1 /* mpihelp-mul.c - MPI helper functions
2 * Copyright (C) 1994, 1996, 1998, 1999,
3 * 2000 Free Software Foundation, Inc.
4 *
5 * This file is part of GnuPG.
6 *
7 * GnuPG is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation; either version 2 of the License, or
10 * (at your option) any later version.
11 *
12 * GnuPG 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 General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * 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 * The GNU MP Library itself is published under the LGPL;
27 * however I decided to publish this code under the plain GPL.
28 */
29
30 #include <linux/string.h>
31 #include "mpi-internal.h"
32 #include "longlong.h"
33
34 #define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \
35 do { \
36 if ((size) < KARATSUBA_THRESHOLD) \
37 mul_n_basecase(prodp, up, vp, size); \
38 else \
39 mul_n(prodp, up, vp, size, tspace); \
40 } while (0);
41
42 #define MPN_SQR_N_RECURSE(prodp, up, size, tspace) \
43 do { \
44 if ((size) < KARATSUBA_THRESHOLD) \
45 mpih_sqr_n_basecase(prodp, up, size); \
46 else \
47 mpih_sqr_n(prodp, up, size, tspace); \
48 } while (0);
49
50 /* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
51 * both with SIZE limbs, and store the result at PRODP. 2 * SIZE limbs are
52 * always stored. Return the most significant limb.
53 *
54 * Argument constraints:
55 * 1. PRODP != UP and PRODP != VP, i.e. the destination
56 * must be distinct from the multiplier and the multiplicand.
57 *
58 *
59 * Handle simple cases with traditional multiplication.
60 *
61 * This is the most critical code of multiplication. All multiplies rely
62 * on this, both small and huge. Small ones arrive here immediately. Huge
63 * ones arrive here as this is the base case for Karatsuba's recursive
64 * algorithm below.
65 */
66
67 static mpi_limb_t
mul_n_basecase(mpi_ptr_t prodp,mpi_ptr_t up,mpi_ptr_t vp,mpi_size_t size)68 mul_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
69 {
70 mpi_size_t i;
71 mpi_limb_t cy;
72 mpi_limb_t v_limb;
73
74 /* Multiply by the first limb in V separately, as the result can be
75 * stored (not added) to PROD. We also avoid a loop for zeroing. */
76 v_limb = vp[0];
77 if (v_limb <= 1) {
78 if (v_limb == 1)
79 MPN_COPY(prodp, up, size);
80 else
81 MPN_ZERO(prodp, size);
82 cy = 0;
83 } else
84 cy = mpihelp_mul_1(prodp, up, size, v_limb);
85
86 prodp[size] = cy;
87 prodp++;
88
89 /* For each iteration in the outer loop, multiply one limb from
90 * U with one limb from V, and add it to PROD. */
91 for (i = 1; i < size; i++) {
92 v_limb = vp[i];
93 if (v_limb <= 1) {
94 cy = 0;
95 if (v_limb == 1)
96 cy = mpihelp_add_n(prodp, prodp, up, size);
97 } else
98 cy = mpihelp_addmul_1(prodp, up, size, v_limb);
99
100 prodp[size] = cy;
101 prodp++;
102 }
103
104 return cy;
105 }
106
107 static void
mul_n(mpi_ptr_t prodp,mpi_ptr_t up,mpi_ptr_t vp,mpi_size_t size,mpi_ptr_t tspace)108 mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp,
109 mpi_size_t size, mpi_ptr_t tspace)
110 {
111 if (size & 1) {
112 /* The size is odd, and the code below doesn't handle that.
113 * Multiply the least significant (size - 1) limbs with a recursive
114 * call, and handle the most significant limb of S1 and S2
115 * separately.
116 * A slightly faster way to do this would be to make the Karatsuba
117 * code below behave as if the size were even, and let it check for
118 * odd size in the end. I.e., in essence move this code to the end.
