Botan  2.12.1
Crypto and TLS for C++11
mp_core.h
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1 /*
2 * MPI Algorithms
3 * (C) 1999-2010,2018 Jack Lloyd
4 * 2006 Luca Piccarreta
5 * 2016 Matthias Gierlings
6 *
7 * Botan is released under the Simplified BSD License (see license.txt)
8 */
9 
10 #ifndef BOTAN_MP_CORE_OPS_H_
11 #define BOTAN_MP_CORE_OPS_H_
12 
13 #include <botan/types.h>
14 #include <botan/exceptn.h>
15 #include <botan/mem_ops.h>
16 #include <botan/internal/mp_asmi.h>
17 #include <botan/internal/ct_utils.h>
18 #include <algorithm>
19 
20 namespace Botan {
21 
22 const word MP_WORD_MAX = ~static_cast<word>(0);
23 
24 /*
25 * If cond == 0, does nothing.
26 * If cond > 0, swaps x[0:size] with y[0:size]
27 * Runs in constant time
28 */
29 inline void bigint_cnd_swap(word cnd, word x[], word y[], size_t size)
30  {
31  const auto mask = CT::Mask<word>::expand(cnd);
32 
33  for(size_t i = 0; i != size; ++i)
34  {
35  const word a = x[i];
36  const word b = y[i];
37  x[i] = mask.select(b, a);
38  y[i] = mask.select(a, b);
39  }
40  }
41 
42 inline word bigint_cnd_add(word cnd, word x[], word x_size,
43  const word y[], size_t y_size)
44  {
45  BOTAN_ASSERT(x_size >= y_size, "Expected sizes");
46 
47  const auto mask = CT::Mask<word>::expand(cnd);
48 
49  word carry = 0;
50 
51  const size_t blocks = y_size - (y_size % 8);
52  word z[8] = { 0 };
53 
54  for(size_t i = 0; i != blocks; i += 8)
55  {
56  carry = word8_add3(z, x + i, y + i, carry);
57  mask.select_n(x + i, z, x + i, 8);
58  }
59 
60  for(size_t i = blocks; i != y_size; ++i)
61  {
62  z[0] = word_add(x[i], y[i], &carry);
63  x[i] = mask.select(z[0], x[i]);
64  }
65 
66  for(size_t i = y_size; i != x_size; ++i)
67  {
68  z[0] = word_add(x[i], 0, &carry);
69  x[i] = mask.select(z[0], x[i]);
70  }
71 
72  return mask.if_set_return(carry);
73  }
74 
75 /*
76 * If cond > 0 adds x[0:size] and y[0:size] and returns carry
77 * Runs in constant time
78 */
79 inline word bigint_cnd_add(word cnd, word x[], const word y[], size_t size)
80  {
81  return bigint_cnd_add(cnd, x, size, y, size);
82  }
83 
84 /*
85 * If cond > 0 subtracts x[0:size] and y[0:size] and returns borrow
86 * Runs in constant time
87 */
88 inline word bigint_cnd_sub(word cnd,
89  word x[], size_t x_size,
90  const word y[], size_t y_size)
91  {
92  BOTAN_ASSERT(x_size >= y_size, "Expected sizes");
93 
94  const auto mask = CT::Mask<word>::expand(cnd);
95 
96  word carry = 0;
97 
98  const size_t blocks = y_size - (y_size % 8);
99  word z[8] = { 0 };
100 
101  for(size_t i = 0; i != blocks; i += 8)
102  {
103  carry = word8_sub3(z, x + i, y + i, carry);
104  mask.select_n(x + i, z, x + i, 8);
105  }
106 
107  for(size_t i = blocks; i != y_size; ++i)
108  {
109  z[0] = word_sub(x[i], y[i], &carry);
110  x[i] = mask.select(z[0], x[i]);
111  }
112 
113  for(size_t i = y_size; i != x_size; ++i)
114  {
115  z[0] = word_sub(x[i], 0, &carry);
116  x[i] = mask.select(z[0], x[i]);
117  }
118 
119  return mask.if_set_return(carry);
120  }
121 
122 /*
123 * If cond > 0 adds x[0:size] and y[0:size] and returns carry
124 * Runs in constant time
125 */
126 inline word bigint_cnd_sub(word cnd, word x[], const word y[], size_t size)
127  {
128  return bigint_cnd_sub(cnd, x, size, y, size);
129  }
130 
131 
132 /*
133 * Equivalent to
134 * bigint_cnd_add( mask, x, y, size);
135 * bigint_cnd_sub(~mask, x, y, size);
136 *
137 * Mask must be either 0 or all 1 bits
138 */
139 inline void bigint_cnd_add_or_sub(CT::Mask<word> mask, word x[], const word y[], size_t size)
140  {
141  const size_t blocks = size - (size % 8);
142 
143  word carry = 0;
144  word borrow = 0;
145 
146  word t0[8] = { 0 };
