2 * Minimal code for RSA support from LibTomMath 0.41
4 * http://libtom.org/files/ltm-0.41.tar.bz2
5 * This library was released in public domain by Tom St Denis.
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
13 * If CONFIG_INTERNAL_LIBTOMMATH is defined, bignum.c includes this
14 * libtommath.c file instead of using the external LibTomMath library.
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
27 #define BN_S_MP_MUL_HIGH_DIGS_C /* Note: #undef in tommath_superclass.h; this
28 * would require other than mp_reduce */
32 /* Use faster div at the cost of about 1 kB */
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
42 /* Include faster sqr at the cost of about 0.5 kB in code */
43 #define BN_FAST_S_MP_SQR_C
47 #define BN_MP_DIV_SMALL
48 #define BN_MP_INIT_MULTI_C
49 #define BN_MP_CLEAR_MULTI_C
53 /* Current uses do not require support for negative exponent in exptmod, so we
54 * can save about 1.5 kB in leaving out invmod. */
55 #define LTM_NO_NEG_EXP
60 #define MIN(x,y) ((x)<(y)?(x):(y))
64 #define MAX(x,y) ((x)>(y)?(x):(y))
69 typedef unsigned long mp_digit;
76 #define XMALLOC os_malloc
78 #define XREALLOC os_realloc
81 #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
83 #define MP_LT -1 /* less than */
84 #define MP_EQ 0 /* equal to */
85 #define MP_GT 1 /* greater than */
87 #define MP_ZPOS 0 /* positive integer */
88 #define MP_NEG 1 /* negative */
90 #define MP_OKAY 0 /* ok result */
91 #define MP_MEM -2 /* out of mem */
92 #define MP_VAL -3 /* invalid input */
94 #define MP_YES 1 /* yes response */
95 #define MP_NO 0 /* no response */
99 /* define this to use lower memory usage routines (exptmods mostly) */
102 /* default precision */
105 #define MP_PREC 32 /* default digits of precision */
107 #define MP_PREC 8 /* default digits of precision */
111 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
112 #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
114 /* the infamous mp_int structure */
116 int used, alloc, sign;
121 /* ---> Basic Manipulations <--- */
122 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
123 #define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
124 #define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
127 /* prototypes for copied functions */
128 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
129 static int s_mp_exptmod(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
130 static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
131 static int s_mp_sqr(mp_int * a, mp_int * b);
132 static int s_mp_mul_high_digs(mp_int * a, mp_int * b, mp_int * c, int digs);
134 static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
136 #ifdef BN_MP_INIT_MULTI_C
137 static int mp_init_multi(mp_int *mp, ...);
139 #ifdef BN_MP_CLEAR_MULTI_C
140 static void mp_clear_multi(mp_int *mp, ...);
142 static int mp_lshd(mp_int * a, int b);
143 static void mp_set(mp_int * a, mp_digit b);
144 static void mp_clamp(mp_int * a);
145 static void mp_exch(mp_int * a, mp_int * b);
146 static void mp_rshd(mp_int * a, int b);
147 static void mp_zero(mp_int * a);
148 static int mp_mod_2d(mp_int * a, int b, mp_int * c);
149 static int mp_div_2d(mp_int * a, int b, mp_int * c, mp_int * d);
150 static int mp_init_copy(mp_int * a, mp_int * b);
151 static int mp_mul_2d(mp_int * a, int b, mp_int * c);
152 #ifndef LTM_NO_NEG_EXP
153 static int mp_div_2(mp_int * a, mp_int * b);
154 static int mp_invmod(mp_int * a, mp_int * b, mp_int * c);
155 static int mp_invmod_slow(mp_int * a, mp_int * b, mp_int * c);
156 #endif /* LTM_NO_NEG_EXP */
157 static int mp_copy(mp_int * a, mp_int * b);
158 static int mp_count_bits(mp_int * a);
159 static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
160 static int mp_mod(mp_int * a, mp_int * b, mp_int * c);
161 static int mp_grow(mp_int * a, int size);
162 static int mp_cmp_mag(mp_int * a, mp_int * b);
164 static int mp_abs(mp_int * a, mp_int * b);
166 static int mp_sqr(mp_int * a, mp_int * b);
167 static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
168 static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
169 static int mp_2expt(mp_int * a, int b);
170 static int mp_reduce_setup(mp_int * a, mp_int * b);
171 static int mp_reduce(mp_int * x, mp_int * m, mp_int * mu);
172 static int mp_init_size(mp_int * a, int size);
173 #ifdef BN_MP_EXPTMOD_FAST_C
174 static int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
175 #endif /* BN_MP_EXPTMOD_FAST_C */
176 #ifdef BN_FAST_S_MP_SQR_C
177 static int fast_s_mp_sqr (mp_int * a, mp_int * b);
178 #endif /* BN_FAST_S_MP_SQR_C */
180 static int mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
181 #endif /* BN_MP_MUL_D_C */
185 /* functions from bn_<func name>.c */
188 /* reverse an array, used for radix code */
189 static void bn_reverse (unsigned char *s, int len)
206 /* low level addition, based on HAC pp.594, Algorithm 14.7 */
207 static int s_mp_add (mp_int * a, mp_int * b, mp_int * c)
210 int olduse, res, min, max;
212 /* find sizes, we let |a| <= |b| which means we have to sort
213 * them. "x" will point to the input with the most digits
215 if (a->used > b->used) {
226 if (c->alloc < max + 1) {
227 if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
232 /* get old used digit count and set new one */
237 register mp_digit u, *tmpa, *tmpb, *tmpc;
240 /* alias for digit pointers */
253 for (i = 0; i < min; i++) {
254 /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
255 *tmpc = *tmpa++ + *tmpb++ + u;
257 /* U = carry bit of T[i] */
258 u = *tmpc >> ((mp_digit)DIGIT_BIT);
260 /* take away carry bit from T[i] */
264 /* now copy higher words if any, that is in A+B
265 * if A or B has more digits add those in
268 for (; i < max; i++) {
269 /* T[i] = X[i] + U */
270 *tmpc = x->dp[i] + u;
272 /* U = carry bit of T[i] */
273 u = *tmpc >> ((mp_digit)DIGIT_BIT);
275 /* take away carry bit from T[i] */
283 /* clear digits above oldused */
284 for (i = c->used; i < olduse; i++) {
294 /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
295 static int s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
297 int olduse, res, min, max;
304 if (c->alloc < max) {
305 if ((res = mp_grow (c, max)) != MP_OKAY) {
313 register mp_digit u, *tmpa, *tmpb, *tmpc;
316 /* alias for digit pointers */
321 /* set carry to zero */
323 for (i = 0; i < min; i++) {
324 /* T[i] = A[i] - B[i] - U */
325 *tmpc = *tmpa++ - *tmpb++ - u;
327 /* U = carry bit of T[i]
328 * Note this saves performing an AND operation since
329 * if a carry does occur it will propagate all the way to the
330 * MSB. As a result a single shift is enough to get the carry
332 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
334 /* Clear carry from T[i] */
338 /* now copy higher words if any, e.g. if A has more digits than B */
339 for (; i < max; i++) {
340 /* T[i] = A[i] - U */
343 /* U = carry bit of T[i] */
344 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
346 /* Clear carry from T[i] */
350 /* clear digits above used (since we may not have grown result above) */
351 for (i = c->used; i < olduse; i++) {
361 /* init a new mp_int */
