Line data Source code
1 : /* mpih-mul.c - MPI helper functions
2 : * Copyright (C) 1994, 1996, 1998, 1999, 2000,
3 : * 2001, 2002 Free Software Foundation, Inc.
4 : *
5 : * This file is part of Libgcrypt.
6 : *
7 : * Libgcrypt is free software; you can redistribute it and/or modify
8 : * it under the terms of the GNU Lesser General Public License as
9 : * published by the Free Software Foundation; either version 2.1 of
10 : * the License, or (at your option) any later version.
11 : *
12 : * Libgcrypt is distributed in the hope that it will be useful,
13 : * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 : * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 : * GNU Lesser General Public License for more details.
16 : *
17 : * You should have received a copy of the GNU Lesser General Public
18 : * License along with this program; if not, write to the Free Software
19 : * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
20 : *
21 : * Note: This code is heavily based on the GNU MP Library.
22 : * Actually it's the same code with only minor changes in the
23 : * way the data is stored; this is to support the abstraction
24 : * of an optional secure memory allocation which may be used
25 : * to avoid revealing of sensitive data due to paging etc.
26 : */
27 :
28 : #include <config.h>
29 : #include <stdio.h>
30 : #include <stdlib.h>
31 : #include <string.h>
32 : #include "mpi-internal.h"
33 : #include "longlong.h"
34 : #include "g10lib.h"
35 :
36 : #define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \
37 : do { \
38 : if( (size) < KARATSUBA_THRESHOLD ) \
39 : mul_n_basecase (prodp, up, vp, size); \
40 : else \
41 : mul_n (prodp, up, vp, size, tspace); \
42 : } while (0);
43 :
44 : #define MPN_SQR_N_RECURSE(prodp, up, size, tspace) \
45 : do { \
46 : if ((size) < KARATSUBA_THRESHOLD) \
47 : _gcry_mpih_sqr_n_basecase (prodp, up, size); \
48 : else \
49 : _gcry_mpih_sqr_n (prodp, up, size, tspace); \
50 : } while (0);
51 :
52 :
53 :
54 :
55 : /* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
56 : * both with SIZE limbs, and store the result at PRODP. 2 * SIZE limbs are
57 : * always stored. Return the most significant limb.
58 : *
59 : * Argument constraints:
60 : * 1. PRODP != UP and PRODP != VP, i.e. the destination
61 : * must be distinct from the multiplier and the multiplicand.
62 : *
63 : *
64 : * Handle simple cases with traditional multiplication.
65 : *
66 : * This is the most critical code of multiplication. All multiplies rely
67 : * on this, both small and huge. Small ones arrive here immediately. Huge
68 : * ones arrive here as this is the base case for Karatsuba's recursive
69 : * algorithm below.
70 : */
71 :
72 : static mpi_limb_t
73 41657037 : mul_n_basecase( mpi_ptr_t prodp, mpi_ptr_t up,
74 : mpi_ptr_t vp, mpi_size_t size)
75 : {
76 : mpi_size_t i;
77 : mpi_limb_t cy;
78 : mpi_limb_t v_limb;
79 :
80 : /* Multiply by the first limb in V separately, as the result can be
81 : * stored (not added) to PROD. We also avoid a loop for zeroing. */
82 41657037 : v_limb = vp[0];
83 41657037 : if( v_limb <= 1 ) {
84 508482 : if( v_limb == 1 )
85 260 : MPN_COPY( prodp, up, size );
86 : else
87 508222 : MPN_ZERO( prodp, size );
88 508482 : cy = 0;
89 : }
90 : else
91 41148555 : cy = _gcry_mpih_mul_1( prodp, up, size, v_limb );
92 :
93 41657037 : prodp[size] = cy;
94 41657037 : prodp++;
95 :
96 : /* For each iteration in the outer loop, multiply one limb from
97 : * U with one limb from V, and add it to PROD. */
98 361255137 : for( i = 1; i < size; i++ ) {
99 319598100 : v_limb = vp[i];
100 319598100 : if( v_limb <= 1 ) {
101 10967972 : cy = 0;
102 10967972 : if( v_limb == 1 )
103 3713 : cy = _gcry_mpih_add_n(prodp, prodp, up, size);
104 : }
105 : else
106 308630128 : cy = _gcry_mpih_addmul_1(prodp, up, size, v_limb);
107 :
108 319598100 : prodp[size] = cy;
109 319598100 : prodp++;
110 : }
111 :
112 41657037 : return cy;
113 : }
114 :
115 :
116 : static void
117 17587489 : mul_n( mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp,
118 : mpi_size_t size, mpi_ptr_t tspace )
119 : {
120 17587489 : if( size & 1 ) {
121 : /* The size is odd, and the code below doesn't handle that.