147  word t1[8] = { 0 };
148 
149  for(size_t i = 0; i != blocks; i += 8)
150  {
151  carry = word8_add3(t0, x + i, y + i, carry);
152  borrow = word8_sub3(t1, x + i, y + i, borrow);
153 
154  for(size_t j = 0; j != 8; ++j)
155  x[i+j] = mask.select(t0[j], t1[j]);
156  }
157 
158  for(size_t i = blocks; i != size; ++i)
159  {
160  const word a = word_add(x[i], y[i], &carry);
161  const word s = word_sub(x[i], y[i], &borrow);
162 
163  x[i] = mask.select(a, s);
164  }
165  }
166 
167 /*
168 * Equivalent to
169 * bigint_cnd_add( mask, x, size, y, size);
170 * bigint_cnd_sub(~mask, x, size, z, size);
171 *
172 * Mask must be either 0 or all 1 bits
173 *
174 * Returns the carry or borrow resp
175 */
176 inline word bigint_cnd_addsub(CT::Mask<word> mask, word x[],
177  const word y[], const word z[],
178  size_t size)
179  {
180  const size_t blocks = size - (size % 8);
181 
182  word carry = 0;
183  word borrow = 0;
184 
185  word t0[8] = { 0 };
186  word t1[8] = { 0 };
187 
188  for(size_t i = 0; i != blocks; i += 8)
189  {
190  carry = word8_add3(t0, x + i, y + i, carry);
191  borrow = word8_sub3(t1, x + i, z + i, borrow);
192 
193  for(size_t j = 0; j != 8; ++j)
194  x[i+j] = mask.select(t0[j], t1[j]);
195  }
196 
197  for(size_t i = blocks; i != size; ++i)
198  {
199  t0[0] = word_add(x[i], y[i], &carry);
200  t1[0] = word_sub(x[i], z[i], &borrow);
201  x[i] = mask.select(t0[0], t1[0]);
202  }
203 
204  return mask.select(carry, borrow);
205  }
206 
207 /*
208 * 2s complement absolute value
209 * If cond > 0 sets x to ~x + 1
210 * Runs in constant time
211 */
212 inline void bigint_cnd_abs(word cnd, word x[], size_t size)
213  {
214  const auto mask = CT::Mask<word>::expand(cnd);
215 
216  word carry = mask.if_set_return(1);
217  for(size_t i = 0; i != size; ++i)
218  {
219  const word z = word_add(~x[i], 0, &carry);
220  x[i] = mask.select(z, x[i]);
221  }
222  }
223 
224 /**
225 * Two operand addition with carry out
226 */
227 inline word bigint_add2_nc(word x[], size_t x_size, const word y[], size_t y_size)
228  {
229  word carry = 0;
230 
231  BOTAN_ASSERT(x_size >= y_size, "Expected sizes");
232 
233  const size_t blocks = y_size - (y_size % 8);
234 
235  for(size_t i = 0; i != blocks; i += 8)
236  carry = word8_add2(x + i, y + i, carry);
237 
238  for(size_t i = blocks; i != y_size; ++i)
239  x[i] = word_add(x[i], y[i], &carry);
240 
241  for(size_t i = y_size; i != x_size; ++i)
242  x[i] = word_add(x[i], 0, &carry);
243 
244  return carry;
245  }
246 
247 /**
248 * Three operand addition with carry out
249 */
250 inline word bigint_add3_nc(word z[],
251  const word x[], size_t x_size,
252  const word y[], size_t y_size)
253  {
254  if(x_size < y_size)
255  { return bigint_add3_nc(z, y, y_size, x, x_size); }
256 
257  word carry = 0;
258 
259  const size_t blocks = y_size - (y_size % 8);
260 
261  for(size_t i = 0; i != blocks; i += 8)
262  carry = word8_add3(z + i, x + i, y + i, carry);
263 
264  for(size_t i = blocks; i != y_size; ++i)
265  z[i] = word_add(x[i], y[i], &carry);
266 
267  for(size_t i = y_size; i != x_size; ++i)
268  z[i] = word_add(x[i], 0, &carry);
269 
270  return carry;
271  }
272 
273 /**
274 * Two operand addition
275 * @param x the first operand (and output)
276 * @param x_size size of x
277 * @param y the second operand
278 * @param y_size size of y (must be >= x_size)
279 */
280 inline void bigint_add2(word x[], size_t x_size,
281  const word y[], size_t y_size)
282  {
283  x[x_size] += bigint_add2_nc(x, x_size, y, y_size);
284  }
285 
286 /**
287 * Three operand addition
288 */
289 inline void bigint_add3(word z[],
290  const word x[], size_t x_size,
291  const word y[], size_t y_size)
