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
45 /* About 0.25 kB of code, but ~1.7kB of stack space! */
46 #define BN_FAST_S_MP_MUL_DIGS_C
50 #define BN_MP_DIV_SMALL
51 #define BN_MP_INIT_MULTI_C
52 #define BN_MP_CLEAR_MULTI_C
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
63 #define MIN(x,y) ((x)<(y)?(x):(y))
67 #define MAX(x,y) ((x)>(y)?(x):(y))
73 typedef unsigned long mp_digit;
74 typedef unsigned long mp_word __attribute__((mode(TI)));
79 typedef unsigned long mp_digit;
87 #define XMALLOC os_malloc
89 #define XREALLOC os_realloc
92 #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
94 #define MP_LT -1 /* less than */
95 #define MP_EQ 0 /* equal to */
96 #define MP_GT 1 /* greater than */
98 #define MP_ZPOS 0 /* positive integer */
99 #define MP_NEG 1 /* negative */
101 #define MP_OKAY 0 /* ok result */
102 #define MP_MEM -2 /* out of mem */
103 #define MP_VAL -3 /* invalid input */
105 #define MP_YES 1 /* yes response */
106 #define MP_NO 0 /* no response */
110 /* define this to use lower memory usage routines (exptmods mostly) */
113 /* default precision */
116 #define MP_PREC 32 /* default digits of precision */
118 #define MP_PREC 8 /* default digits of precision */
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))
125 /* the infamous mp_int structure */
127 int used, alloc, sign;
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)
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);
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);
149 #ifdef BN_MP_INIT_MULTI_C
150 static int mp_init_multi(mp_int *mp, ...);
152 #ifdef BN_MP_CLEAR_MULTI_C
153 static void mp_clear_multi(mp_int *mp, ...);
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);
177 static int mp_abs(mp_int * a, mp_int * b);
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 */
193 static int mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
194 #endif /* BN_MP_MUL_D_C */
198 /* functions from bn_<func name>.c */
201 /* reverse an array, used for radix code */
202 static void bn_reverse (unsigned char *s, int len)
219 /* low level addition, based on HAC pp.594, Algorithm 14.7 */
220 static int s_mp_add (mp_int * a, mp_int * b, mp_int * c)
223 int olduse, res, min, max;
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
228 if (a->used > b->used) {
239 if (c->alloc < max + 1) {
240 if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
245 /* get old used digit count and set new one */
250 register mp_digit u, *tmpa, *tmpb, *tmpc;
253 /* alias for digit pointers */
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;
270 /* U = carry bit of T[i] */
271 u = *tmpc >> ((mp_digit)DIGIT_BIT);
273 /* take away carry bit from T[i] */
277 /* now copy higher words if any, that is in A+B
278 * if A or B has more digits add those in
281 for (; i < max; i++) {
282 /* T[i] = X[i] + U */
283 *tmpc = x->dp[i] + u;
285 /* U = carry bit of T[i] */
286 u = *tmpc >> ((mp_digit)DIGIT_BIT);
288 /* take away carry bit from T[i] */
296 /* clear digits above oldused */
297 for (i = c->used; i < olduse; i++) {
307 /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
308 static int s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
310 int olduse, res, min, max;
317 if (c->alloc < max) {
318 if ((res = mp_grow (c, max)) != MP_OKAY) {
326 register mp_digit u, *tmpa, *tmpb, *tmpc;
329 /* alias for digit pointers */
334 /* set carry to zero */
336 for (i = 0; i < min; i++) {
337 /* T[i] = A[i] - B[i] - U */
338 *tmpc = *tmpa++ - *tmpb++ - u;
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
345 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
347 /* Clear carry from T[i] */
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 */
356 /* U = carry bit of T[i] */
357 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
359 /* Clear carry from T[i] */
363 /* clear digits above used (since we may not have grown result above) */
364 for (i = c->used; i < olduse; i++) {
374 /* init a new mp_int */
375 static int mp_init (mp_int * a)
379 /* allocate memory required and clear it */
380 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
385 /* set the digits to zero */
386 for (i = 0; i < MP_PREC; i++) {
390 /* set the used to zero, allocated digits to the default precision
391 * and sign to positive */
400 /* clear one (frees) */
401 static void mp_clear (mp_int * a)
405 /* only do anything if a hasn't been freed previously */
407 /* first zero the digits */
408 for (i = 0; i < a->used; i++) {
415 /* reset members to make debugging easier */
417 a->alloc = a->used = 0;
423 /* high level addition (handles signs) */
424 static int mp_add (mp_int * a, mp_int * b, mp_int * c)
428 /* get sign of both inputs */
432 /* handle two cases, not four */
434 /* both positive or both negative */
435 /* add their magnitudes, copy the sign */
437 res = s_mp_add (a, b, c);
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) {
445 res = s_mp_sub (b, a, c);
448 res = s_mp_sub (a, b, c);
455 /* high level subtraction (handles signs) */
456 static int mp_sub (mp_int * a, mp_int * b, mp_int * c)
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. */
469 res = s_mp_add (a, b, c);
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 */
478 /* The first has a larger or equal magnitude */
479 res = s_mp_sub (a, b, c);
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);
492 /* high level multiplication (handles sign) */
493 static int mp_mul (mp_int * a, mp_int * b, mp_int * c)
496 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
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);
504 #ifdef BN_MP_KARATSUBA_MUL_C
506 if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
507 res = mp_karatsuba_mul (a, b, c);
511 /* can we use the fast multiplier?