362 static int mp_init (mp_int * a)
366 /* allocate memory required and clear it */
367 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
372 /* set the digits to zero */
373 for (i = 0; i < MP_PREC; i++) {
377 /* set the used to zero, allocated digits to the default precision
378 * and sign to positive */
387 /* clear one (frees) */
388 static void mp_clear (mp_int * a)
392 /* only do anything if a hasn't been freed previously */
394 /* first zero the digits */
395 for (i = 0; i < a->used; i++) {
402 /* reset members to make debugging easier */
404 a->alloc = a->used = 0;
410 /* high level addition (handles signs) */
411 static int mp_add (mp_int * a, mp_int * b, mp_int * c)
415 /* get sign of both inputs */
419 /* handle two cases, not four */
421 /* both positive or both negative */
422 /* add their magnitudes, copy the sign */
424 res = s_mp_add (a, b, c);
426 /* one positive, the other negative */
427 /* subtract the one with the greater magnitude from */
428 /* the one of the lesser magnitude. The result gets */
429 /* the sign of the one with the greater magnitude. */
430 if (mp_cmp_mag (a, b) == MP_LT) {
432 res = s_mp_sub (b, a, c);
435 res = s_mp_sub (a, b, c);
442 /* high level subtraction (handles signs) */
443 static int mp_sub (mp_int * a, mp_int * b, mp_int * c)
451 /* subtract a negative from a positive, OR */
452 /* subtract a positive from a negative. */
453 /* In either case, ADD their magnitudes, */
454 /* and use the sign of the first number. */
456 res = s_mp_add (a, b, c);
458 /* subtract a positive from a positive, OR */
459 /* subtract a negative from a negative. */
460 /* First, take the difference between their */
461 /* magnitudes, then... */
462 if (mp_cmp_mag (a, b) != MP_LT) {
463 /* Copy the sign from the first */
465 /* The first has a larger or equal magnitude */
466 res = s_mp_sub (a, b, c);
468 /* The result has the *opposite* sign from */
469 /* the first number. */
470 c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
471 /* The second has a larger magnitude */
472 res = s_mp_sub (b, a, c);
479 /* high level multiplication (handles sign) */
480 static int mp_mul (mp_int * a, mp_int * b, mp_int * c)
483 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
486 #ifdef BN_MP_TOOM_MUL_C
487 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
488 res = mp_toom_mul(a, b, c);
491 #ifdef BN_MP_KARATSUBA_MUL_C
493 if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
494 res = mp_karatsuba_mul (a, b, c);
498 /* can we use the fast multiplier?
500 * The fast multiplier can be used if the output will
501 * have less than MP_WARRAY digits and the number of
502 * digits won't affect carry propagation
504 #ifdef BN_FAST_S_MP_MUL_DIGS_C
505 int digs = a->used + b->used + 1;
507 if ((digs < MP_WARRAY) &&
508 MIN(a->used, b->used) <=
509 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
510 res = fast_s_mp_mul_digs (a, b, c, digs);
513 #ifdef BN_S_MP_MUL_DIGS_C
514 res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
516 #error mp_mul could fail
521 c->sign = (c->used > 0) ? neg : MP_ZPOS;
526 /* d = a * b (mod c) */
527 static int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
532 if ((res = mp_init (&t)) != MP_OKAY) {
536 if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
540 res = mp_mod (&t, c, d);
546 /* c = a mod b, 0 <= c < b */
547 static int mp_mod (mp_int * a, mp_int * b, mp_int * c)
552 if ((res = mp_init (&t)) != MP_OKAY) {
556 if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
561 if (t.sign != b->sign) {
562 res = mp_add (b, &t, c);
573 /* this is a shell function that calls either the normal or Montgomery
574 * exptmod functions. Originally the call to the montgomery code was
575 * embedded in the normal function but that wasted alot of stack space
576 * for nothing (since 99% of the time the Montgomery code would be called)
578 static int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
582 /* modulus P must be positive */
583 if (P->sign == MP_NEG) {
587 /* if exponent X is negative we have to recurse */
588 if (X->sign == MP_NEG) {
589 #ifdef LTM_NO_NEG_EXP
591 #else /* LTM_NO_NEG_EXP */
592 #ifdef BN_MP_INVMOD_C
596 /* first compute 1/G mod P */
597 if ((err = mp_init(&tmpG)) != MP_OKAY) {
600 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
606 if ((err = mp_init(&tmpX)) != MP_OKAY) {
610 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
611 mp_clear_multi(&tmpG, &tmpX, NULL);
615 /* and now compute (1/G)**|X| instead of G**X [X < 0] */
616 err = mp_exptmod(&tmpG, &tmpX, P, Y);
617 mp_clear_multi(&tmpG, &tmpX, NULL);
620 #error mp_exptmod would always fail
624 #endif /* LTM_NO_NEG_EXP */
627 /* modified diminished radix reduction */
628 #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
629 if (mp_reduce_is_2k_l(P) == MP_YES) {
630 return s_mp_exptmod(G, X, P, Y, 1);
634 #ifdef BN_MP_DR_IS_MODULUS_C
635 /* is it a DR modulus? */
636 dr = mp_dr_is_modulus(P);
642 #ifdef BN_MP_REDUCE_IS_2K_C
643 /* if not, is it a unrestricted DR modulus? */
645 dr = mp_reduce_is_2k(P) << 1;
649 /* if the modulus is odd or dr != 0 use the montgomery method */
650 #ifdef BN_MP_EXPTMOD_FAST_C
651 if (mp_isodd (P) == 1 || dr != 0) {
652 return mp_exptmod_fast (G, X, P, Y, dr);
655 #ifdef BN_S_MP_EXPTMOD_C
656 /* otherwise use the generic Barrett reduction technique */
657 return s_mp_exptmod (G, X, P, Y, 0);
659 #error mp_exptmod could fail
660 /* no exptmod for evens */
663 #ifdef BN_MP_EXPTMOD_FAST_C
669 /* compare two ints (signed)*/
670 static int mp_cmp (mp_int * a, mp_int * b)
672 /* compare based on sign */
673 if (a->sign != b->sign) {
674 if (a->sign == MP_NEG) {
682 if (a->sign == MP_NEG) {
683 /* if negative compare opposite direction */
684 return mp_cmp_mag(b, a);
686 return mp_cmp_mag(a, b);
691 /* compare a digit */
692 static int mp_cmp_d(mp_int * a, mp_digit b)
694 /* compare based on sign */
695 if (a->sign == MP_NEG) {
699 /* compare based on magnitude */
704 /* compare the only digit of a to b */
707 } else if (a->dp[0] < b) {
715 #ifndef LTM_NO_NEG_EXP
716 /* hac 14.61, pp608 */
717 static int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
719 /* b cannot be negative */
720 if (b->sign == MP_NEG || mp_iszero(b) == 1) {
724 #ifdef BN_FAST_MP_INVMOD_C
725 /* if the modulus is odd we can use a faster routine instead */
726 if (mp_isodd (b) == 1) {
727 return fast_mp_invmod (a, b, c);
731 #ifdef BN_MP_INVMOD_SLOW_C
732 return mp_invmod_slow(a, b, c);
735 #ifndef BN_FAST_MP_INVMOD_C
736 #ifndef BN_MP_INVMOD_SLOW_C
737 #error mp_invmod would always fail
742 #endif /* LTM_NO_NEG_EXP */
745 /* get the size for an unsigned equivalent */
746 static int mp_unsigned_bin_size (mp_int * a)
748 int size = mp_count_bits (a);
749 return (size / 8 + ((size & 7) != 0 ? 1 : 0));
753 #ifndef LTM_NO_NEG_EXP
754 /* hac 14.61, pp608 */
755 static int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
757 mp_int x, y, u, v, A, B, C, D;
760 /* b cannot be negative */
761 if (b->sign == MP_NEG || mp_iszero(b) == 1) {
766 if ((res = mp_init_multi(&x, &y, &u, &v,
