wpa_supplicant: Initial Revision 0.8.X
Based on:
commit 0725cc7b7efc434910e89865c42eda7ce61bbf08
Author: Jouni Malinen <j@w1.fi>
Date: Thu Apr 21 20:41:01 2011 +0300
Enable CONFIG_DRIVER_NL80211=y in the default configuration
nl80211 should be preferred over WEXT with any recent Linux
kernel version.
Change-Id: I26aec5afbbd4f4a1f5fd900912545b6f5050de64
Signed-off-by: Dmitry Shmidt <dimitrysh@google.com>
diff --git a/src/tls/libtommath.c b/src/tls/libtommath.c
new file mode 100644
index 0000000..1374264
--- /dev/null
+++ b/src/tls/libtommath.c
@@ -0,0 +1,3381 @@
+/*
+ * Minimal code for RSA support from LibTomMath 0.41
+ * http://libtom.org/
+ * http://libtom.org/files/ltm-0.41.tar.bz2
+ * This library was released in public domain by Tom St Denis.
+ *
+ * The combination in this file may not use all of the optimized algorithms
+ * from LibTomMath and may be considerable slower than the LibTomMath with its
+ * default settings. The main purpose of having this version here is to make it
+ * easier to build bignum.c wrapper without having to install and build an
+ * external library.
+ *
+ * If CONFIG_INTERNAL_LIBTOMMATH is defined, bignum.c includes this
+ * libtommath.c file instead of using the external LibTomMath library.
+ */
+
+#ifndef CHAR_BIT
+#define CHAR_BIT 8
+#endif
+
+#define BN_MP_INVMOD_C
+#define BN_S_MP_EXPTMOD_C /* Note: #undef in tommath_superclass.h; this would
+ * require BN_MP_EXPTMOD_FAST_C instead */
+#define BN_S_MP_MUL_DIGS_C
+#define BN_MP_INVMOD_SLOW_C
+#define BN_S_MP_SQR_C
+#define BN_S_MP_MUL_HIGH_DIGS_C /* Note: #undef in tommath_superclass.h; this
+ * would require other than mp_reduce */
+
+#ifdef LTM_FAST
+
+/* Use faster div at the cost of about 1 kB */
+#define BN_MP_MUL_D_C
+
+/* Include faster exptmod (Montgomery) at the cost of about 2.5 kB in code */
+#define BN_MP_EXPTMOD_FAST_C
+#define BN_MP_MONTGOMERY_SETUP_C
+#define BN_FAST_MP_MONTGOMERY_REDUCE_C
+#define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+#define BN_MP_MUL_2_C
+
+/* Include faster sqr at the cost of about 0.5 kB in code */
+#define BN_FAST_S_MP_SQR_C
+
+#else /* LTM_FAST */
+
+#define BN_MP_DIV_SMALL
+#define BN_MP_INIT_MULTI_C
+#define BN_MP_CLEAR_MULTI_C
+#define BN_MP_ABS_C
+#endif /* LTM_FAST */
+
+/* Current uses do not require support for negative exponent in exptmod, so we
+ * can save about 1.5 kB in leaving out invmod. */
+#define LTM_NO_NEG_EXP
+
+/* from tommath.h */
+
+#ifndef MIN
+ #define MIN(x,y) ((x)<(y)?(x):(y))
+#endif
+
+#ifndef MAX
+ #define MAX(x,y) ((x)>(y)?(x):(y))
+#endif
+
+#define OPT_CAST(x)
+
+typedef unsigned long mp_digit;
+typedef u64 mp_word;
+
+#define DIGIT_BIT 28
+#define MP_28BIT
+
+
+#define XMALLOC os_malloc
+#define XFREE os_free
+#define XREALLOC os_realloc
+
+
+#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
+
+#define MP_LT -1 /* less than */
+#define MP_EQ 0 /* equal to */
+#define MP_GT 1 /* greater than */
+
+#define MP_ZPOS 0 /* positive integer */
+#define MP_NEG 1 /* negative */
+
+#define MP_OKAY 0 /* ok result */
+#define MP_MEM -2 /* out of mem */
+#define MP_VAL -3 /* invalid input */
+
+#define MP_YES 1 /* yes response */
+#define MP_NO 0 /* no response */
+
+typedef int mp_err;
+
+/* define this to use lower memory usage routines (exptmods mostly) */
+#define MP_LOW_MEM
+
+/* default precision */
+#ifndef MP_PREC
+ #ifndef MP_LOW_MEM
+ #define MP_PREC 32 /* default digits of precision */
+ #else
+ #define MP_PREC 8 /* default digits of precision */
+ #endif
+#endif
+
+/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
+#define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
+
+/* the infamous mp_int structure */
+typedef struct {
+ int used, alloc, sign;
+ mp_digit *dp;
+} mp_int;
+
+
+/* ---> Basic Manipulations <--- */
+#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
+#define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
+#define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
+
+
+/* prototypes for copied functions */
+#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
+static int s_mp_exptmod(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
+static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
+static int s_mp_sqr(mp_int * a, mp_int * b);
+static int s_mp_mul_high_digs(mp_int * a, mp_int * b, mp_int * c, int digs);
+
+static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
+
+#ifdef BN_MP_INIT_MULTI_C
+static int mp_init_multi(mp_int *mp, ...);
+#endif
+#ifdef BN_MP_CLEAR_MULTI_C
+static void mp_clear_multi(mp_int *mp, ...);
+#endif
+static int mp_lshd(mp_int * a, int b);
+static void mp_set(mp_int * a, mp_digit b);
+static void mp_clamp(mp_int * a);
+static void mp_exch(mp_int * a, mp_int * b);
+static void mp_rshd(mp_int * a, int b);
+static void mp_zero(mp_int * a);
+static int mp_mod_2d(mp_int * a, int b, mp_int * c);
+static int mp_div_2d(mp_int * a, int b, mp_int * c, mp_int * d);
+static int mp_init_copy(mp_int * a, mp_int * b);
+static int mp_mul_2d(mp_int * a, int b, mp_int * c);
+#ifndef LTM_NO_NEG_EXP
+static int mp_div_2(mp_int * a, mp_int * b);
+static int mp_invmod(mp_int * a, mp_int * b, mp_int * c);
+static int mp_invmod_slow(mp_int * a, mp_int * b, mp_int * c);
+#endif /* LTM_NO_NEG_EXP */
+static int mp_copy(mp_int * a, mp_int * b);
+static int mp_count_bits(mp_int * a);
+static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
+static int mp_mod(mp_int * a, mp_int * b, mp_int * c);
+static int mp_grow(mp_int * a, int size);
+static int mp_cmp_mag(mp_int * a, mp_int * b);
+#ifdef BN_MP_ABS_C
+static int mp_abs(mp_int * a, mp_int * b);
+#endif
+static int mp_sqr(mp_int * a, mp_int * b);
+static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
+static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
+static int mp_2expt(mp_int * a, int b);
+static int mp_reduce_setup(mp_int * a, mp_int * b);
+static int mp_reduce(mp_int * x, mp_int * m, mp_int * mu);
+static int mp_init_size(mp_int * a, int size);
+#ifdef BN_MP_EXPTMOD_FAST_C
+static int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
+#endif /* BN_MP_EXPTMOD_FAST_C */
+#ifdef BN_FAST_S_MP_SQR_C
+static int fast_s_mp_sqr (mp_int * a, mp_int * b);
+#endif /* BN_FAST_S_MP_SQR_C */
+#ifdef BN_MP_MUL_D_C
+static int mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
+#endif /* BN_MP_MUL_D_C */
+
+
+
+/* functions from bn_<func name>.c */
+
+
+/* reverse an array, used for radix code */
+static void bn_reverse (unsigned char *s, int len)
+{
+ int ix, iy;
+ unsigned char t;
+
+ ix = 0;
+ iy = len - 1;
+ while (ix < iy) {
+ t = s[ix];
+ s[ix] = s[iy];
+ s[iy] = t;
+ ++ix;
+ --iy;
+ }
+}
+
+
+/* low level addition, based on HAC pp.594, Algorithm 14.7 */
+static int s_mp_add (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int *x;
+ int olduse, res, min, max;
+
+ /* find sizes, we let |a| <= |b| which means we have to sort
+ * them. "x" will point to the input with the most digits
+ */
+ if (a->used > b->used) {
+ min = b->used;
+ max = a->used;
+ x = a;
+ } else {
+ min = a->used;
+ max = b->used;
+ x = b;
+ }
+
+ /* init result */
+ if (c->alloc < max + 1) {
+ if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* get old used digit count and set new one */
+ olduse = c->used;
+ c->used = max + 1;
+
+ {
+ register mp_digit u, *tmpa, *tmpb, *tmpc;
+ register int i;
+
+ /* alias for digit pointers */
+
+ /* first input */
+ tmpa = a->dp;
+
+ /* second input */
+ tmpb = b->dp;
+
+ /* destination */
+ tmpc = c->dp;
+
+ /* zero the carry */
+ u = 0;
+ for (i = 0; i < min; i++) {
+ /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
+ *tmpc = *tmpa++ + *tmpb++ + u;
+
+ /* U = carry bit of T[i] */
+ u = *tmpc >> ((mp_digit)DIGIT_BIT);
+
+ /* take away carry bit from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+
+ /* now copy higher words if any, that is in A+B
+ * if A or B has more digits add those in
+ */
+ if (min != max) {
+ for (; i < max; i++) {
+ /* T[i] = X[i] + U */
+ *tmpc = x->dp[i] + u;
+
+ /* U = carry bit of T[i] */
+ u = *tmpc >> ((mp_digit)DIGIT_BIT);
+
+ /* take away carry bit from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+ }
+
+ /* add carry */
+ *tmpc++ = u;
+
+ /* clear digits above oldused */
+ for (i = c->used; i < olduse; i++) {
+ *tmpc++ = 0;
+ }
+ }
+
+ mp_clamp (c);
+ return MP_OKAY;
+}
+
+
+/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