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
517 #ifdef BN_FAST_S_MP_MUL_DIGS_C
518 int digs = a->used + b->used + 1;
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);
526 #ifdef BN_S_MP_MUL_DIGS_C
527 res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
529 #error mp_mul could fail
534 c->sign = (c->used > 0) ? neg : MP_ZPOS;
539 /* d = a * b (mod c) */
540 static int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
545 if ((res = mp_init (&t)) != MP_OKAY) {
549 if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
553 res = mp_mod (&t, c, d);
559 /* c = a mod b, 0 <= c < b */
560 static int mp_mod (mp_int * a, mp_int * b, mp_int * c)
565 if ((res = mp_init (&t)) != MP_OKAY) {
569 if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
574 if (t.sign != b->sign) {
575 res = mp_add (b, &t, c);
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)
591 static int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
595 /* modulus P must be positive */
596 if (P->sign == MP_NEG) {
600 /* if exponent X is negative we have to recurse */
601 if (X->sign == MP_NEG) {
602 #ifdef LTM_NO_NEG_EXP
604 #else /* LTM_NO_NEG_EXP */
605 #ifdef BN_MP_INVMOD_C
609 /* first compute 1/G mod P */
610 if ((err = mp_init(&tmpG)) != MP_OKAY) {
613 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
619 if ((err = mp_init(&tmpX)) != MP_OKAY) {
623 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
624 mp_clear_multi(&tmpG, &tmpX, NULL);
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);
633 #error mp_exptmod would always fail
637 #endif /* LTM_NO_NEG_EXP */
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);
647 #ifdef BN_MP_DR_IS_MODULUS_C
648 /* is it a DR modulus? */
649 dr = mp_dr_is_modulus(P);
655 #ifdef BN_MP_REDUCE_IS_2K_C
656 /* if not, is it a unrestricted DR modulus? */
658 dr = mp_reduce_is_2k(P) << 1;
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);
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);
672 #error mp_exptmod could fail
673 /* no exptmod for evens */
676 #ifdef BN_MP_EXPTMOD_FAST_C
680 /* avoid compiler warnings about possibly unused variable */
685 /* compare two ints (signed)*/
686 static int mp_cmp (mp_int * a, mp_int * b)
688 /* compare based on sign */
689 if (a->sign != b->sign) {
690 if (a->sign == MP_NEG) {
698 if (a->sign == MP_NEG) {
699 /* if negative compare opposite direction */
700 return mp_cmp_mag(b, a);
702 return mp_cmp_mag(a, b);
707 /* compare a digit */
708 static int mp_cmp_d(mp_int * a, mp_digit b)
710 /* compare based on sign */
711 if (a->sign == MP_NEG) {
715 /* compare based on magnitude */
720 /* compare the only digit of a to b */
723 } else if (a->dp[0] < b) {
731 #ifndef LTM_NO_NEG_EXP
732 /* hac 14.61, pp608 */
733 static int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
735 /* b cannot be negative */
736 if (b->sign == MP_NEG || mp_iszero(b) == 1) {
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);
747 #ifdef BN_MP_INVMOD_SLOW_C
748 return mp_invmod_slow(a, b, c);
751 #ifndef BN_FAST_MP_INVMOD_C
752 #ifndef BN_MP_INVMOD_SLOW_C
753 #error mp_invmod would always fail
758 #endif /* LTM_NO_NEG_EXP */
761 /* get the size for an unsigned equivalent */
762 static int mp_unsigned_bin_size (mp_int * a)
764 int size = mp_count_bits (a);
765 return (size / 8 + ((size & 7) != 0 ? 1 : 0));
769 #ifndef LTM_NO_NEG_EXP
770 /* hac 14.61, pp608 */
771 static int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
773 mp_int x, y, u, v, A, B, C, D;
776 /* b cannot be negative */
777 if (b->sign == MP_NEG || mp_iszero(b) == 1) {
782 if ((res = mp_init_multi(&x, &y, &u, &v,
783 &A, &B, &C, &D, NULL)) != MP_OKAY) {
788 if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
791 if ((res = mp_copy (b, &y)) != MP_OKAY) {
795 /* 2. [modified] if x,y are both even then return an error! */
796 if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
801 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
802 if ((res = mp_copy (&x, &u)) != MP_OKAY) {
805 if ((res = mp_copy (&y, &v)) != MP_OKAY) {
812 /* 4. while u is even do */
813 while (mp_iseven (&u) == 1) {
815 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
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) {
824 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
828 /* A = A/2, B = B/2 */
829 if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
832 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
837 /* 5. while v is even do */
838 while (mp_iseven (&v) == 1) {
840 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
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) {
849 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
853 /* C = C/2, D = D/2 */
854 if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
857 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
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) {
869 if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
873 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
877 /* v - v - u, C = C - A, D = D - B */
878 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
882 if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
886 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
891 /* if not zero goto step 4 */
892 if (mp_iszero (&u) == 0)
895 /* now a = C, b = D, gcd == g*v */
897 /* if v != 1 then there is no inverse */
898 if (mp_cmp_d (&v, 1) != MP_EQ) {
904 while (mp_cmp_d(&C, 0) == MP_LT) {
905 if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
911 while (mp_cmp_mag(&C, b) != MP_LT) {
912 if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
917 /* C is now the inverse */
920 LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
923 #endif /* LTM_NO_NEG_EXP */
926 /* compare maginitude of two ints (unsigned) */
927 static int mp_cmp_mag (mp_int * a, mp_int * b)
930 mp_digit *tmpa, *tmpb;
932 /* compare based on # of non-zero digits */
933 if (a->used > b->used) {
937 if (a->used < b->used) {
942 tmpa = a->dp + (a->used - 1);
945 tmpb = b->dp + (a->used - 1);
947 /* compare based on digits */
948 for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
961 /* reads a unsigned char array, assumes the msb is stored first [big endian] */
962 static int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
966 /* make sure there are at least two digits */
968 if ((res = mp_grow(a, 2)) != MP_OKAY) {
976 /* read the bytes in */
978 if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
986 a->dp[0] = (*b & MP_MASK);
987 a->dp[1] |= ((*b++ >> 7U) & 1);
996 /* store in unsigned [big endian] format */
997 static int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
