1 // SPDX-License-Identifier: GPL-2.0-or-later
2 /* mpihelp-mul.c - MPI helper functions
3 * Copyright (C) 1994, 1996, 1998, 1999,
4 * 2000 Free Software Foundation, Inc.
5 *
6 * This file is part of GnuPG.
7 *
8 * Note: This code is heavily based on the GNU MP Library.
9 * Actually it's the same code with only minor changes in the
10 * way the data is stored; this is to support the abstraction
11 * of an optional secure memory allocation which may be used
12 * to avoid revealing of sensitive data due to paging etc.
13 * The GNU MP Library itself is published under the LGPL;
14 * however I decided to publish this code under the plain GPL.
15 */
16
17 #include <linux/string.h>
18 #include "mpi-internal.h"
19 #include "longlong.h"
20
21 #define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \
22 do { \
23 if ((size) < KARATSUBA_THRESHOLD) \
24 mul_n_basecase(prodp, up, vp, size); \
25 else \
26 mul_n(prodp, up, vp, size, tspace); \
27 } while (0);
28
29 #define MPN_SQR_N_RECURSE(prodp, up, size, tspace) \
30 do { \
31 if ((size) < KARATSUBA_THRESHOLD) \
32 mpih_sqr_n_basecase(prodp, up, size); \
33 else \
34 mpih_sqr_n(prodp, up, size, tspace); \
35 } while (0);
36
37 /* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
38 * both with SIZE limbs, and store the result at PRODP. 2 * SIZE limbs are
39 * always stored. Return the most significant limb.
40 *
41 * Argument constraints:
42 * 1. PRODP != UP and PRODP != VP, i.e. the destination
43 * must be distinct from the multiplier and the multiplicand.
44 *
45 *
46 * Handle simple cases with traditional multiplication.
47 *
48 * This is the most critical code of multiplication. All multiplies rely
49 * on this, both small and huge. Small ones arrive here immediately. Huge
50 * ones arrive here as this is the base case for Karatsuba's recursive
51 * algorithm below.
52 */
53
54 static mpi_limb_t
mul_n_basecase(mpi_ptr_t prodp,mpi_ptr_t up,mpi_ptr_t vp,mpi_size_t size)55 mul_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
56 {
57 mpi_size_t i;
58 mpi_limb_t cy;
59 mpi_limb_t v_limb;
60
61 /* Multiply by the first limb in V separately, as the result can be
62 * stored (not added) to PROD. We also avoid a loop for zeroing. */
63 v_limb = vp[0];
64 if (v_limb <= 1) {
65 if (v_limb == 1)
66 MPN_COPY(prodp, up, size);
67 else
68 MPN_ZERO(prodp, size);
69 cy = 0;
70 } else
71 cy = mpihelp_mul_1(prodp, up, size, v_limb);
72
73 prodp[size] = cy;
74 prodp++;
75
76 /* For each iteration in the outer loop, multiply one limb from
77 * U with one limb from V, and add it to PROD. */
78 for (i = 1; i < size; i++) {
79 v_limb = vp[i];
80 if (v_limb <= 1) {
81 cy = 0;
82 if (v_limb == 1)
83 cy = mpihelp_add_n(prodp, prodp, up, size);
84 } else
85 cy = mpihelp_addmul_1(prodp, up, size, v_limb);
86
87 prodp[size] = cy;
88 prodp++;
89 }
90
91 return cy;
92 }
93
94 static void
mul_n(mpi_ptr_t prodp,mpi_ptr_t up,mpi_ptr_t vp,mpi_size_t size,mpi_ptr_t tspace)95 mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp,
96 mpi_size_t size, mpi_ptr_t tspace)
97 {
98 if (size & 1) {
99 /* The size is odd, and the code below doesn't handle that.
100 * Multiply the least significant (size - 1) limbs with a recursive
101 * call, and handle the most significant limb of S1 and S2
102 * separately.
103 * A slightly faster way to do this would be to make the Karatsuba
104 * code below behave as if the size were even, and let it check for
105 * odd size in the end. I.e., in essence move this code to the end.
106 * Doing so would save us a recursive call, and potentially make the
107 * stack grow a lot less.