+static int s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
+{
+ int olduse, res, min, max;
+
+ /* find sizes */
+ min = b->used;
+ max = a->used;
+
+ /* init result */
+ if (c->alloc < max) {
+ if ((res = mp_grow (c, max)) != MP_OKAY) {
+ return res;
+ }
+ }
+ olduse = c->used;
+ c->used = max;
+
+ {
+ register mp_digit u, *tmpa, *tmpb, *tmpc;
+ register int i;
+
+ /* alias for digit pointers */
+ tmpa = a->dp;
+ tmpb = b->dp;
+ tmpc = c->dp;
+
+ /* set carry to zero */
+ u = 0;
+ for (i = 0; i < min; i++) {
+ /* T[i] = A[i] - B[i] - U */
+ *tmpc = *tmpa++ - *tmpb++ - u;
+
+ /* U = carry bit of T[i]
+ * Note this saves performing an AND operation since
+ * if a carry does occur it will propagate all the way to the
+ * MSB. As a result a single shift is enough to get the carry
+ */
+ u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
+
+ /* Clear carry from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+
+ /* now copy higher words if any, e.g. if A has more digits than B */
+ for (; i < max; i++) {
+ /* T[i] = A[i] - U */
+ *tmpc = *tmpa++ - u;
+
+ /* U = carry bit of T[i] */
+ u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
+
+ /* Clear carry from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+
+ /* clear digits above used (since we may not have grown result above) */
+ for (i = c->used; i < olduse; i++) {
+ *tmpc++ = 0;
+ }
+ }
+
+ mp_clamp (c);
+ return MP_OKAY;
+}
+
+
+/* init a new mp_int */
+static int mp_init (mp_int * a)
+{
+ int i;
+
+ /* allocate memory required and clear it */
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
+ if (a->dp == NULL) {
+ return MP_MEM;
+ }
+
+ /* set the digits to zero */
+ for (i = 0; i < MP_PREC; i++) {
+ a->dp[i] = 0;
+ }
+
+ /* set the used to zero, allocated digits to the default precision
+ * and sign to positive */
+ a->used = 0;
+ a->alloc = MP_PREC;
+ a->sign = MP_ZPOS;
+
+ return MP_OKAY;
+}
+
+
+/* clear one (frees) */
+static void mp_clear (mp_int * a)
+{
+ int i;
+
+ /* only do anything if a hasn't been freed previously */
+ if (a->dp != NULL) {
+ /* first zero the digits */
+ for (i = 0; i < a->used; i++) {
+ a->dp[i] = 0;
+ }
+
+ /* free ram */
+ XFREE(a->dp);
+
+ /* reset members to make debugging easier */
+ a->dp = NULL;
+ a->alloc = a->used = 0;
+ a->sign = MP_ZPOS;
+ }
+}
+
+
+/* high level addition (handles signs) */
+static int mp_add (mp_int * a, mp_int * b, mp_int * c)
+{
+ int sa, sb, res;
+
+ /* get sign of both inputs */
+ sa = a->sign;
+ sb = b->sign;
+
+ /* handle two cases, not four */
+ if (sa == sb) {
+ /* both positive or both negative */
+ /* add their magnitudes, copy the sign */
+ c->sign = sa;
+ res = s_mp_add (a, b, c);
+ } else {
+ /* one positive, the other negative */
+ /* subtract the one with the greater magnitude from */
+ /* the one of the lesser magnitude. The result gets */
+ /* the sign of the one with the greater magnitude. */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ c->sign = sb;
+ res = s_mp_sub (b, a, c);
+ } else {
+ c->sign = sa;
+ res = s_mp_sub (a, b, c);
+ }
+ }
+ return res;
+}
+
+
+/* high level subtraction (handles signs) */
+static int mp_sub (mp_int * a, mp_int * b, mp_int * c)
+{
+ int sa, sb, res;
+
+ sa = a->sign;
+ sb = b->sign;
+
+ if (sa != sb) {
+ /* subtract a negative from a positive, OR */
+ /* subtract a positive from a negative. */
+ /* In either case, ADD their magnitudes, */
+ /* and use the sign of the first number. */
+ c->sign = sa;
+ res = s_mp_add (a, b, c);
+ } else {
+ /* subtract a positive from a positive, OR */
+ /* subtract a negative from a negative. */
+ /* First, take the difference between their */
+ /* magnitudes, then... */
+ if (mp_cmp_mag (a, b) != MP_LT) {
+ /* Copy the sign from the first */
+ c->sign = sa;
+ /* The first has a larger or equal magnitude */
+ res = s_mp_sub (a, b, c);
+ } else {
+ /* The result has the *opposite* sign from */
+ /* the first number. */
+ c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+ /* The second has a larger magnitude */
+ res = s_mp_sub (b, a, c);
+ }
+ }
+ return res;
+}
+
+
+/* high level multiplication (handles sign) */
+static int mp_mul (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, neg;
+ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+
+ /* use Toom-Cook? */
+#ifdef BN_MP_TOOM_MUL_C
+ if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
+ res = mp_toom_mul(a, b, c);
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_MUL_C
+ /* use Karatsuba? */
+ if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
+ res = mp_karatsuba_mul (a, b, c);
+ } else
+#endif
+ {
+ /* can we use the fast multiplier?
+ *
+ * The fast multiplier can be used if the output will
+ * have less than MP_WARRAY digits and the number of
+ * digits won't affect carry propagation
+ */
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
+ int digs = a->used + b->used + 1;
+
+ if ((digs < MP_WARRAY) &&
+ MIN(a->used, b->used) <=
+ (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ res = fast_s_mp_mul_digs (a, b, c, digs);
+ } else
+#endif
+#ifdef BN_S_MP_MUL_DIGS_C
+ res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+#else
+#error mp_mul could fail
+ res = MP_VAL;
+#endif
+
+ }
+ c->sign = (c->used > 0) ? neg : MP_ZPOS;
+ return res;
+}
+
+
+/* d = a * b (mod c) */
+static int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+ return res;
+}
+
+
+/* c = a mod b, 0 <= c < b */
+static int mp_mod (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int t;
+ int res;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+
+ if (t.sign != b->sign) {
+ res = mp_add (b, &t, c);
+ } else {
+ res = MP_OKAY;
+ mp_exch (&t, c);
+ }
+
+ mp_clear (&t);
+ return res;
+}
+
+
+/* this is a shell function that calls either the normal or Montgomery
+ * exptmod functions. Originally the call to the montgomery code was
+ * embedded in the normal function but that wasted alot of stack space
+ * for nothing (since 99% of the time the Montgomery code would be called)
+ */
+static int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
+{
+ int dr;
+
+ /* modulus P must be positive */
+ if (P->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* if exponent X is negative we have to recurse */
+ if (X->sign == MP_NEG) {
+#ifdef LTM_NO_NEG_EXP
+ return MP_VAL;
+#else /* LTM_NO_NEG_EXP */
+#ifdef BN_MP_INVMOD_C
+ mp_int tmpG, tmpX;
+ int err;
+
+ /* first compute 1/G mod P */
+ if ((err = mp_init(&tmpG)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
+ mp_clear(&tmpG);
+ return err;
+ }
+
+ /* now get |X| */
+ if ((err = mp_init(&tmpX)) != MP_OKAY) {
+ mp_clear(&tmpG);
+ return err;
+ }
+ if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
+ mp_clear_multi(&tmpG, &tmpX, NULL);
+ return err;
+ }
+
+ /* and now compute (1/G)**|X| instead of G**X [X < 0] */
+ err = mp_exptmod(&tmpG, &tmpX, P, Y);
+ mp_clear_multi(&tmpG, &tmpX, NULL);
+ return err;
+#else
+#error mp_exptmod would always fail
+ /* no invmod */
+ return MP_VAL;
+#endif
+#endif /* LTM_NO_NEG_EXP */
+ }
+
+/* modified diminished radix reduction */
+#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
+ if (mp_reduce_is_2k_l(P) == MP_YES) {
+ return s_mp_exptmod(G, X, P, Y, 1);
+ }
+#endif
+
+#ifdef BN_MP_DR_IS_MODULUS_C
+ /* is it a DR modulus? */
+ dr = mp_dr_is_modulus(P);
+#else
+ /* default to no */
+ dr = 0;
+#endif
+
+#ifdef BN_MP_REDUCE_IS_2K_C
+ /* if not, is it a unrestricted DR modulus? */
+ if (dr == 0) {
+ dr = mp_reduce_is_2k(P) << 1;
+ }
+#endif
+
+ /* if the modulus is odd or dr != 0 use the montgomery method */
+#ifdef BN_MP_EXPTMOD_FAST_C
+ if (mp_isodd (P) == 1 || dr != 0) {
+ return mp_exptmod_fast (G, X, P, Y, dr);
+ } else {
+#endif
+#ifdef BN_S_MP_EXPTMOD_C
+ /* otherwise use the generic Barrett reduction technique */
+ return s_mp_exptmod (G, X, P, Y, 0);
+#else
+#error mp_exptmod could fail
+ /* no exptmod for evens */
+ return MP_VAL;
+#endif
+#ifdef BN_MP_EXPTMOD_FAST_C
+ }
+#endif
+}
+
+
+/* compare two ints (signed)*/
+static int mp_cmp (mp_int * a, mp_int * b)
+{
+ /* compare based on sign */
+ if (a->sign != b->sign) {
+ if (a->sign == MP_NEG) {
+ return MP_LT;
+ } else {
+ return MP_GT;
+ }
+ }
+
+ /* compare digits */
+ if (a->sign == MP_NEG) {
+ /* if negative compare opposite direction */
+ return mp_cmp_mag(b, a);
+ } else {
+ return mp_cmp_mag(a, b);
+ }
+}
+
+