1002 if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
1007 while (mp_iszero (&t) == 0) {
1009 b[x++] = (unsigned char) (t.dp[0] & 255);
1011 b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
1013 if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
1024 /* shift right by a certain bit count (store quotient in c, optional remainder in d) */
1025 static int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
1032 /* if the shift count is <= 0 then we do no work */
1034 res = mp_copy (a, c);
1041 if ((res = mp_init (&t)) != MP_OKAY) {
1045 /* get the remainder */
1047 if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
1054 if ((res = mp_copy (a, c)) != MP_OKAY) {
1059 /* shift by as many digits in the bit count */
1060 if (b >= (int)DIGIT_BIT) {
1061 mp_rshd (c, b / DIGIT_BIT);
1064 /* shift any bit count < DIGIT_BIT */
1065 D = (mp_digit) (b % DIGIT_BIT);
1067 register mp_digit *tmpc, mask, shift;
1070 mask = (((mp_digit)1) << D) - 1;
1073 shift = DIGIT_BIT - D;
1076 tmpc = c->dp + (c->used - 1);
1080 for (x = c->used - 1; x >= 0; x--) {
1081 /* get the lower bits of this word in a temp */
1084 /* shift the current word and mix in the carry bits from the previous word */
1085 *tmpc = (*tmpc >> D) | (r << shift);
1088 /* set the carry to the carry bits of the current word found above */
1101 static int mp_init_copy (mp_int * a, mp_int * b)
1105 if ((res = mp_init (a)) != MP_OKAY) {
1108 return mp_copy (b, a);
1113 static void mp_zero (mp_int * a)
1122 for (n = 0; n < a->alloc; n++) {
1129 static int mp_copy (mp_int * a, mp_int * b)
1133 /* if dst == src do nothing */
1139 if (b->alloc < a->used) {
1140 if ((res = mp_grow (b, a->used)) != MP_OKAY) {
1145 /* zero b and copy the parameters over */
1147 register mp_digit *tmpa, *tmpb;
1149 /* pointer aliases */
1157 /* copy all the digits */
1158 for (n = 0; n < a->used; n++) {
1162 /* clear high digits */
1163 for (; n < b->used; n++) {
1168 /* copy used count and sign */
1175 /* shift right a certain amount of digits */
1176 static void mp_rshd (mp_int * a, int b)
1180 /* if b <= 0 then ignore it */
1185 /* if b > used then simply zero it and return */
1192 register mp_digit *bottom, *top;
1194 /* shift the digits down */
1199 /* top [offset into digits] */
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
1208 b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
1210 \-------------------/ ---->
1212 for (x = 0; x < (a->used - b); x++) {
1216 /* zero the top digits */
1217 for (; x < a->used; x++) {
1222 /* remove excess digits */
1227 /* swap the elements of two integers, for cases where you can't simply swap the
1228 * mp_int pointers around
1230 static void mp_exch (mp_int * a, mp_int * b)
1240 /* trim unused digits
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
1247 static void mp_clamp (mp_int * a)
1249 /* decrease used while the most significant digit is
1252 while (a->used > 0 && a->dp[a->used - 1] == 0) {
1256 /* reset the sign flag if used == 0 */
1263 /* grow as required */
1264 static int mp_grow (mp_int * a, int size)
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);
1274 /* reallocate the array a->dp
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.
1280 tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
1282 /* reallocation failed but "a" is still valid [can be freed] */
1286 /* reallocation succeeded so set a->dp */
1289 /* zero excess digits */
1292 for (; i < a->alloc; i++) {
1303 * Simple function copies the input and fixes the sign to positive
1305 static int mp_abs (mp_int * a, mp_int * b)
1311 if ((res = mp_copy (a, b)) != MP_OKAY) {
1316 /* force the sign of b to positive */
1324 /* set to a digit */
1325 static void mp_set (mp_int * a, mp_digit b)
1328 a->dp[0] = b & MP_MASK;
1329 a->used = (a->dp[0] != 0) ? 1 : 0;
1333 #ifndef LTM_NO_NEG_EXP
1335 static int mp_div_2(mp_int * a, mp_int * b)
1337 int x, res, oldused;
1340 if (b->alloc < a->used) {
1341 if ((res = mp_grow (b, a->used)) != MP_OKAY) {
1349 register mp_digit r, rr, *tmpa, *tmpb;
1352 tmpa = a->dp + b->used - 1;
1355 tmpb = b->dp + b->used - 1;
1359 for (x = b->used - 1; x >= 0; x--) {
1360 /* get the carry for the next iteration */
1363 /* shift the current digit, add in carry and store */
1364 *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
1366 /* forward carry to next iteration */
1370 /* zero excess digits */
1371 tmpb = b->dp + b->used;
1372 for (x = b->used; x < oldused; x++) {
1380 #endif /* LTM_NO_NEG_EXP */
1383 /* shift left by a certain bit count */
1384 static int mp_mul_2d (mp_int * a, int b, mp_int * c)
1391 if ((res = mp_copy (a, c)) != MP_OKAY) {
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) {
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) {
1409 /* shift any bit count < DIGIT_BIT */
1410 d = (mp_digit) (b % DIGIT_BIT);
1412 register mp_digit *tmpc, shift, mask, r, rr;
1415 /* bitmask for carries */
1416 mask = (((mp_digit)1) << d) - 1;
1418 /* shift for msbs */
1419 shift = DIGIT_BIT - d;
1426 for (x = 0; x < c->used; x++) {
1427 /* get the higher bits of the current word */
1428 rr = (*tmpc >> shift) & mask;
1430 /* shift the current word and OR in the carry */
1431 *tmpc = ((*tmpc << d) | r) & MP_MASK;
1434 /* set the carry to the carry bits of the current word */
1438 /* set final carry */
1440 c->dp[(c->used)++] = r;
1448 #ifdef BN_MP_INIT_MULTI_C
1449 static int mp_init_multi(mp_int *mp, ...)
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;
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.
1464 /* end the current list */
1467 /* now start cleaning up */
1469 va_start(clean_args, mp);
1472 cur_arg = va_arg(clean_args, mp_int*);
1479 cur_arg = va_arg(args, mp_int*);
1482 return res; /* Assumed ok, if error flagged above. */
1487 #ifdef BN_MP_CLEAR_MULTI_C
1488 static void mp_clear_multi(mp_int *mp, ...)
1490 mp_int* next_mp = mp;
1493 while (next_mp != NULL) {
1495 next_mp = va_arg(args, mp_int*);
1502 /* shift left a certain amount of digits */
1503 static int mp_lshd (mp_int * a, int b)
1507 /* if its less than zero return */
1512 /* grow to fit the new digits */
1513 if (a->alloc < a->used + b) {
1514 if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
1520 register mp_digit *top, *bottom;
1522 /* increment the used by the shift amount then copy upwards */
1526 top = a->dp + a->used - 1;
1529 bottom = a->dp + a->used - 1 - b;
1531 /* much like mp_rshd this is implemented using a sliding window
1532 * except the window goes the otherway around. Copying from
1533 * the bottom to the top. see bn_mp_rshd.c for more info.
