201 | #define MP_COPY(m) ((m)->ref++, (m)) |
202 | |
203 | /* --- @mp_drop@ --- * |
d03ab969 |
204 | * |
d3409d5e |
205 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
206 | * |
207 | * Returns: --- |
208 | * |
d3409d5e |
209 | * Use: Drops a reference to an integer which isn't wanted any more. |
210 | * If there are no more references, the integer is destroyed. |
d03ab969 |
211 | */ |
212 | |
d3409d5e |
213 | extern void mp_drop(mp */*m*/); |
d03ab969 |
214 | |
d3409d5e |
215 | #define MP_DROP(m) do { \ |
216 | mp *_mm = (m); \ |
d34decd2 |
217 | _mm->ref--; \ |
218 | if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \ |
d3409d5e |
219 | mp_destroy(_mm); \ |
220 | } while (0) |
221 | |
222 | /* --- @mp_split@ --- * |
d03ab969 |
223 | * |
d3409d5e |
224 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
225 | * |
d3409d5e |
226 | * Returns: A reference to the same integer, possibly with a different |
227 | * address. |
d03ab969 |
228 | * |
d3409d5e |
229 | * Use: Splits off a modifiable version of the integer referred to. |
d03ab969 |
230 | */ |
231 | |
d3409d5e |
232 | extern mp *mp_split(mp */*m*/); |
233 | |
234 | #define MP_SPLIT(m) do { \ |
d34decd2 |
235 | mp *_m = (m); \ |
236 | if ((_m->f & MP_CONST) || _m->ref > 1) { \ |
237 | size_t _len = MP_LEN(_m); \ |
238 | mp *_mm = mp_new(_len, _m->f); \ |
239 | if (!(_m->f & MP_UNDEF)) \ |
240 | memcpy(_mm->v, _m->v, MPWS(_len)); \ |
241 | _m->ref--; \ |
242 | _m = _mm; \ |
d3409d5e |
243 | } \ |
d34decd2 |
244 | (m) = _m; \ |
d3409d5e |
245 | } while (0) |
d03ab969 |
246 | |
d3409d5e |
247 | /* --- @mp_resize@ --- * |
d03ab969 |
248 | * |
d3409d5e |
249 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
250 | * @size_t sz@ = new size |
d03ab969 |
251 | * |
d3409d5e |
252 | * Returns: --- |
d03ab969 |
253 | * |
d3409d5e |
254 | * Use: Resizes the vector containing the integer's digits. The new |
255 | * size must be at least as large as the current integer's |
d34decd2 |
256 | * length. This isn't really intended for client use. |
d03ab969 |
257 | */ |
258 | |
d3409d5e |
259 | extern void mp_resize(mp */*m*/, size_t /*sz*/); |
260 | |
261 | #define MP_RESIZE(m, ssz) do { \ |
262 | mp *_m = (m); \ |
263 | size_t _sz = (ssz); \ |
d34decd2 |
264 | mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \ |
265 | mpw *_v; \ |
d3409d5e |
266 | size_t _len = MP_LEN(_m); \ |
d34decd2 |
267 | assert(((void)"can't make size less than length", _sz >= _len)); \ |
268 | _v = mpalloc(_a, _sz); \ |
d9a8ae10 |
269 | if (!(_m->f & MP_UNDEF)) \ |
270 | memcpy(_v, _m->v, MPWS(_len)); \ |
d3409d5e |
271 | if (_m->f & MP_BURN) \ |
272 | memset(_m->v, 0, MPWS(_m->sz)); \ |
d34decd2 |
273 | mpfree(_m->a, _m->v); \ |
274 | _m->a = _a; \ |
d3409d5e |
275 | _m->v = _v; \ |
276 | _m->vl = _v + _len; \ |
d3409d5e |
277 | } while (0) |
d03ab969 |
278 | |
d3409d5e |
279 | /* --- @mp_ensure@ --- * |
d03ab969 |
280 | * |
d3409d5e |
281 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
282 | * @size_t sz@ = required size |
d03ab969 |
283 | * |
284 | * Returns: --- |
285 | * |
d3409d5e |
286 | * Use: Ensures that the integer has enough space for @sz@ digits. |
287 | * The value is not changed. |
d03ab969 |
288 | */ |
289 | |
d3409d5e |
290 | extern void mp_ensure(mp */*m*/, size_t /*sz*/); |
291 | |
292 | #define MP_ENSURE(m, ssz) do { \ |
d34decd2 |
293 | mp *_m = (m); \ |
d3409d5e |
294 | size_t _ssz = (ssz); \ |
d34decd2 |
295 | size_t _len = MP_LEN(_m); \ |
296 | if (_ssz >= _len) { \ |
297 | if (_ssz > _m->sz) \ |
298 | mp_resize(_m, _ssz); \ |
299 | if (!(_m->f & MP_UNDEF) && _ssz > _len) \ |
300 | memset(_m->vl, 0, MPWS(_ssz - _len)); \ |