108 */
109 mpi_size_t esize = size - 1; /* even size */
110 mpi_limb_t cy_limb;
111
112 MPN_MUL_N_RECURSE(prodp, up, vp, esize, tspace);
113 cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, vp[esize]);
114 prodp[esize + esize] = cy_limb;
115 cy_limb = mpihelp_addmul_1(prodp + esize, vp, size, up[esize]);
116 prodp[esize + size] = cy_limb;
117 } else {
118 /* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
119 *
120 * Split U in two pieces, U1 and U0, such that
121 * U = U0 + U1*(B**n),
122 * and V in V1 and V0, such that
123 * V = V0 + V1*(B**n).
124 *
125 * UV is then computed recursively using the identity
126 *
127 * 2n n n n
128 * UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V
129 * 1 1 1 0 0 1 0 0
130 *
131 * Where B = 2**BITS_PER_MP_LIMB.
132 */
133 mpi_size_t hsize = size >> 1;
134 mpi_limb_t cy;
135 int negflg;
136
137 /* Product H. ________________ ________________
138 * |_____U1 x V1____||____U0 x V0_____|
139 * Put result in upper part of PROD and pass low part of TSPACE
140 * as new TSPACE.
141 */
142 MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize,
143 tspace);
144
145 /* Product M. ________________
146 * |_(U1-U0)(V0-V1)_|
147 */
148 if (mpihelp_cmp(up + hsize, up, hsize) >= 0) {
149 mpihelp_sub_n(prodp, up + hsize, up, hsize);
150 negflg = 0;
151 } else {
152 mpihelp_sub_n(prodp, up, up + hsize, hsize);
153 negflg = 1;
154 }
155 if (mpihelp_cmp(vp + hsize, vp, hsize) >= 0) {
156 mpihelp_sub_n(prodp + hsize, vp + hsize, vp, hsize);
157 negflg ^= 1;
158 } else {
159 mpihelp_sub_n(prodp + hsize, vp, vp + hsize, hsize);
160 /* No change of NEGFLG. */
161 }
162 /* Read temporary operands from low part of PROD.
163 * Put result in low part of TSPACE using upper part of TSPACE
164 * as new TSPACE.
165 */
166 MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize,
167 tspace + size);
168
169 /* Add/copy product H. */
170 MPN_COPY(prodp + hsize, prodp + size, hsize);
171 cy = mpihelp_add_n(prodp + size, prodp + size,
172 prodp + size + hsize, hsize);
173
174 /* Add product M (if NEGFLG M is a negative number) */
175 if (negflg)
176 cy -=
177 mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace,
178 size);
179 else
180 cy +=
181 mpihelp_add_n(prodp + hsize, prodp + hsize, tspace,
182 size);
183
184 /* Product L. ________________ ________________
185 * |________________||____U0 x V0_____|
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 MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size);
191
192 /* Add/copy Product L (twice) */
193
194 cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
195 if (cy)
196 mpihelp_add_1(prodp + hsize + size,
197 prodp + hsize + size, hsize, cy);
198
199 MPN_COPY(prodp, tspace, hsize);
200 cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
201 hsize);
202 if (cy)
203 mpihelp_add_1(prodp + size, prodp + size, size, 1);
204 }
205 }
206
mpih_sqr_n_basecase(mpi_ptr_t prodp,mpi_ptr_t up,mpi_size_t size)207 void mpih_sqr_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size)
208 {
209 mpi_size_t i;
210 mpi_limb_t cy_limb;
211 mpi_limb_t v_limb;
212
213 /* Multiply by the first limb in V separately, as the result can be
214 * stored (not added) to PROD. We also avoid a loop for zeroing. */
215 v_limb = up[0];
216 if (v_limb <= 1) {
217 if (v_limb == 1)
218 MPN_COPY(prodp, up, size);
219 else
220 MPN_ZERO(prodp, size);
221 cy_limb = 0;
222 } else
223 cy_limb = mpihelp_mul_1(prodp, up, size, v_limb);
224
225 prodp[size] = cy_limb;
226 prodp++;
227
228 /* For each iteration in the outer loop, multiply one limb from
229 * U with one limb from V, and add it to PROD. */
230 for (i = 1; i < size; i++) {
231 v_limb = up[i];
232 if (v_limb <= 1) {
233 cy_limb = 0;
234 if (v_limb == 1)
235 cy_limb = mpihelp_add_n(prodp, prodp, up, size);
236 } else
237 cy_limb = mpihelp_addmul_1(prodp, up, size, v_limb);
238
239 prodp[size] = cy_limb;
240 prodp++;
241 }
242 }
243
244 void
mpih_sqr_n(mpi_ptr_t prodp,mpi_ptr_t up,mpi_size_t size,mpi_ptr_t tspace)245 mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace)
246 {
247 if (size & 1) {
248 /* The size is odd, and the code below doesn't handle that.
