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/*
* 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.
*/
#include "os.h"
#include "stdarg.h"
#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) (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 a lot 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)
{
#if defined(BN_MP_DR_IS_MODULUS_C)||defined(BN_MP_REDUCE_IS_2K_C)||defined(BN_MP_EXPTMOD_FAST_C)
int dr = 0;
#endif
/* 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);
#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 accommodate 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 up to 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 accommodate 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 up to just under
* the leading bit of b. This saves a lot 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
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