1 /*
2 * Minimal code for RSA support from LibTomMath 0.41
3 * http://libtom.org/
4 * http://libtom.org/files/ltm-0.41.tar.bz2
5 * This library was released in public domain by Tom St Denis.
6 *
7 * The combination in this file may not use all of the optimized algorithms
8 * from LibTomMath and may be considerable slower than the LibTomMath with its
9 * default settings. The main purpose of having this version here is to make it
10 * easier to build bignum.c wrapper without having to install and build an
11 * external library.
12 *
13 * If CONFIG_INTERNAL_LIBTOMMATH is defined, bignum.c includes this
14 * libtommath.c file instead of using the external LibTomMath library.
15 */
16
17 #ifndef CHAR_BIT
18 #define CHAR_BIT 8
19 #endif
20
21 #define BN_MP_INVMOD_C
22 #define BN_S_MP_EXPTMOD_C /* Note: #undef in tommath_superclass.h; this would
23 * require BN_MP_EXPTMOD_FAST_C instead */
24 #define BN_S_MP_MUL_DIGS_C
25 #define BN_MP_INVMOD_SLOW_C
26 #define BN_S_MP_SQR_C
27 #define BN_S_MP_MUL_HIGH_DIGS_C /* Note: #undef in tommath_superclass.h; this
28 * would require other than mp_reduce */
29
30 #ifdef LTM_FAST
31
32 /* Use faster div at the cost of about 1 kB */
33 #define BN_MP_MUL_D_C
34
35 /* Include faster exptmod (Montgomery) at the cost of about 2.5 kB in code */
36 #define BN_MP_EXPTMOD_FAST_C
37 #define BN_MP_MONTGOMERY_SETUP_C
38 #define BN_FAST_MP_MONTGOMERY_REDUCE_C
39 #define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
40 #define BN_MP_MUL_2_C
41
42 /* Include faster sqr at the cost of about 0.5 kB in code */
43 #define BN_FAST_S_MP_SQR_C
44
45 /* About 0.25 kB of code, but ~1.7kB of stack space! */
46 #define BN_FAST_S_MP_MUL_DIGS_C
47
48 #else /* LTM_FAST */
49
50 #define BN_MP_DIV_SMALL
51 #define BN_MP_INIT_MULTI_C
52 #define BN_MP_CLEAR_MULTI_C
53 #define BN_MP_ABS_C
54 #endif /* LTM_FAST */
55
56 /* Current uses do not require support for negative exponent in exptmod, so we
57 * can save about 1.5 kB in leaving out invmod. */
58 #define LTM_NO_NEG_EXP
59
60 /* from tommath.h */
61
62 #ifndef MIN
63 #define MIN(x,y) ((x)<(y)?(x):(y))
64 #endif
65
66 #ifndef MAX
67 #define MAX(x,y) ((x)>(y)?(x):(y))
68 #endif
69
70 #define OPT_CAST(x)
71
72 #ifdef __x86_64__
73 typedef unsigned long mp_digit;
74 typedef unsigned long mp_word __attribute__((mode(TI)));
75
76 #define DIGIT_BIT 60
77 #define MP_64BIT
78 #else
79 typedef unsigned long mp_digit;
80 typedef u64 mp_word;
81
82 #define DIGIT_BIT 28
83 #define MP_28BIT
84 #endif
85
86
87 #define XMALLOC os_malloc
88 #define XFREE os_free
89 #define XREALLOC os_realloc
90
91
92 #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
93
94 #define MP_LT -1 /* less than */
95 #define MP_EQ 0 /* equal to */
96 #define MP_GT 1 /* greater than */
97
98 #define MP_ZPOS 0 /* positive integer */
99 #define MP_NEG 1 /* negative */
100
101 #define MP_OKAY 0 /* ok result */
102 #define MP_MEM -2 /* out of mem */
103 #define MP_VAL -3 /* invalid input */
104
105 #define MP_YES 1 /* yes response */
106 #define MP_NO 0 /* no response */
107
108 typedef int mp_err;
109
110 /* define this to use lower memory usage routines (exptmods mostly) */
111 #define MP_LOW_MEM
112
113 /* default precision */
114 #ifndef MP_PREC
115 #ifndef MP_LOW_MEM
116 #define MP_PREC 32 /* default digits of precision */
117 #else
118 #define MP_PREC 8 /* default digits of precision */
119 #endif
120 #endif
121
122 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
123 #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
124
125 /* the infamous mp_int structure */
126 typedef struct {
127 int used, alloc, sign;
128 mp_digit *dp;
129 } mp_int;
130
131
132 /* ---> Basic Manipulations <--- */
133 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
134 #define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
135 #define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
136
137
138 /* prototypes for copied functions */
139 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
140 static int s_mp_exptmod(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
141 static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
142 static int s_mp_sqr(mp_int * a, mp_int * b);
143 static int s_mp_mul_high_digs(mp_int * a, mp_int * b, mp_int * c, int digs);
144
145 #ifdef BN_FAST_S_MP_MUL_DIGS_C
146 static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
147 #endif
148
149 #ifdef BN_MP_INIT_MULTI_C
150 static int mp_init_multi(mp_int *mp, ...);
151 #endif
152 #ifdef BN_MP_CLEAR_MULTI_C
153 static void mp_clear_multi(mp_int *mp, ...);
154 #endif
155 static int mp_lshd(mp_int * a, int b);
156 static void mp_set(mp_int * a, mp_digit b);
157 static void mp_clamp(mp_int * a);
158 static void mp_exch(mp_int * a, mp_int * b);
159 static void mp_rshd(mp_int * a, int b);
160 static void mp_zero(mp_int * a);
161 static int mp_mod_2d(mp_int * a, int b, mp_int * c);
162 static int mp_div_2d(mp_int * a, int b, mp_int * c, mp_int * d);
163 static int mp_init_copy(mp_int * a, mp_int * b);
164 static int mp_mul_2d(mp_int * a, int b, mp_int * c);
165 #ifndef LTM_NO_NEG_EXP
166 static int mp_div_2(mp_int * a, mp_int * b);
167 static int mp_invmod(mp_int * a, mp_int * b, mp_int * c);
168 static int mp_invmod_slow(mp_int * a, mp_int * b, mp_int * c);
169 #endif /* LTM_NO_NEG_EXP */
170 static int mp_copy(mp_int * a, mp_int * b);
171 static int mp_count_bits(mp_int * a);
172 static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
173 static int mp_mod(mp_int * a, mp_int * b, mp_int * c);
174 static int mp_grow(mp_int * a, int size);
175 static int mp_cmp_mag(mp_int * a, mp_int * b);
176 #ifdef BN_MP_ABS_C
177 static int mp_abs(mp_int * a, mp_int * b);
178 #endif
179 static int mp_sqr(mp_int * a, mp_int * b);
180 static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
181 static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
182 static int mp_2expt(mp_int * a, int b);
183 static int mp_reduce_setup(mp_int * a, mp_int * b);
184 static int mp_reduce(mp_int * x, mp_int * m, mp_int * mu);
185 static int mp_init_size(mp_int * a, int size);
186 #ifdef BN_MP_EXPTMOD_FAST_C
187 static int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
188 #endif /* BN_MP_EXPTMOD_FAST_C */
189 #ifdef BN_FAST_S_MP_SQR_C
190 static int fast_s_mp_sqr (mp_int * a, mp_int * b);
191 #endif /* BN_FAST_S_MP_SQR_C */
192 #ifdef BN_MP_MUL_D_C
193 static int mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
194 #endif /* BN_MP_MUL_D_C */
195
196
197
198 /* functions from bn_<func name>.c */
199
200
201 /* reverse an array, used for radix code */
bn_reverse(unsigned char * s,int len)202 static void bn_reverse (unsigned char *s, int len)
203 {
204 int ix, iy;
205 unsigned char t;
206
207 ix = 0;
208 iy = len - 1;
209 while (ix < iy) {
210 t = s[ix];
211 s[ix] = s[iy];
212 s[iy] = t;
213 ++ix;
214 --iy;
215 }
216 }
217
218
219 /* low level addition, based on HAC pp.594, Algorithm 14.7 */
s_mp_add(mp_int * a,mp_int * b,mp_int * c)220 static int s_mp_add (mp_int * a, mp_int * b, mp_int * c)
221 {
222 mp_int *x;
223 int olduse, res, min, max;
224
225 /* find sizes, we let |a| <= |b| which means we have to sort
226 * them. "x" will point to the input with the most digits
227 */
228 if (a->used > b->used) {
229 min = b->used;
230 max = a->used;
231 x = a;
232 } else {
233 min = a->used;
234 max = b->used;
235 x = b;
236 }
237
238 /* init result */
239 if (c->alloc < max + 1) {
240 if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
241 return res;
242 }
243 }
244
245 /* get old used digit count and set new one */
246 olduse = c->used;
247 c->used = max + 1;
248
249 {
250 register mp_digit u, *tmpa, *tmpb, *tmpc;
251 register int i;
252
253 /* alias for digit pointers */
254
255 /* first input */
256 tmpa = a->dp;
257
258 /* second input */
259 tmpb = b->dp;
260
261 /* destination */
262 tmpc = c->dp;
263
264 /* zero the carry */
265 u = 0;
266 for (i = 0; i < min; i++) {
267 /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
268 *tmpc = *tmpa++ + *tmpb++ + u;
269
270 /* U = carry bit of T[i] */
271 u = *tmpc >> ((mp_digit)DIGIT_BIT);
272
273 /* take away carry bit from T[i] */
274 *tmpc++ &= MP_MASK;
275 }
276
277 /* now copy higher words if any, that is in A+B
278 * if A or B has more digits add those in
279 */
280 if (min != max) {
281 for (; i < max; i++) {
282 /* T[i] = X[i] + U */
283 *tmpc = x->dp[i] + u;
284
285 /* U = carry bit of T[i] */
286 u = *tmpc >> ((mp_digit)DIGIT_BIT);
287
288 /* take away carry bit from T[i] */
289 *tmpc++ &= MP_MASK;
290 }
291 }
292
293 /* add carry */
294 *tmpc++ = u;
295
296 /* clear digits above oldused */
297 for (i = c->used; i < olduse; i++) {
298 *tmpc++ = 0;
299 }
300 }
301
302 mp_clamp (c);
303 return MP_OKAY;
304 }
305
306
307 /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
s_mp_sub(mp_int * a,mp_int * b,mp_int * c)308 static int s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
309 {
310 int olduse, res, min, max;
311
312 /* find sizes */
313 min = b->used;
314 max = a->used;
315
316 /* init result */
317 if (c->alloc < max) {
318 if ((res = mp_grow (c, max)) != MP_OKAY) {
319 return res;
320 }
321 }
322 olduse = c->used;
323 c->used = max;
324
325 {
326 register mp_digit u, *tmpa, *tmpb, *tmpc;
327 register int i;
328
329 /* alias for digit pointers */
330 tmpa = a->dp;
331 tmpb = b->dp;
332 tmpc = c->dp;
333
334 /* set carry to zero */
335 u = 0;
336 for (i = 0; i < min; i++) {
337 /* T[i] = A[i] - B[i] - U */
338 *tmpc = *tmpa++ - *tmpb++ - u;
339
340 /* U = carry bit of T[i]
341 * Note this saves performing an AND operation since
342 * if a carry does occur it will propagate all the way to the
343 * MSB. As a result a single shift is enough to get the carry
344 */
345 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
346
347 /* Clear carry from T[i] */
348 *tmpc++ &= MP_MASK;
349 }
350
351 /* now copy higher words if any, e.g. if A has more digits than B */
352 for (; i < max; i++) {
353 /* T[i] = A[i] - U */
354 *tmpc = *tmpa++ - u;
355
356 /* U = carry bit of T[i] */
357 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
358
359 /* Clear carry from T[i] */
360 *tmpc++ &= MP_MASK;
361 }
362
363 /* clear digits above used (since we may not have grown result above) */
364 for (i = c->used; i < olduse; i++) {
365 *tmpc++ = 0;
366 }
367 }
368
369 mp_clamp (c);
370 return MP_OKAY;
371 }
372
373
374 /* init a new mp_int */