249 * Multiply the least significant (size - 1) limbs with a recursive
250 * call, and handle the most significant limb of S1 and S2
251 * separately.
252 * A slightly faster way to do this would be to make the Karatsuba
253 * code below behave as if the size were even, and let it check for
254 * odd size in the end. I.e., in essence move this code to the end.
255 * Doing so would save us a recursive call, and potentially make the
256 * stack grow a lot less.
257 */
258 mpi_size_t esize = size - 1; /* even size */
259 mpi_limb_t cy_limb;
260
261 MPN_SQR_N_RECURSE(prodp, up, esize, tspace);
262 cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, up[esize]);
263 prodp[esize + esize] = cy_limb;
264 cy_limb = mpihelp_addmul_1(prodp + esize, up, size, up[esize]);
265
266 prodp[esize + size] = cy_limb;
267 } else {
268 mpi_size_t hsize = size >> 1;
269 mpi_limb_t cy;
270
271 /* Product H. ________________ ________________
272 * |_____U1 x U1____||____U0 x U0_____|
273 * Put result in upper part of PROD and pass low part of TSPACE
274 * as new TSPACE.
275 */
276 MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace);
277
278 /* Product M. ________________
279 * |_(U1-U0)(U0-U1)_|
280 */
281 if (mpihelp_cmp(up + hsize, up, hsize) >= 0)
282 mpihelp_sub_n(prodp, up + hsize, up, hsize);
283 else
284 mpihelp_sub_n(prodp, up, up + hsize, hsize);
285
286 /* Read temporary operands from low part of PROD.
287 * Put result in low part of TSPACE using upper part of TSPACE
288 * as new TSPACE. */
289 MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size);
290
291 /* Add/copy product H */
292 MPN_COPY(prodp + hsize, prodp + size, hsize);
293 cy = mpihelp_add_n(prodp + size, prodp + size,
294 prodp + size + hsize, hsize);
295
296 /* Add product M (if NEGFLG M is a negative number). */
297 cy -= mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace, size);
298
299 /* Product L. ________________ ________________
300 * |________________||____U0 x U0_____|
301 * Read temporary operands from low part of PROD.
302 * Put result in low part of TSPACE using upper part of TSPACE
303 * as new TSPACE. */
304 MPN_SQR_N_RECURSE(tspace, up, hsize, tspace + size);
305
306 /* Add/copy Product L (twice). */
307 cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
308 if (cy)
309 mpihelp_add_1(prodp + hsize + size,
310 prodp + hsize + size, hsize, cy);
311
312 MPN_COPY(prodp, tspace, hsize);
313 cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
314 hsize);
315 if (cy)
316 mpihelp_add_1(prodp + size, prodp + size, size, 1);
317 }
318 }
319
320 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)321 mpihelp_mul_karatsuba_case(mpi_ptr_t prodp,
322 mpi_ptr_t up, mpi_size_t usize,
323 mpi_ptr_t vp, mpi_size_t vsize,
324 struct karatsuba_ctx *ctx)
325 {
326 mpi_limb_t cy;
327
328 if (!ctx->tspace || ctx->tspace_size < vsize) {
329 if (ctx->tspace)
330 mpi_free_limb_space(ctx->tspace);
331 ctx->tspace = mpi_alloc_limb_space(2 * vsize);
332 if (!ctx->tspace)
333 return -ENOMEM;
334 ctx->tspace_size = vsize;
335 }
336
337 MPN_MUL_N_RECURSE(prodp, up, vp, vsize, ctx->tspace);
338
339 prodp += vsize;
340 up += vsize;
341 usize -= vsize;
342 if (usize >= vsize) {
343 if (!ctx->tp || ctx->tp_size < vsize) {
344 if (ctx->tp)
345 mpi_free_limb_space(ctx->tp);
346 ctx->tp = mpi_alloc_limb_space(2 * vsize);
347 if (!ctx->tp) {
348 if (ctx->tspace)
349 mpi_free_limb_space(ctx->tspace);
350 ctx->tspace = NULL;
351 return -ENOMEM;
352 }