767 &A, &B, &C, &D, NULL)) != MP_OKAY) {
772 if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
775 if ((res = mp_copy (b, &y)) != MP_OKAY) {
779 /* 2. [modified] if x,y are both even then return an error! */
780 if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
785 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
786 if ((res = mp_copy (&x, &u)) != MP_OKAY) {
789 if ((res = mp_copy (&y, &v)) != MP_OKAY) {
796 /* 4. while u is even do */
797 while (mp_iseven (&u) == 1) {
799 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
802 /* 4.2 if A or B is odd then */
803 if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
804 /* A = (A+y)/2, B = (B-x)/2 */
805 if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
808 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
812 /* A = A/2, B = B/2 */
813 if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
816 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
821 /* 5. while v is even do */
822 while (mp_iseven (&v) == 1) {
824 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
827 /* 5.2 if C or D is odd then */
828 if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
829 /* C = (C+y)/2, D = (D-x)/2 */
830 if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
833 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
837 /* C = C/2, D = D/2 */
838 if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
841 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
846 /* 6. if u >= v then */
847 if (mp_cmp (&u, &v) != MP_LT) {
848 /* u = u - v, A = A - C, B = B - D */
849 if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
853 if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
857 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
861 /* v - v - u, C = C - A, D = D - B */
862 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
866 if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
870 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
875 /* if not zero goto step 4 */
876 if (mp_iszero (&u) == 0)
879 /* now a = C, b = D, gcd == g*v */
881 /* if v != 1 then there is no inverse */
882 if (mp_cmp_d (&v, 1) != MP_EQ) {
888 while (mp_cmp_d(&C, 0) == MP_LT) {
889 if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
895 while (mp_cmp_mag(&C, b) != MP_LT) {
896 if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
901 /* C is now the inverse */
904 LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
907 #endif /* LTM_NO_NEG_EXP */
910 /* compare maginitude of two ints (unsigned) */
911 static int mp_cmp_mag (mp_int * a, mp_int * b)
914 mp_digit *tmpa, *tmpb;
916 /* compare based on # of non-zero digits */
917 if (a->used > b->used) {
921 if (a->used < b->used) {
926 tmpa = a->dp + (a->used - 1);
929 tmpb = b->dp + (a->used - 1);
931 /* compare based on digits */
932 for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
945 /* reads a unsigned char array, assumes the msb is stored first [big endian] */
946 static int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
950 /* make sure there are at least two digits */
952 if ((res = mp_grow(a, 2)) != MP_OKAY) {
960 /* read the bytes in */
962 if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
970 a->dp[0] = (*b & MP_MASK);
971 a->dp[1] |= ((*b++ >> 7U) & 1);
980 /* store in unsigned [big endian] format */
981 static int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
986 if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
991 while (mp_iszero (&t) == 0) {
993 b[x++] = (unsigned char) (t.dp[0] & 255);
995 b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
997 if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
1008 /* shift right by a certain bit count (store quotient in c, optional remainder in d) */
1009 static int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
1016 /* if the shift count is <= 0 then we do no work */
1018 res = mp_copy (a, c);
1025 if ((res = mp_init (&t)) != MP_OKAY) {
1029 /* get the remainder */
1031 if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
1038 if ((res = mp_copy (a, c)) != MP_OKAY) {
1043 /* shift by as many digits in the bit count */
1044 if (b >= (int)DIGIT_BIT) {
1045 mp_rshd (c, b / DIGIT_BIT);
1048 /* shift any bit count < DIGIT_BIT */
1049 D = (mp_digit) (b % DIGIT_BIT);
1051 register mp_digit *tmpc, mask, shift;
1054 mask = (((mp_digit)1) << D) - 1;
1057 shift = DIGIT_BIT - D;
1060 tmpc = c->dp + (c->used - 1);
1064 for (x = c->used - 1; x >= 0; x--) {
1065 /* get the lower bits of this word in a temp */
1068 /* shift the current word and mix in the carry bits from the previous word */
1069 *tmpc = (*tmpc >> D) | (r << shift);
1072 /* set the carry to the carry bits of the current word found above */
1085 static int mp_init_copy (mp_int * a, mp_int * b)
1089 if ((res = mp_init (a)) != MP_OKAY) {
1092 return mp_copy (b, a);
1097 static void mp_zero (mp_int * a)
1106 for (n = 0; n < a->alloc; n++) {
1113 static int mp_copy (mp_int * a, mp_int * b)
1117 /* if dst == src do nothing */
1123 if (b->alloc < a->used) {
1124 if ((res = mp_grow (b, a->used)) != MP_OKAY) {
1129 /* zero b and copy the parameters over */
1131 register mp_digit *tmpa, *tmpb;
1133 /* pointer aliases */
1141 /* copy all the digits */
1142 for (n = 0; n < a->used; n++) {
1146 /* clear high digits */
1147 for (; n < b->used; n++) {
1152 /* copy used count and sign */
1159 /* shift right a certain amount of digits */
1160 static void mp_rshd (mp_int * a, int b)
1164 /* if b <= 0 then ignore it */
1169 /* if b > used then simply zero it and return */
1176 register mp_digit *bottom, *top;
1178 /* shift the digits down */
1183 /* top [offset into digits] */
1186 /* this is implemented as a sliding window where
1187 * the window is b-digits long and digits from
1188 * the top of the window are copied to the bottom
1192 b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
1194 \-------------------/ ---->
1196 for (x = 0; x < (a->used - b); x++) {
1200 /* zero the top digits */
1201 for (; x < a->used; x++) {
1206 /* remove excess digits */
1211 /* swap the elements of two integers, for cases where you can't simply swap the
1212 * mp_int pointers around
1214 static void mp_exch (mp_int * a, mp_int * b)
1224 /* trim unused digits
1226 * This is used to ensure that leading zero digits are
1227 * trimed and the leading "used" digit will be non-zero
1228 * Typically very fast. Also fixes the sign if there
1229 * are no more leading digits
1231 static void mp_clamp (mp_int * a)
1233 /* decrease used while the most significant digit is
1236 while (a->used > 0 && a->dp[a->used - 1] == 0) {
1240 /* reset the sign flag if used == 0 */
1247 /* grow as required */
1248 static int mp_grow (mp_int * a, int size)
1253 /* if the alloc size is smaller alloc more ram */
1254 if (a->alloc < size) {
1255 /* ensure there are always at least MP_PREC digits extra on top */
1256 size += (MP_PREC * 2) - (size % MP_PREC);
1258 /* reallocate the array a->dp
1260 * We store the return in a temporary variable
1261 * in case the operation failed we don't want
1262 * to overwrite the dp member of a.