mp_init(mp_int * a)375 static int mp_init (mp_int * a)
376 {
377 int i;
378
379 /* allocate memory required and clear it */
380 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
381 if (a->dp == NULL) {
382 return MP_MEM;
383 }
384
385 /* set the digits to zero */
386 for (i = 0; i < MP_PREC; i++) {
387 a->dp[i] = 0;
388 }
389
390 /* set the used to zero, allocated digits to the default precision
391 * and sign to positive */
392 a->used = 0;
393 a->alloc = MP_PREC;
394 a->sign = MP_ZPOS;
395
396 return MP_OKAY;
397 }
398
399
400 /* clear one (frees) */
mp_clear(mp_int * a)401 static void mp_clear (mp_int * a)
402 {
403 int i;
404
405 /* only do anything if a hasn't been freed previously */
406 if (a->dp != NULL) {
407 /* first zero the digits */
408 for (i = 0; i < a->used; i++) {
409 a->dp[i] = 0;
410 }
411
412 /* free ram */
413 XFREE(a->dp);
414
415 /* reset members to make debugging easier */
416 a->dp = NULL;
417 a->alloc = a->used = 0;
418 a->sign = MP_ZPOS;
419 }
420 }
421
422
423 /* high level addition (handles signs) */
mp_add(mp_int * a,mp_int * b,mp_int * c)424 static int mp_add (mp_int * a, mp_int * b, mp_int * c)
425 {
426 int sa, sb, res;
427
428 /* get sign of both inputs */
429 sa = a->sign;
430 sb = b->sign;
431
432 /* handle two cases, not four */
433 if (sa == sb) {
434 /* both positive or both negative */
435 /* add their magnitudes, copy the sign */
436 c->sign = sa;
437 res = s_mp_add (a, b, c);
438 } else {
439 /* one positive, the other negative */
440 /* subtract the one with the greater magnitude from */
441 /* the one of the lesser magnitude. The result gets */
442 /* the sign of the one with the greater magnitude. */
443 if (mp_cmp_mag (a, b) == MP_LT) {
444 c->sign = sb;
445 res = s_mp_sub (b, a, c);
446 } else {
447 c->sign = sa;
448 res = s_mp_sub (a, b, c);
449 }
450 }
451 return res;
452 }
453
454
455 /* high level subtraction (handles signs) */
mp_sub(mp_int * a,mp_int * b,mp_int * c)456 static int mp_sub (mp_int * a, mp_int * b, mp_int * c)
457 {
458 int sa, sb, res;
459
460 sa = a->sign;
461 sb = b->sign;
462
463 if (sa != sb) {
464 /* subtract a negative from a positive, OR */
465 /* subtract a positive from a negative. */
466 /* In either case, ADD their magnitudes, */
467 /* and use the sign of the first number. */
468 c->sign = sa;
469 res = s_mp_add (a, b, c);
470 } else {
471 /* subtract a positive from a positive, OR */
472 /* subtract a negative from a negative. */
473 /* First, take the difference between their */
474 /* magnitudes, then... */
475 if (mp_cmp_mag (a, b) != MP_LT) {
476 /* Copy the sign from the first */
477 c->sign = sa;
478 /* The first has a larger or equal magnitude */
479 res = s_mp_sub (a, b, c);
480 } else {
481 /* The result has the *opposite* sign from */
482 /* the first number. */
483 c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
484 /* The second has a larger magnitude */
485 res = s_mp_sub (b, a, c);
486 }
487 }
488 return res;
489 }
490
491
492 /* high level multiplication (handles sign) */
mp_mul(mp_int * a,mp_int * b,mp_int * c)493 static int mp_mul (mp_int * a, mp_int * b, mp_int * c)
494 {
495 int res, neg;
496 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
497
498 /* use Toom-Cook? */
499 #ifdef BN_MP_TOOM_MUL_C
500 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
501 res = mp_toom_mul(a, b, c);
502 } else
503 #endif
504 #ifdef BN_MP_KARATSUBA_MUL_C
505 /* use Karatsuba? */
506 if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
507 res = mp_karatsuba_mul (a, b, c);
508 } else
509 #endif
510 {
511 /* can we use the fast multiplier?
512 *
513 * The fast multiplier can be used if the output will
514 * have less than MP_WARRAY digits and the number of
515 * digits won't affect carry propagation
516 */
517 #ifdef BN_FAST_S_MP_MUL_DIGS_C
518 int digs = a->used + b->used + 1;
519
520 if ((digs < MP_WARRAY) &&
521 MIN(a->used, b->used) <=
522 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
523 res = fast_s_mp_mul_digs (a, b, c, digs);
524 } else
525 #endif
526 #ifdef BN_S_MP_MUL_DIGS_C
527 res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
528 #else
529 #error mp_mul could fail
530 res = MP_VAL;
531 #endif
532
533 }
534 c->sign = (c->used > 0) ? neg : MP_ZPOS;
535 return res;
536 }
537
538
539 /* d = a * b (mod c) */
mp_mulmod(mp_int * a,mp_int * b,mp_int * c,mp_int * d)540 static int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
541 {
542 int res;
543 mp_int t;
544
545 if ((res = mp_init (&t)) != MP_OKAY) {
546 return res;
547 }
548
549 if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
550 mp_clear (&t);
551 return res;
552 }
553 res = mp_mod (&t, c, d);
554 mp_clear (&t);
555 return res;
556 }
557
558
559 /* c = a mod b, 0 <= c < b */
mp_mod(mp_int * a,mp_int * b,mp_int * c)560 static int mp_mod (mp_int * a, mp_int * b, mp_int * c)
561 {
562 mp_int t;
563 int res;
564
565 if ((res = mp_init (&t)) != MP_OKAY) {
566 return res;
567 }
568
569 if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
570 mp_clear (&t);
571 return res;
572 }
573
574 if (t.sign != b->sign) {
575 res = mp_add (b, &t, c);
576 } else {
577 res = MP_OKAY;
578 mp_exch (&t, c);
579 }
580
581 mp_clear (&t);
582 return res;
583 }
584
585
586 /* this is a shell function that calls either the normal or Montgomery
587 * exptmod functions. Originally the call to the montgomery code was
588 * embedded in the normal function but that wasted a lot of stack space
589 * for nothing (since 99% of the time the Montgomery code would be called)
590 */
mp_exptmod(mp_int * G,mp_int * X,mp_int * P,mp_int * Y)591 static int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
592 {
593 int dr;
594
595 /* modulus P must be positive */
596 if (P->sign == MP_NEG) {
597 return MP_VAL;
598 }
599
600 /* if exponent X is negative we have to recurse */
601 if (X->sign == MP_NEG) {
602 #ifdef LTM_NO_NEG_EXP
603 return MP_VAL;
604 #else /* LTM_NO_NEG_EXP */
605 #ifdef BN_MP_INVMOD_C
606 mp_int tmpG, tmpX;
607 int err;
608
609 /* first compute 1/G mod P */
610 if ((err = mp_init(&tmpG)) != MP_OKAY) {
611 return err;
612 }
613 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
614 mp_clear(&tmpG);
615 return err;
616 }
617
618 /* now get |X| */
619 if ((err = mp_init(&tmpX)) != MP_OKAY) {
620 mp_clear(&tmpG);
621 return err;
622 }
623 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
624 mp_clear_multi(&tmpG, &tmpX, NULL);
625 return err;
626 }
627
628 /* and now compute (1/G)**|X| instead of G**X [X < 0] */
629 err = mp_exptmod(&tmpG, &tmpX, P, Y);
630 mp_clear_multi(&tmpG, &tmpX, NULL);
631 return err;
632 #else
633 #error mp_exptmod would always fail
634 /* no invmod */
635 return MP_VAL;
636 #endif
637 #endif /* LTM_NO_NEG_EXP */
638 }
639
640 /* modified diminished radix reduction */
641 #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
642 if (mp_reduce_is_2k_l(P) == MP_YES) {
643 return s_mp_exptmod(G, X, P, Y, 1);
644 }
645 #endif
646
647 #ifdef BN_MP_DR_IS_MODULUS_C
648 /* is it a DR modulus? */
649 dr = mp_dr_is_modulus(P);
650 #else
651 /* default to no */
652 dr = 0;
653 #endif
654
655 #ifdef BN_MP_REDUCE_IS_2K_C
656 /* if not, is it a unrestricted DR modulus? */
657 if (dr == 0) {
658 dr = mp_reduce_is_2k(P) << 1;
659 }
660 #endif
661
662 /* if the modulus is odd or dr != 0 use the montgomery method */
663 #ifdef BN_MP_EXPTMOD_FAST_C
664 if (mp_isodd (P) == 1 || dr != 0) {
665 return mp_exptmod_fast (G, X, P, Y, dr);
666 } else {
667 #endif
668 #ifdef BN_S_MP_EXPTMOD_C
669 /* otherwise use the generic Barrett reduction technique */
670 return s_mp_exptmod (G, X, P, Y, 0);
671 #else
672 #error mp_exptmod could fail
673 /* no exptmod for evens */
674 return MP_VAL;
675 #endif
676 #ifdef BN_MP_EXPTMOD_FAST_C
677 }
678 #endif
679 if (dr == 0) {
680 /* avoid compiler warnings about possibly unused variable */
681 }
682 }
683
684
685 /* compare two ints (signed)*/
mp_cmp(mp_int * a,mp_int * b)686 static int mp_cmp (mp_int * a, mp_int * b)
687 {
688 /* compare based on sign */
689 if (a->sign != b->sign) {
690 if (a->sign == MP_NEG) {
691 return MP_LT;
692 } else {
693 return MP_GT;
694 }
695 }
696
697 /* compare digits */
698 if (a->sign == MP_NEG) {
699 /* if negative compare opposite direction */
700 return mp_cmp_mag(b, a);
701 } else {
702 return mp_cmp_mag(a, b);
703 }
704 }
705
706
707 /* compare a digit */
mp_cmp_d(mp_int * a,mp_digit b)708 static int mp_cmp_d(mp_int * a, mp_digit b)
709 {
710 /* compare based on sign */
711 if (a->sign == MP_NEG) {
712 return MP_LT;
713 }
714
715 /* compare based on magnitude */
716 if (a->used > 1) {
717 return MP_GT;
718 }
719
720 /* compare the only digit of a to b */
721 if (a->dp[0] > b) {
722 return MP_GT;
723 } else if (a->dp[0] < b) {
724 return MP_LT;
725 } else {
726 return MP_EQ;
727 }
728 }
729
730
731 #ifndef LTM_NO_NEG_EXP
732 /* hac 14.61, pp608 */
mp_invmod(mp_int * a,mp_int * b,mp_int * c)733 static int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
734 {
735 /* b cannot be negative */
736 if (b->sign == MP_NEG || mp_iszero(b) == 1) {
737 return MP_VAL;
738 }
739
740 #ifdef BN_FAST_MP_INVMOD_C
741 /* if the modulus is odd we can use a faster routine instead */
742 if (mp_isodd (b) == 1) {
743 return fast_mp_invmod (a, b, c);
744 }
745 #endif
746
747 #ifdef BN_MP_INVMOD_SLOW_C
748 return mp_invmod_slow(a, b, c);
749 #endif
750
751 #ifndef BN_FAST_MP_INVMOD_C
752 #ifndef BN_MP_INVMOD_SLOW_C
753 #error mp_invmod would always fail
754 #endif
755 #endif
756 return MP_VAL;
757 }
758 #endif /* LTM_NO_NEG_EXP */
759
760
761 /* get the size for an unsigned equivalent */
mp_unsigned_bin_size(mp_int * a)762 static int mp_unsigned_bin_size (mp_int * a)
763 {
764 int size = mp_count_bits (a);
765 return (size / 8 + ((size & 7) != 0 ? 1 : 0));
766 }
767
768
769 #ifndef LTM_NO_NEG_EXP
770 /* hac 14.61, pp608 */
mp_invmod_slow(mp_int * a,mp_int * b,mp_int * c)771 static int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
772 {
773 mp_int x, y, u, v, A, B, C, D;
774 int res;
775
776 /* b cannot be negative */
777 if (b->sign == MP_NEG || mp_iszero(b) == 1) {
778 return MP_VAL;
779 }
780
781 /* init temps */
782 if ((res = mp_init_multi(&x, &y, &u, &v,
783 &A, &B, &C, &D, NULL)) != MP_OKAY) {
784 return res;
785 }
786
787 /* x = a, y = b */
788 if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
789 goto LBL_ERR;
790 }
791 if ((res = mp_copy (b, &y)) != MP_OKAY) {