301 | _m->vl = _m->v + _ssz; \ |
302 | } \ |
d3409d5e |
303 | } while (0) |
d03ab969 |
304 | |
d34decd2 |
305 | /* --- @mp_dest@ --- * |
d03ab969 |
306 | * |
d34decd2 |
307 | * Arguments: @mp *m@ = a suggested destination integer |
308 | * @size_t sz@ = size required for result, in digits |
309 | * @unsigned f@ = various flags |
310 | * |
311 | * Returns: A pointer to an appropriate destination. |
312 | * |
313 | * Use: Converts a suggested destination into a real destination with |
314 | * the required properties. If the real destination is @d@, |
315 | * then the following properties will hold: |
316 | * |
317 | * * @d@ will have exactly one reference. |
d03ab969 |
318 | * |
d34decd2 |
319 | * * If @m@ is not @MP_NEW@, then the contents of @m@ will not |
320 | * change, unless @f@ has the @MP_UNDEF@ flag set. |
d03ab969 |
321 | * |
d34decd2 |
322 | * * If @m@ is not @MP_NEW@, then he reference count of @m@ on |
323 | * entry is equal to the sum of the counts of @d@ and @m@ on |
324 | * exit. |
325 | * |
326 | * * The size of @d@ will be at least @sz@. |
327 | * |
328 | * * If @f@ has the @MP_BURN@ flag set, then @d@ will be |
329 | * allocated from @MPARENA_SECURE@. |
330 | * |
331 | * Understanding this function is crucial to using Catacomb's |
332 | * multiprecision integer library effectively. |
d03ab969 |
333 | */ |
334 | |
d34decd2 |
335 | extern mp *mp_dest(mp */*m*/, size_t /*sz*/, unsigned /*f*/); |
d03ab969 |
336 | |
d34decd2 |
337 | #define MP_DEST(m, ssz, f) do { \ |
d3409d5e |
338 | mp *_m = (m); \ |
d34decd2 |
339 | size_t _ssz = (ssz); \ |
340 | unsigned _f = (f); \ |
341 | _m = mp_dest(_m, _ssz, _f); \ |
d3409d5e |
342 | (m) = _m; \ |
343 | } while (0) |
344 | |
345 | /*----- Size manipulation -------------------------------------------------*/ |
346 | |
347 | /* --- @mp_shrink@ --- * |
d03ab969 |
348 | * |
d3409d5e |
349 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
350 | * |
351 | * Returns: --- |
352 | * |
d3409d5e |
353 | * Use: Reduces the recorded length of an integer. This doesn't |
354 | * reduce the amount of memory used, although it can improve |
355 | * performance a bit. To reduce memory, use @mp_minimize@ |
356 | * instead. This can't change the value of an integer, and is |
357 | * therefore safe to use even when there are multiple |
358 | * references. |
d03ab969 |
359 | */ |
360 | |
d3409d5e |
361 | extern void mp_shrink(mp */*m*/); |
d03ab969 |
362 | |
d3409d5e |
363 | #define MP_SHRINK(m) do { \ |
364 | mp *_mm = (m); \ |
365 | MPX_SHRINK(_mm->v, _mm->vl); \ |
a69a3efd |
366 | if (MP_ZEROP(_mm)) \ |
d3409d5e |
367 | _mm->f &= ~MP_NEG; \ |
368 | } while (0) |
369 | |
370 | /* --- @mp_minimize@ --- * |
d03ab969 |
371 | * |
d3409d5e |
372 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
d03ab969 |
373 | * |
374 | * Returns: --- |
375 | * |
d3409d5e |
376 | * Use: Reduces the amount of memory an integer uses. It's best to |
377 | * do this to numbers which aren't going to change in the |
378 | * future. |
d03ab969 |
379 | */ |
380 | |
d3409d5e |
381 | extern void mp_minimize(mp */*m*/); |
d03ab969 |
382 | |
d3409d5e |
383 | /*----- Bit scanning ------------------------------------------------------*/ |
d03ab969 |
384 | |
d9a8ae10 |
385 | #ifndef CATACOMB_MPSCAN_H |
d3409d5e |
386 | # include "mpscan.h" |
387 | #endif |
388 | |
389 | /* --- @mp_scan@ --- * |
d03ab969 |
390 | * |
d3409d5e |
391 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
392 | * @const mp *m@ = pointer to a multiprecision integer |
d03ab969 |
393 | * |
394 | * Returns: --- |
395 | * |
d3409d5e |
396 | * Use: Initializes a bitscanner on a multiprecision integer. |
d03ab969 |
397 | */ |
398 | |