119 * Doing so would save us a recursive call, and potentially make the
120 * stack grow a lot less.
121 */
122 mpi_size_t esize = size - 1; /* even size */
123 mpi_limb_t cy_limb;
124
125 MPN_MUL_N_RECURSE(prodp, up, vp, esize, tspace);
126 cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, vp[esize]);
127 prodp[esize + esize] = cy_limb;
128 cy_limb = mpihelp_addmul_1(prodp + esize, vp, size, up[esize]);
129 prodp[esize + size] = cy_limb;
130 } else {
131 /* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
132 *
133 * Split U in two pieces, U1 and U0, such that
134 * U = U0 + U1*(B**n),
135 * and V in V1 and V0, such that
136 * V = V0 + V1*(B**n).
137 *
138 * UV is then computed recursively using the identity
139 *
140 * 2n n n n
141 * UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V
142 * 1 1 1 0 0 1 0 0
143 *
144 * Where B = 2**BITS_PER_MP_LIMB.
145 */
146 mpi_size_t hsize = size >> 1;
147 mpi_limb_t cy;
148 int negflg;
149
150 /* Product H. ________________ ________________
151 * |_____U1 x V1____||____U0 x V0_____|
152 * Put result in upper part of PROD and pass low part of TSPACE
153 * as new TSPACE.
154 */
155 MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize,
156 tspace);
157
158 /* Product M. ________________
159 * |_(U1-U0)(V0-V1)_|
160 */
161 if (mpihelp_cmp(up + hsize, up, hsize) >= 0) {
162 mpihelp_sub_n(prodp, up + hsize, up, hsize);
163 negflg = 0;
164 } else {
165 mpihelp_sub_n(prodp, up, up + hsize, hsize);
166 negflg = 1;
167 }
168 if (mpihelp_cmp(vp + hsize, vp, hsize) >= 0) {
169 mpihelp_sub_n(prodp + hsize, vp + hsize, vp, hsize);
170 negflg ^= 1;
171 } else {
172 mpihelp_sub_n(prodp + hsize, vp, vp + hsize, hsize);
173 /* No change of NEGFLG. */
174 }
175 /* Read temporary operands from low part of PROD.
176 * Put result in low part of TSPACE using upper part of TSPACE
177 * as new TSPACE.
178 */
179 MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize,
180 tspace + size);
181
182 /* Add/copy product H. */
183 MPN_COPY(prodp + hsize, prodp + size, hsize);
184 cy = mpihelp_add_n(prodp + size, prodp + size,
185 prodp + size + hsize, hsize);
186
187 /* Add product M (if NEGFLG M is a negative number) */
188 if (negflg)
189 cy -=
190 mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace,
191 size);
192 else
193 cy +=
194 mpihelp_add_n(prodp + hsize, prodp + hsize, tspace,
195 size);
196
197 /* Product L. ________________ ________________
198 * |________________||____U0 x V0_____|
199 * Read temporary operands from low part of PROD.
200 * Put result in low part of TSPACE using upper part of TSPACE
201 * as new TSPACE.