122 : * Multiply the least significant (size - 1) limbs with a recursive
123 : * call, and handle the most significant limb of S1 and S2
124 : * separately.
125 : * A slightly faster way to do this would be to make the Karatsuba
126 : * code below behave as if the size were even, and let it check for
127 : * odd size in the end. I.e., in essence move this code to the end.
128 : * Doing so would save us a recursive call, and potentially make the
129 : * stack grow a lot less.
130 : */
131 681546 : mpi_size_t esize = size - 1; /* even size */
132 : mpi_limb_t cy_limb;
133 :
134 681546 : MPN_MUL_N_RECURSE( prodp, up, vp, esize, tspace );
135 681546 : cy_limb = _gcry_mpih_addmul_1( prodp + esize, up, esize, vp[esize] );
136 681546 : prodp[esize + esize] = cy_limb;
137 681546 : cy_limb = _gcry_mpih_addmul_1( prodp + esize, vp, size, up[esize] );
138 681546 : prodp[esize + size] = cy_limb;
139 : }
140 : else {
141 : /* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
142 : *
143 : * Split U in two pieces, U1 and U0, such that
144 : * U = U0 + U1*(B**n),
145 : * and V in V1 and V0, such that
146 : * V = V0 + V1*(B**n).
147 : *
148 : * UV is then computed recursively using the identity
149 : *
150 : * 2n n n n
151 : * UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V
152 : * 1 1 1 0 0 1 0 0
153 : *
154 : * Where B = 2**BITS_PER_MP_LIMB.
155 : */
156 16905943 : mpi_size_t hsize = size >> 1;
157 : mpi_limb_t cy;
158 : int negflg;
159 :
160 : /* Product H. ________________ ________________
161 : * |_____U1 x V1____||____U0 x V0_____|
162 : * Put result in upper part of PROD and pass low part of TSPACE
163 : * as new TSPACE.
164 : */
165 16905943 : MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize, tspace);
166 :
167 : /* Product M. ________________
168 : * |_(U1-U0)(V0-V1)_|
169 : */
170 16905943 : if( _gcry_mpih_cmp(up + hsize, up, hsize) >= 0 ) {
171 6666260 : _gcry_mpih_sub_n(prodp, up + hsize, up, hsize);
172 6666260 : negflg = 0;
173 : }
174 : else {
175 10239683 : _gcry_mpih_sub_n(prodp, up, up + hsize, hsize);
176 10239683 : negflg = 1;
177 : }
178 16905943 : if( _gcry_mpih_cmp(vp + hsize, vp, hsize) >= 0 ) {
179 6509968 : _gcry_mpih_sub_n(prodp + hsize, vp + hsize, vp, hsize);
180 6509968 : negflg ^= 1;
181 : }
182 : else {
183 10395975 : _gcry_mpih_sub_n(prodp + hsize, vp, vp + hsize, hsize);
184 : /* No change of NEGFLG. */
185 : }
186 : /* Read temporary operands from low part of PROD.