d3409d5e |
399 | extern void mp_scan(mpscan */*sc*/, const mp */*m*/); |
400 | |
401 | #define MP_SCAN(sc, m) do { \ |
a790733d |
402 | const mp *_mm = (m); \ |
d3409d5e |
403 | mpscan *_sc = (sc); \ |
404 | MPSCAN_INITX(_sc, _mm->v, _mm->vl); \ |
405 | } while (0) |
406 | |
5fbe3846 |
407 | /* --- @mp_rscan@ --- * |
408 | * |
409 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
410 | * @const mp *m@ = pointer to a multiprecision integer |
411 | * |
412 | * Returns: --- |
413 | * |
414 | * Use: Initializes a reverse bitscanner on a multiprecision |
415 | * integer. |
416 | */ |
417 | |
418 | extern void mp_rscan(mpscan */*sc*/, const mp */*m*/); |
419 | |
420 | #define MP_RSCAN(sc, m) do { \ |
421 | const mp *_mm = (m); \ |
422 | mpscan *_sc = (sc); \ |
423 | MPSCAN_RINITX(_sc, _mm->v, _mm->vl); \ |
424 | } while (0) |
425 | |
d3409d5e |
426 | /* --- Other bitscanning aliases --- */ |
427 | |
428 | #define mp_step mpscan_step |
429 | #define mp_bit mpscan_bit |
5fbe3846 |
430 | #define mp_rstep mpscan_rstep |
431 | #define mp_rbit mpscan_rbit |
d3409d5e |
432 | |
433 | #define MP_STEP MPSCAN_STEP |
434 | #define MP_BIT MPSCAN_BIT |
5fbe3846 |
435 | #define MP_RSTEP MPSCAN_RSTEP |
436 | #define MP_RBIT MPSCAN_RBIT |
d3409d5e |
437 | |
438 | /*----- Loading and storing -----------------------------------------------*/ |
d03ab969 |
439 | |
d3409d5e |
440 | /* --- @mp_octets@ --- * |
d03ab969 |
441 | * |
d3409d5e |
442 | * Arguments: @const mp *m@ = a multiprecision integer |
d03ab969 |
443 | * |
d3409d5e |
444 | * Returns: The number of octets required to represent @m@. |
d03ab969 |
445 | * |
d3409d5e |
446 | * Use: Calculates the external storage required for a multiprecision |
447 | * integer. |
d03ab969 |
448 | */ |
449 | |
24e1e862 |
450 | extern size_t mp_octets(const mp */*m*/); |
451 | |
f09e814a |
452 | /* --- @mp_octets2c@ --- * |
453 | * |
454 | * Arguments: @const mp *m@ = a multiprecision integer |
455 | * |
456 | * Returns: The number of octets required to represent @m@. |
457 | * |
458 | * Use: Calculates the external storage required for a multiprecision |
459 | * integer represented as two's complement. |
460 | */ |
461 | |
462 | extern size_t mp_octets2c(const mp */*m*/); |
463 | |
24e1e862 |
464 | /* --- @mp_bits@ --- * |
465 | * |
466 | * Arguments: @const mp *m@ = a multiprecision integer |
467 | * |
468 | * Returns: The number of bits required to represent @m@. |
469 | * |
470 | * Use: Calculates the external storage required for a multiprecision |
471 | * integer. |
472 | */ |
473 | |
474 | extern unsigned long mp_bits(const mp */*m*/); |
d03ab969 |
475 | |
d3409d5e |
476 | /* --- @mp_loadl@ --- * |
d03ab969 |
477 | * |
d3409d5e |
478 | * Arguments: @mp *d@ = destination |
479 | * @const void *pv@ = pointer to source data |
480 | * @size_t sz@ = size of the source data |
d03ab969 |
481 | * |
d3409d5e |
482 | * Returns: Resulting multiprecision number. |
d03ab969 |
483 | * |
d3409d5e |
484 | * Use: Loads a multiprecision number from an array of octets. The |
485 | * first byte in the array is the least significant. More |
486 | * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$% |
487 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
488 | */ |
489 | |
d3409d5e |
490 | extern mp *mp_loadl(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
491 | |
d3409d5e |
492 | /* --- @mp_storel@ --- * |
493 | * |
494 | * Arguments: @const mp *m@ = source |
495 | * @void *pv@ = pointer to output array |
496 | * @size_t sz@ = size of the output array |
497 | * |
498 | * Returns: --- |
499 | * |
500 | * Use: Stores a multiprecision number in an array of octets. The |