1535 for (x = a->used - 1; x >= b; x--) {
1539 /* zero the lower digits */
1541 for (x = 0; x < b; x++) {
1549 /* returns the number of bits in an int */
1550 static int mp_count_bits (mp_int * a)
1560 /* get number of digits and add that */
1561 r = (a->used - 1) * DIGIT_BIT;
1563 /* take the last digit and count the bits in it */
1564 q = a->dp[a->used - 1];
1565 while (q > ((mp_digit) 0)) {
1567 q >>= ((mp_digit) 1);
1573 /* calc a value mod 2**b */
1574 static int mp_mod_2d (mp_int * a, int b, mp_int * c)
1578 /* if b is <= 0 then zero the int */
1584 /* if the modulus is larger than the value than return */
1585 if (b >= (int) (a->used * DIGIT_BIT)) {
1586 res = mp_copy (a, c);
1591 if ((res = mp_copy (a, c)) != MP_OKAY) {
1595 /* zero digits above the last digit of the modulus */
1596 for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
1599 /* clear the digit that is not completely outside/inside the modulus */
1600 c->dp[b / DIGIT_BIT] &=
1601 (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
1607 #ifdef BN_MP_DIV_SMALL
1609 /* slower bit-bang division... also smaller */
1610 static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
1612 mp_int ta, tb, tq, q;
1615 /* is divisor zero ? */
1616 if (mp_iszero (b) == 1) {
1620 /* if a < b then q=0, r = a */
1621 if (mp_cmp_mag (a, b) == MP_LT) {
1623 res = mp_copy (a, d);
1633 /* init our temps */
1634 if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
1640 n = mp_count_bits(a) - mp_count_bits(b);
1641 if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
1642 ((res = mp_abs(b, &tb)) != MP_OKAY) ||
1643 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
1644 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
1649 if (mp_cmp(&tb, &ta) != MP_GT) {
1650 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
1651 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
1655 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
1656 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
1661 /* now q == quotient and ta == remainder */
1663 n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
1666 c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
1670 d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
1673 mp_clear_multi(&ta, &tb, &tq, &q, NULL);
1679 /* integer signed division.
1680 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
1681 * HAC pp.598 Algorithm 14.20
1683 * Note that the description in HAC is horribly
1684 * incomplete. For example, it doesn't consider
1685 * the case where digits are removed from 'x' in
1686 * the inner loop. It also doesn't consider the
1687 * case that y has fewer than three digits, etc..
1689 * The overall algorithm is as described as
1690 * 14.20 from HAC but fixed to treat these cases.
1692 static int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
1694 mp_int q, x, y, t1, t2;
1695 int res, n, t, i, norm, neg;
1697 /* is divisor zero ? */
1698 if (mp_iszero (b) == 1) {
1702 /* if a < b then q=0, r = a */
1703 if (mp_cmp_mag (a, b) == MP_LT) {
1705 res = mp_copy (a, d);
1715 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
1718 q.used = a->used + 2;
1720 if ((res = mp_init (&t1)) != MP_OKAY) {
1724 if ((res = mp_init (&t2)) != MP_OKAY) {
1728 if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
1732 if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
1737 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
1738 x.sign = y.sign = MP_ZPOS;
1740 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
1741 norm = mp_count_bits(&y) % DIGIT_BIT;
1742 if (norm < (int)(DIGIT_BIT-1)) {
1743 norm = (DIGIT_BIT-1) - norm;
1744 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
1747 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
1754 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
1758 /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
1759 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
1763 while (mp_cmp (&x, &y) != MP_LT) {
1765 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
1770 /* reset y by shifting it back down */
1771 mp_rshd (&y, n - t);
1773 /* step 3. for i from n down to (t + 1) */
1774 for (i = n; i >= (t + 1); i--) {
1779 /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
1780 * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
1781 if (x.dp[i] == y.dp[t]) {
1782 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
1785 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
1786 tmp |= ((mp_word) x.dp[i - 1]);
1787 tmp /= ((mp_word) y.dp[t]);
1788 if (tmp > (mp_word) MP_MASK)
1790 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
1793 /* while (q{i-t-1} * (yt * b + y{t-1})) >
1794 xi * b**2 + xi-1 * b + xi-2
1798 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
1800 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
1802 /* find left hand */
1804 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
1807 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
1811 /* find right hand */
1812 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
1813 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
1816 } while (mp_cmp_mag(&t1, &t2) == MP_GT);
1818 /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
1819 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
1823 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
1827 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
1831 /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
1832 if (x.sign == MP_NEG) {
1833 if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
1836 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
1839 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
1843 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
1847 /* now q is the quotient and x is the remainder
1848 * [which we have to normalize]
1851 /* get sign before writing to c */
1852 x.sign = x.used == 0 ? MP_ZPOS : a->sign;
1861 mp_div_2d (&x, norm, &x, NULL);
1867 LBL_Y:mp_clear (&y);
1868 LBL_X:mp_clear (&x);
1869 LBL_T2:mp_clear (&t2);
1870 LBL_T1:mp_clear (&t1);
1871 LBL_Q:mp_clear (&q);
1881 #define TAB_SIZE 256
1884 static int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
1886 mp_int M[TAB_SIZE], res, mu;
1888 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
1889 int (*redux)(mp_int*,mp_int*,mp_int*);
1891 /* find window size */
1892 x = mp_count_bits (X);
1895 } else if (x <= 36) {
1897 } else if (x <= 140) {
1899 } else if (x <= 450) {
1901 } else if (x <= 1303) {
1903 } else if (x <= 3529) {
1916 /* init first cell */
1917 if ((err = mp_init(&M[1])) != MP_OKAY) {
1921 /* now init the second half of the array */
1922 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
1923 if ((err = mp_init(&M[x])) != MP_OKAY) {
1924 for (y = 1<<(winsize-1); y < x; y++) {
1932 /* create mu, used for Barrett reduction */
1933 if ((err = mp_init (&mu)) != MP_OKAY) {