792 goto LBL_ERR;
793 }
794
795 /* 2. [modified] if x,y are both even then return an error! */
796 if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
797 res = MP_VAL;
798 goto LBL_ERR;
799 }
800
801 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
802 if ((res = mp_copy (&x, &u)) != MP_OKAY) {
803 goto LBL_ERR;
804 }
805 if ((res = mp_copy (&y, &v)) != MP_OKAY) {
806 goto LBL_ERR;
807 }
808 mp_set (&A, 1);
809 mp_set (&D, 1);
810
811 top:
812 /* 4. while u is even do */
813 while (mp_iseven (&u) == 1) {
814 /* 4.1 u = u/2 */
815 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
816 goto LBL_ERR;
817 }
818 /* 4.2 if A or B is odd then */
819 if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
820 /* A = (A+y)/2, B = (B-x)/2 */
821 if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
822 goto LBL_ERR;
823 }
824 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
825 goto LBL_ERR;
826 }
827 }
828 /* A = A/2, B = B/2 */
829 if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
830 goto LBL_ERR;
831 }
832 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
833 goto LBL_ERR;
834 }
835 }
836
837 /* 5. while v is even do */
838 while (mp_iseven (&v) == 1) {
839 /* 5.1 v = v/2 */
840 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
841 goto LBL_ERR;
842 }
843 /* 5.2 if C or D is odd then */
844 if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
845 /* C = (C+y)/2, D = (D-x)/2 */
846 if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
847 goto LBL_ERR;
848 }
849 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
850 goto LBL_ERR;
851 }
852 }
853 /* C = C/2, D = D/2 */
854 if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
855 goto LBL_ERR;
856 }
857 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
858 goto LBL_ERR;
859 }
860 }
861
862 /* 6. if u >= v then */
863 if (mp_cmp (&u, &v) != MP_LT) {
864 /* u = u - v, A = A - C, B = B - D */
865 if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
866 goto LBL_ERR;
867 }
868
869 if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
870 goto LBL_ERR;
871 }
872
873 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
874 goto LBL_ERR;
875 }
876 } else {
877 /* v - v - u, C = C - A, D = D - B */
878 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
879 goto LBL_ERR;
880 }
881
882 if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
883 goto LBL_ERR;
884 }
885
886 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
887 goto LBL_ERR;
888 }
889 }
890
891 /* if not zero goto step 4 */
892 if (mp_iszero (&u) == 0)
893 goto top;
894
895 /* now a = C, b = D, gcd == g*v */
896
897 /* if v != 1 then there is no inverse */
898 if (mp_cmp_d (&v, 1) != MP_EQ) {
899 res = MP_VAL;
900 goto LBL_ERR;
901 }
902
903 /* if its too low */
904 while (mp_cmp_d(&C, 0) == MP_LT) {
905 if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
906 goto LBL_ERR;
907 }
908 }
909
910 /* too big */
911 while (mp_cmp_mag(&C, b) != MP_LT) {
912 if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
913 goto LBL_ERR;
914 }
915 }
916
917 /* C is now the inverse */
918 mp_exch (&C, c);
919 res = MP_OKAY;
920 LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
921 return res;
922 }
923 #endif /* LTM_NO_NEG_EXP */
924
925
926 /* compare maginitude of two ints (unsigned) */
mp_cmp_mag(mp_int * a,mp_int * b)927 static int mp_cmp_mag (mp_int * a, mp_int * b)
928 {
929 int n;
930 mp_digit *tmpa, *tmpb;
931
932 /* compare based on # of non-zero digits */
933 if (a->used > b->used) {
934 return MP_GT;
935 }
936
937 if (a->used < b->used) {
938 return MP_LT;
939 }
940
941 /* alias for a */
942 tmpa = a->dp + (a->used - 1);
943
944 /* alias for b */
945 tmpb = b->dp + (a->used - 1);
946
947 /* compare based on digits */
948 for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
949 if (*tmpa > *tmpb) {
950 return MP_GT;
951 }
952
953 if (*tmpa < *tmpb) {
954 return MP_LT;
955 }
956 }
957 return MP_EQ;
958 }
959
960
961 /* reads a unsigned char array, assumes the msb is stored first [big endian] */
mp_read_unsigned_bin(mp_int * a,const unsigned char * b,int c)962 static int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
963 {
964 int res;
965
966 /* make sure there are at least two digits */
967 if (a->alloc < 2) {
968 if ((res = mp_grow(a, 2)) != MP_OKAY) {
969 return res;
970 }
971 }
972
973 /* zero the int */
974 mp_zero (a);
975
976 /* read the bytes in */
977 while (c-- > 0) {
978 if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
979 return res;
980 }
981
982 #ifndef MP_8BIT
983 a->dp[0] |= *b++;
984 a->used += 1;
985 #else
986 a->dp[0] = (*b & MP_MASK);
987 a->dp[1] |= ((*b++ >> 7U) & 1);
988 a->used += 2;
989 #endif
990 }
991 mp_clamp (a);
992 return MP_OKAY;
993 }
994
995
996 /* store in unsigned [big endian] format */
mp_to_unsigned_bin(mp_int * a,unsigned char * b)997 static int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
998 {
999 int x, res;
1000 mp_int t;
1001
1002 if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
1003 return res;
1004 }
1005
1006 x = 0;
1007 while (mp_iszero (&t) == 0) {
1008 #ifndef MP_8BIT
1009 b[x++] = (unsigned char) (t.dp[0] & 255);
1010 #else
1011 b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
1012 #endif
1013 if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
1014 mp_clear (&t);
1015 return res;
1016 }
1017 }
1018 bn_reverse (b, x);
1019 mp_clear (&t);
1020 return MP_OKAY;
1021 }
1022
1023
1024 /* shift right by a certain bit count (store quotient in c, optional remainder in d) */
mp_div_2d(mp_int * a,int b,mp_int * c,mp_int * d)1025 static int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
1026 {
1027 mp_digit D, r, rr;
1028 int x, res;
1029 mp_int t;
1030
1031
1032 /* if the shift count is <= 0 then we do no work */
1033 if (b <= 0) {
1034 res = mp_copy (a, c);
1035 if (d != NULL) {
1036 mp_zero (d);
1037 }
1038 return res;
1039 }
1040
1041 if ((res = mp_init (&t)) != MP_OKAY) {
1042 return res;
1043 }
1044
1045 /* get the remainder */
1046 if (d != NULL) {
1047 if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
1048 mp_clear (&t);
1049 return res;
1050 }
1051 }
1052
1053 /* copy */
1054 if ((res = mp_copy (a, c)) != MP_OKAY) {
1055 mp_clear (&t);
1056 return res;
1057 }
1058
1059 /* shift by as many digits in the bit count */
1060 if (b >= (int)DIGIT_BIT) {
1061 mp_rshd (c, b / DIGIT_BIT);
1062 }
1063
1064 /* shift any bit count < DIGIT_BIT */
1065 D = (mp_digit) (b % DIGIT_BIT);
1066 if (D != 0) {
1067 register mp_digit *tmpc, mask, shift;
1068
1069 /* mask */
1070 mask = (((mp_digit)1) << D) - 1;
1071
1072 /* shift for lsb */
1073 shift = DIGIT_BIT - D;
1074
1075 /* alias */
1076 tmpc = c->dp + (c->used - 1);
1077
1078 /* carry */
1079 r = 0;
1080 for (x = c->used - 1; x >= 0; x--) {
1081 /* get the lower bits of this word in a temp */
1082 rr = *tmpc & mask;
1083
1084 /* shift the current word and mix in the carry bits from the previous word */
1085 *tmpc = (*tmpc >> D) | (r << shift);
1086 --tmpc;
1087
1088 /* set the carry to the carry bits of the current word found above */
1089 r = rr;
1090 }
1091 }
1092 mp_clamp (c);
1093 if (d != NULL) {
1094 mp_exch (&t, d);
1095 }
1096 mp_clear (&t);
1097 return MP_OKAY;
1098 }
1099
1100
mp_init_copy(mp_int * a,mp_int * b)1101 static int mp_init_copy (mp_int * a, mp_int * b)
1102 {
1103 int res;
1104
1105 if ((res = mp_init (a)) != MP_OKAY) {
1106 return res;
1107 }
1108 return mp_copy (b, a);
1109 }
1110
1111
1112 /* set to zero */
mp_zero(mp_int * a)1113 static void mp_zero (mp_int * a)
1114 {
1115 int n;
1116 mp_digit *tmp;
1117
1118 a->sign = MP_ZPOS;
1119 a->used = 0;
1120
1121 tmp = a->dp;
1122 for (n = 0; n < a->alloc; n++) {
1123 *tmp++ = 0;
1124 }
1125 }
1126
1127
1128 /* copy, b = a */
mp_copy(mp_int * a,mp_int * b)1129 static int mp_copy (mp_int * a, mp_int * b)
1130 {
1131 int res, n;
1132
1133 /* if dst == src do nothing */
1134 if (a == b) {
1135 return MP_OKAY;
1136 }
1137
1138 /* grow dest */
1139 if (b->alloc < a->used) {
1140 if ((res = mp_grow (b, a->used)) != MP_OKAY) {
1141 return res;
1142 }
1143 }
1144
1145 /* zero b and copy the parameters over */
1146 {
1147 register mp_digit *tmpa, *tmpb;
1148
1149 /* pointer aliases */
1150
1151 /* source */
1152 tmpa = a->dp;
1153
1154 /* destination */
1155 tmpb = b->dp;
1156
1157 /* copy all the digits */
1158 for (n = 0; n < a->used; n++) {
1159 *tmpb++ = *tmpa++;
1160 }
1161
1162 /* clear high digits */
1163 for (; n < b->used; n++) {
1164 *tmpb++ = 0;
1165 }
1166 }
1167
1168 /* copy used count and sign */
1169 b->used = a->used;
1170 b->sign = a->sign;
1171 return MP_OKAY;
1172 }
1173
1174
1175 /* shift right a certain amount of digits */
mp_rshd(mp_int * a,int b)1176 static void mp_rshd (mp_int * a, int b)
1177 {
1178 int x;
1179
1180 /* if b <= 0 then ignore it */
1181 if (b <= 0) {
1182 return;
1183 }
1184
1185 /* if b > used then simply zero it and return */
1186 if (a->used <= b) {
1187 mp_zero (a);
1188 return;
1189 }
1190
1191 {
1192 register mp_digit *bottom, *top;
1193
1194 /* shift the digits down */
1195
1196 /* bottom */
1197 bottom = a->dp;
1198
1199 /* top [offset into digits] */
1200 top = a->dp + b;
1201
1202 /* this is implemented as a sliding window where
1203 * the window is b-digits long and digits from
1204 * the top of the window are copied to the bottom
1205 *
1206 * e.g.
1207
1208 b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
1209 /\ | ---->
1210 \-------------------/ ---->
1211 */
1212 for (x = 0; x < (a->used - b); x++) {
1213 *bottom++ = *top++;
1214 }
1215
1216 /* zero the top digits */
1217 for (; x < a->used; x++) {
1218 *bottom++ = 0;
1219 }
1220 }
1221
1222 /* remove excess digits */
1223 a->used -= b;
1224 }
1225
1226
1227 /* swap the elements of two integers, for cases where you can't simply swap the
1228 * mp_int pointers around
1229 */
mp_exch(mp_int * a,mp_int * b)1230 static void mp_exch (mp_int * a, mp_int * b)
1231 {
1232 mp_int t;
1233
1234 t = *a;
1235 *a = *b;
1236 *b = t;
1237 }
1238
1239
1240 /* trim unused digits
1241 *
1242 * This is used to ensure that leading zero digits are
1243 * trimed and the leading "used" digit will be non-zero
1244 * Typically very fast. Also fixes the sign if there
1245 * are no more leading digits
1246 */
mp_clamp(mp_int * a)1247 static void mp_clamp (mp_int * a)
1248 {
1249 /* decrease used while the most significant digit is
1250 * zero.