+/* compare a digit */
+static int mp_cmp_d(mp_int * a, mp_digit b)
+{
+ /* compare based on sign */
+ if (a->sign == MP_NEG) {
+ return MP_LT;
+ }
+
+ /* compare based on magnitude */
+ if (a->used > 1) {
+ return MP_GT;
+ }
+
+ /* compare the only digit of a to b */
+ if (a->dp[0] > b) {
+ return MP_GT;
+ } else if (a->dp[0] < b) {
+ return MP_LT;
+ } else {
+ return MP_EQ;
+ }
+}
+
+
+#ifndef LTM_NO_NEG_EXP
+/* hac 14.61, pp608 */
+static int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+#ifdef BN_FAST_MP_INVMOD_C
+ /* if the modulus is odd we can use a faster routine instead */
+ if (mp_isodd (b) == 1) {
+ return fast_mp_invmod (a, b, c);
+ }
+#endif
+
+#ifdef BN_MP_INVMOD_SLOW_C
+ return mp_invmod_slow(a, b, c);
+#endif
+
+#ifndef BN_FAST_MP_INVMOD_C
+#ifndef BN_MP_INVMOD_SLOW_C
+#error mp_invmod would always fail
+#endif
+#endif
+ return MP_VAL;
+}
+#endif /* LTM_NO_NEG_EXP */
+
+
+/* get the size for an unsigned equivalent */
+static int mp_unsigned_bin_size (mp_int * a)
+{
+ int size = mp_count_bits (a);
+ return (size / 8 + ((size & 7) != 0 ? 1 : 0));
+}
+
+
+#ifndef LTM_NO_NEG_EXP
+/* hac 14.61, pp608 */
+static int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, A, B, C, D;
+ int res;
+
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+ /* init temps */
+ if ((res = mp_init_multi(&x, &y, &u, &v,
+ &A, &B, &C, &D, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* x = a, y = b */
+ if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (b, &y)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* 2. [modified] if x,y are both even then return an error! */
+ if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+ if ((res = mp_copy (&x, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (&y, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ mp_set (&A, 1);
+ mp_set (&D, 1);
+
+top:
+ /* 4. while u is even do */
+ while (mp_iseven (&u) == 1) {
+ /* 4.1 u = u/2 */
+ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 4.2 if A or B is odd then */
+ if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
+ /* A = (A+y)/2, B = (B-x)/2 */
+ if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* A = A/2, B = B/2 */
+ if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 5. while v is even do */
+ while (mp_iseven (&v) == 1) {
+ /* 5.1 v = v/2 */
+ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 5.2 if C or D is odd then */
+ if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
+ /* C = (C+y)/2, D = (D-x)/2 */
+ if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* C = C/2, D = D/2 */
+ if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 6. if u >= v then */
+ if (mp_cmp (&u, &v) != MP_LT) {
+ /* u = u - v, A = A - C, B = B - D */
+ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ } else {
+ /* v - v - u, C = C - A, D = D - B */
+ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* if not zero goto step 4 */
+ if (mp_iszero (&u) == 0)
+ goto top;
+
+ /* now a = C, b = D, gcd == g*v */
+
+ /* if v != 1 then there is no inverse */
+ if (mp_cmp_d (&v, 1) != MP_EQ) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* if its too low */
+ while (mp_cmp_d(&C, 0) == MP_LT) {
+ if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* too big */
+ while (mp_cmp_mag(&C, b) != MP_LT) {
+ if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* C is now the inverse */
+ mp_exch (&C, c);
+ res = MP_OKAY;
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
+ return res;
+}
+#endif /* LTM_NO_NEG_EXP */
+
+
+/* compare maginitude of two ints (unsigned) */
+static int mp_cmp_mag (mp_int * a, mp_int * b)
+{
+ int n;
+ mp_digit *tmpa, *tmpb;
+
+ /* compare based on # of non-zero digits */
+ if (a->used > b->used) {
+ return MP_GT;
+ }
+
+ if (a->used < b->used) {
+ return MP_LT;
+ }
+
+ /* alias for a */
+ tmpa = a->dp + (a->used - 1);
+
+ /* alias for b */
+ tmpb = b->dp + (a->used - 1);
+
+ /* compare based on digits */
+ for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
+ if (*tmpa > *tmpb) {
+ return MP_GT;
+ }
+
+ if (*tmpa < *tmpb) {
+ return MP_LT;
+ }
+ }
+ return MP_EQ;
+}
+
+
+/* reads a unsigned char array, assumes the msb is stored first [big endian] */
+static int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
+{
+ int res;
+
+ /* make sure there are at least two digits */
+ if (a->alloc < 2) {
+ if ((res = mp_grow(a, 2)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* zero the int */
+ mp_zero (a);
+
+ /* read the bytes in */
+ while (c-- > 0) {
+ if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
+ return res;
+ }
+
+#ifndef MP_8BIT
+ a->dp[0] |= *b++;
+ a->used += 1;
+#else
+ a->dp[0] = (*b & MP_MASK);
+ a->dp[1] |= ((*b++ >> 7U) & 1);
+ a->used += 2;
+#endif
+ }
+ mp_clamp (a);
+ return MP_OKAY;
+}
+
+
+/* store in unsigned [big endian] format */
+static int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
+{
+ int x, res;
+ mp_int t;
+
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ x = 0;
+ while (mp_iszero (&t) == 0) {
+#ifndef MP_8BIT
+ b[x++] = (unsigned char) (t.dp[0] & 255);
+#else
+ b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
+#endif
+ if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ }
+ bn_reverse (b, x);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+
+
+/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
+static int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
+{
+ mp_digit D, r, rr;
+ int x, res;
+ mp_int t;
+
+
+ /* if the shift count is <= 0 then we do no work */
+ if (b <= 0) {
+ res = mp_copy (a, c);
+ if (d != NULL) {
+ mp_zero (d);
+ }
+ return res;
+ }
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ /* get the remainder */
+ if (d != NULL) {
+ if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ }
+
+ /* copy */
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+
+ /* shift by as many digits in the bit count */
+ if (b >= (int)DIGIT_BIT) {
+ mp_rshd (c, b / DIGIT_BIT);
+ }
+
+ /* shift any bit count < DIGIT_BIT */
+ D = (mp_digit) (b % DIGIT_BIT);
+ if (D != 0) {
+ register mp_digit *tmpc, mask, shift;
+
+ /* mask */
+ mask = (((mp_digit)1) << D) - 1;
+
+ /* shift for lsb */
+ shift = DIGIT_BIT - D;
+
+ /* alias */
+ tmpc = c->dp + (c->used - 1);
+
+ /* carry */
+ r = 0;
+ for (x = c->used - 1; x >= 0; x--) {
+ /* get the lower bits of this word in a temp */
+ rr = *tmpc & mask;
+
+ /* shift the current word and mix in the carry bits from the previous word */
+ *tmpc = (*tmpc >> D) | (r << shift);
+ --tmpc;
+
+ /* set the carry to the carry bits of the current word found above */
+ r = rr;
+ }
+ }
+ mp_clamp (c);
+ if (d != NULL) {
+ mp_exch (&t, d);
+ }
+ mp_clear (&t);
+ return MP_OKAY;
+}
+
+
+static int mp_init_copy (mp_int * a, mp_int * b)
+{
+ int res;
+
+ if ((res = mp_init (a)) != MP_OKAY) {
+ return res;
+ }
+ return mp_copy (b, a);
+}
+
+
+/* set to zero */
+static void mp_zero (mp_int * a)
+{
+ int n;
+ mp_digit *tmp;
+
+ a->sign = MP_ZPOS;
+ a->used = 0;
+
+ tmp = a->dp;
+ for (n = 0; n < a->alloc; n++) {
+ *tmp++ = 0;
+ }
+}
+
+
+/* copy, b = a */
+static int mp_copy (mp_int * a, mp_int * b)
+{
+ int res, n;
+
+ /* if dst == src do nothing */
+ if (a == b) {
+ return MP_OKAY;
+ }
+
+ /* grow dest */
+ if (b->alloc < a->used) {
+ if ((res = mp_grow (b, a->used)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* zero b and copy the parameters over */
+ {
+ register mp_digit *tmpa, *tmpb;
+
+ /* pointer aliases */
+
+ /* source */
+ tmpa = a->dp;
+
+ /* destination */
+ tmpb = b->dp;
+
+ /* copy all the digits */
+ for (n = 0; n < a->used; n++) {
+ *tmpb++ = *tmpa++;
+ }
+
+ /* clear high digits */
+ for (; n < b->used; n++) {
+ *tmpb++ = 0;
+ }
+ }
+
+ /* copy used count and sign */
+ b->used = a->used;
+ b->sign = a->sign;
+ return MP_OKAY;
+}
+
+
+/* shift right a certain amount of digits */
+static void mp_rshd (mp_int * a, int b)
+{
+ int x;
+
+ /* if b <= 0 then ignore it */
+ if (b <= 0) {
+ return;
+ }
+
+ /* if b > used then simply zero it and return */
+ if (a->used <= b) {
+ mp_zero (a);
+ return;
+ }
+
+ {
+ register mp_digit *bottom, *top;
+
+ /* shift the digits down */
+
+ /* bottom */
+ bottom = a->dp;
+
+ /* top [offset into digits] */
+ top = a->dp + b;
+
+ /* this is implemented as a sliding window where
+ * the window is b-digits long and digits from
+ * the top of the window are copied to the bottom
+ *
+ * e.g.
