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mpih-mul.c
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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
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
108 mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp,
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 
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
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 int
335  mpi_ptr_t up, mpi_size_t usize,
336  mpi_ptr_t vp, mpi_size_t vsize,
337  struct karatsuba_ctx *ctx)
338 {
339  mpi_limb_t cy;
340 
341  if (!ctx->tspace || ctx->tspace_size < vsize) {
342  if (ctx->tspace)
344  ctx->tspace = mpi_alloc_limb_space(2 * vsize);
345  if (!ctx->tspace)
346  return -ENOMEM;
347  ctx->tspace_size = vsize;
348  }
349 
350  MPN_MUL_N_RECURSE(prodp, up, vp, vsize, ctx->tspace);
351 
352  prodp += vsize;
353  up += vsize;
354  usize -= vsize;
355  if (usize >= vsize) {
356  if (!ctx->tp || ctx->tp_size < vsize) {
357  if (ctx->tp)
358  mpi_free_limb_space(ctx->tp);
359  ctx->tp = mpi_alloc_limb_space(2 * vsize);
360  if (!ctx->tp) {
361  if (ctx->tspace)
363  ctx->tspace = NULL;
364  return -ENOMEM;
365  }
366  ctx->tp_size = vsize;
367  }
368 
369  do {
370  MPN_MUL_N_RECURSE(ctx->tp, up, vp, vsize, ctx->tspace);
371  cy = mpihelp_add_n(prodp, prodp, ctx->tp, vsize);
372  mpihelp_add_1(prodp + vsize, ctx->tp + vsize, vsize,
373  cy);
374  prodp += vsize;
375  up += vsize;
376  usize -= vsize;
377  } while (usize >= vsize);
378  }
379 
380  if (usize) {
381  if (usize < KARATSUBA_THRESHOLD) {
382  mpi_limb_t tmp;
383  if (mpihelp_mul(ctx->tspace, vp, vsize, up, usize, &tmp)
384  < 0)
385  return -ENOMEM;
386  } else {
387  if (!ctx->next) {
388  ctx->next = kzalloc(sizeof *ctx, GFP_KERNEL);
389  if (!ctx->next)
390  return -ENOMEM;
391  }
393  vp, vsize,
394  up, usize,
395  ctx->next) < 0)
396  return -ENOMEM;
397  }
398 
399  cy = mpihelp_add_n(prodp, prodp, ctx->tspace, vsize);
400  mpihelp_add_1(prodp + vsize, ctx->tspace + vsize, usize, cy);
401  }
402 
403  return 0;
404 }
405 
407 {
408  struct karatsuba_ctx *ctx2;
409 
410  if (ctx->tp)
411  mpi_free_limb_space(ctx->tp);
412  if (ctx->tspace)
414  for (ctx = ctx->next; ctx; ctx = ctx2) {
415  ctx2 = ctx->next;
416  if (ctx->tp)
417  mpi_free_limb_space(ctx->tp);
418  if (ctx->tspace)
420  kfree(ctx);
421  }
422 }
423 
424 /* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
425  * and v (pointed to by VP, with VSIZE limbs), and store the result at
426  * PRODP. USIZE + VSIZE limbs are always stored, but if the input
427  * operands are normalized. Return the most significant limb of the
428  * result.
429  *
430  * NOTE: The space pointed to by PRODP is overwritten before finished
431  * with U and V, so overlap is an error.
432  *
433  * Argument constraints:
434  * 1. USIZE >= VSIZE.
435  * 2. PRODP != UP and PRODP != VP, i.e. the destination
436  * must be distinct from the multiplier and the multiplicand.
437  */
438 
439 int
441  mpi_ptr_t vp, mpi_size_t vsize, mpi_limb_t *_result)
442 {
443  mpi_ptr_t prod_endp = prodp + usize + vsize - 1;
444  mpi_limb_t cy;
445  struct karatsuba_ctx ctx;
446 
447  if (vsize < KARATSUBA_THRESHOLD) {
448  mpi_size_t i;
449  mpi_limb_t v_limb;
450 
451  if (!vsize) {
452  *_result = 0;
453  return 0;
454  }
455 
456  /* Multiply by the first limb in V separately, as the result can be
457  * stored (not added) to PROD. We also avoid a loop for zeroing. */
458  v_limb = vp[0];
459  if (v_limb <= 1) {
460  if (v_limb == 1)
461  MPN_COPY(prodp, up, usize);
462  else
463  MPN_ZERO(prodp, usize);
464  cy = 0;
465  } else
466  cy = mpihelp_mul_1(prodp, up, usize, v_limb);
467 
468  prodp[usize] = cy;
469  prodp++;
470 
471  /* For each iteration in the outer loop, multiply one limb from
472  * U with one limb from V, and add it to PROD. */
473  for (i = 1; i < vsize; i++) {
474  v_limb = vp[i];
475  if (v_limb <= 1) {
476  cy = 0;
477  if (v_limb == 1)
478  cy = mpihelp_add_n(prodp, prodp, up,
479  usize);
480  } else
481  cy = mpihelp_addmul_1(prodp, up, usize, v_limb);
482 
483  prodp[usize] = cy;
484  prodp++;
485  }
486 
487  *_result = cy;
488  return 0;
489  }
490 
491  memset(&ctx, 0, sizeof ctx);
492  if (mpihelp_mul_karatsuba_case(prodp, up, usize, vp, vsize, &ctx) < 0)
493  return -ENOMEM;
495  *_result = *prod_endp;
496  return 0;
497 }