1264 tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
1266 /* reallocation failed but "a" is still valid [can be freed] */
1270 /* reallocation succeeded so set a->dp */
1273 /* zero excess digits */
1276 for (; i < a->alloc; i++) {
1287 * Simple function copies the input and fixes the sign to positive
1289 static int mp_abs (mp_int * a, mp_int * b)
1295 if ((res = mp_copy (a, b)) != MP_OKAY) {
1300 /* force the sign of b to positive */
1308 /* set to a digit */
1309 static void mp_set (mp_int * a, mp_digit b)
1312 a->dp[0] = b & MP_MASK;
1313 a->used = (a->dp[0] != 0) ? 1 : 0;
1317 #ifndef LTM_NO_NEG_EXP
1319 static int mp_div_2(mp_int * a, mp_int * b)
1321 int x, res, oldused;
1324 if (b->alloc < a->used) {
1325 if ((res = mp_grow (b, a->used)) != MP_OKAY) {
1333 register mp_digit r, rr, *tmpa, *tmpb;
1336 tmpa = a->dp + b->used - 1;
1339 tmpb = b->dp + b->used - 1;
1343 for (x = b->used - 1; x >= 0; x--) {
1344 /* get the carry for the next iteration */
1347 /* shift the current digit, add in carry and store */
1348 *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
1350 /* forward carry to next iteration */
1354 /* zero excess digits */
1355 tmpb = b->dp + b->used;
1356 for (x = b->used; x < oldused; x++) {
1364 #endif /* LTM_NO_NEG_EXP */
1367 /* shift left by a certain bit count */
1368 static int mp_mul_2d (mp_int * a, int b, mp_int * c)
1375 if ((res = mp_copy (a, c)) != MP_OKAY) {
1380 if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
1381 if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
1386 /* shift by as many digits in the bit count */
1387 if (b >= (int)DIGIT_BIT) {
1388 if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
1393 /* shift any bit count < DIGIT_BIT */
1394 d = (mp_digit) (b % DIGIT_BIT);
1396 register mp_digit *tmpc, shift, mask, r, rr;
1399 /* bitmask for carries */
1400 mask = (((mp_digit)1) << d) - 1;
1402 /* shift for msbs */
1403 shift = DIGIT_BIT - d;
1410 for (x = 0; x < c->used; x++) {
1411 /* get the higher bits of the current word */
1412 rr = (*tmpc >> shift) & mask;
1414 /* shift the current word and OR in the carry */
1415 *tmpc = ((*tmpc << d) | r) & MP_MASK;
1418 /* set the carry to the carry bits of the current word */
1422 /* set final carry */
1424 c->dp[(c->used)++] = r;
1432 #ifdef BN_MP_INIT_MULTI_C
1433 static int mp_init_multi(mp_int *mp, ...)
1435 mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
1436 int n = 0; /* Number of ok inits */
1437 mp_int* cur_arg = mp;
1440 va_start(args, mp); /* init args to next argument from caller */
1441 while (cur_arg != NULL) {
1442 if (mp_init(cur_arg) != MP_OKAY) {
1443 /* Oops - error! Back-track and mp_clear what we already
1444 succeeded in init-ing, then return error.
1448 /* end the current list */
1451 /* now start cleaning up */
1453 va_start(clean_args, mp);
1456 cur_arg = va_arg(clean_args, mp_int*);
1463 cur_arg = va_arg(args, mp_int*);
1466 return res; /* Assumed ok, if error flagged above. */
1471 #ifdef BN_MP_CLEAR_MULTI_C
1472 static void mp_clear_multi(mp_int *mp, ...)
1474 mp_int* next_mp = mp;
1477 while (next_mp != NULL) {
1479 next_mp = va_arg(args, mp_int*);
1486 /* shift left a certain amount of digits */
1487 static int mp_lshd (mp_int * a, int b)
1491 /* if its less than zero return */
1496 /* grow to fit the new digits */
1497 if (a->alloc < a->used + b) {
1498 if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
1504 register mp_digit *top, *bottom;
1506 /* increment the used by the shift amount then copy upwards */
1510 top = a->dp + a->used - 1;
1513 bottom = a->dp + a->used - 1 - b;
1515 /* much like mp_rshd this is implemented using a sliding window
1516 * except the window goes the otherway around. Copying from
1517 * the bottom to the top. see bn_mp_rshd.c for more info.
1519 for (x = a->used - 1; x >= b; x--) {
1523 /* zero the lower digits */
1525 for (x = 0; x < b; x++) {
1533 /* returns the number of bits in an int */
1534 static int mp_count_bits (mp_int * a)
1544 /* get number of digits and add that */
1545 r = (a->used - 1) * DIGIT_BIT;
1547 /* take the last digit and count the bits in it */
1548 q = a->dp[a->used - 1];
1549 while (q > ((mp_digit) 0)) {
1551 q >>= ((mp_digit) 1);
1557 /* calc a value mod 2**b */
1558 static int mp_mod_2d (mp_int * a, int b, mp_int * c)
1562 /* if b is <= 0 then zero the int */
1568 /* if the modulus is larger than the value than return */
1569 if (b >= (int) (a->used * DIGIT_BIT)) {
1570 res = mp_copy (a, c);
1575 if ((res = mp_copy (a, c)) != MP_OKAY) {
1579 /* zero digits above the last digit of the modulus */
1580 for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
1583 /* clear the digit that is not completely outside/inside the modulus */
1584 c->dp[b / DIGIT_BIT] &=
1585 (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
1591 #ifdef BN_MP_DIV_SMALL
1593 /* slower bit-bang division... also smaller */
1594 static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
1596 mp_int ta, tb, tq, q;
1599 /* is divisor zero ? */
1600 if (mp_iszero (b) == 1) {
1604 /* if a < b then q=0, r = a */
1605 if (mp_cmp_mag (a, b) == MP_LT) {
1607 res = mp_copy (a, d);
1617 /* init our temps */
1618 if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
1624 n = mp_count_bits(a) - mp_count_bits(b);
1625 if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
1626 ((res = mp_abs(b, &tb)) != MP_OKAY) ||
1627 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
1628 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
1633 if (mp_cmp(&tb, &ta) != MP_GT) {
1634 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
1635 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
1639 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
1640 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
1645 /* now q == quotient and ta == remainder */
1647 n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
1650 c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
1654 d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
1657 mp_clear_multi(&ta, &tb, &tq, &q, NULL);
1663 /* integer signed division.