1251 */
1252 while (a->used > 0 && a->dp[a->used - 1] == 0) {
1253 --(a->used);
1254 }
1255
1256 /* reset the sign flag if used == 0 */
1257 if (a->used == 0) {
1258 a->sign = MP_ZPOS;
1259 }
1260 }
1261
1262
1263 /* grow as required */
mp_grow(mp_int * a,int size)1264 static int mp_grow (mp_int * a, int size)
1265 {
1266 int i;
1267 mp_digit *tmp;
1268
1269 /* if the alloc size is smaller alloc more ram */
1270 if (a->alloc < size) {
1271 /* ensure there are always at least MP_PREC digits extra on top */
1272 size += (MP_PREC * 2) - (size % MP_PREC);
1273
1274 /* reallocate the array a->dp
1275 *
1276 * We store the return in a temporary variable
1277 * in case the operation failed we don't want
1278 * to overwrite the dp member of a.
1279 */
1280 tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
1281 if (tmp == NULL) {
1282 /* reallocation failed but "a" is still valid [can be freed] */
1283 return MP_MEM;
1284 }
1285
1286 /* reallocation succeeded so set a->dp */
1287 a->dp = tmp;
1288
1289 /* zero excess digits */
1290 i = a->alloc;
1291 a->alloc = size;
1292 for (; i < a->alloc; i++) {
1293 a->dp[i] = 0;
1294 }
1295 }
1296 return MP_OKAY;
1297 }
1298
1299
1300 #ifdef BN_MP_ABS_C
1301 /* b = |a|
1302 *
1303 * Simple function copies the input and fixes the sign to positive
1304 */
mp_abs(mp_int * a,mp_int * b)1305 static int mp_abs (mp_int * a, mp_int * b)
1306 {
1307 int res;
1308
1309 /* copy a to b */
1310 if (a != b) {
1311 if ((res = mp_copy (a, b)) != MP_OKAY) {
1312 return res;
1313 }
1314 }
1315
1316 /* force the sign of b to positive */
1317 b->sign = MP_ZPOS;
1318
1319 return MP_OKAY;
1320 }
1321 #endif
1322
1323
1324 /* set to a digit */
mp_set(mp_int * a,mp_digit b)1325 static void mp_set (mp_int * a, mp_digit b)
1326 {
1327 mp_zero (a);
1328 a->dp[0] = b & MP_MASK;
1329 a->used = (a->dp[0] != 0) ? 1 : 0;
1330 }
1331
1332
1333 #ifndef LTM_NO_NEG_EXP
1334 /* b = a/2 */
mp_div_2(mp_int * a,mp_int * b)1335 static int mp_div_2(mp_int * a, mp_int * b)
1336 {
1337 int x, res, oldused;
1338
1339 /* copy */
1340 if (b->alloc < a->used) {
1341 if ((res = mp_grow (b, a->used)) != MP_OKAY) {
1342 return res;
1343 }
1344 }
1345
1346 oldused = b->used;
1347 b->used = a->used;
1348 {
1349 register mp_digit r, rr, *tmpa, *tmpb;
1350
1351 /* source alias */
1352 tmpa = a->dp + b->used - 1;
1353
1354 /* dest alias */
1355 tmpb = b->dp + b->used - 1;
1356
1357 /* carry */
1358 r = 0;
1359 for (x = b->used - 1; x >= 0; x--) {
1360 /* get the carry for the next iteration */
1361 rr = *tmpa & 1;
1362
1363 /* shift the current digit, add in carry and store */
1364 *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
1365
1366 /* forward carry to next iteration */
1367 r = rr;
1368 }
1369
1370 /* zero excess digits */
1371 tmpb = b->dp + b->used;
1372 for (x = b->used; x < oldused; x++) {
1373 *tmpb++ = 0;
1374 }
1375 }
1376 b->sign = a->sign;
1377 mp_clamp (b);
1378 return MP_OKAY;
1379 }
1380 #endif /* LTM_NO_NEG_EXP */
1381
1382
1383 /* shift left by a certain bit count */
mp_mul_2d(mp_int * a,int b,mp_int * c)1384 static int mp_mul_2d (mp_int * a, int b, mp_int * c)
1385 {
1386 mp_digit d;
1387 int res;
1388
1389 /* copy */
1390 if (a != c) {
1391 if ((res = mp_copy (a, c)) != MP_OKAY) {
1392 return res;
1393 }
1394 }
1395
1396 if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
1397 if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
1398 return res;
1399 }
1400 }
1401
1402 /* shift by as many digits in the bit count */
1403 if (b >= (int)DIGIT_BIT) {
1404 if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
1405 return res;
1406 }
1407 }
1408
1409 /* shift any bit count < DIGIT_BIT */
1410 d = (mp_digit) (b % DIGIT_BIT);
1411 if (d != 0) {
1412 register mp_digit *tmpc, shift, mask, r, rr;
1413 register int x;
1414
1415 /* bitmask for carries */
1416 mask = (((mp_digit)1) << d) - 1;
1417
1418 /* shift for msbs */
1419 shift = DIGIT_BIT - d;
1420
1421 /* alias */
1422 tmpc = c->dp;
1423
1424 /* carry */
1425 r = 0;
1426 for (x = 0; x < c->used; x++) {
1427 /* get the higher bits of the current word */
1428 rr = (*tmpc >> shift) & mask;
1429
1430 /* shift the current word and OR in the carry */
1431 *tmpc = ((*tmpc << d) | r) & MP_MASK;
1432 ++tmpc;
1433
1434 /* set the carry to the carry bits of the current word */
1435 r = rr;
1436 }
1437
1438 /* set final carry */
1439 if (r != 0) {
1440 c->dp[(c->used)++] = r;
1441 }
1442 }
1443 mp_clamp (c);
1444 return MP_OKAY;
1445 }
1446
1447
1448 #ifdef BN_MP_INIT_MULTI_C
mp_init_multi(mp_int * mp,...)1449 static int mp_init_multi(mp_int *mp, ...)
1450 {
1451 mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
1452 int n = 0; /* Number of ok inits */
1453 mp_int* cur_arg = mp;
1454 va_list args;
1455
1456 va_start(args, mp); /* init args to next argument from caller */
1457 while (cur_arg != NULL) {
1458 if (mp_init(cur_arg) != MP_OKAY) {
1459 /* Oops - error! Back-track and mp_clear what we already
1460 succeeded in init-ing, then return error.
1461 */
1462 va_list clean_args;
1463
1464 /* end the current list */
1465 va_end(args);
1466
1467 /* now start cleaning up */
1468 cur_arg = mp;
1469 va_start(clean_args, mp);
1470 while (n--) {
1471 mp_clear(cur_arg);
1472 cur_arg = va_arg(clean_args, mp_int*);
1473 }
1474 va_end(clean_args);
1475 return MP_MEM;
1476 }
1477 n++;
1478 cur_arg = va_arg(args, mp_int*);
1479 }
1480 va_end(args);
1481 return res; /* Assumed ok, if error flagged above. */
1482 }
1483 #endif
1484
1485
1486 #ifdef BN_MP_CLEAR_MULTI_C
mp_clear_multi(mp_int * mp,...)1487 static void mp_clear_multi(mp_int *mp, ...)
1488 {
1489 mp_int* next_mp = mp;
1490 va_list args;
1491 va_start(args, mp);
1492 while (next_mp != NULL) {
1493 mp_clear(next_mp);
1494 next_mp = va_arg(args, mp_int*);
1495 }
1496 va_end(args);
1497 }
1498 #endif
1499
1500
1501 /* shift left a certain amount of digits */
mp_lshd(mp_int * a,int b)1502 static int mp_lshd (mp_int * a, int b)
1503 {
1504 int x, res;
1505
1506 /* if its less than zero return */
1507 if (b <= 0) {
1508 return MP_OKAY;
1509 }
1510
1511 /* grow to fit the new digits */
1512 if (a->alloc < a->used + b) {
1513 if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
1514 return res;
1515 }
1516 }
1517
1518 {
1519 register mp_digit *top, *bottom;
1520
1521 /* increment the used by the shift amount then copy upwards */
1522 a->used += b;
1523
1524 /* top */
1525 top = a->dp + a->used - 1;
1526
1527 /* base */
1528 bottom = a->dp + a->used - 1 - b;
1529
1530 /* much like mp_rshd this is implemented using a sliding window
1531 * except the window goes the otherway around. Copying from
1532 * the bottom to the top. see bn_mp_rshd.c for more info.
1533 */
1534 for (x = a->used - 1; x >= b; x--) {
1535 *top-- = *bottom--;
1536 }
1537
1538 /* zero the lower digits */
1539 top = a->dp;
1540 for (x = 0; x < b; x++) {
1541 *top++ = 0;
1542 }
1543 }
1544 return MP_OKAY;
1545 }
1546
1547
1548 /* returns the number of bits in an int */
mp_count_bits(mp_int * a)1549 static int mp_count_bits (mp_int * a)
1550 {
1551 int r;
1552 mp_digit q;
1553
1554 /* shortcut */
1555 if (a->used == 0) {
1556 return 0;
1557 }
1558
1559 /* get number of digits and add that */
1560 r = (a->used - 1) * DIGIT_BIT;
1561
1562 /* take the last digit and count the bits in it */
1563 q = a->dp[a->used - 1];
1564 while (q > ((mp_digit) 0)) {
1565 ++r;
1566 q >>= ((mp_digit) 1);
1567 }
1568 return r;
1569 }
1570
1571
1572 /* calc a value mod 2**b */
mp_mod_2d(mp_int * a,int b,mp_int * c)1573 static int mp_mod_2d (mp_int * a, int b, mp_int * c)
1574 {
1575 int x, res;
1576
1577 /* if b is <= 0 then zero the int */
1578 if (b <= 0) {
1579 mp_zero (c);
1580 return MP_OKAY;
1581 }
1582
1583 /* if the modulus is larger than the value than return */
1584 if (b >= (int) (a->used * DIGIT_BIT)) {
1585 res = mp_copy (a, c);
1586 return res;
1587 }
1588
1589 /* copy */
1590 if ((res = mp_copy (a, c)) != MP_OKAY) {
1591 return res;
1592 }
1593
1594 /* zero digits above the last digit of the modulus */
1595 for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
1596 c->dp[x] = 0;
1597 }
1598 /* clear the digit that is not completely outside/inside the modulus */
1599 c->dp[b / DIGIT_BIT] &=
1600 (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
1601 mp_clamp (c);
1602 return MP_OKAY;
1603 }
1604
1605
1606 #ifdef BN_MP_DIV_SMALL
1607
1608 /* slower bit-bang division... also smaller */
mp_div(mp_int * a,mp_int * b,mp_int * c,mp_int * d)1609 static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
1610 {
1611 mp_int ta, tb, tq, q;
1612 int res, n, n2;
1613
1614 /* is divisor zero ? */
1615 if (mp_iszero (b) == 1) {
1616 return MP_VAL;
1617 }
1618
1619 /* if a < b then q=0, r = a */
1620 if (mp_cmp_mag (a, b) == MP_LT) {
1621 if (d != NULL) {
1622 res = mp_copy (a, d);
1623 } else {
1624 res = MP_OKAY;
1625 }
1626 if (c != NULL) {
1627 mp_zero (c);
1628 }
1629 return res;
1630 }
1631
1632 /* init our temps */
1633 if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) {
1634 return res;
1635 }
1636
1637
1638 mp_set(&tq, 1);
1639 n = mp_count_bits(a) - mp_count_bits(b);
1640 if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
1641 ((res = mp_abs(b, &tb)) != MP_OKAY) ||
1642 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
1643 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
1644 goto LBL_ERR;
1645 }
1646
1647 while (n-- >= 0) {
1648 if (mp_cmp(&tb, &ta) != MP_GT) {
1649 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
1650 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
1651 goto LBL_ERR;
1652 }
1653 }
1654 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
1655 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
1656 goto LBL_ERR;
1657 }
1658 }
1659
1660 /* now q == quotient and ta == remainder */
1661 n = a->sign;
1662 n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
1663 if (c != NULL) {
1664 mp_exch(c, &q);
1665 c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
1666 }
1667 if (d != NULL) {
1668 mp_exch(d, &ta);
1669 d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
1670 }
1671 LBL_ERR:
1672 mp_clear_multi(&ta, &tb, &tq, &q, NULL);
1673 return res;
1674 }
1675
1676 #else
1677
1678 /* integer signed division.