187 : * Put result in low part of TSPACE using upper part of TSPACE
188 : * as new TSPACE.
189 : */
190 16905943 : MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize, tspace + size);
191 :
192 : /* Add/copy product H. */
193 16905943 : MPN_COPY (prodp + hsize, prodp + size, hsize);
194 16905943 : cy = _gcry_mpih_add_n( prodp + size, prodp + size,
195 16905943 : prodp + size + hsize, hsize);
196 :
197 : /* Add product M (if NEGFLG M is a negative number) */
198 16905943 : if(negflg)
199 16274885 : cy -= _gcry_mpih_sub_n(prodp + hsize, prodp + hsize, tspace, size);
200 : else
201 631058 : cy += _gcry_mpih_add_n(prodp + hsize, prodp + hsize, tspace, size);
202 :
203 : /* Product L. ________________ ________________
204 : * |________________||____U0 x V0_____|
205 : * Read temporary operands from low part of PROD.
206 : * Put result in low part of TSPACE using upper part of TSPACE
207 : * as new TSPACE.
208 : */
209 16905943 : MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size);
210 :
211 : /* Add/copy Product L (twice) */
212 :
213 16905943 : cy += _gcry_mpih_add_n(prodp + hsize, prodp + hsize, tspace, size);
214 16905943 : if( cy )
215 6151022 : _gcry_mpih_add_1(prodp + hsize + size, prodp + hsize + size, hsize, cy);
216 :
217 16905943 : MPN_COPY(prodp, tspace, hsize);
218 16905943 : cy = _gcry_mpih_add_n(prodp + hsize, prodp + hsize, tspace + hsize, hsize);
219 16905943 : if( cy )
220 5403784 : _gcry_mpih_add_1(prodp + size, prodp + size, size, 1);
221 : }
222 17587489 : }
223 :
224 :
225 : void
226 0 : _gcry_mpih_sqr_n_basecase( mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size )
227 : {
228 : mpi_size_t i;
229 : mpi_limb_t cy_limb;
230 : mpi_limb_t v_limb;
231 :
232 : /* Multiply by the first limb in V separately, as the result can be
233 : * stored (not added) to PROD. We also avoid a loop for zeroing. */
234 0 : v_limb = up[0];
235 0 : if( v_limb <= 1 ) {
236 0 : if( v_limb == 1 )
237 0 : MPN_COPY( prodp, up, size );
238 : else
239 0 : MPN_ZERO(prodp, size);
240 0 : cy_limb = 0;
241 : }
242 : else
243 0 : cy_limb = _gcry_mpih_mul_1( prodp, up, size, v_limb );
244 :
245 0 : prodp[size] = cy_limb;
246 0 : prodp++;
247 :
248 : /* For each iteration in the outer loop, multiply one limb from
249 : * U with one limb from V, and add it to PROD. */
250 0 : for( i=1; i < size; i++) {
251 0 : v_limb = up[i];
252 0 : if( v_limb <= 1 ) {
253 0 : cy_limb = 0;
254 0 : if( v_limb == 1 )
255 0 : cy_limb = _gcry_mpih_add_n(prodp, prodp, up, size);
256 : }
257 : else
258 0 : cy_limb = _gcry_mpih_addmul_1(prodp, up, size, v_limb);
259 :
260 0 : prodp[size] = cy_limb;
261 0 : prodp++;
262 : }
263 0 : }
264 :
265 :
266 : void
267 0 : _gcry_mpih_sqr_n( mpi_ptr_t prodp,
268 : mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace)
269 : {
270 0 : if( size & 1 ) {
271 : /* The size is odd, and the code below doesn't handle that.
272 : * Multiply the least significant (size - 1) limbs with a recursive
273 : * call, and handle the most significant limb of S1 and S2
274 : * separately.
275 : * A slightly faster way to do this would be to make the Karatsuba
276 : * code below behave as if the size were even, and let it check for
277 : * odd size in the end. I.e., in essence move this code to the end.