501 | * first byte in the array is the least significant. If the |
502 | * array is too small to represent the number, high-order bits |
503 | * are truncated; if the array is too large, high order bytes |
504 | * are filled with zeros. More formally, if the number is |
505 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
506 | * then the array is %$b_0, b_1, \ldots, b_{n-1}$%. |
507 | */ |
d03ab969 |
508 | |
d3409d5e |
509 | extern void mp_storel(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
510 | |
d3409d5e |
511 | /* --- @mp_loadb@ --- * |
d03ab969 |
512 | * |
d3409d5e |
513 | * Arguments: @mp *d@ = destination |
514 | * @const void *pv@ = pointer to source data |
515 | * @size_t sz@ = size of the source data |
d03ab969 |
516 | * |
d3409d5e |
517 | * Returns: Resulting multiprecision number. |
d03ab969 |
518 | * |
d3409d5e |
519 | * Use: Loads a multiprecision number from an array of octets. The |
520 | * last byte in the array is the least significant. More |
521 | * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$% |
522 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
d03ab969 |
523 | */ |
524 | |
d3409d5e |
525 | extern mp *mp_loadb(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d03ab969 |
526 | |
d3409d5e |
527 | /* --- @mp_storeb@ --- * |
d03ab969 |
528 | * |
d3409d5e |
529 | * Arguments: @const mp *m@ = source |
530 | * @void *pv@ = pointer to output array |
531 | * @size_t sz@ = size of the output array |
d03ab969 |
532 | * |
533 | * Returns: --- |
534 | * |
d3409d5e |
535 | * Use: Stores a multiprecision number in an array of octets. The |
536 | * last byte in the array is the least significant. If the |
537 | * array is too small to represent the number, high-order bits |
538 | * are truncated; if the array is too large, high order bytes |
539 | * are filled with zeros. More formally, if the number is |
540 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
541 | * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%. |
d03ab969 |
542 | */ |
543 | |
d3409d5e |
544 | extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
d03ab969 |
545 | |
f09e814a |
546 | /* --- @mp_loadl2c@ --- * |
d03ab969 |
547 | * |
d3409d5e |
548 | * Arguments: @mp *d@ = destination |
f09e814a |
549 | * @const void *pv@ = pointer to source data |
550 | * @size_t sz@ = size of the source data |
551 | * |
552 | * Returns: Resulting multiprecision number. |
d03ab969 |
553 | * |
f09e814a |
554 | * Use: Loads a multiprecision number from an array of octets as |
555 | * two's complement. The first byte in the array is the least |
556 | * significant. |
d3409d5e |
557 | */ |
558 | |
f09e814a |
559 | extern mp *mp_loadl2c(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
d3409d5e |
560 | |
f09e814a |
561 | /* --- @mp_storel2c@ --- * |
562 | * |
563 | * Arguments: @const mp *m@ = source |
564 | * @void *pv@ = pointer to output array |
565 | * @size_t sz@ = size of the output array |
566 | * |
567 | * Returns: --- |
568 | * |
569 | * Use: Stores a multiprecision number in an array of octets as two's |
570 | * complement. The first byte in the array is the least |
571 | * significant. If the array is too small to represent the |
572 | * number, high-order bits are truncated; if the array is too |
573 | * large, high order bytes are sign-extended. |
574 | */ |
575 | |
576 | extern void mp_storel2c(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
577 | |
578 | /* --- @mp_loadb2c@ --- * |
d3409d5e |
579 | * |
580 | * Arguments: @mp *d@ = destination |
f09e814a |
581 | * @const void *pv@ = pointer to source data |
582 | * @size_t sz@ = size of the source data |
d03ab969 |
583 | * |
f09e814a |
