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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