292  {
293  z[x_size > y_size ? x_size : y_size] +=
294  bigint_add3_nc(z, x, x_size, y, y_size);
295  }
296 
297 /**
298 * Two operand subtraction
299 */
300 inline word bigint_sub2(word x[], size_t x_size,
301  const word y[], size_t y_size)
302  {
303  word borrow = 0;
304 
305  BOTAN_ASSERT(x_size >= y_size, "Expected sizes");
306 
307  const size_t blocks = y_size - (y_size % 8);
308 
309  for(size_t i = 0; i != blocks; i += 8)
310  borrow = word8_sub2(x + i, y + i, borrow);
311 
312  for(size_t i = blocks; i != y_size; ++i)
313  x[i] = word_sub(x[i], y[i], &borrow);
314 
315  for(size_t i = y_size; i != x_size; ++i)
316  x[i] = word_sub(x[i], 0, &borrow);
317 
318  return borrow;
319  }
320 
321 /**
322 * Two operand subtraction, x = y - x; assumes y >= x
323 */
324 inline void bigint_sub2_rev(word x[], const word y[], size_t y_size)
325  {
326  word borrow = 0;
327 
328  const size_t blocks = y_size - (y_size % 8);
329 
330  for(size_t i = 0; i != blocks; i += 8)
331  borrow = word8_sub2_rev(x + i, y + i, borrow);
332 
333  for(size_t i = blocks; i != y_size; ++i)
334  x[i] = word_sub(y[i], x[i], &borrow);
335 
336  BOTAN_ASSERT(borrow == 0, "y must be greater than x");
337  }
338 
339 /**
340 * Three operand subtraction
341 */
342 inline word bigint_sub3(word z[],
343  const word x[], size_t x_size,
344  const word y[], size_t y_size)
345  {
346  word borrow = 0;
347 
348  BOTAN_ASSERT(x_size >= y_size, "Expected sizes");
349 
350  const size_t blocks = y_size - (y_size % 8);
351 
352  for(size_t i = 0; i != blocks; i += 8)
353  borrow = word8_sub3(z + i, x + i, y + i, borrow);
354 
355  for(size_t i = blocks; i != y_size; ++i)
356  z[i] = word_sub(x[i], y[i], &borrow);
357 
358  for(size_t i = y_size; i != x_size; ++i)
359  z[i] = word_sub(x[i], 0, &borrow);
360 
361  return borrow;
362  }
363 
364 /**
365 * Return abs(x-y), ie if x >= y, then compute z = x - y
366 * Otherwise compute z = y - x
367 * No borrow is possible since the result is always >= 0
368 *
369 * Returns ~0 if x >= y or 0 if x < y
370 * @param z output array of at least N words
371 * @param x input array of N words
372 * @param y input array of N words
373 * @param N length of x and y
374 * @param ws array of at least 2*N words
375 */
376 inline CT::Mask<word>
377 bigint_sub_abs(word z[],
378  const word x[], const word y[], size_t N,
379  word ws[])
380  {
381  // Subtract in both direction then conditional copy out the result
382 
383  word* ws0 = ws;
384  word* ws1 = ws + N;
385 
386  word borrow0 = 0;
387  word borrow1 = 0;
388 
389  const size_t blocks = N - (N % 8);
390 
391  for(size_t i = 0; i != blocks; i += 8)
392  {
393  borrow0 = word8_sub3(ws0 + i, x + i, y + i, borrow0);
394  borrow1 = word8_sub3(ws1 + i, y + i, x + i, borrow1);
395  }
396 
397  for(size_t i = blocks; i != N; ++i)
398  {
399  ws0[i] = word_sub(x[i], y[i], &borrow0);
400  ws1[i] = word_sub(y[i], x[i], &borrow1);
401  }
402 
403  return CT::conditional_copy_mem(borrow0, z, ws1, ws0, N);
404  }
405 
406 /*
407 * Shift Operations
408 */
409 inline void bigint_shl1(word x[], size_t x_size, size_t x_words,
410  size_t word_shift, size_t bit_shift)
411  {
412  copy_mem(x + word_shift, x, x_words);
413  clear_mem(x, word_shift);
414 
415  const auto carry_mask = CT::Mask<word>::expand(bit_shift);
416  const size_t carry_shift = carry_mask.if_set_return(BOTAN_MP_WORD_BITS - bit_shift);
417 
418  word carry = 0;
419  for(size_t i = word_shift; i != x_size; ++i)
420  {
421  const word w = x[i];
422  x[i] = (w << bit_shift) | carry;
423  carry = carry_mask.if_set_return(w >> carry_shift);
424  }
425  }
426 
427 inline void bigint_shr1(word x[], size_t x_size,