+
+ b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
+ /\ | ---->
+ \-------------------/ ---->
+ */
+ for (x = 0; x < (a->used - b); x++) {
+ *bottom++ = *top++;
+ }
+
+ /* zero the top digits */
+ for (; x < a->used; x++) {
+ *bottom++ = 0;
+ }
+ }
+
+ /* remove excess digits */
+ a->used -= b;
+}
+
+
+/* swap the elements of two integers, for cases where you can't simply swap the
+ * mp_int pointers around
+ */
+static void mp_exch (mp_int * a, mp_int * b)
+{
+ mp_int t;
+
+ t = *a;
+ *a = *b;
+ *b = t;
+}
+
+
+/* trim unused digits
+ *
+ * This is used to ensure that leading zero digits are
+ * trimed and the leading "used" digit will be non-zero
+ * Typically very fast. Also fixes the sign if there
+ * are no more leading digits
+ */
+static void mp_clamp (mp_int * a)
+{
+ /* decrease used while the most significant digit is
+ * zero.
+ */
+ while (a->used > 0 && a->dp[a->used - 1] == 0) {
+ --(a->used);
+ }
+
+ /* reset the sign flag if used == 0 */
+ if (a->used == 0) {
+ a->sign = MP_ZPOS;
+ }
+}
+
+
+/* grow as required */
+static int mp_grow (mp_int * a, int size)
+{
+ int i;
+ mp_digit *tmp;
+
+ /* if the alloc size is smaller alloc more ram */
+ if (a->alloc < size) {
+ /* ensure there are always at least MP_PREC digits extra on top */
+ size += (MP_PREC * 2) - (size % MP_PREC);
+
+ /* reallocate the array a->dp
+ *
+ * We store the return in a temporary variable
+ * in case the operation failed we don't want
+ * to overwrite the dp member of a.
+ */
+ tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
+ if (tmp == NULL) {
+ /* reallocation failed but "a" is still valid [can be freed] */
+ return MP_MEM;
+ }
+
+ /* reallocation succeeded so set a->dp */
+ a->dp = tmp;
+
+ /* zero excess digits */
+ i = a->alloc;
+ a->alloc = size;
+ for (; i < a->alloc; i++) {
+ a->dp[i] = 0;
+ }
+ }
+ return MP_OKAY;
+}
+
+
+#ifdef BN_MP_ABS_C
+/* b = |a|
+ *
+ * Simple function copies the input and fixes the sign to positive
+ */
+static int mp_abs (mp_int * a, mp_int * b)
+{
+ int res;
+
+ /* copy a to b */
+ if (a != b) {
+ if ((res = mp_copy (a, b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* force the sign of b to positive */
+ b->sign = MP_ZPOS;
+
+ return MP_OKAY;
+}
+#endif
+
+
+/* set to a digit */
+static void mp_set (mp_int * a, mp_digit b)
+{
+ mp_zero (a);
+ a->dp[0] = b & MP_MASK;
+ a->used = (a->dp[0] != 0) ? 1 : 0;
+}
+
+
+#ifndef LTM_NO_NEG_EXP
+/* b = a/2 */
+static int mp_div_2(mp_int * a, mp_int * b)
+{
+ int x, res, oldused;
+
+ /* copy */
+ if (b->alloc < a->used) {
+ if ((res = mp_grow (b, a->used)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ oldused = b->used;
+ b->used = a->used;
+ {
+ register mp_digit r, rr, *tmpa, *tmpb;
+
+ /* source alias */
+ tmpa = a->dp + b->used - 1;
+
+ /* dest alias */
+ tmpb = b->dp + b->used - 1;
+
+ /* carry */
+ r = 0;
+ for (x = b->used - 1; x >= 0; x--) {
+ /* get the carry for the next iteration */
+ rr = *tmpa & 1;
+
+ /* shift the current digit, add in carry and store */
+ *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
+
+ /* forward carry to next iteration */
+ r = rr;
+ }
+
+ /* zero excess digits */
+ tmpb = b->dp + b->used;
+ for (x = b->used; x < oldused; x++) {
+ *tmpb++ = 0;
+ }
+ }
+ b->sign = a->sign;
+ mp_clamp (b);
+ return MP_OKAY;
+}
+#endif /* LTM_NO_NEG_EXP */
+
+
+/* shift left by a certain bit count */
+static int mp_mul_2d (mp_int * a, int b, mp_int * c)
+{
+ mp_digit d;
+ int res;
+
+ /* copy */
+ if (a != c) {
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
+ if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* shift by as many digits in the bit count */
+ if (b >= (int)DIGIT_BIT) {
+ if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* shift any bit count < DIGIT_BIT */
+ d = (mp_digit) (b % DIGIT_BIT);
+ if (d != 0) {
+ register mp_digit *tmpc, shift, mask, r, rr;
+ register int x;
+
+ /* bitmask for carries */
+ mask = (((mp_digit)1) << d) - 1;
+
+ /* shift for msbs */
+ shift = DIGIT_BIT - d;
+
+ /* alias */
+ tmpc = c->dp;
+
+ /* carry */
+ r = 0;
+ for (x = 0; x < c->used; x++) {
+ /* get the higher bits of the current word */
+ rr = (*tmpc >> shift) & mask;
+
+ /* shift the current word and OR in the carry */
+ *tmpc = ((*tmpc << d) | r) & MP_MASK;
+ ++tmpc;
+
+ /* set the carry to the carry bits of the current word */
+ r = rr;
+ }
+
+ /* set final carry */
+ if (r != 0) {
+ c->dp[(c->used)++] = r;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+
+
+#ifdef BN_MP_INIT_MULTI_C
+static int mp_init_multi(mp_int *mp, ...)
+{
+ mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
+ int n = 0; /* Number of ok inits */
+ mp_int* cur_arg = mp;
+ va_list args;
+
+ va_start(args, mp); /* init args to next argument from caller */
+ while (cur_arg != NULL) {
+ if (mp_init(cur_arg) != MP_OKAY) {
+ /* Oops - error! Back-track and mp_clear what we already
+ succeeded in init-ing, then return error.
+ */
+ va_list clean_args;
+
+ /* end the current list */
+ va_end(args);
+
+ /* now start cleaning up */
+ cur_arg = mp;
+ va_start(clean_args, mp);
+ while (n--) {
+ mp_clear(cur_arg);
+ cur_arg = va_arg(clean_args, mp_int*);
+ }
+ va_end(clean_args);
+ res = MP_MEM;
+ break;
+ }
+ n++;
+ cur_arg = va_arg(args, mp_int*);
+ }
+ va_end(args);
+ return res; /* Assumed ok, if error flagged above. */
+}
+#endif
+
+
+#ifdef BN_MP_CLEAR_MULTI_C
+static void mp_clear_multi(mp_int *mp, ...)
+{
+ mp_int* next_mp = mp;
+ va_list args;
+ va_start(args, mp);
+ while (next_mp != NULL) {
+ mp_clear(next_mp);
+ next_mp = va_arg(args, mp_int*);
+ }
+ va_end(args);
+}
+#endif
+
+
+/* shift left a certain amount of digits */
+static int mp_lshd (mp_int * a, int b)
+{
+ int x, res;
+
+ /* if its less than zero return */
+ if (b <= 0) {
+ return MP_OKAY;
+ }
+
+ /* grow to fit the new digits */
+ if (a->alloc < a->used + b) {
+ if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ {
+ register mp_digit *top, *bottom;
+
+ /* increment the used by the shift amount then copy upwards */
+ a->used += b;
+
+ /* top */
+ top = a->dp + a->used - 1;
+
+ /* base */
+ bottom = a->dp + a->used - 1 - b;
+
+ /* much like mp_rshd this is implemented using a sliding window
+ * except the window goes the otherway around. Copying from
+ * the bottom to the top. see bn_mp_rshd.c for more info.