1938 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
1943 if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
1946 redux = mp_reduce_2k_l;
1951 * The M table contains powers of the base,
1952 * e.g. M[x] = G**x mod P
1954 * The first half of the table is not
1955 * computed though accept for M[0] and M[1]
1957 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
1961 /* compute the value at M[1<<(winsize-1)] by squaring
1962 * M[1] (winsize-1) times
1964 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
1968 for (x = 0; x < (winsize - 1); x++) {
1970 if ((err = mp_sqr (&M[1 << (winsize - 1)],
1971 &M[1 << (winsize - 1)])) != MP_OKAY) {
1975 /* reduce modulo P */
1976 if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
1981 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
1982 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
1984 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
1985 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
1988 if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
1994 if ((err = mp_init (&res)) != MP_OKAY) {
1999 /* set initial mode and bit cnt */
2003 digidx = X->used - 1;
2008 /* grab next digit as required */
2009 if (--bitcnt == 0) {
2010 /* if digidx == -1 we are out of digits */
2014 /* read next digit and reset the bitcnt */
2015 buf = X->dp[digidx--];
2016 bitcnt = (int) DIGIT_BIT;
2019 /* grab the next msb from the exponent */
2020 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
2021 buf <<= (mp_digit)1;
2023 /* if the bit is zero and mode == 0 then we ignore it
2024 * These represent the leading zero bits before the first 1 bit
2025 * in the exponent. Technically this opt is not required but it
2026 * does lower the # of trivial squaring/reductions used
2028 if (mode == 0 && y == 0) {
2032 /* if the bit is zero and mode == 1 then we square */
2033 if (mode == 1 && y == 0) {
2034 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2037 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2043 /* else we add it to the window */
2044 bitbuf |= (y << (winsize - ++bitcpy));
2047 if (bitcpy == winsize) {
2048 /* ok window is filled so square as required and multiply */
2050 for (x = 0; x < winsize; x++) {
2051 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2054 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2060 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
2063 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2067 /* empty window and reset */
2074 /* if bits remain then square/multiply */
2075 if (mode == 2 && bitcpy > 0) {
2076 /* square then multiply if the bit is set */
2077 for (x = 0; x < bitcpy; x++) {
2078 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
2081 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2086 if ((bitbuf & (1 << winsize)) != 0) {
2088 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
2091 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
2100 LBL_RES:mp_clear (&res);
2101 LBL_MU:mp_clear (&mu);
2104 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
2111 /* computes b = a*a */
2112 static int mp_sqr (mp_int * a, mp_int * b)
2116 #ifdef BN_MP_TOOM_SQR_C
2117 /* use Toom-Cook? */
2118 if (a->used >= TOOM_SQR_CUTOFF) {
2119 res = mp_toom_sqr(a, b);
2123 #ifdef BN_MP_KARATSUBA_SQR_C
2124 if (a->used >= KARATSUBA_SQR_CUTOFF) {
2125 res = mp_karatsuba_sqr (a, b);
2129 #ifdef BN_FAST_S_MP_SQR_C
2130 /* can we use the fast comba multiplier? */
2131 if ((a->used * 2 + 1) < MP_WARRAY &&
2133 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
2134 res = fast_s_mp_sqr (a, b);
2137 #ifdef BN_S_MP_SQR_C
2138 res = s_mp_sqr (a, b);
2140 #error mp_sqr could fail
2149 /* reduces a modulo n where n is of the form 2**p - d
2150 This differs from reduce_2k since "d" can be larger
2151 than a single digit.
2153 static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
2158 if ((res = mp_init(&q)) != MP_OKAY) {
2162 p = mp_count_bits(n);
2164 /* q = a/2**p, a = a mod 2**p */
2165 if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
2170 if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
2175 if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
2179 if (mp_cmp_mag(a, n) != MP_LT) {
2190 /* determines the setup value */
2191 static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
2196 if ((res = mp_init(&tmp)) != MP_OKAY) {
2200 if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
2204 if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
2214 /* computes a = 2**b
2216 * Simple algorithm which zeroes the int, grows it then just sets one bit
2219 static int mp_2expt (mp_int * a, int b)
2223 /* zero a as per default */
2226 /* grow a to accommodate the single bit */
2227 if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
2231 /* set the used count of where the bit will go */
2232 a->used = b / DIGIT_BIT + 1;
2234 /* put the single bit in its place */
2235 a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
2241 /* pre-calculate the value required for Barrett reduction
2242 * For a given modulus "b" it calulates the value required in "a"
2244 static int mp_reduce_setup (mp_int * a, mp_int * b)
2248 if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
2251 return mp_div (a, b, a, NULL);
2255 /* reduces x mod m, assumes 0 < x < m**2, mu is
2256 * precomputed via mp_reduce_setup.
2257 * From HAC pp.604 Algorithm 14.42
2259 static int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
2262 int res, um = m->used;
2265 if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
2269 /* q1 = x / b**(k-1) */
2270 mp_rshd (&q, um - 1);
2272 /* according to HAC this optimization is ok */
2273 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
2274 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
2278 #ifdef BN_S_MP_MUL_HIGH_DIGS_C
2279 if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
2282 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
2283 if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
2288 #error mp_reduce would always fail
2295 /* q3 = q2 / b**(k+1) */
2296 mp_rshd (&q, um + 1);
2298 /* x = x mod b**(k+1), quick (no division) */
2299 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
2303 /* q = q * m mod b**(k+1), quick (no division) */
2304 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
2309 if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
2313 /* If x < 0, add b**(k+1) to it */
2314 if (mp_cmp_d (x, 0) == MP_LT) {
2316 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) {
2319 if ((res = mp_add (x, &q, x)) != MP_OKAY) {
2324 /* Back off if it's too big */
2325 while (mp_cmp (x, m) != MP_LT) {
2326 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
2338 /* multiplies |a| * |b| and only computes up to digs digits of result
2339 * HAC pp. 595, Algorithm 14.12 Modified so you can control how
2340 * many digits of output are created.