1679 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
1680 * HAC pp.598 Algorithm 14.20
1681 *
1682 * Note that the description in HAC is horribly
1683 * incomplete. For example, it doesn't consider
1684 * the case where digits are removed from 'x' in
1685 * the inner loop. It also doesn't consider the
1686 * case that y has fewer than three digits, etc..
1687 *
1688 * The overall algorithm is as described as
1689 * 14.20 from HAC but fixed to treat these cases.
1690 */
mp_div(mp_int * a,mp_int * b,mp_int * c,mp_int * d)1691 static int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
1692 {
1693 mp_int q, x, y, t1, t2;
1694 int res, n, t, i, norm, neg;
1695
1696 /* is divisor zero ? */
1697 if (mp_iszero (b) == 1) {
1698 return MP_VAL;
1699 }
1700
1701 /* if a < b then q=0, r = a */
1702 if (mp_cmp_mag (a, b) == MP_LT) {
1703 if (d != NULL) {
1704 res = mp_copy (a, d);
1705 } else {
1706 res = MP_OKAY;
1707 }
1708 if (c != NULL) {
1709 mp_zero (c);
1710 }
1711 return res;
1712 }
1713
1714 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
1715 return res;
1716 }
1717 q.used = a->used + 2;
1718
1719 if ((res = mp_init (&t1)) != MP_OKAY) {
1720 goto LBL_Q;
1721 }
1722
1723 if ((res = mp_init (&t2)) != MP_OKAY) {
1724 goto LBL_T1;
1725 }
1726
1727 if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
1728 goto LBL_T2;
1729 }
1730
1731 if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
1732 goto LBL_X;
1733 }
1734
1735 /* fix the sign */
1736 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
1737 x.sign = y.sign = MP_ZPOS;
1738
1739 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
1740 norm = mp_count_bits(&y) % DIGIT_BIT;
1741 if (norm < (int)(DIGIT_BIT-1)) {
1742 norm = (DIGIT_BIT-1) - norm;
1743 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
1744 goto LBL_Y;
1745 }
1746 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
1747 goto LBL_Y;
1748 }
1749 } else {
1750 norm = 0;
1751 }
1752
1753 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
1754 n = x.used - 1;
1755 t = y.used - 1;
1756
1757 /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
1758 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
1759 goto LBL_Y;
1760 }
1761
1762 while (mp_cmp (&x, &y) != MP_LT) {
1763 ++(q.dp[n - t]);
1764 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
1765 goto LBL_Y;
1766 }
1767 }
1768
1769 /* reset y by shifting it back down */
1770 mp_rshd (&y, n - t);
1771
1772 /* step 3. for i from n down to (t + 1) */
1773 for (i = n; i >= (t + 1); i--) {
1774 if (i > x.used) {
1775 continue;
1776 }
1777
1778 /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
1779 * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
1780 if (x.dp[i] == y.dp[t]) {
1781 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
1782 } else {
1783 mp_word tmp;
1784 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
1785 tmp |= ((mp_word) x.dp[i - 1]);
1786 tmp /= ((mp_word) y.dp[t]);
1787 if (tmp > (mp_word) MP_MASK)
1788 tmp = MP_MASK;
1789 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
1790 }
1791
1792 /* while (q{i-t-1} * (yt * b + y{t-1})) >
1793 xi * b**2 + xi-1 * b + xi-2
1794
1795 do q{i-t-1} -= 1;
1796 */
1797 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
1798 do {
1799 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
1800
1801 /* find left hand */
1802 mp_zero (&t1);
1803 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
1804 t1.dp[1] = y.dp[t];
1805 t1.used = 2;
1806 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
1807 goto LBL_Y;
1808 }
1809
1810 /* find right hand */
1811 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
1812 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
1813 t2.dp[2] = x.dp[i];
1814 t2.used = 3;
1815 } while (mp_cmp_mag(&t1, &t2) == MP_GT);
1816
1817 /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
1818 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
1819 goto LBL_Y;
1820 }
1821
1822 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
1823 goto LBL_Y;
1824 }
1825
1826 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
1827 goto LBL_Y;
1828 }
1829
1830 /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
1831 if (x.sign == MP_NEG) {
1832 if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
1833 goto LBL_Y;
1834 }
1835 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
1836 goto LBL_Y;
1837 }
1838 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
1839 goto LBL_Y;
1840 }
1841
1842 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
1843 }
1844 }
1845
1846 /* now q is the quotient and x is the remainder
1847 * [which we have to normalize]
1848 */
1849
1850 /* get sign before writing to c */
1851 x.sign = x.used == 0 ? MP_ZPOS : a->sign;
1852
1853 if (c != NULL) {
1854 mp_clamp (&q);
1855 mp_exch (&q, c);
1856 c->sign = neg;
1857 }
1858
1859 if (d != NULL) {
1860 mp_div_2d (&x, norm, &x, NULL);
1861 mp_exch (&x, d);
1862 }
1863
1864 res = MP_OKAY;
1865
1866 LBL_Y:mp_clear (&y);
1867 LBL_X:mp_clear (&x);
1868 LBL_T2:mp_clear (&t2);
1869 LBL_T1:mp_clear (&t1);
1870 LBL_Q:mp_clear (&q);
1871 return res;
1872 }
1873
1874 #endif
1875
1876
1877 #ifdef MP_LOW_MEM
1878 #define TAB_SIZE 32
1879 #else
1880 #define TAB_SIZE 256
1881 #endif
1882
s_mp_exptmod(mp_int * G,mp_int * X,mp_int * P,mp_int * Y,int redmode)1883 static int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
1884 {
1885 mp_int M[TAB_SIZE], res, mu;
1886 mp_digit buf;
1887 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
1888 int (*redux)(mp_int*,mp_int*,mp_int*);
1889
1890 /* find window size */
1891 x = mp_count_bits (X);
1892 if (x <= 7) {
1893 winsize = 2;
1894 } else if (x <= 36) {
1895 winsize = 3;
1896 } else if (x <= 140) {
1897 winsize = 4;
1898 } else if (x <= 450) {
1899 winsize = 5;
1900 } else if (x <= 1303) {
1901 winsize = 6;
1902 } else if (x <= 3529) {
1903 winsize = 7;
1904 } else {
1905 winsize = 8;
1906 }
1907
1908 #ifdef MP_LOW_MEM
1909 if (winsize > 5) {
1910 winsize = 5;
1911 }
1912 #endif
1913
1914 /* init M array */
1915 /* init first cell */
1916 if ((err = mp_init(&M[1])) != MP_OKAY) {
1917 return err;
1918 }
1919
1920 /* now init the second half of the array */
1921 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
1922 if ((err = mp_init(&M[x])) != MP_OKAY) {
1923 for (y = 1<<(winsize-1); y < x; y++) {
1924 mp_clear (&M[y]);
1925 }
1926 mp_clear(&M[1]);
1927 return err;
1928 }
1929 }
1930
1931 /* create mu, used for Barrett reduction */
1932 if ((err = mp_init (&mu)) != MP_OKAY) {
1933 goto LBL_M;
1934 }
1935
1936 if (redmode == 0) {
1937 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
1938 goto LBL_MU;
1939 }
1940 redux = mp_reduce;
1941 } else {
1942 if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
1943 goto LBL_MU;
1944 }
1945 redux = mp_reduce_2k_l;
1946 }
1947
1948 /* create M table
1949 *
1950 * The M table contains powers of the base,
1951 * e.g. M[x] = G**x mod P
1952 *
1953 * The first half of the table is not
1954 * computed though accept for M[0] and M[1]
1955 */
1956 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
1957 goto LBL_MU;
1958 }
1959
1960 /* compute the value at M[1<<(winsize-1)] by squaring
1961 * M[1] (winsize-1) times
1962 */
1963 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
1964 goto LBL_MU;
1965 }
1966
1967 for (x = 0; x < (winsize - 1); x++) {
1968 /* square it */
1969 if ((err = mp_sqr (&M[1 << (winsize - 1)],
1970 &M[1 << (winsize - 1)])) != MP_OKAY) {
1971 goto LBL_MU;
1972 }
1973
1974 /* reduce modulo P */
1975 if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
1976 goto LBL_MU;
1977 }
1978 }
1979
1980 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
1981 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
1982 */
1983 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
1984 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
1985 goto LBL_MU;
1986 }
1987 if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
1988 goto LBL_MU;
1989 }
1990 }
1991
1992 /* setup result */
1993 if ((err = mp_init (&res)) != MP_OKAY) {
1994 goto LBL_MU;
1995 }
1996 mp_set (&res, 1);
1997
1998 /* set initial mode and bit cnt */
1999 mode = 0;
2000 bitcnt = 1;
2001 buf = 0;
2002 digidx = X->used - 1;
2003 bitcpy = 0;
2004 bitbuf = 0;
2005
2006 for (;;) {
2007 /* grab next digit as required */
2008 if (--bitcnt == 0) {
2009 /* if digidx == -1 we are out of digits */
2010 if (digidx == -1) {
2011 break;
2012 }
2013 /* read next digit and reset the bitcnt */
2014 buf = X->dp[digidx--];
2015 bitcnt = (int) DIGIT_BIT;
2016 }
2017
2018 /* grab the next msb from the exponent */
2019 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
2020 buf <<= (mp_digit)1;
2021
2022 /* if the bit is zero and mode == 0 then we ignore it
2023 * These represent the leading zero bits before the first 1 bit
2024 * in the exponent. Technically this opt is not required but it
2025 * does lower the # of trivial squaring/reductions used
2026 */
2027 if (mode == 0 && y == 0) {
2028 continue;
2029 }
2030
2031 /* if the bit is zero and mode == 1 then we square */
2032 if (mode == 1 && y == 0) {
2033 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2034 goto LBL_RES;
2035 }
2036 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2037 goto LBL_RES;
2038 }
2039 continue;
2040 }
2041
2042 /* else we add it to the window */
2043 bitbuf |= (y << (winsize - ++bitcpy));
2044 mode = 2;
2045
2046 if (bitcpy == winsize) {
2047 /* ok window is filled so square as required and multiply */
2048 /* square first */
2049 for (x = 0; x < winsize; x++) {
2050 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2051 goto LBL_RES;
2052 }
2053 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2054 goto LBL_RES;
2055 }
2056 }
2057
2058 /* then multiply */
2059 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
2060 goto LBL_RES;
2061 }
2062 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2063 goto LBL_RES;
2064 }
2065
2066 /* empty window and reset */
2067 bitcpy = 0;
2068 bitbuf = 0;
2069 mode = 1;
2070 }
2071 }
2072
2073 /* if bits remain then square/multiply */
2074 if (mode == 2 && bitcpy > 0) {
2075 /* square then multiply if the bit is set */
2076 for (x = 0; x < bitcpy; x++) {
2077 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2078 goto LBL_RES;
2079 }
2080 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2081 goto LBL_RES;
2082 }
2083
2084 bitbuf <<= 1;
2085 if ((bitbuf & (1 << winsize)) != 0) {
2086 /* then multiply */
2087 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
2088 goto LBL_RES;
2089 }
2090 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2091 goto LBL_RES;
2092 }
2093 }
2094 }
2095 }
2096
2097 mp_exch (&res, Y);
2098 err = MP_OKAY;
2099 LBL_RES:mp_clear (&res);
2100 LBL_MU:mp_clear (&mu);
2101 LBL_M:
2102 mp_clear(&M[1]);
2103 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
2104 mp_clear (&M[x]);
2105 }
2106 return err;
2107 }
2108
2109
2110 /* computes b = a*a */
mp_sqr(mp_int * a,mp_int * b)2111 static int mp_sqr (mp_int * a, mp_int * b)
2112 {
2113 int res;
2114
2115 #ifdef BN_MP_TOOM_SQR_C
2116 /* use Toom-Cook? */
2117 if (a->used >= TOOM_SQR_CUTOFF) {
2118 res = mp_toom_sqr(a, b);
2119 /* Karatsuba? */
2120 } else
2121 #endif
2122 #ifdef BN_MP_KARATSUBA_SQR_C
2123 if (a->used >= KARATSUBA_SQR_CUTOFF) {
2124 res = mp_karatsuba_sqr (a, b);
2125 } else
2126 #endif
2127 {
2128 #ifdef BN_FAST_S_MP_SQR_C
2129 /* can we use the fast comba multiplier? */
2130 if ((a->used * 2 + 1) < MP_WARRAY &&
2131 a->used <
2132 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
2133 res = fast_s_mp_sqr (a, b);
2134 } else
2135 #endif
2136 #ifdef BN_S_MP_SQR_C
2137 res = s_mp_sqr (a, b);
2138 #else
2139 #error mp_sqr could fail
2140 res = MP_VAL;
2141 #endif
2142 }
2143 b->sign = MP_ZPOS;
2144 return res;
2145 }
2146
2147
2148 /* reduces a modulo n where n is of the form 2**p - d
2149 This differs from reduce_2k since "d" can be larger
2150 than a single digit.