278 : * Doing so would save us a recursive call, and potentially make the
279 : * stack grow a lot less.
280 : */
281 0 : mpi_size_t esize = size - 1; /* even size */
282 : mpi_limb_t cy_limb;
283 :
284 0 : MPN_SQR_N_RECURSE( prodp, up, esize, tspace );
285 0 : cy_limb = _gcry_mpih_addmul_1( prodp + esize, up, esize, up[esize] );
286 0 : prodp[esize + esize] = cy_limb;
287 0 : cy_limb = _gcry_mpih_addmul_1( prodp + esize, up, size, up[esize] );
288 :
289 0 : prodp[esize + size] = cy_limb;
290 : }
291 : else {
292 0 : mpi_size_t hsize = size >> 1;
293 : mpi_limb_t cy;
294 :
295 : /* Product H. ________________ ________________
296 : * |_____U1 x U1____||____U0 x U0_____|
297 : * Put result in upper part of PROD and pass low part of TSPACE
298 : * as new TSPACE.
299 : */
300 0 : MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace);
301 :
302 : /* Product M. ________________
303 : * |_(U1-U0)(U0-U1)_|
304 : */
305 0 : if( _gcry_mpih_cmp( up + hsize, up, hsize) >= 0 )
306 0 : _gcry_mpih_sub_n( prodp, up + hsize, up, hsize);
307 : else
308 0 : _gcry_mpih_sub_n (prodp, up, up + hsize, hsize);
309 :
310 : /* Read temporary operands from low part of PROD.
311 : * Put result in low part of TSPACE using upper part of TSPACE
312 : * as new TSPACE. */
313 0 : MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size);
314 :
315 : /* Add/copy product H */
316 0 : MPN_COPY(prodp + hsize, prodp + size, hsize);
317 0 : cy = _gcry_mpih_add_n(prodp + size, prodp + size,
318 0 : prodp + size + hsize, hsize);
319 :
320 : /* Add product M (if NEGFLG M is a negative number). */
321 0 : cy -= _gcry_mpih_sub_n (prodp + hsize, prodp + hsize, tspace, size);
322 :
323 : /* Product L. ________________ ________________
324 : * |________________||____U0 x U0_____|
325 : * Read temporary operands from low part of PROD.
326 : * Put result in low part of TSPACE using upper part of TSPACE
327 : * as new TSPACE. */
328 0 : MPN_SQR_N_RECURSE (tspace, up, hsize, tspace + size);
329 :
330 : /* Add/copy Product L (twice). */
331 0 : cy += _gcry_mpih_add_n (prodp + hsize, prodp + hsize, tspace, size);
332 0 : if( cy )
333 0 : _gcry_mpih_add_1(prodp + hsize + size, prodp + hsize + size,
334 : hsize, cy);
335 :
336 0 : MPN_COPY(prodp, tspace, hsize);
337 0 : cy = _gcry_mpih_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize);
338 0 : if( cy )
339 0 : _gcry_mpih_add_1 (prodp + size, prodp + size, size, 1);
340 : }
341 0 : }
342 :
343 :
344 : /* This should be made into an inline function in gmp.h. */
345 : void
346 0 : _gcry_mpih_mul_n( mpi_ptr_t prodp,
347 : mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
348 : {
349 : int secure;
350 :
351 0 : if( up == vp ) {
352 0 : if( size < KARATSUBA_THRESHOLD )
353 0 : _gcry_mpih_sqr_n_basecase( prodp, up, size );
354 : else {
355 : mpi_ptr_t tspace;
356 0 : secure = _gcry_is_secure( up );
357 0 : tspace = mpi_alloc_limb_space( 2 * size, secure );
358 0 : _gcry_mpih_sqr_n( prodp, up, size, tspace );
359 0 : _gcry_mpi_free_limb_space (tspace, 2 * size );
360 : }
361 : }
362 : else {
363 0 : if( size < KARATSUBA_THRESHOLD )
364 0 : mul_n_basecase( prodp, up, vp, size );
365 : else {
366 : mpi_ptr_t tspace;
367 0 : secure = _gcry_is_secure( up ) || _gcry_is_secure( vp );