+ */
+ for (x = a->used - 1; x >= b; x--) {
+ *top-- = *bottom--;
+ }
+
+ /* zero the lower digits */
+ top = a->dp;
+ for (x = 0; x < b; x++) {
+ *top++ = 0;
+ }
+ }
+ return MP_OKAY;
+}
+
+
+/* returns the number of bits in an int */
+static int mp_count_bits (mp_int * a)
+{
+ int r;
+ mp_digit q;
+
+ /* shortcut */
+ if (a->used == 0) {
+ return 0;
+ }
+
+ /* get number of digits and add that */
+ r = (a->used - 1) * DIGIT_BIT;
+
+ /* take the last digit and count the bits in it */
+ q = a->dp[a->used - 1];
+ while (q > ((mp_digit) 0)) {
+ ++r;
+ q >>= ((mp_digit) 1);
+ }
+ return r;
+}
+
+
+/* calc a value mod 2**b */
+static int mp_mod_2d (mp_int * a, int b, mp_int * c)
+{
+ int x, res;
+
+ /* if b is <= 0 then zero the int */
+ if (b <= 0) {
+ mp_zero (c);
+ return MP_OKAY;
+ }
+
+ /* if the modulus is larger than the value than return */
+ if (b >= (int) (a->used * DIGIT_BIT)) {
+ res = mp_copy (a, c);
+ return res;
+ }
+
+ /* copy */
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ return res;
+ }
+
+ /* zero digits above the last digit of the modulus */
+ for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
+ c->dp[x] = 0;
+ }
+ /* clear the digit that is not completely outside/inside the modulus */
+ c->dp[b / DIGIT_BIT] &=
+ (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
+ mp_clamp (c);
+ return MP_OKAY;
+}
+
+
+#ifdef BN_MP_DIV_SMALL
+
+/* slower bit-bang division... also smaller */
+static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int ta, tb, tq, q;
+ int res, n, n2;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ /* init our temps */
+ if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
+ return res;
+ }
+
+
+ mp_set(&tq, 1);
+ n = mp_count_bits(a) - mp_count_bits(b);
+ if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
+ ((res = mp_abs(b, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+
+ while (n-- >= 0) {
+ if (mp_cmp(&tb, &ta) != MP_GT) {
+ if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+ ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+ }
+ if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+ ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* now q == quotient and ta == remainder */
+ n = a->sign;
+ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+ if (c != NULL) {
+ mp_exch(c, &q);
+ c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
+ }
+ if (d != NULL) {
+ mp_exch(d, &ta);
+ d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
+ }
+LBL_ERR:
+ mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+ return res;
+}
+
+#else
+
+/* integer signed division.
+ * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
+ * HAC pp.598 Algorithm 14.20
+ *
+ * Note that the description in HAC is horribly
+ * incomplete. For example, it doesn't consider
+ * the case where digits are removed from 'x' in
+ * the inner loop. It also doesn't consider the
+ * case that y has fewer than three digits, etc..
+ *
+ * The overall algorithm is as described as
+ * 14.20 from HAC but fixed to treat these cases.
+*/
+static int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int q, x, y, t1, t2;
+ int res, n, t, i, norm, neg;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
+ return res;
+ }
+ q.used = a->used + 2;
+
+ if ((res = mp_init (&t1)) != MP_OKAY) {
+ goto LBL_Q;
+ }
+
+ if ((res = mp_init (&t2)) != MP_OKAY) {
+ goto LBL_T1;
+ }
+
+ if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
+ goto LBL_T2;
+ }
+
+ if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
+ goto LBL_X;
+ }
+
+ /* fix the sign */
+ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+ x.sign = y.sign = MP_ZPOS;
+
+ /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
+ norm = mp_count_bits(&y) % DIGIT_BIT;
+ if (norm < (int)(DIGIT_BIT-1)) {
+ norm = (DIGIT_BIT-1) - norm;
+ if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ } else {
+ norm = 0;
+ }
+
+ /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
+ n = x.used - 1;
+ t = y.used - 1;
+
+ /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
+ if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
+ goto LBL_Y;
+ }
+
+ while (mp_cmp (&x, &y) != MP_LT) {
+ ++(q.dp[n - t]);
+ if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ }
+
+ /* reset y by shifting it back down */
+ mp_rshd (&y, n - t);
+
+ /* step 3. for i from n down to (t + 1) */
+ for (i = n; i >= (t + 1); i--) {
+ if (i > x.used) {
+ continue;
+ }
+
+ /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
+ * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
+ if (x.dp[i] == y.dp[t]) {
+ q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
+ } else {
+ mp_word tmp;
+ tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
+ tmp |= ((mp_word) x.dp[i - 1]);
+ tmp /= ((mp_word) y.dp[t]);
+ if (tmp > (mp_word) MP_MASK)
+ tmp = MP_MASK;
+ q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
+ }
+
+ /* while (q{i-t-1} * (yt * b + y{t-1})) >
+ xi * b**2 + xi-1 * b + xi-2
+
+ do q{i-t-1} -= 1;
+ */
+ q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
+ do {
+ q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
+
+ /* find left hand */
+ mp_zero (&t1);
+ t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
+ t1.dp[1] = y.dp[t];
+ t1.used = 2;
+ if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* find right hand */
+ t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
+ t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
+ t2.dp[2] = x.dp[i];
+ t2.used = 3;
+ } while (mp_cmp_mag(&t1, &t2) == MP_GT);
+
+ /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
+ if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
+ if (x.sign == MP_NEG) {
+ if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
+ }
+ }
+
+ /* now q is the quotient and x is the remainder
+ * [which we have to normalize]
+ */
+
+ /* get sign before writing to c */
+ x.sign = x.used == 0 ? MP_ZPOS : a->sign;
+
+ if (c != NULL) {
+ mp_clamp (&q);
+ mp_exch (&q, c);
+ c->sign = neg;
+ }
+
+ if (d != NULL) {
+ mp_div_2d (&x, norm, &x, NULL);
+ mp_exch (&x, d);
+ }
+
+ res = MP_OKAY;
+
+LBL_Y:mp_clear (&y);
+LBL_X:mp_clear (&x);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
+LBL_Q:mp_clear (&q);
+ return res;
+}
+
+#endif
+
+
+#ifdef MP_LOW_MEM
+ #define TAB_SIZE 32
+#else
+ #define TAB_SIZE 256
+#endif
+
+static int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+{
+ mp_int M[TAB_SIZE], res, mu;
+ mp_digit buf;
+ int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+ int (*redux)(mp_int*,mp_int*,mp_int*);
+
+ /* find window size */
+ x = mp_count_bits (X);
+ if (x <= 7) {
+ winsize = 2;
+ } else if (x <= 36) {
+ winsize = 3;
+ } else if (x <= 140) {
+ winsize = 4;
+ } else if (x <= 450) {
+ winsize = 5;
+ } else if (x <= 1303) {
+ winsize = 6;
+ } else if (x <= 3529) {
+ winsize = 7;
+ } else {
+ winsize = 8;
+ }
+
+#ifdef MP_LOW_MEM
+ if (winsize > 5) {
+ winsize = 5;
+ }
+#endif
+
+ /* init M array */
+ /* init first cell */
+ if ((err = mp_init(&M[1])) != MP_OKAY) {
+ return err;
+ }
+
+ /* now init the second half of the array */
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ if ((err = mp_init(&M[x])) != MP_OKAY) {
+ for (y = 1<<(winsize-1); y < x; y++) {
+ mp_clear (&M[y]);
+ }
+ mp_clear(&M[1]);
+ return err;
+ }
+ }
+
+ /* create mu, used for Barrett reduction */
+ if ((err = mp_init (&mu)) != MP_OKAY) {
+ goto LBL_M;
+ }
+
+ if (redmode == 0) {
+ if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ redux = mp_reduce;
+ } else {
+ if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ redux = mp_reduce_2k_l;
+ }
+
+ /* create M table
+ *
+ * The M table contains powers of the base,
+ * e.g. M[x] = G**x mod P
+ *
+ * The first half of the table is not
+ * computed though accept for M[0] and M[1]
+ */
+ if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* compute the value at M[1<<(winsize-1)] by squaring
+ * M[1] (winsize-1) times
+ */
+ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ for (x = 0; x < (winsize - 1); x++) {
+ /* square it */
+ if ((err = mp_sqr (&M[1 << (winsize - 1)],
+ &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* reduce modulo P */
+ if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
+ * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
+ */
+ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
+ if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* setup result */
+ if ((err = mp_init (&res)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ mp_set (&res, 1);
+
+ /* set initial mode and bit cnt */
+ mode = 0;
+ bitcnt = 1;
+ buf = 0;
+ digidx = X->used - 1;
+ bitcpy = 0;
+ bitbuf = 0;
+
+ for (;;) {
+ /* grab next digit as required */
+ if (--bitcnt == 0) {
+ /* if digidx == -1 we are out of digits */
+ if (digidx == -1) {
+ break;
+ }
+ /* read next digit and reset the bitcnt */
+ buf = X->dp[digidx--];
+ bitcnt = (int) DIGIT_BIT;
+ }
+
+ /* grab the next msb from the exponent */
+ y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
+ buf <<= (mp_digit)1;
+
+ /* if the bit is zero and mode == 0 then we ignore it
+ * These represent the leading zero bits before the first 1 bit
+ * in the exponent. Technically this opt is not required but it
+ * does lower the # of trivial squaring/reductions used
+ */
+ if (mode == 0 && y == 0) {
+ continue;
+ }
+
+ /* if the bit is zero and mode == 1 then we square */
+ if (mode == 1 && y == 0) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ continue;
+ }
+
+ /* else we add it to the window */
+ bitbuf |= (y << (winsize - ++bitcpy));
+ mode = 2;
+
+ if (bitcpy == winsize) {
+ /* ok window is filled so square as required and multiply */
+ /* square first */
+ for (x = 0; x < winsize; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* empty window and reset */
+ bitcpy = 0;
+ bitbuf = 0;
+ mode = 1;
+ }
+ }
+
+ /* if bits remain then square/multiply */
+ if (mode == 2 && bitcpy > 0) {
+ /* square then multiply if the bit is set */
+ for (x = 0; x < bitcpy; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ bitbuf <<= 1;
+ if ((bitbuf & (1 << winsize)) != 0) {
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+ }
+ }
+
+ mp_exch (&res, Y);
+ err = MP_OKAY;
+LBL_RES:mp_clear (&res);
+LBL_MU:mp_clear (&mu);
+LBL_M:
+ mp_clear(&M[1]);
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ mp_clear (&M[x]);
+ }
+ return err;
+}
+
+
+/* computes b = a*a */
+static int mp_sqr (mp_int * a, mp_int * b)
+{
+ int res;
+
+#ifdef BN_MP_TOOM_SQR_C
+ /* use Toom-Cook? */
+ if (a->used >= TOOM_SQR_CUTOFF) {
+ res = mp_toom_sqr(a, b);
+ /* Karatsuba? */
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_SQR_C
+if (a->used >= KARATSUBA_SQR_CUTOFF) {
+ res = mp_karatsuba_sqr (a, b);
+ } else
+#endif
+ {
+#ifdef BN_FAST_S_MP_SQR_C
+ /* can we use the fast comba multiplier? */
+ if ((a->used * 2 + 1) < MP_WARRAY &&
+ a->used <
+ (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
+ res = fast_s_mp_sqr (a, b);
+ } else
+#endif
+#ifdef BN_S_MP_SQR_C
+ res = s_mp_sqr (a, b);
+#else
+#error mp_sqr could fail
+ res = MP_VAL;
+#endif
+ }
+ b->sign = MP_ZPOS;
+ return res;
+}
+
+
+/* reduces a modulo n where n is of the form 2**p - d
+ This differs from reduce_2k since "d" can be larger
+ than a single digit.