202 */
203 MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size);
204
205 /* Add/copy Product L (twice) */
206
207 cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
208 if (cy)
209 mpihelp_add_1(prodp + hsize + size,
210 prodp + hsize + size, hsize, cy);
211
212 MPN_COPY(prodp, tspace, hsize);
213 cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
214 hsize);
215 if (cy)
216 mpihelp_add_1(prodp + size, prodp + size, size, 1);
217 }
218 }
219
mpih_sqr_n_basecase(mpi_ptr_t prodp,mpi_ptr_t up,mpi_size_t size)220 void mpih_sqr_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size)
221 {
222 mpi_size_t i;
223 mpi_limb_t cy_limb;
224 mpi_limb_t v_limb;
225
226 /* Multiply by the first limb in V separately, as the result can be
227 * stored (not added) to PROD. We also avoid a loop for zeroing. */
228 v_limb = up[0];
229 if (v_limb <= 1) {
230 if (v_limb == 1)
231 MPN_COPY(prodp, up, size);
232 else
233 MPN_ZERO(prodp, size);
234 cy_limb = 0;
235 } else
236 cy_limb = mpihelp_mul_1(prodp, up, size, v_limb);
237
238 prodp[size] = cy_limb;
239 prodp++;
240
241 /* For each iteration in the outer loop, multiply one limb from
242 * U with one limb from V, and add it to PROD. */
243 for (i = 1; i < size; i++) {
244 v_limb = up[i];
245 if (v_limb <= 1) {
246 cy_limb = 0;
247 if (v_limb == 1)
248 cy_limb = mpihelp_add_n(prodp, prodp, up, size);
249 } else
250 cy_limb = mpihelp_addmul_1(prodp, up, size, v_limb);
251
252 prodp[size] = cy_limb;
253 prodp++;
254 }
255 }
256
257 void
mpih_sqr_n(mpi_ptr_t prodp,mpi_ptr_t up,mpi_size_t size,mpi_ptr_t tspace)258 mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace)
259 {
260 if (size & 1) {
261 /* The size is odd, and the code below doesn't handle that.
262 * Multiply the least significant (size - 1) limbs with a recursive
263 * call, and handle the most significant limb of S1 and S2
264 * separately.
265 * A slightly faster way to do this would be to make the Karatsuba
266 * code below behave as if the size were even, and let it check for
267 * odd size in the end. I.e., in essence move this code to the end.
268 * Doing so would save us a recursive call, and potentially make the
269 * stack grow a lot less.
270 */
271 mpi_size_t esize = size - 1; /* even size */
272 mpi_limb_t cy_limb;
273
274 MPN_SQR_N_RECURSE(prodp, up, esize, tspace);
275 cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, up[esize]);
276 prodp[esize + esize] = cy_limb;
277 cy_limb = mpihelp_addmul_1(prodp + esize, up, size, up[esize]);
278
279 prodp[esize + size] = cy_limb;
280 } else {
281 mpi_size_t hsize = size >> 1;
282 mpi_limb_t cy;
283
284 /* Product H. ________________ ________________
285 * |_____U1 x U1____||____U0 x U0_____|
286 * Put result in upper part of PROD and pass low part of TSPACE
287 * as new TSPACE.
288 */
289 MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace);
290
291 /* Product M. ________________
292 * |_(U1-U0)(U0-U1)_|
293 */
294 if (mpihelp_cmp(up + hsize, up, hsize) >= 0)
295 mpihelp_sub_n(prodp, up + hsize, up, hsize);
296 else
297 mpihelp_sub_n(prodp, up, up + hsize, hsize);
298
299 /* Read temporary operands from low part of PROD.
300 * Put result in low part of TSPACE using upper part of TSPACE
301 * as new TSPACE. */
302 MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size);
303
304 /* Add/copy product H */
305 MPN_COPY(prodp + hsize, prodp + size, hsize);
306 cy = mpihelp_add_n(prodp + size, prodp + size,
307 prodp + size + hsize, hsize);
308
309 /* Add product M (if NEGFLG M is a negative number). */
310 cy -= mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace, size);
311
312 /* Product L. ________________ ________________
313 * |________________||____U0 x U0_____|
314 * Read temporary operands from low part of PROD.