428  size_t word_shift, size_t bit_shift)
429  {
430  const size_t top = x_size >= word_shift ? (x_size - word_shift) : 0;
431 
432  copy_mem(x, x + word_shift, top);
433  clear_mem(x + top, std::min(word_shift, x_size));
434 
435  const auto carry_mask = CT::Mask<word>::expand(bit_shift);
436  const size_t carry_shift = carry_mask.if_set_return(BOTAN_MP_WORD_BITS - bit_shift);
437 
438  word carry = 0;
439 
440  for(size_t i = 0; i != top; ++i)
441  {
442  const word w = x[top - i - 1];
443  x[top-i-1] = (w >> bit_shift) | carry;
444  carry = carry_mask.if_set_return(w << carry_shift);
445  }
446  }
447 
448 inline void bigint_shl2(word y[], const word x[], size_t x_size,
449  size_t word_shift, size_t bit_shift)
450  {
451  copy_mem(y + word_shift, x, x_size);
452 
453  const auto carry_mask = CT::Mask<word>::expand(bit_shift);
454  const size_t carry_shift = carry_mask.if_set_return(BOTAN_MP_WORD_BITS - bit_shift);
455 
456  word carry = 0;
457  for(size_t i = word_shift; i != x_size + word_shift + 1; ++i)
458  {
459  const word w = y[i];
460  y[i] = (w << bit_shift) | carry;
461  carry = carry_mask.if_set_return(w >> carry_shift);
462  }
463  }
464 
465 inline void bigint_shr2(word y[], const word x[], size_t x_size,
466  size_t word_shift, size_t bit_shift)
467  {
468  const size_t new_size = x_size < word_shift ? 0 : (x_size - word_shift);
469 
470  copy_mem(y, x + word_shift, new_size);
471 
472  const auto carry_mask = CT::Mask<word>::expand(bit_shift);
473  const size_t carry_shift = carry_mask.if_set_return(BOTAN_MP_WORD_BITS - bit_shift);
474 
475  word carry = 0;
476  for(size_t i = new_size; i > 0; --i)
477  {
478  word w = y[i-1];
479  y[i-1] = (w >> bit_shift) | carry;
480  carry = carry_mask.if_set_return(w << carry_shift);
481  }
482  }
483 
484 /*
485 * Linear Multiply - returns the carry
486 */
487 inline word BOTAN_WARN_UNUSED_RESULT bigint_linmul2(word x[], size_t x_size, word y)
488  {
489  const size_t blocks = x_size - (x_size % 8);
490 
491  word carry = 0;
492 
493  for(size_t i = 0; i != blocks; i += 8)
494  carry = word8_linmul2(x + i, y, carry);
495 
496  for(size_t i = blocks; i != x_size; ++i)
497  x[i] = word_madd2(x[i], y, &carry);
498 
499  return carry;
500  }
501 
502 inline void bigint_linmul3(word z[], const word x[], size_t x_size, word y)
503  {
504  const size_t blocks = x_size - (x_size % 8);
505 
506  word carry = 0;
507 
508  for(size_t i = 0; i != blocks; i += 8)
509  carry = word8_linmul3(z + i, x + i, y, carry);
510 
511  for(size_t i = blocks; i != x_size; ++i)
512  z[i] = word_madd2(x[i], y, &carry);
513 
514  z[x_size] = carry;
515  }
516 
517 /**
518 * Compare x and y
519 * Return -1 if x < y
520 * Return 0 if x == y
521 * Return 1 if x > y
522 */
523 inline int32_t bigint_cmp(const word x[], size_t x_size,
524  const word y[], size_t y_size)
525  {
526  static_assert(sizeof(word) >= sizeof(uint32_t), "Size assumption");
527 
528  const word LT = static_cast<word>(-1);
529  const word EQ = 0;
530  const word GT = 1;
531 
532  const size_t common_elems = std::min(x_size, y_size);
533 
534  word result = EQ; // until found otherwise
535 
536  for(size_t i = 0; i != common_elems; i++)
537  {
538  const auto is_eq = CT::Mask<word>::is_equal(x[i], y[i]);
539  const auto is_lt = CT::Mask<word>::is_lt(x[i], y[i]);
540 
541  result = is_eq.select(result, is_lt.select(LT, GT));
542  }
543 
544  if(x_size < y_size)
545  {
546  word mask = 0;
547  for(size_t i = x_size; i != y_size; i++)
548  mask |= y[i];
549 
550  // If any bits were set in high part of y, then x < y
551  result = CT::Mask<word>::is_zero(mask).select(result, LT);
552  }