584 | * Returns: Resulting multiprecision number. |
585 | * |
586 | * Use: Loads a multiprecision number from an array of octets as |
587 | * two's complement. The last byte in the array is the least |
588 | * significant. |
d03ab969 |
589 | */ |
590 | |
f09e814a |
591 | extern mp *mp_loadb2c(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
592 | |
593 | /* --- @mp_storeb2c@ --- * |
594 | * |
595 | * Arguments: @const mp *m@ = source |
596 | * @void *pv@ = pointer to output array |
597 | * @size_t sz@ = size of the output array |
598 | * |
599 | * Returns: --- |
600 | * |
601 | * Use: Stores a multiprecision number in an array of octets, as |
602 | * two's complement. The last byte in the array is the least |
603 | * significant. If the array is too small to represent the |
604 | * number, high-order bits are truncated; if the array is too |
605 | * large, high order bytes are sign-extended. |
606 | */ |
607 | |
608 | extern void mp_storeb2c(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
609 | |
397041a9 |
610 | /*----- Bit operations ----------------------------------------------------*/ |
d03ab969 |
611 | |
397041a9 |
612 | /* --- @mp_not@ --- * |
d03ab969 |
613 | * |
d3409d5e |
614 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
615 | * @mp *a@ = source |
d03ab969 |
616 | * |
397041a9 |
617 | * Returns: The bitwise complement of the source. |
618 | */ |
d3409d5e |
619 | |
397041a9 |
620 | extern mp *mp_not(mp */*d*/, mp */*a*/); |
d3409d5e |
621 | |
397041a9 |
622 | /* --- @mp_bitop@ --- * |
d3409d5e |
623 | * |
624 | * Arguments: @mp *d@ = destination |
397041a9 |
625 | * @mp *a, *b@ = sources |
d03ab969 |
626 | * |
397041a9 |
627 | * Returns: The result of the given bitwise operation. These functions |
628 | * don't handle negative numbers at all sensibly. For that, use |
629 | * the @...2c@ variants. The functions are named after the |
630 | * truth tables they generate: |
631 | * |
632 | * a: 0011 |
633 | * b: 0101 |
634 | * @mpx_bitXXXX@ |
d03ab969 |
635 | */ |
636 | |
397041a9 |
637 | #define MP_BITDECL(string) \ |
638 | extern mp *mp_bit##string(mp */*d*/, mp */*a*/, mp */*b*/); |
639 | MPX_DOBIN(MP_BITDECL) |
f09e814a |
640 | |
397041a9 |
641 | /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- * |
f09e814a |
642 | * |
397041a9 |
643 | * Synonyms for the commonly-used functions. |
f09e814a |
644 | */ |
645 | |
397041a9 |
646 | #define mp_and mp_bit0001 |
647 | #define mp_or mp_bit0111 |
648 | #define mp_nand mp_bit1110 |
649 | #define mp_nor mp_bit1000 |
650 | #define mp_xor mp_bit0110 |
f09e814a |
651 | |
397041a9 |
652 | /* --- @mp_testbit@ --- * |
f09e814a |
653 | * |
654 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
655 | * @unsigned long n@ = which bit to test |
f09e814a |
656 | * |
397041a9 |
657 | * Returns: Nonzero if the bit is set, zero if not. |
d3409d5e |
658 | */ |
659 | |
397041a9 |
660 | extern int mp_testbit(mp */*x*/, unsigned long /*n*/); |
d3409d5e |
661 | |
09d00c6b |
662 | /* --- @mp_setbit@, @mp_clearbit@ --- * |
663 | * |
664 | * Arguments: @mp *d@ = a destination |
665 | * @mp *x@ = a large integer |
666 | * @unsigned long n@ = which bit to modify |
667 | * |
668 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
669 | */ |
670 | |
671 | extern mp *mp_setbit(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
672 | extern mp *mp_clearbit(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
673 | |
81578196 |
674 | /* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- * |
0f32e0f8 |
675 | * |
676 | * Arguments: @mp *d@ = destination |
397041a9 |
677 | * @mp *a@ = source |
678 | * @size_t n@ = number of bits to move |
f09e814a |