+*/
+static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
+{
+ mp_int q;
+ int p, res;
+
+ if ((res = mp_init(&q)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(n);
+top:
+ /* q = a/2**p, a = a mod 2**p */
+ if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* q = q * d */
+ if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* a = a + q */
+ if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (mp_cmp_mag(a, n) != MP_LT) {
+ s_mp_sub(a, n, a);
+ goto top;
+ }
+
+ERR:
+ mp_clear(&q);
+ return res;
+}
+
+
+/* determines the setup value */
+static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
+{
+ int res;
+ mp_int tmp;
+
+ if ((res = mp_init(&tmp)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear(&tmp);
+ return res;
+}
+
+
+/* computes a = 2**b
+ *
+ * Simple algorithm which zeroes the int, grows it then just sets one bit
+ * as required.
+ */
+static int mp_2expt (mp_int * a, int b)
+{
+ int res;
+
+ /* zero a as per default */
+ mp_zero (a);
+
+ /* grow a to accomodate the single bit */
+ if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
+ return res;
+ }
+
+ /* set the used count of where the bit will go */
+ a->used = b / DIGIT_BIT + 1;
+
+ /* put the single bit in its place */
+ a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
+
+ return MP_OKAY;
+}
+
+
+/* pre-calculate the value required for Barrett reduction
+ * For a given modulus "b" it calulates the value required in "a"
+ */
+static int mp_reduce_setup (mp_int * a, mp_int * b)
+{
+ int res;
+
+ if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
+ return res;
+ }
+ return mp_div (a, b, a, NULL);
+}
+
+
+/* reduces x mod m, assumes 0 < x < m**2, mu is
+ * precomputed via mp_reduce_setup.
+ * From HAC pp.604 Algorithm 14.42
+ */
+static int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
+{
+ mp_int q;
+ int res, um = m->used;
+
+ /* q = x */
+ if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
+ return res;
+ }
+
+ /* q1 = x / b**(k-1) */
+ mp_rshd (&q, um - 1);
+
+ /* according to HAC this optimization is ok */
+ if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
+ if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+ } else {
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
+ if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#else
+ {
+#error mp_reduce would always fail
+ res = MP_VAL;
+ goto CLEANUP;
+ }
+#endif
+ }
+
+ /* q3 = q2 / b**(k+1) */
+ mp_rshd (&q, um + 1);
+
+ /* x = x mod b**(k+1), quick (no division) */
+ if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* q = q * m mod b**(k+1), quick (no division) */
+ if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* x = x - q */
+ if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* If x < 0, add b**(k+1) to it */
+ if (mp_cmp_d (x, 0) == MP_LT) {
+ mp_set (&q, 1);
+ if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+ if ((res = mp_add (x, &q, x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+ }
+
+ /* Back off if it's too big */
+ while (mp_cmp (x, m) != MP_LT) {
+ if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+ }
+
+CLEANUP:
+ mp_clear (&q);
+
+ return res;
+}
+
+
+/* multiplies |a| * |b| and only computes upto digs digits of result
+ * HAC pp. 595, Algorithm 14.12 Modified so you can control how
+ * many digits of output are created.
+ */
+static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ mp_int t;
+ int res, pa, pb, ix, iy;
+ mp_digit u;
+ mp_word r;
+ mp_digit tmpx, *tmpt, *tmpy;
+
+ /* can we use the fast multiplier? */
+ if (((digs) < MP_WARRAY) &&
+ MIN (a->used, b->used) <
+ (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ return fast_s_mp_mul_digs (a, b, c, digs);
+ }
+
+ if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
+ return res;
+ }
+ t.used = digs;
+
+ /* compute the digits of the product directly */
+ pa = a->used;
+ for (ix = 0; ix < pa; ix++) {
+ /* set the carry to zero */
+ u = 0;
+
+ /* limit ourselves to making digs digits of output */
+ pb = MIN (b->used, digs - ix);
+
+ /* setup some aliases */
+ /* copy of the digit from a used within the nested loop */
+ tmpx = a->dp[ix];
+
+ /* an alias for the destination shifted ix places */
+ tmpt = t.dp + ix;
+
+ /* an alias for the digits of b */
+ tmpy = b->dp;
+
+ /* compute the columns of the output and propagate the carry */
+ for (iy = 0; iy < pb; iy++) {
+ /* compute the column as a mp_word */
+ r = ((mp_word)*tmpt) +
+ ((mp_word)tmpx) * ((mp_word)*tmpy++) +
+ ((mp_word) u);
+
+ /* the new column is the lower part of the result */
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* get the carry word from the result */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
+ /* set carry if it is placed below digs */
+ if (ix + iy < digs) {
+ *tmpt = u;
+ }
+ }
+
+ mp_clamp (&t);
+ mp_exch (&t, c);
+
+ mp_clear (&t);
+ return MP_OKAY;
+}
+
+
+/* Fast (comba) multiplier
+ *
+ * This is the fast column-array [comba] multiplier. It is
+ * designed to compute the columns of the product first
+ * then handle the carries afterwards. This has the effect
+ * of making the nested loops that compute the columns very
+ * simple and schedulable on super-scalar processors.
+ *
+ * This has been modified to produce a variable number of
+ * digits of output so if say only a half-product is required
+ * you don't have to compute the upper half (a feature
+ * required for fast Barrett reduction).
+ *
+ * Based on Algorithm 14.12 on pp.595 of HAC.