553  else if(y_size < x_size)
554  {
555  word mask = 0;
556  for(size_t i = y_size; i != x_size; i++)
557  mask |= x[i];
558 
559  // If any bits were set in high part of x, then x > y
560  result = CT::Mask<word>::is_zero(mask).select(result, GT);
561  }
562 
563  CT::unpoison(result);
564  BOTAN_DEBUG_ASSERT(result == LT || result == GT || result == EQ);
565  return static_cast<int32_t>(result);
566  }
567 
568 /**
569 * Compare x and y
570 * Return ~0 if x[0:x_size] < y[0:y_size] or 0 otherwise
571 * If lt_or_equal is true, returns ~0 also for x == y
572 */
573 inline CT::Mask<word>
574 bigint_ct_is_lt(const word x[], size_t x_size,
575  const word y[], size_t y_size,
576  bool lt_or_equal = false)
577  {
578  const size_t common_elems = std::min(x_size, y_size);
579 
580  auto is_lt = CT::Mask<word>::expand(lt_or_equal);
581 
582  for(size_t i = 0; i != common_elems; i++)
583  {
584  const auto eq = CT::Mask<word>::is_equal(x[i], y[i]);
585  const auto lt = CT::Mask<word>::is_lt(x[i], y[i]);
586  is_lt = eq.select_mask(is_lt, lt);
587  }
588 
589  if(x_size < y_size)
590  {
591  word mask = 0;
592  for(size_t i = x_size; i != y_size; i++)
593  mask |= y[i];
594  // If any bits were set in high part of y, then is_lt should be forced true
595  is_lt |= CT::Mask<word>::expand(mask);
596  }
597  else if(y_size < x_size)
598  {
599  word mask = 0;
600  for(size_t i = y_size; i != x_size; i++)
601  mask |= x[i];
602 
603  // If any bits were set in high part of x, then is_lt should be false
604  is_lt &= CT::Mask<word>::is_zero(mask);
605  }
606 
607  return is_lt;
608  }
609 
610 inline CT::Mask<word>
611 bigint_ct_is_eq(const word x[], size_t x_size,
612  const word y[], size_t y_size)
613  {
614  const size_t common_elems = std::min(x_size, y_size);
615 
616  word diff = 0;
617 
618  for(size_t i = 0; i != common_elems; i++)
619  {
620  diff |= (x[i] ^ y[i]);
621  }
622 
623  // If any bits were set in high part of x/y, then they are not equal
624  if(x_size < y_size)
625  {
626  for(size_t i = x_size; i != y_size; i++)
627  diff |= y[i];
628  }
629  else if(y_size < x_size)
630  {
631  for(size_t i = y_size; i != x_size; i++)
632  diff |= x[i];
633  }
634 
635  return CT::Mask<word>::is_zero(diff);
636  }
637 
638 /**
639 * Set z to abs(x-y), ie if x >= y, then compute z = x - y
640 * Otherwise compute z = y - x
641 * No borrow is possible since the result is always >= 0
642 *
643 * Return the relative size of x vs y (-1, 0, 1)
644 *
645 * @param z output array of max(x_size,y_size) words
646 * @param x input param
647 * @param x_size length of x
648 * @param y input param
649 * @param y_size length of y
650 */
651 inline int32_t
652 bigint_sub_abs(word z[],
653  const word x[], size_t x_size,
654  const word y[], size_t y_size)
655  {
656  const int32_t relative_size = bigint_cmp(x, x_size, y, y_size);
657 
658  // Swap if relative_size == -1
659  CT::conditional_swap_ptr(relative_size < 0, x, y);
660  CT::conditional_swap(relative_size < 0, x_size, y_size);
661 
662  /*
663  * We know at this point that x >= y so if y_size is larger than
664  * x_size, we are guaranteed they are just leading zeros which can
665  * be ignored
666  */
667  y_size = std::min(x_size, y_size);
668 
669  bigint_sub3(z, x, x_size, y, y_size);
670 
671  return relative_size;
672  }
673 
674 /**
675 * Set t to t-s modulo mod
676 *
677 * @param t first integer
678 * @param s second integer
679 * @param mod the modulus
680 * @param mod_sw size of t, s, and mod
681 * @param ws workspace of size mod_sw
682 */
683 inline void
684 bigint_mod_sub(word t[], const word s[], const word mod[], size_t mod_sw, word ws[])
685  {
686  // is t < s or not?