679 | * |
397041a9 |
680 | * Returns: Result, @a@ shifted left or right by @n@. |
81578196 |
681 | * |
682 | * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced |
683 | * on the right with ones instead of zeroes: it's used |
684 | * internally by @mp_lsl2c@, though it may be useful on its |
685 | * own. |
f09e814a |
686 | */ |
687 | |
397041a9 |
688 | extern mp *mp_lsl(mp */*d*/, mp */*a*/, size_t /*n*/); |
81578196 |
689 | extern mp *mp_lslc(mp */*d*/, mp */*a*/, size_t /*n*/); |
397041a9 |
690 | extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/); |
f09e814a |
691 | |
397041a9 |
692 | /* --- @mp_not2c@ --- * |
f09e814a |
693 | * |
694 | * Arguments: @mp *d@ = destination |
695 | * @mp *a@ = source |
696 | * |
397041a9 |
697 | * Returns: The sign-extended complement of the argument. |
698 | */ |
f09e814a |
699 | |
397041a9 |
700 | extern mp *mp_not2c(mp */*d*/, mp */*a*/); |
0f32e0f8 |
701 | |
f09e814a |
702 | /* --- @mp_bitop2c@ --- * |
703 | * |
704 | * Arguments: @mp *d@ = destination |
705 | * @mp *a, *b@ = sources |
706 | * |
707 | * Returns: The result of the given bitwise operation. Negative numbers |
708 | * are treated as two's complement, sign-extended infinitely to |
709 | * the left. The functions are named after the truth tables |
710 | * they generate: |
711 | * |
712 | * a: 0011 |
713 | * b: 0101 |
714 | * @mpx_bitXXXX@ |
715 | */ |
716 | |
717 | #define MP_BIT2CDECL(string) \ |
718 | extern mp *mp_bit##string##2c(mp */*d*/, mp */*a*/, mp */*b*/); |
719 | MPX_DOBIN(MP_BIT2CDECL) |
720 | |
721 | /* --- @mp_[n]and@, @mp_[n]or@, @mp_[n]xor@, @mp_not@ --- * |
722 | * |
723 | * Synonyms for the commonly-used functions. |
724 | */ |
725 | |
726 | #define mp_and2c mp_bit00012c |
727 | #define mp_or2c mp_bit01112c |
728 | #define mp_nand2c mp_bit11102c |
729 | #define mp_nor2c mp_bit10002c |
730 | #define mp_xor2c mp_bit01102c |
731 | |
397041a9 |
732 | /* --- @mp_lsl2c@, @mp_lsr2c@ --- * |
f09e814a |
733 | * |
734 | * Arguments: @mp *d@ = destination |
735 | * @mp *a@ = source |
397041a9 |
736 | * @size_t n@ = number of bits to move |
f09e814a |
737 | * |
397041a9 |
738 | * Returns: Result, @a@ shifted left or right by @n@. Handles the |
739 | * pretence of sign-extension for negative numbers. |
f09e814a |
740 | */ |
741 | |
397041a9 |
742 | extern mp *mp_lsl2c(mp */*d*/, mp */*a*/, size_t /*n*/); |
743 | extern mp *mp_lsr2c(mp */*d*/, mp */*a*/, size_t /*n*/); |
744 | |
745 | /* --- @mp_testbit2c@ --- * |
746 | * |
747 | * Arguments: @mp *x@ = a large integer |
748 | * @unsigned long n@ = which bit to test |
749 | * |
750 | * Returns: Nonzero if the bit is set, zero if not. Fakes up two's |
751 | * complement representation. |
752 | */ |
753 | |
754 | extern int mp_testbit2c(mp */*x*/, unsigned long /*n*/); |
755 | |
756 | /* --- @mp_setbit2c@, @mp_clearbit2c@ --- * |
757 | * |
758 | * Arguments: @mp *d@ = a destination |
759 | * @mp *x@ = a large integer |
760 | * @unsigned long n@ = which bit to modify |
761 | * |
762 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
763 | * Fakes up two's complement representation. |
764 | */ |
765 | |
766 | extern mp *mp_setbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
767 | extern mp *mp_clearbit2c(mp */*d*/, mp */*x*/, unsigned long /*n*/); |
768 | |
769 | /*----- Comparisons -------------------------------------------------------*/ |
770 | |
771 | /* --- @mp_eq@ --- * |
772 | * |
773 | * Arguments: @const mp *a, *b@ = two numbers |
774 | * |
775 | * Returns: Nonzero if the numbers are equal. |
776 | */ |
777 | |
778 | extern int mp_eq(const mp */*a*/, const mp */*b*/); |
779 | |
780 | #define MP_EQ(a, b) \ |