+ *
+ */
+static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ register mp_word _W;
+
+ /* grow the destination as required */
+ if (c->alloc < digs) {
+ if ((res = mp_grow (c, digs)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ pa = MIN(digs, a->used + b->used);
+
+ /* clear the carry */
+ _W = 0;
+ for (ix = 0; ix < pa; ix++) {
+ int tx, ty;
+ int iy;
+ mp_digit *tmpx, *tmpy;
+
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; ++iz) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+
+ }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = c->used;
+ c->used = pa;
+
+ {
+ register mp_digit *tmpc;
+ tmpc = c->dp;
+ for (ix = 0; ix < pa+1; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+
+
+/* init an mp_init for a given size */
+static int mp_init_size (mp_int * a, int size)
+{
+ int x;
+
+ /* pad size so there are always extra digits */
+ size += (MP_PREC * 2) - (size % MP_PREC);
+
+ /* alloc mem */
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
+ if (a->dp == NULL) {
+ return MP_MEM;
+ }
+
+ /* set the members */
+ a->used = 0;
+ a->alloc = size;
+ a->sign = MP_ZPOS;
+
+ /* zero the digits */
+ for (x = 0; x < size; x++) {
+ a->dp[x] = 0;
+ }
+
+ return MP_OKAY;
+}
+
+
+/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
+static int s_mp_sqr (mp_int * a, mp_int * b)
+{
+ mp_int t;
+ int res, ix, iy, pa;
+ mp_word r;
+ mp_digit u, tmpx, *tmpt;
+
+ pa = a->used;
+ if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
+ return res;
+ }
+
+ /* default used is maximum possible size */
+ t.used = 2*pa + 1;
+
+ for (ix = 0; ix < pa; ix++) {
+ /* first calculate the digit at 2*ix */
+ /* calculate double precision result */
+ r = ((mp_word) t.dp[2*ix]) +
+ ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
+
+ /* store lower part in result */
+ t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* get the carry */
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+
+ /* left hand side of A[ix] * A[iy] */
+ tmpx = a->dp[ix];
+
+ /* alias for where to store the results */
+ tmpt = t.dp + (2*ix + 1);
+
+ for (iy = ix + 1; iy < pa; iy++) {
+ /* first calculate the product */
+ r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
+
+ /* now calculate the double precision result, note we use
+ * addition instead of *2 since it's easier to optimize
+ */
+ r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
+
+ /* store lower part */
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* get carry */
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+ }
+ /* propagate upwards */
+ while (u != ((mp_digit) 0)) {
+ r = ((mp_word) *tmpt) + ((mp_word) u);
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+ }
+ }
+
+ mp_clamp (&t);
+ mp_exch (&t, b);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+
+
+/* multiplies |a| * |b| and does not compute the lower digs digits
+ * [meant to get the higher part of the product]
+ */
+static int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ mp_int t;
+ int res, pa, pb, ix, iy;
+ mp_digit u;
+ mp_word r;
+ mp_digit tmpx, *tmpt, *tmpy;
+
+ /* can we use the fast multiplier? */
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ if (((a->used + b->used + 1) < MP_WARRAY)
+ && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ return fast_s_mp_mul_high_digs (a, b, c, digs);
+ }
+#endif
+
+ if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ t.used = a->used + b->used + 1;
+
+ pa = a->used;
+ pb = b->used;
+ for (ix = 0; ix < pa; ix++) {
+ /* clear the carry */
+ u = 0;
+
+ /* left hand side of A[ix] * B[iy] */
+ tmpx = a->dp[ix];
+
+ /* alias to the address of where the digits will be stored */
+ tmpt = &(t.dp[digs]);
+
+ /* alias for where to read the right hand side from */
+ tmpy = b->dp + (digs - ix);
+
+ for (iy = digs - ix; iy < pb; iy++) {
+ /* calculate the double precision result */
+ r = ((mp_word)*tmpt) +
+ ((mp_word)tmpx) * ((mp_word)*tmpy++) +
+ ((mp_word) u);
+
+ /* get the lower part */
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* carry the carry */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
+ *tmpt = u;
+ }
+ mp_clamp (&t);
+ mp_exch (&t, c);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+
+
+#ifdef BN_MP_MONTGOMERY_SETUP_C
+/* setups the montgomery reduction stuff */
+static int
+mp_montgomery_setup (mp_int * n, mp_digit * rho)
+{
+ mp_digit x, b;
+
+/* fast inversion mod 2**k
+ *
+ * Based on the fact that
+ *
+ * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
+ * => 2*X*A - X*X*A*A = 1
+ * => 2*(1) - (1) = 1
+ */
+ b = n->dp[0];
+
+ if ((b & 1) == 0) {
+ return MP_VAL;
+ }
+
+ x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
+ x *= 2 - b * x; /* here x*a==1 mod 2**8 */
+#if !defined(MP_8BIT)
+ x *= 2 - b * x; /* here x*a==1 mod 2**16 */
+#endif
+#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
+ x *= 2 - b * x; /* here x*a==1 mod 2**32 */
+#endif
+#ifdef MP_64BIT
+ x *= 2 - b * x; /* here x*a==1 mod 2**64 */
+#endif
+
+ /* rho = -1/m mod b */
+ *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
+
+ return MP_OKAY;
+}
+#endif
+
+
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
+/* computes xR**-1 == x (mod N) via Montgomery Reduction
+ *
+ * This is an optimized implementation of montgomery_reduce
+ * which uses the comba method to quickly calculate the columns of the
+ * reduction.
+ *
+ * Based on Algorithm 14.32 on pp.601 of HAC.
+*/
+int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+{
+ int ix, res, olduse;
+ mp_word W[MP_WARRAY];
+
+ /* get old used count */
+ olduse = x->used;
+
+ /* grow a as required */
+ if (x->alloc < n->used + 1) {
+ if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* first we have to get the digits of the input into
+ * an array of double precision words W[...]
+ */
+ {
+ register mp_word *_W;
+ register mp_digit *tmpx;
+
+ /* alias for the W[] array */
+ _W = W;
+
+ /* alias for the digits of x*/
+ tmpx = x->dp;
+
+ /* copy the digits of a into W[0..a->used-1] */
+ for (ix = 0; ix < x->used; ix++) {
+ *_W++ = *tmpx++;
+ }
+
+ /* zero the high words of W[a->used..m->used*2] */
+ for (; ix < n->used * 2 + 1; ix++) {
+ *_W++ = 0;
+ }
+ }
+
+ /* now we proceed to zero successive digits
+ * from the least significant upwards
+ */
+ for (ix = 0; ix < n->used; ix++) {
+ /* mu = ai * m' mod b
+ *
+ * We avoid a double precision multiplication (which isn't required)
+ * by casting the value down to a mp_digit. Note this requires
+ * that W[ix-1] have the carry cleared (see after the inner loop)
+ */
+ register mp_digit mu;
+ mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
+
+ /* a = a + mu * m * b**i
+ *
+ * This is computed in place and on the fly. The multiplication
+ * by b**i is handled by offseting which columns the results
+ * are added to.
+ *
+ * Note the comba method normally doesn't handle carries in the
+ * inner loop In this case we fix the carry from the previous
+ * column since the Montgomery reduction requires digits of the
+ * result (so far) [see above] to work. This is
+ * handled by fixing up one carry after the inner loop. The
+ * carry fixups are done in order so after these loops the
+ * first m->used words of W[] have the carries fixed
+ */
+ {
+ register int iy;
+ register mp_digit *tmpn;
+ register mp_word *_W;
+
+ /* alias for the digits of the modulus */
+ tmpn = n->dp;
+
+ /* Alias for the columns set by an offset of ix */
+ _W = W + ix;
+
+ /* inner loop */
+ for (iy = 0; iy < n->used; iy++) {
+ *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
+ }
+ }
+
+ /* now fix carry for next digit, W[ix+1] */
+ W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
+ }
+
+ /* now we have to propagate the carries and
+ * shift the words downward [all those least
+ * significant digits we zeroed].
+ */
+ {
+ register mp_digit *tmpx;
+ register mp_word *_W, *_W1;
+
+ /* nox fix rest of carries */
+
+ /* alias for current word */
+ _W1 = W + ix;
+
+ /* alias for next word, where the carry goes */
+ _W = W + ++ix;
+
+ for (; ix <= n->used * 2 + 1; ix++) {
+ *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
+ }
+
+ /* copy out, A = A/b**n
+ *
+ * The result is A/b**n but instead of converting from an
+ * array of mp_word to mp_digit than calling mp_rshd
+ * we just copy them in the right order
+ */
+
+ /* alias for destination word */
+ tmpx = x->dp;
+
+ /* alias for shifted double precision result */
+ _W = W + n->used;
+
+ for (ix = 0; ix < n->used + 1; ix++) {
+ *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
+ }
+
+ /* zero oldused digits, if the input a was larger than
+ * m->used+1 we'll have to clear the digits
+ */
+ for (; ix < olduse; ix++) {
+ *tmpx++ = 0;
+ }
+ }
+
+ /* set the max used and clamp */
+ x->used = n->used + 1;
+ mp_clamp (x);
+
+ /* if A >= m then A = A - m */
+ if (mp_cmp_mag (x, n) != MP_LT) {
+ return s_mp_sub (x, n, x);
+ }
+ return MP_OKAY;
+}
+#endif
+
+
+#ifdef BN_MP_MUL_2_C
+/* b = a*2 */
+static int mp_mul_2(mp_int * a, mp_int * b)
+{
+ int x, res, oldused;
+
+ /* grow to accomodate result */
+ if (b->alloc < a->used + 1) {
+ if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ oldused = b->used;
+ b->used = a->used;
+
+ {
+ register mp_digit r, rr, *tmpa, *tmpb;
+
+ /* alias for source */
+ tmpa = a->dp;
+
+ /* alias for dest */
+ tmpb = b->dp;
+
+ /* carry */
+ r = 0;
+ for (x = 0; x < a->used; x++) {
+
+ /* get what will be the *next* carry bit from the
+ * MSB of the current digit
+ */
+ rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
+
+ /* now shift up this digit, add in the carry [from the previous] */
+ *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
+
+ /* copy the carry that would be from the source
+ * digit into the next iteration
+ */
+ r = rr;
+ }
+
+ /* new leading digit? */
+ if (r != 0) {
+ /* add a MSB which is always 1 at this point */
+ *tmpb = 1;
+ ++(b->used);
+ }
+
+ /* now zero any excess digits on the destination
+ * that we didn't write to
+ */
+ tmpb = b->dp + b->used;
+ for (x = b->used; x < oldused; x++) {
+ *tmpb++ = 0;
+ }
+ }
+ b->sign = a->sign;
+ return MP_OKAY;
+}
+#endif
+
+
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+/*
+ * shifts with subtractions when the result is greater than b.