368 0 : tspace = mpi_alloc_limb_space( 2 * size, secure );
369 0 : mul_n (prodp, up, vp, size, tspace);
370 0 : _gcry_mpi_free_limb_space (tspace, 2 * size );
371 : }
372 : }
373 0 : }
374 :
375 :
376 :
377 : void
378 7821503 : _gcry_mpih_mul_karatsuba_case( mpi_ptr_t prodp,
379 : mpi_ptr_t up, mpi_size_t usize,
380 : mpi_ptr_t vp, mpi_size_t vsize,
381 : struct karatsuba_ctx *ctx )
382 : {
383 : mpi_limb_t cy;
384 :
385 7821503 : if( !ctx->tspace || ctx->tspace_size < vsize ) {
386 71123 : if( ctx->tspace )
387 625 : _gcry_mpi_free_limb_space( ctx->tspace, ctx->tspace_nlimbs );
388 71123 : ctx->tspace_nlimbs = 2 * vsize;
389 71123 : ctx->tspace = mpi_alloc_limb_space (2 * vsize,
390 : (_gcry_is_secure (up)
391 : || _gcry_is_secure (vp)));
392 71123 : ctx->tspace_size = vsize;
393 : }
394 :
395 7821503 : MPN_MUL_N_RECURSE( prodp, up, vp, vsize, ctx->tspace );
396 :
397 7821503 : prodp += vsize;
398 7821503 : up += vsize;
399 7821503 : usize -= vsize;
400 7821503 : if( usize >= vsize ) {
401 23648 : if( !ctx->tp || ctx->tp_size < vsize ) {
402 387 : if( ctx->tp )
403 203 : _gcry_mpi_free_limb_space( ctx->tp, ctx->tp_nlimbs );
404 387 : ctx->tp_nlimbs = 2 * vsize;
405 387 : ctx->tp = mpi_alloc_limb_space (2 * vsize,
406 : (_gcry_is_secure (up)
407 : || _gcry_is_secure (vp)));
408 387 : ctx->tp_size = vsize;
409 : }
410 :
411 : do {
412 23648 : MPN_MUL_N_RECURSE( ctx->tp, up, vp, vsize, ctx->tspace );
413 23648 : cy = _gcry_mpih_add_n( prodp, prodp, ctx->tp, vsize );
414 23648 : _gcry_mpih_add_1( prodp + vsize, ctx->tp + vsize, vsize, cy );
415 23648 : prodp += vsize;
416 23648 : up += vsize;
417 23648 : usize -= vsize;
418 23648 : } while( usize >= vsize );
419 : }
420 :
421 7821503 : if( usize ) {
422 204278 : if( usize < KARATSUBA_THRESHOLD ) {
423 180743 : _gcry_mpih_mul( ctx->tspace, vp, vsize, up, usize );
424 : }
425 : else {
426 23535 : if( !ctx->next ) {
427 184 : ctx->next = xcalloc( 1, sizeof *ctx );
428 : }
429 23535 : _gcry_mpih_mul_karatsuba_case( ctx->tspace,
430 : vp, vsize,
431 : up, usize,
432 : ctx->next );
433 : }
434 :
435 204278 : cy = _gcry_mpih_add_n( prodp, prodp, ctx->tspace, vsize);
436 204278 : _gcry_mpih_add_1( prodp + vsize, ctx->tspace + vsize, usize, cy );
437 : }
438 7821503 : }
439 :
440 :
441 : void
442 355396 : _gcry_mpih_release_karatsuba_ctx( struct karatsuba_ctx *ctx )
443 : {
444 : struct karatsuba_ctx *ctx2;
445 :
446 355396 : if( ctx->tp )
447 184 : _gcry_mpi_free_limb_space( ctx->tp, ctx->tp_nlimbs );
448 355396 : if( ctx->tspace )
449 70314 : _gcry_mpi_free_limb_space( ctx->tspace, ctx->tspace_nlimbs );
450 355580 : for( ctx=ctx->next; ctx; ctx = ctx2 ) {
451 184 : ctx2 = ctx->next;
452 184 : if( ctx->tp )
453 0 : _gcry_mpi_free_limb_space( ctx->tp, ctx->tp_nlimbs );
454 184 : if( ctx->tspace )
455 184 : _gcry_mpi_free_limb_space( ctx->tspace, ctx->tspace_nlimbs );
456 184 : xfree( ctx );
457 : }
458 355396 : }
459 :
460 : /* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
461 : * and v (pointed to by VP, with VSIZE limbs), and store the result at
462 : * PRODP. USIZE + VSIZE limbs are always stored, but if the input
463 : * operands are normalized. Return the most significant limb of the
464 : * result.