781 | ((((a)->f ^ (b)->f) & MP_NEG) == 0 && \ |
782 | mpx_ueq((a)->v, (a)->vl, (b)->v, (b)->vl)) |
783 | |
784 | /* --- @mp_cmp@ --- * |
785 | * |
786 | * Arguments: @const mp *a, *b@ = two numbers |
787 | * |
788 | * Returns: Less than, equal to or greater than zero, according to |
789 | * whether @a@ is less than, equal to or greater than @b@. |
790 | */ |
791 | |
792 | extern int mp_cmp(const mp */*a*/, const mp */*b*/); |
793 | |
794 | #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0) |
795 | |
3cd24abb |
796 | /* --- Other handy macros --- */ |
797 | |
a69a3efd |
798 | #define MP_NEGP(x) ((x)->f & MP_NEG) |
799 | #define MP_ZEROP(x) (!MP_LEN(x)) |
800 | #define MP_POSP(x) (!MP_NEGP(x) && !MP_ZEROP(x)) |
801 | #define MP_ODDP(x) (!MP_ZEROP(x) && ((x)->v[0] & 1u)) |
802 | #define MP_EVENP(x) (!MP_ODDP(x)) |
3cd24abb |
803 | |
397041a9 |
804 | /*----- Arithmetic operations ---------------------------------------------*/ |
805 | |
806 | /* --- @mp_neg@ --- * |
807 | * |
808 | * Arguments: @mp *d@ = destination |
809 | * @mp *a@ = argument |
810 | * |
811 | * Returns: The negation of the argument. |
812 | * |
813 | * Use: Negates its argument. |
814 | */ |
815 | |
816 | extern mp *mp_neg(mp */*d*/, mp */*a*/); |
f09e814a |
817 | |
d3409d5e |
818 | /* --- @mp_add@ --- * |
d03ab969 |
819 | * |
d3409d5e |
820 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
821 | * @mp *a, *b@ = sources |
d3409d5e |
822 | * |
823 | * Returns: Result, @a@ added to @b@. |
d03ab969 |
824 | */ |
825 | |
d9a8ae10 |
826 | extern mp *mp_add(mp */*d*/, mp */*a*/, mp */*b*/); |
d03ab969 |
827 | |
d3409d5e |
828 | /* --- @mp_sub@ --- * |
829 | * |
830 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
831 | * @mp *a, *b@ = sources |
d3409d5e |
832 | * |
833 | * Returns: Result, @b@ subtracted from @a@. |
834 | */ |
d03ab969 |
835 | |
d9a8ae10 |
836 | extern mp *mp_sub(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
837 | |
838 | /* --- @mp_mul@ --- * |
d03ab969 |
839 | * |
d3409d5e |
840 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
841 | * @mp *a, *b@ = sources |
d03ab969 |
842 | * |
d3409d5e |
843 | * Returns: Result, @a@ multiplied by @b@. |
844 | */ |
845 | |
d9a8ae10 |
846 | extern mp *mp_mul(mp */*d*/, mp */*a*/, mp */*b*/); |
d3409d5e |
847 | |
848 | /* --- @mp_sqr@ --- * |
849 | * |
850 | * Arguments: @mp *d@ = destination |
d9a8ae10 |
851 | * @mp *a@ = source |
d3409d5e |
852 | * |
853 | * Returns: Result, @a@ squared. |
854 | */ |
855 | |
d9a8ae10 |
856 | extern mp *mp_sqr(mp */*d*/, mp */*a*/); |
d3409d5e |
857 | |
858 | /* --- @mp_div@ --- * |
d03ab969 |
859 | * |
d3409d5e |
860 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
d9a8ae10 |
861 | * @mp *a, *b@ = sources |
d3409d5e |
862 | * |
863 | * Use: Calculates the quotient and remainder when @a@ is divided by |
864 | * @b@. |
d03ab969 |
865 | */ |
866 | |
d9a8ae10 |
867 | extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/); |
d3409d5e |
868 | |
f4535c64 |
869 | /* --- @mp_exp@ --- * |
870 | * |
871 | * Arguments: @mp *d@ = fake destination |
872 | * @mp *a@ = base |
873 | * @mp *e@ = exponent |
874 | * |
875 | * Returns: Result, %$a^e$%. |
876 | */ |
877 | |
878 | extern mp *mp_exp(mp */*d*/, mp */*a*/, mp */*e*/); |
879 | |
22a073c0 |
880 | /* --- @mp_odd@ --- * |
881 | * |
882 | * Arguments: @mp *d@ = pointer to destination integer |
883 | * @mp *m@ = pointer to source integer |
884 | * @size_t *s@ = where to store the power of 2 |
885 | * |
886 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
887 | * |
888 | * Use: Computes a power of two and an odd integer which, when |
889 | * multiplied, give a specified result. This sort of thing is |