687  const auto is_lt = bigint_ct_is_lt(t, mod_sw, s, mod_sw);
688 
689  // ws = p - s
690  const word borrow = bigint_sub3(ws, mod, mod_sw, s, mod_sw);
691 
692  // Compute either (t - s) or (t + (p - s)) depending on mask
693  const word carry = bigint_cnd_addsub(is_lt, t, ws, s, mod_sw);
694 
695  BOTAN_DEBUG_ASSERT(borrow == 0 && carry == 0);
696  BOTAN_UNUSED(carry, borrow);
697  }
698 
699 template<size_t N>
700 inline void bigint_mod_sub_n(word t[], const word s[], const word mod[], word ws[])
701  {
702  // is t < s or not?
703  const auto is_lt = bigint_ct_is_lt(t, N, s, N);
704 
705  // ws = p - s
706  const word borrow = bigint_sub3(ws, mod, N, s, N);
707 
708  // Compute either (t - s) or (t + (p - s)) depending on mask
709  const word carry = bigint_cnd_addsub(is_lt, t, ws, s, N);
710 
711  BOTAN_DEBUG_ASSERT(borrow == 0 && carry == 0);
712  BOTAN_UNUSED(carry, borrow);
713  }
714 
715 /**
716 * Compute ((n1<<bits) + n0) / d
717 */
718 inline word bigint_divop(word n1, word n0, word d)
719  {
720  if(d == 0)
721  throw Invalid_Argument("bigint_divop divide by zero");
722 
723 #if defined(BOTAN_HAS_MP_DWORD)
724  return ((static_cast<dword>(n1) << BOTAN_MP_WORD_BITS) | n0) / d;
725 #else
726 
727  word high = n1 % d;
728  word quotient = 0;
729 
730  for(size_t i = 0; i != BOTAN_MP_WORD_BITS; ++i)
731  {
732  const word high_top_bit = high >> (BOTAN_MP_WORD_BITS-1);
733 
734  high <<= 1;
735  high |= (n0 >> (BOTAN_MP_WORD_BITS-1-i)) & 1;
736  quotient <<= 1;
737 
738  if(high_top_bit || high >= d)
739  {
740  high -= d;
741  quotient |= 1;
742  }
743  }
744 
745  return quotient;
746 #endif
747  }
748 
749 /**
750 * Compute ((n1<<bits) + n0) % d
751 */
752 inline word bigint_modop(word n1, word n0, word d)
753  {
754  if(d == 0)
755  throw Invalid_Argument("bigint_modop divide by zero");
756 
757 #if defined(BOTAN_HAS_MP_DWORD)
758  return ((static_cast<dword>(n1) << BOTAN_MP_WORD_BITS) | n0) % d;
759 #else
760  word z = bigint_divop(n1, n0, d);
761  word dummy = 0;
762  z = word_madd2(z, d, &dummy);
763  return (n0-z);
764 #endif
765  }
766 
767 /*
768 * Comba Multiplication / Squaring
769 */
770 void bigint_comba_mul4(word z[8], const word x[4], const word y[4]);
771 void bigint_comba_mul6(word z[12], const word x[6], const word y[6]);
772 void bigint_comba_mul8(word z[16], const word x[8], const word y[8]);
773 void bigint_comba_mul9(word z[18], const word x[9], const word y[9]);
774 void bigint_comba_mul16(word z[32], const word x[16], const word y[16]);
775 void bigint_comba_mul24(word z[48], const word x[24], const word y[24]);
776 
777 void bigint_comba_sqr4(word out[8], const word in[4]);
778 void bigint_comba_sqr6(word out[12], const word in[6]);
779 void bigint_comba_sqr8(word out[16], const word in[8]);
780 void bigint_comba_sqr9(word out[18], const word in[9]);
781 void bigint_comba_sqr16(word out[32], const word in[16]);
782 void bigint_comba_sqr24(word out[48], const word in[24]);
783 
784 /**
785 * Montgomery Reduction
786 * @param z integer to reduce, of size exactly 2*(p_size+1).