353 ctx->tp_size = vsize;
354 }
355
356 do {
357 MPN_MUL_N_RECURSE(ctx->tp, up, vp, vsize, ctx->tspace);
358 cy = mpihelp_add_n(prodp, prodp, ctx->tp, vsize);
359 mpihelp_add_1(prodp + vsize, ctx->tp + vsize, vsize,
360 cy);
361 prodp += vsize;
362 up += vsize;
363 usize -= vsize;
364 } while (usize >= vsize);
365 }
366
367 if (usize) {
368 if (usize < KARATSUBA_THRESHOLD) {
369 mpi_limb_t tmp;
370 if (mpihelp_mul(ctx->tspace, vp, vsize, up, usize, &tmp)
371 < 0)
372 return -ENOMEM;
373 } else {
374 if (!ctx->next) {
375 ctx->next = kzalloc(sizeof *ctx, GFP_KERNEL);
376 if (!ctx->next)
377 return -ENOMEM;
378 }
379 if (mpihelp_mul_karatsuba_case(ctx->tspace,
380 vp, vsize,
381 up, usize,
382 ctx->next) < 0)
383 return -ENOMEM;
384 }
385
386 cy = mpihelp_add_n(prodp, prodp, ctx->tspace, vsize);
387 mpihelp_add_1(prodp + vsize, ctx->tspace + vsize, usize, cy);
388 }
389
390 return 0;
391 }
392
mpihelp_release_karatsuba_ctx(struct karatsuba_ctx * ctx)393 void mpihelp_release_karatsuba_ctx(struct karatsuba_ctx *ctx)
394 {
395 struct karatsuba_ctx *ctx2;
396
397 if (ctx->tp)
398 mpi_free_limb_space(ctx->tp);
399 if (ctx->tspace)
400 mpi_free_limb_space(ctx->tspace);
401 for (ctx = ctx->next; ctx; ctx = ctx2) {
402 ctx2 = ctx->next;
403 if (ctx->tp)
404 mpi_free_limb_space(ctx->tp);
405 if (ctx->tspace)
406 mpi_free_limb_space(ctx->tspace);
407 kfree(ctx);
408 }
409 }
410
411 /* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
412 * and v (pointed to by VP, with VSIZE limbs), and store the result at
413 * PRODP. USIZE + VSIZE limbs are always stored, but if the input
414 * operands are normalized. Return the most significant limb of the
415 * result.
416 *
417 * NOTE: The space pointed to by PRODP is overwritten before finished
418 * with U and V, so overlap is an error.
419 *
420 * Argument constraints:
421 * 1. USIZE >= VSIZE.
422 * 2. PRODP != UP and PRODP != VP, i.e. the destination
423 * must be distinct from the multiplier and the multiplicand.
424 */
425
426 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)427 mpihelp_mul(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize,
428 mpi_ptr_t vp, mpi_size_t vsize, mpi_limb_t *_result)
429 {
430 mpi_ptr_t prod_endp = prodp + usize + vsize - 1;
431 mpi_limb_t cy;
432 struct karatsuba_ctx ctx;
433
434 if (vsize < KARATSUBA_THRESHOLD) {
435 mpi_size_t i;
436 mpi_limb_t v_limb;
437
438 if (!vsize) {
439 *_result = 0;
440 return 0;
441 }
442
443 /* Multiply by the first limb in V separately, as the result can be
444 * stored (not added) to PROD. We also avoid a loop for zeroing. */
445 v_limb = vp[0];
446 if (v_limb <= 1) {
447 if (v_limb == 1)
448 MPN_COPY(prodp, up, usize);
449 else
450 MPN_ZERO(prodp, usize);
451 cy = 0;
452 } else
453 cy = mpihelp_mul_1(prodp, up, usize, v_limb);
454
455 prodp[usize] = cy;
456 prodp++;
457
458 /* For each iteration in the outer loop, multiply one limb from
459 * U with one limb from V, and add it to PROD. */
460 for (i = 1; i < vsize; i++) {
461 v_limb = vp[i];
462 if (v_limb <= 1) {
463 cy = 0;
464 if (v_limb == 1)
465 cy = mpihelp_add_n(prodp, prodp, up,
466 usize);
467 } else
468 cy = mpihelp_addmul_1(prodp, up, usize, v_limb);
469
470 prodp[usize] = cy;
471 prodp++;
472 }
473
474 *_result = cy;
475 return 0;
476 }
477
478 memset(&ctx, 0, sizeof ctx);
479 if (mpihelp_mul_karatsuba_case(prodp, up, usize, vp, vsize, &ctx) < 0)
480 return -ENOMEM;
481 mpihelp_release_karatsuba_ctx(&ctx);
482 *_result = *prod_endp;
483 return 0;
484 }
485