2151 */
mp_reduce_2k_l(mp_int * a,mp_int * n,mp_int * d)2152 static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
2153 {
2154 mp_int q;
2155 int p, res;
2156
2157 if ((res = mp_init(&q)) != MP_OKAY) {
2158 return res;
2159 }
2160
2161 p = mp_count_bits(n);
2162 top:
2163 /* q = a/2**p, a = a mod 2**p */
2164 if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
2165 goto ERR;
2166 }
2167
2168 /* q = q * d */
2169 if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
2170 goto ERR;
2171 }
2172
2173 /* a = a + q */
2174 if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
2175 goto ERR;
2176 }
2177
2178 if (mp_cmp_mag(a, n) != MP_LT) {
2179 s_mp_sub(a, n, a);
2180 goto top;
2181 }
2182
2183 ERR:
2184 mp_clear(&q);
2185 return res;
2186 }
2187
2188
2189 /* determines the setup value */
mp_reduce_2k_setup_l(mp_int * a,mp_int * d)2190 static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
2191 {
2192 int res;
2193 mp_int tmp;
2194
2195 if ((res = mp_init(&tmp)) != MP_OKAY) {
2196 return res;
2197 }
2198
2199 if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
2200 goto ERR;
2201 }
2202
2203 if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
2204 goto ERR;
2205 }
2206
2207 ERR:
2208 mp_clear(&tmp);
2209 return res;
2210 }
2211
2212
2213 /* computes a = 2**b
2214 *
2215 * Simple algorithm which zeroes the int, grows it then just sets one bit
2216 * as required.
2217 */
mp_2expt(mp_int * a,int b)2218 static int mp_2expt (mp_int * a, int b)
2219 {
2220 int res;
2221
2222 /* zero a as per default */
2223 mp_zero (a);
2224
2225 /* grow a to accommodate the single bit */
2226 if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
2227 return res;
2228 }
2229
2230 /* set the used count of where the bit will go */
2231 a->used = b / DIGIT_BIT + 1;
2232
2233 /* put the single bit in its place */
2234 a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
2235
2236 return MP_OKAY;
2237 }
2238
2239
2240 /* pre-calculate the value required for Barrett reduction
2241 * For a given modulus "b" it calulates the value required in "a"
2242 */
mp_reduce_setup(mp_int * a,mp_int * b)2243 static int mp_reduce_setup (mp_int * a, mp_int * b)
2244 {
2245 int res;
2246
2247 if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
2248 return res;
2249 }
2250 return mp_div (a, b, a, NULL);
2251 }
2252
2253
2254 /* reduces x mod m, assumes 0 < x < m**2, mu is
2255 * precomputed via mp_reduce_setup.
2256 * From HAC pp.604 Algorithm 14.42
2257 */
mp_reduce(mp_int * x,mp_int * m,mp_int * mu)2258 static int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
2259 {
2260 mp_int q;
2261 int res, um = m->used;
2262
2263 /* q = x */
2264 if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
2265 return res;
2266 }
2267
2268 /* q1 = x / b**(k-1) */
2269 mp_rshd (&q, um - 1);
2270
2271 /* according to HAC this optimization is ok */
2272 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
2273 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
2274 goto CLEANUP;
2275 }
2276 } else {
2277 #ifdef BN_S_MP_MUL_HIGH_DIGS_C
2278 if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
2279 goto CLEANUP;
2280 }
2281 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
2282 if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
2283 goto CLEANUP;
2284 }
2285 #else
2286 {
2287 #error mp_reduce would always fail
2288 res = MP_VAL;
2289 goto CLEANUP;
2290 }
2291 #endif
2292 }
2293
2294 /* q3 = q2 / b**(k+1) */
2295 mp_rshd (&q, um + 1);
2296
2297 /* x = x mod b**(k+1), quick (no division) */
2298 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
2299 goto CLEANUP;
2300 }
2301
2302 /* q = q * m mod b**(k+1), quick (no division) */
2303 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
2304 goto CLEANUP;
2305 }
2306
2307 /* x = x - q */
2308 if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
2309 goto CLEANUP;
2310 }
2311
2312 /* If x < 0, add b**(k+1) to it */
2313 if (mp_cmp_d (x, 0) == MP_LT) {
2314 mp_set (&q, 1);
2315 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) {
2316 goto CLEANUP;
2317 }
2318 if ((res = mp_add (x, &q, x)) != MP_OKAY) {
2319 goto CLEANUP;
2320 }
2321 }
2322
2323 /* Back off if it's too big */
2324 while (mp_cmp (x, m) != MP_LT) {
2325 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
2326 goto CLEANUP;
2327 }
2328 }
2329
2330 CLEANUP:
2331 mp_clear (&q);
2332
2333 return res;
2334 }
2335
2336
2337 /* multiplies |a| * |b| and only computes up to digs digits of result
2338 * HAC pp. 595, Algorithm 14.12 Modified so you can control how
2339 * many digits of output are created.
2340 */
s_mp_mul_digs(mp_int * a,mp_int * b,mp_int * c,int digs)2341 static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2342 {
2343 mp_int t;
2344 int res, pa, pb, ix, iy;
2345 mp_digit u;
2346 mp_word r;
2347 mp_digit tmpx, *tmpt, *tmpy;
2348
2349 #ifdef BN_FAST_S_MP_MUL_DIGS_C
2350 /* can we use the fast multiplier? */
2351 if (((digs) < MP_WARRAY) &&
2352 MIN (a->used, b->used) <
2353 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
2354 return fast_s_mp_mul_digs (a, b, c, digs);
2355 }
2356 #endif
2357
2358 if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
2359 return res;
2360 }
2361 t.used = digs;
2362
2363 /* compute the digits of the product directly */
2364 pa = a->used;
2365 for (ix = 0; ix < pa; ix++) {
2366 /* set the carry to zero */
2367 u = 0;
2368
2369 /* limit ourselves to making digs digits of output */
2370 pb = MIN (b->used, digs - ix);
2371
2372 /* setup some aliases */
2373 /* copy of the digit from a used within the nested loop */
2374 tmpx = a->dp[ix];
2375
2376 /* an alias for the destination shifted ix places */
2377 tmpt = t.dp + ix;
2378
2379 /* an alias for the digits of b */
2380 tmpy = b->dp;
2381
2382 /* compute the columns of the output and propagate the carry */
2383 for (iy = 0; iy < pb; iy++) {
2384 /* compute the column as a mp_word */
2385 r = ((mp_word)*tmpt) +
2386 ((mp_word)tmpx) * ((mp_word)*tmpy++) +
2387 ((mp_word) u);
2388
2389 /* the new column is the lower part of the result */
2390 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2391
2392 /* get the carry word from the result */
2393 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
2394 }
2395 /* set carry if it is placed below digs */
2396 if (ix + iy < digs) {
2397 *tmpt = u;
2398 }
2399 }
2400
2401 mp_clamp (&t);
2402 mp_exch (&t, c);
2403
2404 mp_clear (&t);
2405 return MP_OKAY;
2406 }
2407
2408
2409 #ifdef BN_FAST_S_MP_MUL_DIGS_C
2410 /* Fast (comba) multiplier
2411 *
2412 * This is the fast column-array [comba] multiplier. It is
2413 * designed to compute the columns of the product first
2414 * then handle the carries afterwards. This has the effect
2415 * of making the nested loops that compute the columns very
2416 * simple and schedulable on super-scalar processors.
2417 *
2418 * This has been modified to produce a variable number of
2419 * digits of output so if say only a half-product is required
2420 * you don't have to compute the upper half (a feature
2421 * required for fast Barrett reduction).
2422 *
2423 * Based on Algorithm 14.12 on pp.595 of HAC.