315 * Put result in low part of TSPACE using upper part of TSPACE
316 * as new TSPACE. */
317 MPN_SQR_N_RECURSE(tspace, up, hsize, tspace + size);
318
319 /* Add/copy Product L (twice). */
320 cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
321 if (cy)
322 mpihelp_add_1(prodp + hsize + size,
323 prodp + hsize + size, hsize, cy);
324
325 MPN_COPY(prodp, tspace, hsize);
326 cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
327 hsize);
328 if (cy)
329 mpihelp_add_1(prodp + size, prodp + size, size, 1);
330 }
331 }
332
333 /* This should be made into an inline function in gmp.h. */
mpihelp_mul_n(mpi_ptr_t prodp,mpi_ptr_t up,mpi_ptr_t vp,mpi_size_t size)334 int mpihelp_mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
335 {
336 if (up == vp) {
337 if (size < KARATSUBA_THRESHOLD)
338 mpih_sqr_n_basecase(prodp, up, size);
339 else {
340 mpi_ptr_t tspace;
341 tspace = mpi_alloc_limb_space(2 * size);
342 if (!tspace)
343 return -ENOMEM;
344 mpih_sqr_n(prodp, up, size, tspace);
345 mpi_free_limb_space(tspace);
346 }
347 } else {
348 if (size < KARATSUBA_THRESHOLD)
349 mul_n_basecase(prodp, up, vp, size);
350 else {
351 mpi_ptr_t tspace;
352 tspace = mpi_alloc_limb_space(2 * size);
353 if (!tspace)
354 return -ENOMEM;
355 mul_n(prodp, up, vp, size, tspace);
356 mpi_free_limb_space(tspace);
357 }
358 }
359
360 return 0;
361 }
362
363 int
mpihelp_mul_karatsuba_case(mpi_ptr_t prodp,mpi_ptr_t up,mpi_size_t usize,mpi_ptr_t vp,mpi_size_t vsize,struct karatsuba_ctx * ctx)364 mpihelp_mul_karatsuba_case(mpi_ptr_t prodp,
365 mpi_ptr_t up, mpi_size_t usize,
366 mpi_ptr_t vp, mpi_size_t vsize,
367 struct karatsuba_ctx *ctx)
368 {
369 mpi_limb_t cy;
370
371 if (!ctx->tspace || ctx->tspace_size < vsize) {
372 if (ctx->tspace)
373 mpi_free_limb_space(ctx->tspace);
374 ctx->tspace = mpi_alloc_limb_space(2 * vsize);
375 if (!ctx->tspace)
376 return -ENOMEM;
377 ctx->tspace_size = vsize;
378 }
379
380 MPN_MUL_N_RECURSE(prodp, up, vp, vsize, ctx->tspace);
381
382 prodp += vsize;
383 up += vsize;
384 usize -= vsize;
385 if (usize >= vsize) {
386 if (!ctx->tp || ctx->tp_size < vsize) {
387 if (ctx->tp)
388 mpi_free_limb_space(ctx->tp);
389 ctx->tp = mpi_alloc_limb_space(2 * vsize);
390 if (!ctx->tp) {
391 if (ctx->tspace)
392 mpi_free_limb_space(ctx->tspace);
393 ctx->tspace = NULL;
394 return -ENOMEM;
395 }
396 ctx->tp_size = vsize;
397 }
398
399 do {
400 MPN_MUL_N_RECURSE(ctx->tp, up, vp, vsize, ctx->tspace);
401 cy = mpihelp_add_n(prodp, prodp, ctx->tp, vsize);
402 mpihelp_add_1(prodp + vsize, ctx->tp + vsize, vsize,
403 cy);
404 prodp += vsize;
405 up += vsize;
406 usize -= vsize;
407 } while (usize >= vsize);
408 }
409
410 if (usize) {
411 if (usize < KARATSUBA_THRESHOLD) {
412 mpi_limb_t tmp;
413 if (mpihelp_mul(ctx->tspace, vp, vsize, up, usize, &tmp)
414 < 0)
415 return -ENOMEM;
416 } else {
417 if (!ctx->next) {
418 ctx->next = kzalloc(sizeof *ctx, GFP_KERNEL);
419 if (!ctx->next)
420 return -ENOMEM;