787  Output is in the first p_size+1 words, higher
788  words are set to zero.
789 * @param p modulus
790 * @param p_size size of p
791 * @param p_dash Montgomery value
792 * @param workspace array of at least 2*(p_size+1) words
793 * @param ws_size size of workspace in words
794 */
795 void bigint_monty_redc(word z[],
796  const word p[], size_t p_size,
797  word p_dash,
798  word workspace[],
799  size_t ws_size);
800 
801 /*
802 * High Level Multiplication/Squaring Interfaces
803 */
804 
805 void bigint_mul(word z[], size_t z_size,
806  const word x[], size_t x_size, size_t x_sw,
807  const word y[], size_t y_size, size_t y_sw,
808  word workspace[], size_t ws_size);
809 
810 void bigint_sqr(word z[], size_t z_size,
811  const word x[], size_t x_size, size_t x_sw,
812  word workspace[], size_t ws_size);
813 
814 }
815 
816 #endif
void bigint_shr1(word x[], size_t x_size, size_t word_shift, size_t bit_shift)
Definition: mp_core.h:427
void bigint_sub2_rev(word x[], const word y[], size_t y_size)
Definition: mp_core.h:324
word word8_sub2_rev(word x[8], const word y[8], word carry)
Definition: mp_asmi.h:381
void conditional_swap_ptr(bool cnd, T &x, T &y)
Definition: ct_utils.h:362
word word8_add2(word x[8], const word y[8], word carry)
Definition: mp_asmi.h:138
word word8_linmul3(word z[8], const word x[8], word y, word carry)
Definition: mp_asmi.h:585
void bigint_shr2(word y[], const word x[], size_t x_size, size_t word_shift, size_t bit_shift)
Definition: mp_core.h:465
void carry(int64_t &h0, int64_t &h1)
word BOTAN_WARN_UNUSED_RESULT bigint_linmul2(word x[], size_t x_size, word y)
Definition: mp_core.h:487
void bigint_mod_sub_n(word t[], const word s[], const word mod[], word ws[])
Definition: mp_core.h:700
int32_t bigint_cmp(const word x[], size_t x_size, const word y[], size_t y_size)
Definition: mp_core.h:523
void clear_mem(T *ptr, size_t n)
Definition: mem_ops.h:111
word bigint_sub2(word x[], size_t x_size, const word y[], size_t y_size)
Definition: mp_core.h:300
word bigint_add3_nc(word z[], const word x[], size_t x_size, const word y[], size_t y_size)
Definition: mp_core.h:250
void bigint_comba_mul4(word z[8], const word x[4], const word y[4])
Definition: mp_comba.cpp:50
#define BOTAN_WARN_UNUSED_RESULT
Definition: compiler.h:80
word word8_sub2(word x[8], const word y[8], word carry)
Definition: mp_asmi.h:311
word bigint_sub3(word z[], const word x[], size_t x_size, const word y[], size_t y_size)
Definition: mp_core.h:342
word bigint_divop(word n1, word n0, word d)
Definition: mp_core.h:718
void bigint_comba_mul9(word z[18], const word x[9], const word y[9])
Definition: mp_comba.cpp:474
void bigint_sqr(word z[], size_t z_size, const word x[], size_t x_size, size_t x_sw, word workspace[], size_t ws_size)
Definition: mp_karat.cpp:357
uint64_t carry_shift(const donna128 &a, size_t shift)
Definition: donna128.h:116
word bigint_cnd_addsub(CT::Mask< word > mask, word x[], const word y[], const word z[], size_t size)
Definition: mp_core.h:176
void bigint_comba_mul24(word z[48], const word x[24], const word y[24])
Definition: mp_comba.cpp:1535
word word_madd2(word a, word b, word *c)
Definition: mp_madd.h:48
#define BOTAN_ASSERT(expr, assertion_made)
Definition: assert.h:55
void bigint_linmul3(word z[], const word x[], size_t x_size, word y)
Definition: mp_core.h:502
void bigint_comba_sqr16(word z[32], const word x[16])
Definition: mp_comba.cpp:598
static Mask< T > expand(T v)
Definition: ct_utils.h:123
word bigint_cnd_sub(word cnd, word x[], size_t x_size, const word y[], size_t y_size)
Definition: mp_core.h:88
void bigint_shl1(word x[], size_t x_size, size_t x_words, size_t word_shift, size_t bit_shift)