2424 *
2425 */
fast_s_mp_mul_digs(mp_int * a,mp_int * b,mp_int * c,int digs)2426 static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2427 {
2428 int olduse, res, pa, ix, iz;
2429 mp_digit W[MP_WARRAY];
2430 register mp_word _W;
2431
2432 /* grow the destination as required */
2433 if (c->alloc < digs) {
2434 if ((res = mp_grow (c, digs)) != MP_OKAY) {
2435 return res;
2436 }
2437 }
2438
2439 /* number of output digits to produce */
2440 pa = MIN(digs, a->used + b->used);
2441
2442 /* clear the carry */
2443 _W = 0;
2444 for (ix = 0; ix < pa; ix++) {
2445 int tx, ty;
2446 int iy;
2447 mp_digit *tmpx, *tmpy;
2448
2449 /* get offsets into the two bignums */
2450 ty = MIN(b->used-1, ix);
2451 tx = ix - ty;
2452
2453 /* setup temp aliases */
2454 tmpx = a->dp + tx;
2455 tmpy = b->dp + ty;
2456
2457 /* this is the number of times the loop will iterrate, essentially
2458 while (tx++ < a->used && ty-- >= 0) { ... }
2459 */
2460 iy = MIN(a->used-tx, ty+1);
2461
2462 /* execute loop */
2463 for (iz = 0; iz < iy; ++iz) {
2464 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
2465
2466 }
2467
2468 /* store term */
2469 W[ix] = ((mp_digit)_W) & MP_MASK;
2470
2471 /* make next carry */
2472 _W = _W >> ((mp_word)DIGIT_BIT);
2473 }
2474
2475 /* setup dest */
2476 olduse = c->used;
2477 c->used = pa;
2478
2479 {
2480 register mp_digit *tmpc;
2481 tmpc = c->dp;
2482 for (ix = 0; ix < pa+1; ix++) {
2483 /* now extract the previous digit [below the carry] */
2484 *tmpc++ = W[ix];
2485 }
2486
2487 /* clear unused digits [that existed in the old copy of c] */
2488 for (; ix < olduse; ix++) {
2489 *tmpc++ = 0;
2490 }
2491 }
2492 mp_clamp (c);
2493 return MP_OKAY;
2494 }
2495 #endif /* BN_FAST_S_MP_MUL_DIGS_C */
2496
2497
2498 /* init an mp_init for a given size */
mp_init_size(mp_int * a,int size)2499 static int mp_init_size (mp_int * a, int size)
2500 {
2501 int x;
2502
2503 /* pad size so there are always extra digits */
2504 size += (MP_PREC * 2) - (size % MP_PREC);
2505
2506 /* alloc mem */
2507 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
2508 if (a->dp == NULL) {
2509 return MP_MEM;
2510 }
2511
2512 /* set the members */
2513 a->used = 0;
2514 a->alloc = size;
2515 a->sign = MP_ZPOS;
2516
2517 /* zero the digits */
2518 for (x = 0; x < size; x++) {
2519 a->dp[x] = 0;
2520 }
2521
2522 return MP_OKAY;
2523 }
2524
2525
2526 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
s_mp_sqr(mp_int * a,mp_int * b)2527 static int s_mp_sqr (mp_int * a, mp_int * b)
2528 {
2529 mp_int t;
2530 int res, ix, iy, pa;
2531 mp_word r;
2532 mp_digit u, tmpx, *tmpt;
2533
2534 pa = a->used;
2535 if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
2536 return res;
2537 }
2538
2539 /* default used is maximum possible size */
2540 t.used = 2*pa + 1;
2541
2542 for (ix = 0; ix < pa; ix++) {
2543 /* first calculate the digit at 2*ix */
2544 /* calculate double precision result */
2545 r = ((mp_word) t.dp[2*ix]) +
2546 ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
2547
2548 /* store lower part in result */
2549 t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
2550
2551 /* get the carry */
2552 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2553
2554 /* left hand side of A[ix] * A[iy] */
2555 tmpx = a->dp[ix];
2556
2557 /* alias for where to store the results */
2558 tmpt = t.dp + (2*ix + 1);
2559
2560 for (iy = ix + 1; iy < pa; iy++) {
2561 /* first calculate the product */
2562 r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
2563
2564 /* now calculate the double precision result, note we use
2565 * addition instead of *2 since it's easier to optimize
2566 */
2567 r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
2568
2569 /* store lower part */
2570 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2571
2572 /* get carry */
2573 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2574 }
2575 /* propagate upwards */
2576 while (u != ((mp_digit) 0)) {
2577 r = ((mp_word) *tmpt) + ((mp_word) u);
2578 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2579 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2580 }
2581 }
2582
2583 mp_clamp (&t);
2584 mp_exch (&t, b);
2585 mp_clear (&t);
2586 return MP_OKAY;
2587 }
2588
2589
2590 /* multiplies |a| * |b| and does not compute the lower digs digits
2591 * [meant to get the higher part of the product]
2592 */
s_mp_mul_high_digs(mp_int * a,mp_int * b,mp_int * c,int digs)2593 static int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2594 {
2595 mp_int t;
2596 int res, pa, pb, ix, iy;
2597 mp_digit u;
2598 mp_word r;
2599 mp_digit tmpx, *tmpt, *tmpy;
2600
2601 /* can we use the fast multiplier? */
2602 #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
2603 if (((a->used + b->used + 1) < MP_WARRAY)
2604 && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
2605 return fast_s_mp_mul_high_digs (a, b, c, digs);
2606 }
2607 #endif
2608
2609 if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
2610 return res;
2611 }
2612 t.used = a->used + b->used + 1;
2613
2614 pa = a->used;
2615 pb = b->used;
2616 for (ix = 0; ix < pa; ix++) {
2617 /* clear the carry */
2618 u = 0;
2619
2620 /* left hand side of A[ix] * B[iy] */
2621 tmpx = a->dp[ix];
2622
2623 /* alias to the address of where the digits will be stored */
2624 tmpt = &(t.dp[digs]);
2625
2626 /* alias for where to read the right hand side from */
2627 tmpy = b->dp + (digs - ix);
2628
2629 for (iy = digs - ix; iy < pb; iy++) {
2630 /* calculate the double precision result */
2631 r = ((mp_word)*tmpt) +
2632 ((mp_word)tmpx) * ((mp_word)*tmpy++) +
2633 ((mp_word) u);
2634
2635 /* get the lower part */
2636 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2637
2638 /* carry the carry */
2639 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
2640 }
2641 *tmpt = u;
2642 }
2643 mp_clamp (&t);
2644 mp_exch (&t, c);
2645 mp_clear (&t);
2646 return MP_OKAY;
2647 }
2648
2649
2650 #ifdef BN_MP_MONTGOMERY_SETUP_C
2651 /* setups the montgomery reduction stuff */
2652 static int
mp_montgomery_setup(mp_int * n,mp_digit * rho)2653 mp_montgomery_setup (mp_int * n, mp_digit * rho)
2654 {
2655 mp_digit x, b;
2656
2657 /* fast inversion mod 2**k
2658 *
2659 * Based on the fact that
2660 *
2661 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
2662 * => 2*X*A - X*X*A*A = 1
2663 * => 2*(1) - (1) = 1
2664 */
2665 b = n->dp[0];
2666
2667 if ((b & 1) == 0) {
2668 return MP_VAL;
2669 }
2670
2671 x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
2672 x *= 2 - b * x; /* here x*a==1 mod 2**8 */
2673 #if !defined(MP_8BIT)
2674 x *= 2 - b * x; /* here x*a==1 mod 2**16 */
2675 #endif
2676 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
2677 x *= 2 - b * x; /* here x*a==1 mod 2**32 */
2678 #endif
2679 #ifdef MP_64BIT
2680 x *= 2 - b * x; /* here x*a==1 mod 2**64 */
2681 #endif
2682
2683 /* rho = -1/m mod b */
2684 *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
2685
2686 return MP_OKAY;
2687 }
2688 #endif
2689
2690
2691 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
2692 /* computes xR**-1 == x (mod N) via Montgomery Reduction
2693 *
2694 * This is an optimized implementation of montgomery_reduce
2695 * which uses the comba method to quickly calculate the columns of the
2696 * reduction.
2697 *
2698 * Based on Algorithm 14.32 on pp.601 of HAC.
2699 */
fast_mp_montgomery_reduce(mp_int * x,mp_int * n,mp_digit rho)2700 static int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
2701 {
2702 int ix, res, olduse;
2703 mp_word W[MP_WARRAY];
2704
2705 /* get old used count */
2706 olduse = x->used;
2707
2708 /* grow a as required */
2709 if (x->alloc < n->used + 1) {
2710 if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
2711 return res;
2712 }
2713 }
2714
2715 /* first we have to get the digits of the input into
2716 * an array of double precision words W[...]
2717 */
2718 {
2719 register mp_word *_W;
2720 register mp_digit *tmpx;
2721
2722 /* alias for the W[] array */
2723 _W = W;
2724
2725 /* alias for the digits of x*/
2726 tmpx = x->dp;
2727
2728 /* copy the digits of a into W[0..a->used-1] */
2729 for (ix = 0; ix < x->used; ix++) {
2730 *_W++ = *tmpx++;
2731 }
2732
2733 /* zero the high words of W[a->used..m->used*2] */
2734 for (; ix < n->used * 2 + 1; ix++) {
2735 *_W++ = 0;
2736 }
2737 }
2738
2739 /* now we proceed to zero successive digits
2740 * from the least significant upwards
2741 */
2742 for (ix = 0; ix < n->used; ix++) {
2743 /* mu = ai * m' mod b
2744 *
2745 * We avoid a double precision multiplication (which isn't required)
2746 * by casting the value down to a mp_digit. Note this requires
2747 * that W[ix-1] have the carry cleared (see after the inner loop)
2748 */
2749 register mp_digit mu;
2750 mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
2751
2752 /* a = a + mu * m * b**i
2753 *
2754 * This is computed in place and on the fly. The multiplication
2755 * by b**i is handled by offseting which columns the results
2756 * are added to.
2757 *
2758 * Note the comba method normally doesn't handle carries in the
2759 * inner loop In this case we fix the carry from the previous
2760 * column since the Montgomery reduction requires digits of the
2761 * result (so far) [see above] to work. This is
2762 * handled by fixing up one carry after the inner loop. The
2763 * carry fixups are done in order so after these loops the
2764 * first m->used words of W[] have the carries fixed
2765 */
2766 {
2767 register int iy;
2768 register mp_digit *tmpn;
2769 register mp_word *_W;
2770
2771 /* alias for the digits of the modulus */
2772 tmpn = n->dp;
2773
2774 /* Alias for the columns set by an offset of ix */
2775 _W = W + ix;
2776
2777 /* inner loop */
2778 for (iy = 0; iy < n->used; iy++) {
2779 *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
2780 }
2781 }
2782
2783 /* now fix carry for next digit, W[ix+1] */
2784 W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
2785 }
2786
2787 /* now we have to propagate the carries and
2788 * shift the words downward [all those least
2789 * significant digits we zeroed].
2790 */
2791 {
2792 register mp_digit *tmpx;
2793 register mp_word *_W, *_W1;
2794
2795 /* nox fix rest of carries */
2796
2797 /* alias for current word */
2798 _W1 = W + ix;
2799
2800 /* alias for next word, where the carry goes */
2801 _W = W + ++ix;
2802
2803 for (; ix <= n->used * 2 + 1; ix++) {
2804 *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
2805 }
2806
2807 /* copy out, A = A/b**n
2808 *
2809 * The result is A/b**n but instead of converting from an
2810 * array of mp_word to mp_digit than calling mp_rshd
2811 * we just copy them in the right order
2812 */
2813
2814 /* alias for destination word */
2815 tmpx = x->dp;
2816
2817 /* alias for shifted double precision result */
2818 _W = W + n->used;
2819
2820 for (ix = 0; ix < n->used + 1; ix++) {
2821 *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
2822 }
2823
2824 /* zero oldused digits, if the input a was larger than
2825 * m->used+1 we'll have to clear the digits
2826 */
2827 for (; ix < olduse; ix++) {
2828 *tmpx++ = 0;
2829 }
2830 }
2831
2832 /* set the max used and clamp */
2833 x->used = n->used + 1;
2834 mp_clamp (x);
2835
2836 /* if A >= m then A = A - m */
2837 if (mp_cmp_mag (x, n) != MP_LT) {
2838 return s_mp_sub (x, n, x);
2839 }
2840 return MP_OKAY;
2841 }
2842 #endif
2843
2844
2845 #ifdef BN_MP_MUL_2_C
2846 /* b = a*2 */
mp_mul_2(mp_int * a,mp_int * b)2847 static int mp_mul_2(mp_int * a, mp_int * b)
2848 {
2849 int x, res, oldused;
2850
2851 /* grow to accommodate result */
2852 if (b->alloc < a->used + 1) {
2853 if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
2854 return res;
2855 }
2856 }
2857
2858 oldused = b->used;
2859 b->used = a->used;
2860
2861 {
2862 register mp_digit r, rr, *tmpa, *tmpb;
2863
2864 /* alias for source */
2865 tmpa = a->dp;
2866
2867 /* alias for dest */
2868 tmpb = b->dp;
2869
2870 /* carry */
2871 r = 0;
2872 for (x = 0; x < a->used; x++) {
2873
2874 /* get what will be the *next* carry bit from the
2875 * MSB of the current digit
2876 */
2877 rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
2878
2879 /* now shift up this digit, add in the carry [from the previous] */
2880 *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
2881
2882 /* copy the carry that would be from the source
2883 * digit into the next iteration
2884 */
2885 r = rr;
2886 }
2887
2888 /* new leading digit? */
2889 if (r != 0) {
2890 /* add a MSB which is always 1 at this point */
2891 *tmpb = 1;
2892 ++(b->used);
2893 }
2894
2895 /* now zero any excess digits on the destination
2896 * that we didn't write to
2897 */
2898 tmpb = b->dp + b->used;
2899 for (x = b->used; x < oldused; x++) {
2900 *tmpb++ = 0;
2901 }
2902 }
2903 b->sign = a->sign;
2904 return MP_OKAY;
2905 }
2906 #endif
2907
2908
2909 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
2910 /*
2911 * shifts with subtractions when the result is greater than b.
2912 *
2913 * The method is slightly modified to shift B unconditionally up to just under
2914 * the leading bit of b. This saves a lot of multiple precision shifting.
2915 */
mp_montgomery_calc_normalization(mp_int * a,mp_int * b)2916 static int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
2917 {
2918 int x, bits, res;
2919
2920 /* how many bits of last digit does b use */
2921 bits = mp_count_bits (b) % DIGIT_BIT;
2922
2923 if (b->used > 1) {
2924 if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
2925 return res;
2926 }
2927 } else {
2928 mp_set(a, 1);
2929 bits = 1;
2930 }
2931
2932
2933 /* now compute C = A * B mod b */
2934 for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
2935 if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
2936 return res;
2937 }
2938 if (mp_cmp_mag (a, b) != MP_LT) {
2939 if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
2940 return res;
2941 }
2942 }
2943 }
2944
2945 return MP_OKAY;
2946 }
2947 #endif
2948
2949
2950 #ifdef BN_MP_EXPTMOD_FAST_C
2951 /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
2952 *
2953 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
2954 * The value of k changes based on the size of the exponent.
2955 *
2956 * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
2957 */
2958
mp_exptmod_fast(mp_int * G,mp_int * X,mp_int * P,mp_int * Y,int redmode)2959 static int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
2960 {
2961 mp_int M[TAB_SIZE], res;
2962 mp_digit buf, mp;
2963 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
2964
2965 /* use a pointer to the reduction algorithm. This allows us to use
2966 * one of many reduction algorithms without modding the guts of
2967 * the code with if statements everywhere.