1664 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
1665 * HAC pp.598 Algorithm 14.20
1667 * Note that the description in HAC is horribly
1668 * incomplete. For example, it doesn't consider
1669 * the case where digits are removed from 'x' in
1670 * the inner loop. It also doesn't consider the
1671 * case that y has fewer than three digits, etc..
1673 * The overall algorithm is as described as
1674 * 14.20 from HAC but fixed to treat these cases.
1676 static int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
1678 mp_int q, x, y, t1, t2;
1679 int res, n, t, i, norm, neg;
1681 /* is divisor zero ? */
1682 if (mp_iszero (b) == 1) {
1686 /* if a < b then q=0, r = a */
1687 if (mp_cmp_mag (a, b) == MP_LT) {
1689 res = mp_copy (a, d);
1699 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
1702 q.used = a->used + 2;
1704 if ((res = mp_init (&t1)) != MP_OKAY) {
1708 if ((res = mp_init (&t2)) != MP_OKAY) {
1712 if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
1716 if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
1721 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
1722 x.sign = y.sign = MP_ZPOS;
1724 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
1725 norm = mp_count_bits(&y) % DIGIT_BIT;
1726 if (norm < (int)(DIGIT_BIT-1)) {
1727 norm = (DIGIT_BIT-1) - norm;
1728 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
1731 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
1738 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
1742 /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
1743 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
1747 while (mp_cmp (&x, &y) != MP_LT) {
1749 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
1754 /* reset y by shifting it back down */
1755 mp_rshd (&y, n - t);
1757 /* step 3. for i from n down to (t + 1) */
1758 for (i = n; i >= (t + 1); i--) {
1763 /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
1764 * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
1765 if (x.dp[i] == y.dp[t]) {
1766 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
1769 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
1770 tmp |= ((mp_word) x.dp[i - 1]);
1771 tmp /= ((mp_word) y.dp[t]);
1772 if (tmp > (mp_word) MP_MASK)
1774 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
1777 /* while (q{i-t-1} * (yt * b + y{t-1})) >
1778 xi * b**2 + xi-1 * b + xi-2
1782 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
1784 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
1786 /* find left hand */
1788 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
1791 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
1795 /* find right hand */
1796 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
1797 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
1800 } while (mp_cmp_mag(&t1, &t2) == MP_GT);
1802 /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
1803 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
1807 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
1811 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
1815 /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
1816 if (x.sign == MP_NEG) {
1817 if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
1820 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
1823 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
1827 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
1831 /* now q is the quotient and x is the remainder
1832 * [which we have to normalize]
1835 /* get sign before writing to c */
1836 x.sign = x.used == 0 ? MP_ZPOS : a->sign;
1845 mp_div_2d (&x, norm, &x, NULL);
1851 LBL_Y:mp_clear (&y);
1852 LBL_X:mp_clear (&x);
1853 LBL_T2:mp_clear (&t2);
1854 LBL_T1:mp_clear (&t1);
1855 LBL_Q:mp_clear (&q);
1865 #define TAB_SIZE 256
1868 static int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
1870 mp_int M[TAB_SIZE], res, mu;
1872 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
1873 int (*redux)(mp_int*,mp_int*,mp_int*);
1875 /* find window size */
1876 x = mp_count_bits (X);
1879 } else if (x <= 36) {
1881 } else if (x <= 140) {
1883 } else if (x <= 450) {
1885 } else if (x <= 1303) {
1887 } else if (x <= 3529) {
1900 /* init first cell */
1901 if ((err = mp_init(&M[1])) != MP_OKAY) {
1905 /* now init the second half of the array */
1906 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
1907 if ((err = mp_init(&M[x])) != MP_OKAY) {
1908 for (y = 1<<(winsize-1); y < x; y++) {
1916 /* create mu, used for Barrett reduction */
1917 if ((err = mp_init (&mu)) != MP_OKAY) {
1922 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
1927 if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
1930 redux = mp_reduce_2k_l;
1935 * The M table contains powers of the base,
1936 * e.g. M[x] = G**x mod P
1938 * The first half of the table is not
1939 * computed though accept for M[0] and M[1]
1941 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
1945 /* compute the value at M[1<<(winsize-1)] by squaring
1946 * M[1] (winsize-1) times
1948 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
1952 for (x = 0; x < (winsize - 1); x++) {
1954 if ((err = mp_sqr (&M[1 << (winsize - 1)],
1955 &M[1 << (winsize - 1)])) != MP_OKAY) {
1959 /* reduce modulo P */
1960 if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
1965 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
1966 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
1968 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
1969 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
1972 if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
1978 if ((err = mp_init (&res)) != MP_OKAY) {
1983 /* set initial mode and bit cnt */
1987 digidx = X->used - 1;
1992 /* grab next digit as required */
1993 if (--bitcnt == 0) {
1994 /* if digidx == -1 we are out of digits */
1998 /* read next digit and reset the bitcnt */
1999 buf = X->dp[digidx--];
2000 bitcnt = (int) DIGIT_BIT;
2003 /* grab the next msb from the exponent */
2004 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
2005 buf <<= (mp_digit)1;
2007 /* if the bit is zero and mode == 0 then we ignore it
2008 * These represent the leading zero bits before the first 1 bit
2009 * in the exponent. Technically this opt is not required but it
2010 * does lower the # of trivial squaring/reductions used
2012 if (mode == 0 && y == 0) {
2016 /* if the bit is zero and mode == 1 then we square */
2017 if (mode == 1 && y == 0) {
2018 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2021 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2027 /* else we add it to the window */
2028 bitbuf |= (y << (winsize - ++bitcpy));
2031 if (bitcpy == winsize) {
2032 /* ok window is filled so square as required and multiply */
2034 for (x = 0; x < winsize; x++) {
2035 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2038 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2044 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
2047 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2051 /* empty window and reset */
2058 /* if bits remain then square/multiply */
2059 if (mode == 2 && bitcpy > 0) {
2060 /* square then multiply if the bit is set */
2061 for (x = 0; x < bitcpy; x++) {
2062 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2065 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2070 if ((bitbuf & (1 << winsize)) != 0) {
2072 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
2075 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2084 LBL_RES:mp_clear (&res);
2085 LBL_MU:mp_clear (&mu);
2088 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
2095 /* computes b = a*a */
2096 static int mp_sqr (mp_int * a, mp_int * b)
2100 #ifdef BN_MP_TOOM_SQR_C
2101 /* use Toom-Cook? */
2102 if (a->used >= TOOM_SQR_CUTOFF) {
2103 res = mp_toom_sqr(a, b);
2107 #ifdef BN_MP_KARATSUBA_SQR_C
2108 if (a->used >= KARATSUBA_SQR_CUTOFF) {
2109 res = mp_karatsuba_sqr (a, b);
2113 #ifdef BN_FAST_S_MP_SQR_C
2114 /* can we use the fast comba multiplier? */
2115 if ((a->used * 2 + 1) < MP_WARRAY &&
2117 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
2118 res = fast_s_mp_sqr (a, b);
2121 #ifdef BN_S_MP_SQR_C
2122 res = s_mp_sqr (a, b);
2124 #error mp_sqr could fail
2133 /* reduces a modulo n where n is of the form 2**p - d
2134 This differs from reduce_2k since "d" can be larger
2135 than a single digit.