+ *
+ * The method is slightly modified to shift B unconditionally upto just under
+ * the leading bit of b. This saves alot of multiple precision shifting.
+ */
+static int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
+{
+ int x, bits, res;
+
+ /* how many bits of last digit does b use */
+ bits = mp_count_bits (b) % DIGIT_BIT;
+
+ if (b->used > 1) {
+ if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ mp_set(a, 1);
+ bits = 1;
+ }
+
+
+ /* now compute C = A * B mod b */
+ for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
+ if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
+ return res;
+ }
+ if (mp_cmp_mag (a, b) != MP_LT) {
+ if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
+ return res;
+ }
+ }
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+
+#ifdef BN_MP_EXPTMOD_FAST_C
+/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
+ *
+ * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
+ * The value of k changes based on the size of the exponent.
+ *
+ * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
+ */
+
+static int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+{
+ mp_int M[TAB_SIZE], res;
+ mp_digit buf, mp;
+ int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+
+ /* use a pointer to the reduction algorithm. This allows us to use
+ * one of many reduction algorithms without modding the guts of
+ * the code with if statements everywhere.
+ */
+ int (*redux)(mp_int*,mp_int*,mp_digit);
+
+ /* find window size */
+ x = mp_count_bits (X);
+ if (x <= 7) {
+ winsize = 2;
+ } else if (x <= 36) {
+ winsize = 3;
+ } else if (x <= 140) {
+ winsize = 4;
+ } else if (x <= 450) {
+ winsize = 5;
+ } else if (x <= 1303) {
+ winsize = 6;
+ } else if (x <= 3529) {
+ winsize = 7;
+ } else {
+ winsize = 8;
+ }
+
+#ifdef MP_LOW_MEM
+ if (winsize > 5) {
+ winsize = 5;
+ }
+#endif
+
+ /* init M array */
+ /* init first cell */
+ if ((err = mp_init(&M[1])) != MP_OKAY) {
+ return err;
+ }
+
+ /* now init the second half of the array */
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ if ((err = mp_init(&M[x])) != MP_OKAY) {
+ for (y = 1<<(winsize-1); y < x; y++) {
+ mp_clear (&M[y]);
+ }
+ mp_clear(&M[1]);
+ return err;
+ }
+ }
+
+ /* determine and setup reduction code */
+ if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_SETUP_C
+ /* now setup montgomery */
+ if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
+ goto LBL_M;
+ }
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+
+ /* automatically pick the comba one if available (saves quite a few calls/ifs) */
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
+ if (((P->used * 2 + 1) < MP_WARRAY) &&
+ P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ redux = fast_mp_montgomery_reduce;
+ } else
+#endif
+ {
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
+ /* use slower baseline Montgomery method */
+ redux = mp_montgomery_reduce;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ }
+ } else if (redmode == 1) {
+#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
+ /* setup DR reduction for moduli of the form B**k - b */
+ mp_dr_setup(P, &mp);
+ redux = mp_dr_reduce;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ } else {
+#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
+ /* setup DR reduction for moduli of the form 2**k - b */
+ if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
+ goto LBL_M;
+ }
+ redux = mp_reduce_2k;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ }
+
+ /* setup result */
+ if ((err = mp_init (&res)) != MP_OKAY) {
+ goto LBL_M;
+ }
+
+ /* create M table
+ *
+
+ *
+ * The first half of the table is not computed though accept for M[0] and M[1]
+ */
+
+ if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+ /* now we need R mod m */
+ if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+#else
+ err = MP_VAL;
+ goto LBL_RES;
+#endif
+
+ /* now set M[1] to G * R mod m */
+ if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ } else {
+ mp_set(&res, 1);
+ if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
+ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ for (x = 0; x < (winsize - 1); x++) {
+ if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* create upper table */
+ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
+ if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* set initial mode and bit cnt */
+ mode = 0;
+ bitcnt = 1;
+ buf = 0;
+ digidx = X->used - 1;
+ bitcpy = 0;
+ bitbuf = 0;
+
+ for (;;) {
+ /* grab next digit as required */
+ if (--bitcnt == 0) {
+ /* if digidx == -1 we are out of digits so break */
+ if (digidx == -1) {
+ break;
+ }
+ /* read next digit and reset bitcnt */
+ buf = X->dp[digidx--];
+ bitcnt = (int)DIGIT_BIT;
+ }
+
+ /* grab the next msb from the exponent */
+ y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
+ buf <<= (mp_digit)1;
+
+ /* if the bit is zero and mode == 0 then we ignore it
+ * These represent the leading zero bits before the first 1 bit
+ * in the exponent. Technically this opt is not required but it
+ * does lower the # of trivial squaring/reductions used
+ */
+ if (mode == 0 && y == 0) {
+ continue;
+ }
+
+ /* if the bit is zero and mode == 1 then we square */
+ if (mode == 1 && y == 0) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ continue;
+ }
+
+ /* else we add it to the window */
+ bitbuf |= (y << (winsize - ++bitcpy));
+ mode = 2;
+
+ if (bitcpy == winsize) {
+ /* ok window is filled so square as required and multiply */
+ /* square first */
+ for (x = 0; x < winsize; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* empty window and reset */
+ bitcpy = 0;
+ bitbuf = 0;
+ mode = 1;
+ }
+ }
+
+ /* if bits remain then square/multiply */
+ if (mode == 2 && bitcpy > 0) {
+ /* square then multiply if the bit is set */
+ for (x = 0; x < bitcpy; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* get next bit of the window */
+ bitbuf <<= 1;
+ if ((bitbuf & (1 << winsize)) != 0) {
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+ }
+ }
+
+ if (redmode == 0) {
+ /* fixup result if Montgomery reduction is used
+ * recall that any value in a Montgomery system is
+ * actually multiplied by R mod n. So we have
+ * to reduce one more time to cancel out the factor
+ * of R.
+ */
+ if ((err = redux(&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* swap res with Y */
+ mp_exch (&res, Y);
+ err = MP_OKAY;
+LBL_RES:mp_clear (&res);
+LBL_M:
+ mp_clear(&M[1]);
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ mp_clear (&M[x]);
+ }
+ return err;
+}
+#endif
+
+
+#ifdef BN_FAST_S_MP_SQR_C
+/* the jist of squaring...
+ * you do like mult except the offset of the tmpx [one that
+ * starts closer to zero] can't equal the offset of tmpy.
+ * So basically you set up iy like before then you min it with
+ * (ty-tx) so that it never happens. You double all those
+ * you add in the inner loop
+
+After that loop you do the squares and add them in.
+*/
+
+static int fast_s_mp_sqr (mp_int * a, mp_int * b)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY], *tmpx;
+ mp_word W1;
+
+ /* grow the destination as required */
+ pa = a->used + a->used;
+ if (b->alloc < pa) {
+ if ((res = mp_grow (b, pa)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ W1 = 0;
+ for (ix = 0; ix < pa; ix++) {
+ int tx, ty, iy;
+ mp_word _W;
+ mp_digit *tmpy;
+
+ /* clear counter */
+ _W = 0;
+
+ /* get offsets into the two bignums */
+ ty = MIN(a->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = a->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* now for squaring tx can never equal ty
+ * we halve the distance since they approach at a rate of 2x
+ * and we have to round because odd cases need to be executed
+ */
+ iy = MIN(iy, (ty-tx+1)>>1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+ }
+
+ /* double the inner product and add carry */
+ _W = _W + _W + W1;
+
+ /* even columns have the square term in them */
+ if ((ix&1) == 0) {
+ _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
+ }
+
+ /* store it */
+ W[ix] = (mp_digit)(_W & MP_MASK);
+
+ /* make next carry */
+ W1 = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = b->used;
+ b->used = a->used+a->used;
+
+ {
+ mp_digit *tmpb;
+ tmpb = b->dp;
+ for (ix = 0; ix < pa; ix++) {
+ *tmpb++ = W[ix] & MP_MASK;
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpb++ = 0;
+ }
+ }
+ mp_clamp (b);
+ return MP_OKAY;
+}
+#endif
+
+
+#ifdef BN_MP_MUL_D_C
+/* multiply by a digit */
+static int
+mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ mp_digit u, *tmpa, *tmpc;
+ mp_word r;
+ int ix, res, olduse;
+
+ /* make sure c is big enough to hold a*b */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* get the original destinations used count */
+ olduse = c->used;
+
+ /* set the sign */
+ c->sign = a->sign;
+
+ /* alias for a->dp [source] */
+ tmpa = a->dp;
+
+ /* alias for c->dp [dest] */
+ tmpc = c->dp;
+
+ /* zero carry */
+ u = 0;
+
+ /* compute columns */
+ for (ix = 0; ix < a->used; ix++) {
+ /* compute product and carry sum for this term */
+ r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
+
+ /* mask off higher bits to get a single digit */
+ *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* send carry into next iteration */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
+
+ /* store final carry [if any] and increment ix offset */
+ *tmpc++ = u;
+ ++ix;
+
+ /* now zero digits above the top */
+ while (ix++ < olduse) {
+ *tmpc++ = 0;
+ }
+
+ /* set used count */
+ c->used = a->used + 1;
+ mp_clamp(c);
+
+ return MP_OKAY;
+}
+#endif