890 | * useful in number theory quite often. |
891 | */ |
892 | |
893 | extern mp *mp_odd(mp */*d*/, mp */*m*/, size_t */*s*/); |
894 | |
d3409d5e |
895 | /*----- More advanced algorithms ------------------------------------------*/ |
d03ab969 |
896 | |
22a073c0 |
897 | /* --- @mp_sqrt@ --- * |
898 | * |
899 | * Arguments: @mp *d@ = pointer to destination integer |
900 | * @mp *a@ = (nonnegative) integer to take square root of |
901 | * |
902 | * Returns: The largest integer %$x$% such that %$x^2 \le a$%. |
903 | * |
904 | * Use: Computes integer square roots. |
905 | * |
906 | * The current implementation isn't very good: it uses the |
907 | * Newton-Raphson method to find an approximation to %$a$%. If |
908 | * there's any demand for a better version, I'll write one. |
909 | */ |
910 | |
911 | extern mp *mp_sqrt(mp */*d*/, mp */*a*/); |
912 | |
d3409d5e |
913 | /* --- @mp_gcd@ --- * |
d03ab969 |
914 | * |
d3409d5e |
915 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
916 | * @mp *a, *b@ = sources (must be nonzero) |
d03ab969 |
917 | * |
918 | * Returns: --- |
919 | * |
d3409d5e |
920 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
921 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
d9a8ae10 |
922 | * inverses. Neither @a@ nor @b@ may be zero. |
d03ab969 |
923 | */ |
924 | |
d3409d5e |
925 | extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/, |
926 | mp */*a*/, mp */*b*/); |
927 | |
b817bfc6 |
928 | /* -- @mp_modinv@ --- * |
929 | * |
930 | * Arguments: @mp *d@ = destination |
931 | * @mp *x@ = argument |
932 | * @mp *p@ = modulus |
933 | * |
934 | * Returns: The inverse %$x^{-1} \bmod p$%. |
935 | * |
936 | * Use: Computes a modular inverse. An assertion fails if %$p$% |
937 | * has no inverse. |
938 | */ |
939 | |
940 | extern mp *mp_modinv(mp */*d*/, mp */*x*/, mp */*p*/); |
941 | |
5b00a0ea |
942 | /* --- @mp_jacobi@ --- * |
943 | * |
944 | * Arguments: @mp *a@ = an integer less than @n@ |
945 | * @mp *n@ = an odd integer |
946 | * |
947 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
948 | * |
949 | * Use: Computes the Jacobi symbol. If @n@ is prime, this is the |
950 | * Legendre symbol and is equal to 1 if and only if @a@ is a |
951 | * quadratic residue mod @n@. The result is zero if and only if |
952 | * @a@ and @n@ have a common factor greater than one. |
953 | */ |
954 | |
22a073c0 |
955 | extern int mp_jacobi(mp */*a*/, mp */*n*/); |
956 | |
957 | /* --- @mp_modsqrt@ --- * |
958 | * |
959 | * Arguments: @mp *d@ = destination integer |
960 | * @mp *a@ = source integer |
961 | * @mp *p@ = modulus (must be prime) |
962 | * |
963 | * Returns: If %$a$% is a quadratic residue, a square root of %$a$%; else |
964 | * a null pointer. |
965 | * |
966 | * Use: Returns an integer %$x$% such that %$x^2 \equiv a \pmod{p}$%, |
967 | * if one exists; else a null pointer. This function will not |
968 | * work if %$p$% is composite: you must factor the modulus, take |
969 | * a square root mod each factor, and recombine the results |
970 | * using the Chinese Remainder Theorem. |
971 | */ |
972 | |
973 | extern mp *mp_modsqrt(mp */*d*/, mp */*a*/, mp */*p*/); |
5b00a0ea |
974 | |
d3409d5e |
975 | /*----- Test harness support ----------------------------------------------*/ |
976 | |
977 | #include <mLib/testrig.h> |
978 | |
d9a8ae10 |
979 | #ifndef CATACOMB_MPTEXT_H |
d3409d5e |
980 | # include "mptext.h" |
981 | #endif |
982 | |
983 | extern const test_type type_mp; |
d03ab969 |
984 | |
985 | /*----- That's all, folks -------------------------------------------------*/ |
986 | |
987 | #ifdef __cplusplus |
988 | } |
989 | #endif |
990 | |
991 | #endif |