2137 static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
2142 if ((res = mp_init(&q)) != MP_OKAY) {
2146 p = mp_count_bits(n);
2148 /* q = a/2**p, a = a mod 2**p */
2149 if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
2154 if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
2159 if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
2163 if (mp_cmp_mag(a, n) != MP_LT) {
2174 /* determines the setup value */
2175 static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
2180 if ((res = mp_init(&tmp)) != MP_OKAY) {
2184 if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
2188 if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
2198 /* computes a = 2**b
2200 * Simple algorithm which zeroes the int, grows it then just sets one bit
2203 static int mp_2expt (mp_int * a, int b)
2207 /* zero a as per default */
2210 /* grow a to accomodate the single bit */
2211 if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
2215 /* set the used count of where the bit will go */
2216 a->used = b / DIGIT_BIT + 1;
2218 /* put the single bit in its place */
2219 a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
2225 /* pre-calculate the value required for Barrett reduction
2226 * For a given modulus "b" it calulates the value required in "a"
2228 static int mp_reduce_setup (mp_int * a, mp_int * b)
2232 if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
2235 return mp_div (a, b, a, NULL);
2239 /* reduces x mod m, assumes 0 < x < m**2, mu is
2240 * precomputed via mp_reduce_setup.
2241 * From HAC pp.604 Algorithm 14.42
2243 static int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
2246 int res, um = m->used;
2249 if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
2253 /* q1 = x / b**(k-1) */
2254 mp_rshd (&q, um - 1);
2256 /* according to HAC this optimization is ok */
2257 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
2258 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
2262 #ifdef BN_S_MP_MUL_HIGH_DIGS_C
2263 if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
2266 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
2267 if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
2272 #error mp_reduce would always fail
2279 /* q3 = q2 / b**(k+1) */
2280 mp_rshd (&q, um + 1);
2282 /* x = x mod b**(k+1), quick (no division) */
2283 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
2287 /* q = q * m mod b**(k+1), quick (no division) */
2288 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
2293 if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
2297 /* If x < 0, add b**(k+1) to it */
2298 if (mp_cmp_d (x, 0) == MP_LT) {
2300 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) {
2303 if ((res = mp_add (x, &q, x)) != MP_OKAY) {
2308 /* Back off if it's too big */
2309 while (mp_cmp (x, m) != MP_LT) {
2310 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
2322 /* multiplies |a| * |b| and only computes upto digs digits of result
2323 * HAC pp. 595, Algorithm 14.12 Modified so you can control how
2324 * many digits of output are created.
2326 static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2329 int res, pa, pb, ix, iy;
2332 mp_digit tmpx, *tmpt, *tmpy;
2334 /* can we use the fast multiplier? */
2335 if (((digs) < MP_WARRAY) &&
2336 MIN (a->used, b->used) <
2337 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
2338 return fast_s_mp_mul_digs (a, b, c, digs);
2341 if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
2346 /* compute the digits of the product directly */
2348 for (ix = 0; ix < pa; ix++) {
2349 /* set the carry to zero */
2352 /* limit ourselves to making digs digits of output */
2353 pb = MIN (b->used, digs - ix);
2355 /* setup some aliases */
2356 /* copy of the digit from a used within the nested loop */
2359 /* an alias for the destination shifted ix places */
2362 /* an alias for the digits of b */
2365 /* compute the columns of the output and propagate the carry */
2366 for (iy = 0; iy < pb; iy++) {
2367 /* compute the column as a mp_word */
2368 r = ((mp_word)*tmpt) +
2369 ((mp_word)tmpx) * ((mp_word)*tmpy++) +
2372 /* the new column is the lower part of the result */
2373 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2375 /* get the carry word from the result */
2376 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
2378 /* set carry if it is placed below digs */
2379 if (ix + iy < digs) {
2392 /* Fast (comba) multiplier
2394 * This is the fast column-array [comba] multiplier. It is
2395 * designed to compute the columns of the product first
2396 * then handle the carries afterwards. This has the effect
2397 * of making the nested loops that compute the columns very
2398 * simple and schedulable on super-scalar processors.
2400 * This has been modified to produce a variable number of
2401 * digits of output so if say only a half-product is required
2402 * you don't have to compute the upper half (a feature
2403 * required for fast Barrett reduction).
2405 * Based on Algorithm 14.12 on pp.595 of HAC.
2408 static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2410 int olduse, res, pa, ix, iz;
2411 mp_digit W[MP_WARRAY];
2412 register mp_word _W;
2414 /* grow the destination as required */
2415 if (c->alloc < digs) {
2416 if ((res = mp_grow (c, digs)) != MP_OKAY) {
2421 /* number of output digits to produce */
2422 pa = MIN(digs, a->used + b->used);
2424 /* clear the carry */
2426 for (ix = 0; ix < pa; ix++) {
2429 mp_digit *tmpx, *tmpy;
2431 /* get offsets into the two bignums */
2432 ty = MIN(b->used-1, ix);
2435 /* setup temp aliases */
2439 /* this is the number of times the loop will iterrate, essentially
2440 while (tx++ < a->used && ty-- >= 0) { ... }
2442 iy = MIN(a->used-tx, ty+1);
2445 for (iz = 0; iz < iy; ++iz) {
2446 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
2451 W[ix] = ((mp_digit)_W) & MP_MASK;
2453 /* make next carry */
2454 _W = _W >> ((mp_word)DIGIT_BIT);
2462 register mp_digit *tmpc;
2464 for (ix = 0; ix < pa+1; ix++) {
2465 /* now extract the previous digit [below the carry] */
2469 /* clear unused digits [that existed in the old copy of c] */
2470 for (; ix < olduse; ix++) {
2479 /* init an mp_init for a given size */
2480 static int mp_init_size (mp_int * a, int size)
2484 /* pad size so there are always extra digits */
2485 size += (MP_PREC * 2) - (size % MP_PREC);
2488 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
2489 if (a->dp == NULL) {
2493 /* set the members */
2498 /* zero the digits */
2499 for (x = 0; x < size; x++) {
2507 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
2508 static int s_mp_sqr (mp_int * a, mp_int * b)
2511 int res, ix, iy, pa;
2513 mp_digit u, tmpx, *tmpt;
2516 if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
2520 /* default used is maximum possible size */
2523 for (ix = 0; ix < pa; ix++) {
2524 /* first calculate the digit at 2*ix */
2525 /* calculate double precision result */
2526 r = ((mp_word) t.dp[2*ix]) +
2527 ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
2529 /* store lower part in result */
2530 t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
2533 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2535 /* left hand side of A[ix] * A[iy] */
2538 /* alias for where to store the results */
2539 tmpt = t.dp + (2*ix + 1);
2541 for (iy = ix + 1; iy < pa; iy++) {
2542 /* first calculate the product */
2543 r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
2545 /* now calculate the double precision result, note we use
2546 * addition instead of *2 since it's easier to optimize
2548 r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
2550 /* store lower part */
2551 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2554 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2556 /* propagate upwards */