421 }
422 if (mpihelp_mul_karatsuba_case(ctx->tspace,
423 vp, vsize,
424 up, usize,
425 ctx->next) < 0)
426 return -ENOMEM;
427 }
428
429 cy = mpihelp_add_n(prodp, prodp, ctx->tspace, vsize);
430 mpihelp_add_1(prodp + vsize, ctx->tspace + vsize, usize, cy);
431 }
432
433 return 0;
434 }
435
mpihelp_release_karatsuba_ctx(struct karatsuba_ctx * ctx)436 void mpihelp_release_karatsuba_ctx(struct karatsuba_ctx *ctx)
437 {
438 struct karatsuba_ctx *ctx2;
439
440 if (ctx->tp)
441 mpi_free_limb_space(ctx->tp);
442 if (ctx->tspace)
443 mpi_free_limb_space(ctx->tspace);
444 for (ctx = ctx->next; ctx; ctx = ctx2) {
445 ctx2 = ctx->next;
446 if (ctx->tp)
447 mpi_free_limb_space(ctx->tp);
448 if (ctx->tspace)
449 mpi_free_limb_space(ctx->tspace);
450 kfree(ctx);
451 }
452 }
453
454 /* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
455 * and v (pointed to by VP, with VSIZE limbs), and store the result at
456 * PRODP. USIZE + VSIZE limbs are always stored, but if the input
457 * operands are normalized. Return the most significant limb of the
458 * result.
459 *
460 * NOTE: The space pointed to by PRODP is overwritten before finished
461 * with U and V, so overlap is an error.
462 *
463 * Argument constraints:
464 * 1. USIZE >= VSIZE.
465 * 2. PRODP != UP and PRODP != VP, i.e. the destination
466 * must be distinct from the multiplier and the multiplicand.
467 */
468
469 int
mpihelp_mul(mpi_ptr_t prodp,mpi_ptr_t up,mpi_size_t usize,mpi_ptr_t vp,mpi_size_t vsize,mpi_limb_t * _result)470 mpihelp_mul(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize,
471 mpi_ptr_t vp, mpi_size_t vsize, mpi_limb_t *_result)
472 {
473 mpi_ptr_t prod_endp = prodp + usize + vsize - 1;
474 mpi_limb_t cy;
475 struct karatsuba_ctx ctx;
476
477 if (vsize < KARATSUBA_THRESHOLD) {
478 mpi_size_t i;
479 mpi_limb_t v_limb;
480
481 if (!vsize) {
482 *_result = 0;
483 return 0;
484 }
485
486 /* Multiply by the first limb in V separately, as the result can be
487 * stored (not added) to PROD. We also avoid a loop for zeroing. */
488 v_limb = vp[0];
489 if (v_limb <= 1) {
490 if (v_limb == 1)
491 MPN_COPY(prodp, up, usize);
492 else
493 MPN_ZERO(prodp, usize);
494 cy = 0;
495 } else
496 cy = mpihelp_mul_1(prodp, up, usize, v_limb);
497
498 prodp[usize] = cy;
499 prodp++;
500
501 /* For each iteration in the outer loop, multiply one limb from
502 * U with one limb from V, and add it to PROD. */
503 for (i = 1; i < vsize; i++) {
504 v_limb = vp[i];
505 if (v_limb <= 1) {
506 cy = 0;
507 if (v_limb == 1)
508 cy = mpihelp_add_n(prodp, prodp, up,
509 usize);
510 } else
511 cy = mpihelp_addmul_1(prodp, up, usize, v_limb);
512
513 prodp[usize] = cy;
514 prodp++;
515 }
516
517 *_result = cy;
518 return 0;
519 }
520
521 memset(&ctx, 0, sizeof ctx);
522 if (mpihelp_mul_karatsuba_case(prodp, up, usize, vp, vsize, &ctx) < 0)
523 return -ENOMEM;
524 mpihelp_release_karatsuba_ctx(&ctx);
525 *_result = *prod_endp;
526 return 0;
527 }
528