2342 static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2345 int res, pa, pb, ix, iy;
2348 mp_digit tmpx, *tmpt, *tmpy;
2350 #ifdef BN_FAST_S_MP_MUL_DIGS_C
2351 /* can we use the fast multiplier? */
2352 if (((digs) < MP_WARRAY) &&
2353 MIN (a->used, b->used) <
2354 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
2355 return fast_s_mp_mul_digs (a, b, c, digs);
2359 if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
2364 /* compute the digits of the product directly */
2366 for (ix = 0; ix < pa; ix++) {
2367 /* set the carry to zero */
2370 /* limit ourselves to making digs digits of output */
2371 pb = MIN (b->used, digs - ix);
2373 /* setup some aliases */
2374 /* copy of the digit from a used within the nested loop */
2377 /* an alias for the destination shifted ix places */
2380 /* an alias for the digits of b */
2383 /* compute the columns of the output and propagate the carry */
2384 for (iy = 0; iy < pb; iy++) {
2385 /* compute the column as a mp_word */
2386 r = ((mp_word)*tmpt) +
2387 ((mp_word)tmpx) * ((mp_word)*tmpy++) +
2390 /* the new column is the lower part of the result */
2391 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2393 /* get the carry word from the result */
2394 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
2396 /* set carry if it is placed below digs */
2397 if (ix + iy < digs) {
2410 #ifdef BN_FAST_S_MP_MUL_DIGS_C
2411 /* Fast (comba) multiplier
2413 * This is the fast column-array [comba] multiplier. It is
2414 * designed to compute the columns of the product first
2415 * then handle the carries afterwards. This has the effect
2416 * of making the nested loops that compute the columns very
2417 * simple and schedulable on super-scalar processors.
2419 * This has been modified to produce a variable number of
2420 * digits of output so if say only a half-product is required
2421 * you don't have to compute the upper half (a feature
2422 * required for fast Barrett reduction).
2424 * Based on Algorithm 14.12 on pp.595 of HAC.
2427 static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2429 int olduse, res, pa, ix, iz;
2430 mp_digit W[MP_WARRAY];
2431 register mp_word _W;
2433 /* grow the destination as required */
2434 if (c->alloc < digs) {
2435 if ((res = mp_grow (c, digs)) != MP_OKAY) {
2440 /* number of output digits to produce */
2441 pa = MIN(digs, a->used + b->used);
2443 /* clear the carry */
2445 for (ix = 0; ix < pa; ix++) {
2448 mp_digit *tmpx, *tmpy;
2450 /* get offsets into the two bignums */
2451 ty = MIN(b->used-1, ix);
2454 /* setup temp aliases */
2458 /* this is the number of times the loop will iterrate, essentially
2459 while (tx++ < a->used && ty-- >= 0) { ... }
2461 iy = MIN(a->used-tx, ty+1);
2464 for (iz = 0; iz < iy; ++iz) {
2465 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
2470 W[ix] = ((mp_digit)_W) & MP_MASK;
2472 /* make next carry */
2473 _W = _W >> ((mp_word)DIGIT_BIT);
2481 register mp_digit *tmpc;
2483 for (ix = 0; ix < pa+1; ix++) {
2484 /* now extract the previous digit [below the carry] */
2488 /* clear unused digits [that existed in the old copy of c] */
2489 for (; ix < olduse; ix++) {
2496 #endif /* BN_FAST_S_MP_MUL_DIGS_C */
2499 /* init an mp_init for a given size */
2500 static int mp_init_size (mp_int * a, int size)
2504 /* pad size so there are always extra digits */
2505 size += (MP_PREC * 2) - (size % MP_PREC);
2508 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
2509 if (a->dp == NULL) {
2513 /* set the members */
2518 /* zero the digits */
2519 for (x = 0; x < size; x++) {
2527 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
2528 static int s_mp_sqr (mp_int * a, mp_int * b)
2531 int res, ix, iy, pa;
2533 mp_digit u, tmpx, *tmpt;
2536 if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
2540 /* default used is maximum possible size */
2543 for (ix = 0; ix < pa; ix++) {
2544 /* first calculate the digit at 2*ix */
2545 /* calculate double precision result */
2546 r = ((mp_word) t.dp[2*ix]) +
2547 ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
2549 /* store lower part in result */
2550 t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
2553 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2555 /* left hand side of A[ix] * A[iy] */
2558 /* alias for where to store the results */
2559 tmpt = t.dp + (2*ix + 1);
2561 for (iy = ix + 1; iy < pa; iy++) {
2562 /* first calculate the product */
2563 r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
2565 /* now calculate the double precision result, note we use
2566 * addition instead of *2 since it's easier to optimize
2568 r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
2570 /* store lower part */
2571 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2574 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2576 /* propagate upwards */
2577 while (u != ((mp_digit) 0)) {
2578 r = ((mp_word) *tmpt) + ((mp_word) u);
2579 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2580 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2591 /* multiplies |a| * |b| and does not compute the lower digs digits
2592 * [meant to get the higher part of the product]
2594 static int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2597 int res, pa, pb, ix, iy;
2600 mp_digit tmpx, *tmpt, *tmpy;
2602 /* can we use the fast multiplier? */
2603 #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
2604 if (((a->used + b->used + 1) < MP_WARRAY)
2605 && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
2606 return fast_s_mp_mul_high_digs (a, b, c, digs);
2610 if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
2613 t.used = a->used + b->used + 1;
2617 for (ix = 0; ix < pa; ix++) {
2618 /* clear the carry */
2621 /* left hand side of A[ix] * B[iy] */
2624 /* alias to the address of where the digits will be stored */
2625 tmpt = &(t.dp[digs]);
2627 /* alias for where to read the right hand side from */
2628 tmpy = b->dp + (digs - ix);
2630 for (iy = digs - ix; iy < pb; iy++) {
2631 /* calculate the double precision result */
2632 r = ((mp_word)*tmpt) +
2633 ((mp_word)tmpx) * ((mp_word)*tmpy++) +
2636 /* get the lower part */
2637 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2639 /* carry the carry */
2640 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
2651 #ifdef BN_MP_MONTGOMERY_SETUP_C
2652 /* setups the montgomery reduction stuff */
2654 mp_montgomery_setup (mp_int * n, mp_digit * rho)
2658 /* fast inversion mod 2**k
2660 * Based on the fact that
2662 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
2663 * => 2*X*A - X*X*A*A = 1
2664 * => 2*(1) - (1) = 1
2672 x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
2673 x *= 2 - b * x; /* here x*a==1 mod 2**8 */
2674 #if !defined(MP_8BIT)
2675 x *= 2 - b * x; /* here x*a==1 mod 2**16 */
2677 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
2678 x *= 2 - b * x; /* here x*a==1 mod 2**32 */
2681 x *= 2 - b * x; /* here x*a==1 mod 2**64 */
2684 /* rho = -1/m mod b */
2685 *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
2692 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
2693 /* computes xR**-1 == x (mod N) via Montgomery Reduction
2695 * This is an optimized implementation of montgomery_reduce
2696 * which uses the comba method to quickly calculate the columns of the
2699 * Based on Algorithm 14.32 on pp.601 of HAC.