2968 */
2969 int (*redux)(mp_int*,mp_int*,mp_digit);
2970
2971 /* find window size */
2972 x = mp_count_bits (X);
2973 if (x <= 7) {
2974 winsize = 2;
2975 } else if (x <= 36) {
2976 winsize = 3;
2977 } else if (x <= 140) {
2978 winsize = 4;
2979 } else if (x <= 450) {
2980 winsize = 5;
2981 } else if (x <= 1303) {
2982 winsize = 6;
2983 } else if (x <= 3529) {
2984 winsize = 7;
2985 } else {
2986 winsize = 8;
2987 }
2988
2989 #ifdef MP_LOW_MEM
2990 if (winsize > 5) {
2991 winsize = 5;
2992 }
2993 #endif
2994
2995 /* init M array */
2996 /* init first cell */
2997 if ((err = mp_init(&M[1])) != MP_OKAY) {
2998 return err;
2999 }
3000
3001 /* now init the second half of the array */
3002 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
3003 if ((err = mp_init(&M[x])) != MP_OKAY) {
3004 for (y = 1<<(winsize-1); y < x; y++) {
3005 mp_clear (&M[y]);
3006 }
3007 mp_clear(&M[1]);
3008 return err;
3009 }
3010 }
3011
3012 /* determine and setup reduction code */
3013 if (redmode == 0) {
3014 #ifdef BN_MP_MONTGOMERY_SETUP_C
3015 /* now setup montgomery */
3016 if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
3017 goto LBL_M;
3018 }
3019 #else
3020 err = MP_VAL;
3021 goto LBL_M;
3022 #endif
3023
3024 /* automatically pick the comba one if available (saves quite a few calls/ifs) */
3025 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
3026 if (((P->used * 2 + 1) < MP_WARRAY) &&
3027 P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
3028 redux = fast_mp_montgomery_reduce;
3029 } else
3030 #endif
3031 {
3032 #ifdef BN_MP_MONTGOMERY_REDUCE_C
3033 /* use slower baseline Montgomery method */
3034 redux = mp_montgomery_reduce;
3035 #else
3036 err = MP_VAL;
3037 goto LBL_M;
3038 #endif
3039 }
3040 } else if (redmode == 1) {
3041 #if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
3042 /* setup DR reduction for moduli of the form B**k - b */
3043 mp_dr_setup(P, &mp);
3044 redux = mp_dr_reduce;
3045 #else
3046 err = MP_VAL;
3047 goto LBL_M;
3048 #endif
3049 } else {
3050 #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
3051 /* setup DR reduction for moduli of the form 2**k - b */
3052 if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
3053 goto LBL_M;
3054 }
3055 redux = mp_reduce_2k;
3056 #else
3057 err = MP_VAL;
3058 goto LBL_M;
3059 #endif
3060 }
3061
3062 /* setup result */
3063 if ((err = mp_init (&res)) != MP_OKAY) {
3064 goto LBL_M;
3065 }
3066
3067 /* create M table
3068 *
3069
3070 *
3071 * The first half of the table is not computed though accept for M[0] and M[1]
3072 */
3073
3074 if (redmode == 0) {
3075 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
3076 /* now we need R mod m */
3077 if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
3078 goto LBL_RES;
3079 }
3080 #else
3081 err = MP_VAL;
3082 goto LBL_RES;
3083 #endif
3084
3085 /* now set M[1] to G * R mod m */
3086 if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
3087 goto LBL_RES;
3088 }
3089 } else {
3090 mp_set(&res, 1);
3091 if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
3092 goto LBL_RES;
3093 }
3094 }
3095
3096 /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
3097 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
3098 goto LBL_RES;
3099 }
3100
3101 for (x = 0; x < (winsize - 1); x++) {
3102 if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
3103 goto LBL_RES;
3104 }
3105 if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
3106 goto LBL_RES;
3107 }
3108 }
3109
3110 /* create upper table */
3111 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
3112 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
3113 goto LBL_RES;
3114 }
3115 if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
3116 goto LBL_RES;
3117 }
3118 }
3119
3120 /* set initial mode and bit cnt */
3121 mode = 0;
3122 bitcnt = 1;
3123 buf = 0;
3124 digidx = X->used - 1;
3125 bitcpy = 0;
3126 bitbuf = 0;
3127
3128 for (;;) {
3129 /* grab next digit as required */
3130 if (--bitcnt == 0) {
3131 /* if digidx == -1 we are out of digits so break */
3132 if (digidx == -1) {
3133 break;
3134 }
3135 /* read next digit and reset bitcnt */
3136 buf = X->dp[digidx--];
3137 bitcnt = (int)DIGIT_BIT;
3138 }
3139
3140 /* grab the next msb from the exponent */
3141 y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
3142 buf <<= (mp_digit)1;
3143
3144 /* if the bit is zero and mode == 0 then we ignore it
3145 * These represent the leading zero bits before the first 1 bit
3146 * in the exponent. Technically this opt is not required but it
3147 * does lower the # of trivial squaring/reductions used
3148 */
3149 if (mode == 0 && y == 0) {
3150 continue;
3151 }
3152
3153 /* if the bit is zero and mode == 1 then we square */
3154 if (mode == 1 && y == 0) {
3155 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
3156 goto LBL_RES;
3157 }
3158 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3159 goto LBL_RES;
3160 }
3161 continue;
3162 }
3163
3164 /* else we add it to the window */
3165 bitbuf |= (y << (winsize - ++bitcpy));
3166 mode = 2;
3167
3168 if (bitcpy == winsize) {
3169 /* ok window is filled so square as required and multiply */
3170 /* square first */
3171 for (x = 0; x < winsize; x++) {
3172 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
3173 goto LBL_RES;
3174 }
3175 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3176 goto LBL_RES;
3177 }
3178 }
3179
3180 /* then multiply */
3181 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
3182 goto LBL_RES;
3183 }
3184 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3185 goto LBL_RES;
3186 }
3187
3188 /* empty window and reset */
3189 bitcpy = 0;
3190 bitbuf = 0;
3191 mode = 1;
3192 }
3193 }
3194
3195 /* if bits remain then square/multiply */
3196 if (mode == 2 && bitcpy > 0) {
3197 /* square then multiply if the bit is set */
3198 for (x = 0; x < bitcpy; x++) {
3199 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
3200 goto LBL_RES;
3201 }
3202 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3203 goto LBL_RES;
3204 }
3205
3206 /* get next bit of the window */
3207 bitbuf <<= 1;
3208 if ((bitbuf & (1 << winsize)) != 0) {
3209 /* then multiply */
3210 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
3211 goto LBL_RES;
3212 }
3213 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3214 goto LBL_RES;
3215 }
3216 }
3217 }
3218 }
3219
3220 if (redmode == 0) {
3221 /* fixup result if Montgomery reduction is used
3222 * recall that any value in a Montgomery system is
3223 * actually multiplied by R mod n. So we have
3224 * to reduce one more time to cancel out the factor
3225 * of R.
3226 */
3227 if ((err = redux(&res, P, mp)) != MP_OKAY) {
3228 goto LBL_RES;
3229 }
3230 }
3231
3232 /* swap res with Y */
3233 mp_exch (&res, Y);
3234 err = MP_OKAY;
3235 LBL_RES:mp_clear (&res);
3236 LBL_M:
3237 mp_clear(&M[1]);
3238 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
3239 mp_clear (&M[x]);
3240 }
3241 return err;
3242 }
3243 #endif
3244
3245
3246 #ifdef BN_FAST_S_MP_SQR_C
3247 /* the jist of squaring...
3248 * you do like mult except the offset of the tmpx [one that
3249 * starts closer to zero] can't equal the offset of tmpy.
3250 * So basically you set up iy like before then you min it with
3251 * (ty-tx) so that it never happens. You double all those
3252 * you add in the inner loop
3253
3254 After that loop you do the squares and add them in.
3255 */
3256
fast_s_mp_sqr(mp_int * a,mp_int * b)3257 static int fast_s_mp_sqr (mp_int * a, mp_int * b)
3258 {
3259 int olduse, res, pa, ix, iz;
3260 mp_digit W[MP_WARRAY], *tmpx;
3261 mp_word W1;
3262
3263 /* grow the destination as required */
3264 pa = a->used + a->used;
3265 if (b->alloc < pa) {
3266 if ((res = mp_grow (b, pa)) != MP_OKAY) {
3267 return res;
3268 }
3269 }
3270
3271 /* number of output digits to produce */
3272 W1 = 0;
3273 for (ix = 0; ix < pa; ix++) {
3274 int tx, ty, iy;
3275 mp_word _W;
3276 mp_digit *tmpy;
3277
3278 /* clear counter */
3279 _W = 0;
3280
3281 /* get offsets into the two bignums */
3282 ty = MIN(a->used-1, ix);
3283 tx = ix - ty;
3284
3285 /* setup temp aliases */
3286 tmpx = a->dp + tx;
3287 tmpy = a->dp + ty;
3288
3289 /* this is the number of times the loop will iterrate, essentially
3290 while (tx++ < a->used && ty-- >= 0) { ... }
3291 */
3292 iy = MIN(a->used-tx, ty+1);
3293
3294 /* now for squaring tx can never equal ty
3295 * we halve the distance since they approach at a rate of 2x
3296 * and we have to round because odd cases need to be executed
3297 */
3298 iy = MIN(iy, (ty-tx+1)>>1);
3299
3300 /* execute loop */
3301 for (iz = 0; iz < iy; iz++) {
3302 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
3303 }
3304
3305 /* double the inner product and add carry */
3306 _W = _W + _W + W1;
3307
3308 /* even columns have the square term in them */
3309 if ((ix&1) == 0) {
3310 _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
3311 }
3312
3313 /* store it */
3314 W[ix] = (mp_digit)(_W & MP_MASK);
3315
3316 /* make next carry */
3317 W1 = _W >> ((mp_word)DIGIT_BIT);
3318 }
3319
3320 /* setup dest */
3321 olduse = b->used;
3322 b->used = a->used+a->used;
3323
3324 {
3325 mp_digit *tmpb;
3326 tmpb = b->dp;
3327 for (ix = 0; ix < pa; ix++) {
3328 *tmpb++ = W[ix] & MP_MASK;
3329 }
3330
3331 /* clear unused digits [that existed in the old copy of c] */
3332 for (; ix < olduse; ix++) {
3333 *tmpb++ = 0;
3334 }
3335 }
3336 mp_clamp (b);
3337 return MP_OKAY;
3338 }
3339 #endif
3340
3341
3342 #ifdef BN_MP_MUL_D_C
3343 /* multiply by a digit */
3344 static int
mp_mul_d(mp_int * a,mp_digit b,mp_int * c)3345 mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
3346 {
3347 mp_digit u, *tmpa, *tmpc;
3348 mp_word r;
3349 int ix, res, olduse;
3350
3351 /* make sure c is big enough to hold a*b */
3352 if (c->alloc < a->used + 1) {
3353 if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
3354 return res;
3355 }
3356 }
3357
3358 /* get the original destinations used count */
3359 olduse = c->used;
3360
3361 /* set the sign */
3362 c->sign = a->sign;
3363
3364 /* alias for a->dp [source] */
3365 tmpa = a->dp;
3366
3367 /* alias for c->dp [dest] */
3368 tmpc = c->dp;
3369
3370 /* zero carry */
3371 u = 0;
3372
3373 /* compute columns */
3374 for (ix = 0; ix < a->used; ix++) {
3375 /* compute product and carry sum for this term */
3376 r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
3377
3378 /* mask off higher bits to get a single digit */
3379 *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
3380
3381 /* send carry into next iteration */
3382 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
3383 }
3384
3385 /* store final carry [if any] and increment ix offset */
3386 *tmpc++ = u;
3387 ++ix;
3388
3389 /* now zero digits above the top */
3390 while (ix++ < olduse) {
3391 *tmpc++ = 0;
3392 }
3393
3394 /* set used count */
3395 c->used = a->used + 1;
3396 mp_clamp(c);
3397
3398 return MP_OKAY;
3399 }
3400 #endif
3401