2557 while (u != ((mp_digit) 0)) {
2558 r = ((mp_word) *tmpt) + ((mp_word) u);
2559 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2560 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2571 /* multiplies |a| * |b| and does not compute the lower digs digits
2572 * [meant to get the higher part of the product]
2574 static int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2577 int res, pa, pb, ix, iy;
2580 mp_digit tmpx, *tmpt, *tmpy;
2582 /* can we use the fast multiplier? */
2583 #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
2584 if (((a->used + b->used + 1) < MP_WARRAY)
2585 && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
2586 return fast_s_mp_mul_high_digs (a, b, c, digs);
2590 if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
2593 t.used = a->used + b->used + 1;
2597 for (ix = 0; ix < pa; ix++) {
2598 /* clear the carry */
2601 /* left hand side of A[ix] * B[iy] */
2604 /* alias to the address of where the digits will be stored */
2605 tmpt = &(t.dp[digs]);
2607 /* alias for where to read the right hand side from */
2608 tmpy = b->dp + (digs - ix);
2610 for (iy = digs - ix; iy < pb; iy++) {
2611 /* calculate the double precision result */
2612 r = ((mp_word)*tmpt) +
2613 ((mp_word)tmpx) * ((mp_word)*tmpy++) +
2616 /* get the lower part */
2617 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2619 /* carry the carry */
2620 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
2631 #ifdef BN_MP_MONTGOMERY_SETUP_C
2632 /* setups the montgomery reduction stuff */
2634 mp_montgomery_setup (mp_int * n, mp_digit * rho)
2638 /* fast inversion mod 2**k
2640 * Based on the fact that
2642 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
2643 * => 2*X*A - X*X*A*A = 1
2644 * => 2*(1) - (1) = 1
2652 x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
2653 x *= 2 - b * x; /* here x*a==1 mod 2**8 */
2654 #if !defined(MP_8BIT)
2655 x *= 2 - b * x; /* here x*a==1 mod 2**16 */
2657 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
2658 x *= 2 - b * x; /* here x*a==1 mod 2**32 */
2661 x *= 2 - b * x; /* here x*a==1 mod 2**64 */
2664 /* rho = -1/m mod b */
2665 *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
2672 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
2673 /* computes xR**-1 == x (mod N) via Montgomery Reduction
2675 * This is an optimized implementation of montgomery_reduce
2676 * which uses the comba method to quickly calculate the columns of the
2679 * Based on Algorithm 14.32 on pp.601 of HAC.
2681 int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
2683 int ix, res, olduse;
2684 mp_word W[MP_WARRAY];
2686 /* get old used count */
2689 /* grow a as required */
2690 if (x->alloc < n->used + 1) {
2691 if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
2696 /* first we have to get the digits of the input into
2697 * an array of double precision words W[...]
2700 register mp_word *_W;
2701 register mp_digit *tmpx;
2703 /* alias for the W[] array */
2706 /* alias for the digits of x*/
2709 /* copy the digits of a into W[0..a->used-1] */
2710 for (ix = 0; ix < x->used; ix++) {
2714 /* zero the high words of W[a->used..m->used*2] */
2715 for (; ix < n->used * 2 + 1; ix++) {
2720 /* now we proceed to zero successive digits
2721 * from the least significant upwards
2723 for (ix = 0; ix < n->used; ix++) {
2724 /* mu = ai * m' mod b
2726 * We avoid a double precision multiplication (which isn't required)
2727 * by casting the value down to a mp_digit. Note this requires
2728 * that W[ix-1] have the carry cleared (see after the inner loop)
2730 register mp_digit mu;
2731 mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
2733 /* a = a + mu * m * b**i
2735 * This is computed in place and on the fly. The multiplication
2736 * by b**i is handled by offseting which columns the results
2739 * Note the comba method normally doesn't handle carries in the
2740 * inner loop In this case we fix the carry from the previous
2741 * column since the Montgomery reduction requires digits of the
2742 * result (so far) [see above] to work. This is
2743 * handled by fixing up one carry after the inner loop. The
2744 * carry fixups are done in order so after these loops the
2745 * first m->used words of W[] have the carries fixed
2749 register mp_digit *tmpn;
2750 register mp_word *_W;
2752 /* alias for the digits of the modulus */
2755 /* Alias for the columns set by an offset of ix */
2759 for (iy = 0; iy < n->used; iy++) {
2760 *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
2764 /* now fix carry for next digit, W[ix+1] */
2765 W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
2768 /* now we have to propagate the carries and
2769 * shift the words downward [all those least
2770 * significant digits we zeroed].
2773 register mp_digit *tmpx;
2774 register mp_word *_W, *_W1;
2776 /* nox fix rest of carries */
2778 /* alias for current word */
2781 /* alias for next word, where the carry goes */
2784 for (; ix <= n->used * 2 + 1; ix++) {
2785 *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
2788 /* copy out, A = A/b**n
2790 * The result is A/b**n but instead of converting from an
2791 * array of mp_word to mp_digit than calling mp_rshd
2792 * we just copy them in the right order
2795 /* alias for destination word */
2798 /* alias for shifted double precision result */
2801 for (ix = 0; ix < n->used + 1; ix++) {
2802 *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
2805 /* zero oldused digits, if the input a was larger than
2806 * m->used+1 we'll have to clear the digits
2808 for (; ix < olduse; ix++) {
2813 /* set the max used and clamp */
2814 x->used = n->used + 1;
2817 /* if A >= m then A = A - m */
2818 if (mp_cmp_mag (x, n) != MP_LT) {
2819 return s_mp_sub (x, n, x);
2826 #ifdef BN_MP_MUL_2_C
2828 static int mp_mul_2(mp_int * a, mp_int * b)
2830 int x, res, oldused;
2832 /* grow to accomodate result */
2833 if (b->alloc < a->used + 1) {
2834 if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
2843 register mp_digit r, rr, *tmpa, *tmpb;
2845 /* alias for source */
2848 /* alias for dest */
2853 for (x = 0; x < a->used; x++) {
2855 /* get what will be the *next* carry bit from the
2856 * MSB of the current digit
2858 rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
2860 /* now shift up this digit, add in the carry [from the previous] */
2861 *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
2863 /* copy the carry that would be from the source
2864 * digit into the next iteration
2869 /* new leading digit? */
2871 /* add a MSB which is always 1 at this point */
2876 /* now zero any excess digits on the destination
2877 * that we didn't write to
2879 tmpb = b->dp + b->used;
2880 for (x = b->used; x < oldused; x++) {
2890 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
2892 * shifts with subtractions when the result is greater than b.
2894 * The method is slightly modified to shift B unconditionally upto just under
2895 * the leading bit of b. This saves alot of multiple precision shifting.
2897 static int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
2901 /* how many bits of last digit does b use */
2902 bits = mp_count_bits (b) % DIGIT_BIT;
2905 if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
2914 /* now compute C = A * B mod b */
2915 for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
2916 if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
2919 if (mp_cmp_mag (a, b) != MP_LT) {
2920 if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
2931 #ifdef BN_MP_EXPTMOD_FAST_C
2932 /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
2934 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
2935 * The value of k changes based on the size of the exponent.