2701 static int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
2703 int ix, res, olduse;
2704 mp_word W[MP_WARRAY];
2706 /* get old used count */
2709 /* grow a as required */
2710 if (x->alloc < n->used + 1) {
2711 if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
2716 /* first we have to get the digits of the input into
2717 * an array of double precision words W[...]
2720 register mp_word *_W;
2721 register mp_digit *tmpx;
2723 /* alias for the W[] array */
2726 /* alias for the digits of x*/
2729 /* copy the digits of a into W[0..a->used-1] */
2730 for (ix = 0; ix < x->used; ix++) {
2734 /* zero the high words of W[a->used..m->used*2] */
2735 for (; ix < n->used * 2 + 1; ix++) {
2740 /* now we proceed to zero successive digits
2741 * from the least significant upwards
2743 for (ix = 0; ix < n->used; ix++) {
2744 /* mu = ai * m' mod b
2746 * We avoid a double precision multiplication (which isn't required)
2747 * by casting the value down to a mp_digit. Note this requires
2748 * that W[ix-1] have the carry cleared (see after the inner loop)
2750 register mp_digit mu;
2751 mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
2753 /* a = a + mu * m * b**i
2755 * This is computed in place and on the fly. The multiplication
2756 * by b**i is handled by offseting which columns the results
2759 * Note the comba method normally doesn't handle carries in the
2760 * inner loop In this case we fix the carry from the previous
2761 * column since the Montgomery reduction requires digits of the
2762 * result (so far) [see above] to work. This is
2763 * handled by fixing up one carry after the inner loop. The
2764 * carry fixups are done in order so after these loops the
2765 * first m->used words of W[] have the carries fixed
2769 register mp_digit *tmpn;
2770 register mp_word *_W;
2772 /* alias for the digits of the modulus */
2775 /* Alias for the columns set by an offset of ix */
2779 for (iy = 0; iy < n->used; iy++) {
2780 *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
2784 /* now fix carry for next digit, W[ix+1] */
2785 W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
2788 /* now we have to propagate the carries and
2789 * shift the words downward [all those least
2790 * significant digits we zeroed].
2793 register mp_digit *tmpx;
2794 register mp_word *_W, *_W1;
2796 /* nox fix rest of carries */
2798 /* alias for current word */
2801 /* alias for next word, where the carry goes */
2804 for (; ix <= n->used * 2 + 1; ix++) {
2805 *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
2808 /* copy out, A = A/b**n
2810 * The result is A/b**n but instead of converting from an
2811 * array of mp_word to mp_digit than calling mp_rshd
2812 * we just copy them in the right order
2815 /* alias for destination word */
2818 /* alias for shifted double precision result */
2821 for (ix = 0; ix < n->used + 1; ix++) {
2822 *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
2825 /* zero oldused digits, if the input a was larger than
2826 * m->used+1 we'll have to clear the digits
2828 for (; ix < olduse; ix++) {
2833 /* set the max used and clamp */
2834 x->used = n->used + 1;
2837 /* if A >= m then A = A - m */
2838 if (mp_cmp_mag (x, n) != MP_LT) {
2839 return s_mp_sub (x, n, x);
2846 #ifdef BN_MP_MUL_2_C
2848 static int mp_mul_2(mp_int * a, mp_int * b)
2850 int x, res, oldused;
2852 /* grow to accommodate result */
2853 if (b->alloc < a->used + 1) {
2854 if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
2863 register mp_digit r, rr, *tmpa, *tmpb;
2865 /* alias for source */
2868 /* alias for dest */
2873 for (x = 0; x < a->used; x++) {
2875 /* get what will be the *next* carry bit from the
2876 * MSB of the current digit
2878 rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
2880 /* now shift up this digit, add in the carry [from the previous] */
2881 *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
2883 /* copy the carry that would be from the source
2884 * digit into the next iteration
2889 /* new leading digit? */
2891 /* add a MSB which is always 1 at this point */
2896 /* now zero any excess digits on the destination
2897 * that we didn't write to
2899 tmpb = b->dp + b->used;
2900 for (x = b->used; x < oldused; x++) {
2910 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
2912 * shifts with subtractions when the result is greater than b.
2914 * The method is slightly modified to shift B unconditionally up to just under
2915 * the leading bit of b. This saves a lot of multiple precision shifting.
2917 static int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
2921 /* how many bits of last digit does b use */
2922 bits = mp_count_bits (b) % DIGIT_BIT;
2925 if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
2934 /* now compute C = A * B mod b */
2935 for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
2936 if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
2939 if (mp_cmp_mag (a, b) != MP_LT) {
2940 if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
2951 #ifdef BN_MP_EXPTMOD_FAST_C
2952 /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
2954 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
2955 * The value of k changes based on the size of the exponent.
2957 * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
2960 static int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
2962 mp_int M[TAB_SIZE], res;
2964 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
2966 /* use a pointer to the reduction algorithm. This allows us to use
2967 * one of many reduction algorithms without modding the guts of
2968 * the code with if statements everywhere.