Definition: mp_core.h:409
#define BOTAN_DEBUG_ASSERT(expr)
Definition: assert.h:123
CT::Mask< word > bigint_sub_abs(word z[], const word x[], const word y[], size_t N, word ws[])
Definition: mp_core.h:377
T select(T x, T y) const
Definition: ct_utils.h:264
void bigint_comba_sqr24(word z[48], const word x[24])
Definition: mp_comba.cpp:1132
void bigint_cnd_swap(word cnd, word x[], word y[], size_t size)
Definition: mp_core.h:29
word word8_linmul2(word x[8], word y, word carry)
Definition: mp_asmi.h:488
word bigint_cnd_add(word cnd, word x[], word x_size, const word y[], size_t y_size)
Definition: mp_core.h:42
CT::Mask< word > bigint_ct_is_eq(const word x[], size_t x_size, const word y[], size_t y_size)
Definition: mp_core.h:611
word bigint_add2_nc(word x[], size_t x_size, const word y[], size_t y_size)
Definition: mp_core.h:227
void bigint_cnd_add_or_sub(CT::Mask< word > mask, word x[], const word y[], size_t size)
Definition: mp_core.h:139
void copy_mem(T *out, const T *in, size_t n)
Definition: mem_ops.h:122
Definition: alg_id.cpp:13
Mask< T > conditional_copy_mem(T cnd, T *to, const T *from0, const T *from1, size_t elems)
Definition: ct_utils.h:339
void bigint_comba_sqr9(word z[18], const word x[9])
Definition: mp_comba.cpp:386
#define BOTAN_UNUSED(...)
Definition: assert.h:142
void bigint_mul(word z[], size_t z_size, const word x[], size_t x_size, size_t x_sw, const word y[], size_t y_size, size_t y_sw, word workspace[], size_t ws_size)
Definition: mp_karat.cpp:298
word word8_add3(word z[8], const word x[8], const word y[8], word carry)
Definition: mp_asmi.h:200
void bigint_monty_redc(word z[], const word p[], size_t p_size, word p_dash, word workspace[], size_t ws_size)
Definition: mp_monty.cpp:109
void bigint_shl2(word y[], const word x[], size_t x_size, size_t word_shift, size_t bit_shift)
Definition: mp_core.h:448
void bigint_comba_mul8(word z[16], const word x[8], const word y[8])
Definition: mp_comba.cpp:283
const word MP_WORD_MAX
Definition: mp_core.h:22
word word_sub(word x, word y, word *carry)
Definition: mp_asmi.h:280
CT::Mask< word > bigint_ct_is_lt(const word x[], size_t x_size, const word y[], size_t y_size, bool lt_or_equal=false)
Definition: mp_core.h:574
void bigint_comba_sqr8(word z[16], const word x[8])
Definition: mp_comba.cpp:208
void bigint_add2(word x[], size_t x_size, const word y[], size_t y_size)
Definition: mp_core.h:280
void bigint_comba_mul16(word z[32], const word x[16], const word y[16])
Definition: mp_comba.cpp:805
word word_add(word x, word y, word *carry)
Definition: mp_asmi.h:107
void unpoison(const T *p, size_t n)
Definition: ct_utils.h:59
void bigint_comba_mul6(word z[12], const word x[6], const word y[6])
Definition: mp_comba.cpp:141
void bigint_cnd_abs(word cnd, word x[], size_t size)
Definition: mp_core.h:212
static Mask< T > is_zero(T x)
Definition: ct_utils.h:141
word word8_sub3(word z[8], const word x[8], const word y[8], word carry)
Definition: mp_asmi.h:416
static Mask< T > is_equal(T x, T y)
Definition: ct_utils.h:149
void bigint_mod_sub(word t[], const word s[], const word mod[], size_t mod_sw, word ws[])
Definition: mp_core.h:684
void bigint_comba_sqr4(word z[8], const word x[4])
Definition: mp_comba.cpp:17
void bigint_comba_sqr6(word z[12], const word x[6])
Definition: mp_comba.cpp:89
void bigint_add3(word z[], const word x[], size_t x_size, const word y[], size_t y_size)
Definition: mp_core.h:289
word bigint_modop(word n1, word n0, word d)
Definition: mp_core.h:752
static Mask< T > is_lt(T x, T y)
Definition: ct_utils.h:157
void conditional_swap(bool cnd, T &x, T &y)
Definition: ct_utils.h:351