465 : *
466 : * NOTE: The space pointed to by PRODP is overwritten before finished
467 : * with U and V, so overlap is an error.
468 : *
469 : * Argument constraints:
470 : * 1. USIZE >= VSIZE.
471 : * 2. PRODP != UP and PRODP != VP, i.e. the destination
472 : * must be distinct from the multiplier and the multiplicand.
473 : */
474 :
475 : mpi_limb_t
476 33278126 : _gcry_mpih_mul( mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize,
477 : mpi_ptr_t vp, mpi_size_t vsize)
478 : {
479 33278126 : mpi_ptr_t prod_endp = prodp + usize + vsize - 1;
480 : mpi_limb_t cy;
481 : struct karatsuba_ctx ctx;
482 :
483 33278126 : if( vsize < KARATSUBA_THRESHOLD ) {
484 : mpi_size_t i;
485 : mpi_limb_t v_limb;
486 :
487 33218692 : if( !vsize )
488 0 : return 0;
489 :
490 : /* Multiply by the first limb in V separately, as the result can be
491 : * stored (not added) to PROD. We also avoid a loop for zeroing. */
492 33218692 : v_limb = vp[0];
493 33218692 : if( v_limb <= 1 ) {
494 1380072 : if( v_limb == 1 )
495 1294036 : MPN_COPY( prodp, up, usize );
496 : else
497 86036 : MPN_ZERO( prodp, usize );
498 1380072 : cy = 0;
499 : }
500 : else
501 31838620 : cy = _gcry_mpih_mul_1( prodp, up, usize, v_limb );
502 :
503 33218692 : prodp[usize] = cy;
504 33218692 : prodp++;
505 :
506 : /* For each iteration in the outer loop, multiply one limb from
507 : * U with one limb from V, and add it to PROD. */
508 140314615 : for( i = 1; i < vsize; i++ ) {
509 107095923 : v_limb = vp[i];
510 107095923 : if( v_limb <= 1 ) {
511 4350937 : cy = 0;
512 4350937 : if( v_limb == 1 )
513 2977 : cy = _gcry_mpih_add_n(prodp, prodp, up, usize);
514 : }
515 : else
516 102744986 : cy = _gcry_mpih_addmul_1(prodp, up, usize, v_limb);
517 :
518 107095923 : prodp[usize] = cy;
519 107095923 : prodp++;
520 : }
521 :
522 33218692 : return cy;
523 : }
524 :
525 59434 : memset( &ctx, 0, sizeof ctx );
526 59434 : _gcry_mpih_mul_karatsuba_case( prodp, up, usize, vp, vsize, &ctx );
527 59434 : _gcry_mpih_release_karatsuba_ctx( &ctx );
528 59434 : return *prod_endp;
529 : }
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