2937 * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
2940 static int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
2942 mp_int M[TAB_SIZE], res;
2944 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
2946 /* use a pointer to the reduction algorithm. This allows us to use
2947 * one of many reduction algorithms without modding the guts of
2948 * the code with if statements everywhere.
2950 int (*redux)(mp_int*,mp_int*,mp_digit);
2952 /* find window size */
2953 x = mp_count_bits (X);
2956 } else if (x <= 36) {
2958 } else if (x <= 140) {
2960 } else if (x <= 450) {
2962 } else if (x <= 1303) {
2964 } else if (x <= 3529) {
2977 /* init first cell */
2978 if ((err = mp_init(&M[1])) != MP_OKAY) {
2982 /* now init the second half of the array */
2983 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
2984 if ((err = mp_init(&M[x])) != MP_OKAY) {
2985 for (y = 1<<(winsize-1); y < x; y++) {
2993 /* determine and setup reduction code */
2995 #ifdef BN_MP_MONTGOMERY_SETUP_C
2996 /* now setup montgomery */
2997 if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
3005 /* automatically pick the comba one if available (saves quite a few calls/ifs) */
3006 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
3007 if (((P->used * 2 + 1) < MP_WARRAY) &&
3008 P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
3009 redux = fast_mp_montgomery_reduce;
3013 #ifdef BN_MP_MONTGOMERY_REDUCE_C
3014 /* use slower baseline Montgomery method */
3015 redux = mp_montgomery_reduce;
3021 } else if (redmode == 1) {
3022 #if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
3023 /* setup DR reduction for moduli of the form B**k - b */
3024 mp_dr_setup(P, &mp);
3025 redux = mp_dr_reduce;
3031 #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
3032 /* setup DR reduction for moduli of the form 2**k - b */
3033 if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
3036 redux = mp_reduce_2k;
3044 if ((err = mp_init (&res)) != MP_OKAY) {
3052 * The first half of the table is not computed though accept for M[0] and M[1]
3056 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
3057 /* now we need R mod m */
3058 if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
3066 /* now set M[1] to G * R mod m */
3067 if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
3072 if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
3077 /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
3078 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
3082 for (x = 0; x < (winsize - 1); x++) {
3083 if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
3086 if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
3091 /* create upper table */
3092 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
3093 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
3096 if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
3101 /* set initial mode and bit cnt */
3105 digidx = X->used - 1;
3110 /* grab next digit as required */
3111 if (--bitcnt == 0) {
3112 /* if digidx == -1 we are out of digits so break */
3116 /* read next digit and reset bitcnt */
3117 buf = X->dp[digidx--];
3118 bitcnt = (int)DIGIT_BIT;
3121 /* grab the next msb from the exponent */
3122 y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
3123 buf <<= (mp_digit)1;
3125 /* if the bit is zero and mode == 0 then we ignore it
3126 * These represent the leading zero bits before the first 1 bit
3127 * in the exponent. Technically this opt is not required but it
3128 * does lower the # of trivial squaring/reductions used
3130 if (mode == 0 && y == 0) {
3134 /* if the bit is zero and mode == 1 then we square */
3135 if (mode == 1 && y == 0) {
3136 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
3139 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3145 /* else we add it to the window */
3146 bitbuf |= (y << (winsize - ++bitcpy));
3149 if (bitcpy == winsize) {
3150 /* ok window is filled so square as required and multiply */
3152 for (x = 0; x < winsize; x++) {
3153 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
3156 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3162 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
3165 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3169 /* empty window and reset */
3176 /* if bits remain then square/multiply */
3177 if (mode == 2 && bitcpy > 0) {
3178 /* square then multiply if the bit is set */
3179 for (x = 0; x < bitcpy; x++) {
3180 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
3183 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3187 /* get next bit of the window */
3189 if ((bitbuf & (1 << winsize)) != 0) {
3191 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
3194 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3202 /* fixup result if Montgomery reduction is used
3203 * recall that any value in a Montgomery system is
3204 * actually multiplied by R mod n. So we have
3205 * to reduce one more time to cancel out the factor
3208 if ((err = redux(&res, P, mp)) != MP_OKAY) {
3213 /* swap res with Y */
3216 LBL_RES:mp_clear (&res);
3219 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
3227 #ifdef BN_FAST_S_MP_SQR_C
3228 /* the jist of squaring...
3229 * you do like mult except the offset of the tmpx [one that
3230 * starts closer to zero] can't equal the offset of tmpy.
3231 * So basically you set up iy like before then you min it with
3232 * (ty-tx) so that it never happens. You double all those
3233 * you add in the inner loop
3235 After that loop you do the squares and add them in.
3238 static int fast_s_mp_sqr (mp_int * a, mp_int * b)
3240 int olduse, res, pa, ix, iz;
3241 mp_digit W[MP_WARRAY], *tmpx;
3244 /* grow the destination as required */
3245 pa = a->used + a->used;
3246 if (b->alloc < pa) {
3247 if ((res = mp_grow (b, pa)) != MP_OKAY) {
3252 /* number of output digits to produce */
3254 for (ix = 0; ix < pa; ix++) {
3262 /* get offsets into the two bignums */
3263 ty = MIN(a->used-1, ix);
3266 /* setup temp aliases */
3270 /* this is the number of times the loop will iterrate, essentially
3271 while (tx++ < a->used && ty-- >= 0) { ... }
3273 iy = MIN(a->used-tx, ty+1);
3275 /* now for squaring tx can never equal ty
3276 * we halve the distance since they approach at a rate of 2x
3277 * and we have to round because odd cases need to be executed
3279 iy = MIN(iy, (ty-tx+1)>>1);
3282 for (iz = 0; iz < iy; iz++) {
3283 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
3286 /* double the inner product and add carry */
3289 /* even columns have the square term in them */
3291 _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
3295 W[ix] = (mp_digit)(_W & MP_MASK);
3297 /* make next carry */
3298 W1 = _W >> ((mp_word)DIGIT_BIT);
3303 b->used = a->used+a->used;
3308 for (ix = 0; ix < pa; ix++) {
3309 *tmpb++ = W[ix] & MP_MASK;
3312 /* clear unused digits [that existed in the old copy of c] */
3313 for (; ix < olduse; ix++) {
3323 #ifdef BN_MP_MUL_D_C
3324 /* multiply by a digit */
3326 mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
3328 mp_digit u, *tmpa, *tmpc;
3330 int ix, res, olduse;
3332 /* make sure c is big enough to hold a*b */
3333 if (c->alloc < a->used + 1) {
3334 if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
3339 /* get the original destinations used count */
3345 /* alias for a->dp [source] */
3348 /* alias for c->dp [dest] */
3354 /* compute columns */
3355 for (ix = 0; ix < a->used; ix++) {
3356 /* compute product and carry sum for this term */
3357 r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
3359 /* mask off higher bits to get a single digit */
3360 *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
3362 /* send carry into next iteration */
3363 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
3366 /* store final carry [if any] and increment ix offset */
3370 /* now zero digits above the top */
3371 while (ix++ < olduse) {
3375 /* set used count */
3376 c->used = a->used + 1;