2970 int (*redux)(mp_int*,mp_int*,mp_digit);
2972 /* find window size */
2973 x = mp_count_bits (X);
2976 } else if (x <= 36) {
2978 } else if (x <= 140) {
2980 } else if (x <= 450) {
2982 } else if (x <= 1303) {
2984 } else if (x <= 3529) {
2997 /* init first cell */
2998 if ((err = mp_init(&M[1])) != MP_OKAY) {
3002 /* now init the second half of the array */
3003 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
3004 if ((err = mp_init(&M[x])) != MP_OKAY) {
3005 for (y = 1<<(winsize-1); y < x; y++) {
3013 /* determine and setup reduction code */
3015 #ifdef BN_MP_MONTGOMERY_SETUP_C
3016 /* now setup montgomery */
3017 if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
3025 /* automatically pick the comba one if available (saves quite a few calls/ifs) */
3026 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
3027 if (((P->used * 2 + 1) < MP_WARRAY) &&
3028 P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
3029 redux = fast_mp_montgomery_reduce;
3033 #ifdef BN_MP_MONTGOMERY_REDUCE_C
3034 /* use slower baseline Montgomery method */
3035 redux = mp_montgomery_reduce;
3041 } else if (redmode == 1) {
3042 #if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
3043 /* setup DR reduction for moduli of the form B**k - b */
3044 mp_dr_setup(P, &mp);
3045 redux = mp_dr_reduce;
3051 #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
3052 /* setup DR reduction for moduli of the form 2**k - b */
3053 if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
3056 redux = mp_reduce_2k;
3064 if ((err = mp_init (&res)) != MP_OKAY) {
3072 * The first half of the table is not computed though accept for M[0] and M[1]
3076 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
3077 /* now we need R mod m */
3078 if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
3086 /* now set M[1] to G * R mod m */
3087 if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
3092 if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
3097 /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
3098 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
3102 for (x = 0; x < (winsize - 1); x++) {
3103 if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
3106 if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
3111 /* create upper table */
3112 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
3113 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
3116 if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
3121 /* set initial mode and bit cnt */
3125 digidx = X->used - 1;
3130 /* grab next digit as required */
3131 if (--bitcnt == 0) {
3132 /* if digidx == -1 we are out of digits so break */
3136 /* read next digit and reset bitcnt */
3137 buf = X->dp[digidx--];
3138 bitcnt = (int)DIGIT_BIT;
3141 /* grab the next msb from the exponent */
3142 y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
3143 buf <<= (mp_digit)1;
3145 /* if the bit is zero and mode == 0 then we ignore it
3146 * These represent the leading zero bits before the first 1 bit
3147 * in the exponent. Technically this opt is not required but it
3148 * does lower the # of trivial squaring/reductions used
3150 if (mode == 0 && y == 0) {
3154 /* if the bit is zero and mode == 1 then we square */
3155 if (mode == 1 && y == 0) {
3156 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
3159 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3165 /* else we add it to the window */
3166 bitbuf |= (y << (winsize - ++bitcpy));
3169 if (bitcpy == winsize) {
3170 /* ok window is filled so square as required and multiply */
3172 for (x = 0; x < winsize; x++) {
3173 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
3176 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3182 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
3185 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3189 /* empty window and reset */
3196 /* if bits remain then square/multiply */
3197 if (mode == 2 && bitcpy > 0) {
3198 /* square then multiply if the bit is set */
3199 for (x = 0; x < bitcpy; x++) {
3200 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
3203 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3207 /* get next bit of the window */
3209 if ((bitbuf & (1 << winsize)) != 0) {
3211 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
3214 if ((err = redux (&res, P, mp)) != MP_OKAY) {
3222 /* fixup result if Montgomery reduction is used
3223 * recall that any value in a Montgomery system is
3224 * actually multiplied by R mod n. So we have
3225 * to reduce one more time to cancel out the factor
3228 if ((err = redux(&res, P, mp)) != MP_OKAY) {
3233 /* swap res with Y */
3236 LBL_RES:mp_clear (&res);
3239 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
3247 #ifdef BN_FAST_S_MP_SQR_C
3248 /* the jist of squaring...
3249 * you do like mult except the offset of the tmpx [one that
3250 * starts closer to zero] can't equal the offset of tmpy.
3251 * So basically you set up iy like before then you min it with
3252 * (ty-tx) so that it never happens. You double all those
3253 * you add in the inner loop
3255 After that loop you do the squares and add them in.
3258 static int fast_s_mp_sqr (mp_int * a, mp_int * b)
3260 int olduse, res, pa, ix, iz;
3261 mp_digit W[MP_WARRAY], *tmpx;
3264 /* grow the destination as required */
3265 pa = a->used + a->used;
3266 if (b->alloc < pa) {
3267 if ((res = mp_grow (b, pa)) != MP_OKAY) {
3272 /* number of output digits to produce */
3274 for (ix = 0; ix < pa; ix++) {
3282 /* get offsets into the two bignums */
3283 ty = MIN(a->used-1, ix);
3286 /* setup temp aliases */
3290 /* this is the number of times the loop will iterrate, essentially
3291 while (tx++ < a->used && ty-- >= 0) { ... }
3293 iy = MIN(a->used-tx, ty+1);
3295 /* now for squaring tx can never equal ty
3296 * we halve the distance since they approach at a rate of 2x
3297 * and we have to round because odd cases need to be executed
3299 iy = MIN(iy, (ty-tx+1)>>1);
3302 for (iz = 0; iz < iy; iz++) {
3303 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
3306 /* double the inner product and add carry */
3309 /* even columns have the square term in them */
3311 _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
3315 W[ix] = (mp_digit)(_W & MP_MASK);
3317 /* make next carry */
3318 W1 = _W >> ((mp_word)DIGIT_BIT);
3323 b->used = a->used+a->used;
3328 for (ix = 0; ix < pa; ix++) {
3329 *tmpb++ = W[ix] & MP_MASK;
3332 /* clear unused digits [that existed in the old copy of c] */
3333 for (; ix < olduse; ix++) {
3343 #ifdef BN_MP_MUL_D_C
3344 /* multiply by a digit */
3346 mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
3348 mp_digit u, *tmpa, *tmpc;
3350 int ix, res, olduse;
3352 /* make sure c is big enough to hold a*b */
3353 if (c->alloc < a->used + 1) {
3354 if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
3359 /* get the original destinations used count */
3365 /* alias for a->dp [source] */
3368 /* alias for c->dp [dest] */
3374 /* compute columns */
3375 for (ix = 0; ix < a->used; ix++) {
3376 /* compute product and carry sum for this term */
3377 r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
3379 /* mask off higher bits to get a single digit */
3380 *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
3382 /* send carry into next iteration */
3383 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
3386 /* store final carry [if any] and increment ix offset */
3390 /* now zero digits above the top */
3391 while (ix++ < olduse) {
3395 /* set used count */
3396 c->used = a->used + 1;