mpi.c File Reference

#include <stdarg.h>
#include <windef.h>
#include <winbase.h>
#include "tomcrypt.h"

Include dependency graph for mpi.c:

Go to the source code of this file.

Macros
#define	s_mp_mul(a, b, c)   s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)

Functions
static void	mp_clamp (mp_int *a)
static int	mp_cmp_mag (const mp_int *a, const mp_int *b)
static int	mp_cnt_lsb (const mp_int *a)
static int	mp_montgomery_calc_normalization (mp_int *a, const mp_int *b)
static int	mp_montgomery_reduce (mp_int *a, const mp_int *m, mp_digit mp)
static int	mp_montgomery_setup (const mp_int *a, mp_digit *mp)
static int	mp_reduce (mp_int *a, const mp_int *b, const mp_int *c)
static int	mp_reduce_2k (mp_int *a, const mp_int *n, mp_digit d)
static int	mp_reduce_2k_setup (const mp_int *a, mp_digit *d)
static int	mp_reduce_setup (mp_int *a, const mp_int *b)
static void	mp_set (mp_int *a, mp_digit b)
static int	mp_sqr (const mp_int *a, mp_int *b)
static int	mp_sqrmod (const mp_int *a, mp_int *b, mp_int *c)
static void	bn_reverse (unsigned char *s, int len)
static int	s_mp_add (mp_int *a, mp_int *b, mp_int *c)
static int	s_mp_exptmod (const mp_int *G, const mp_int *X, mp_int *P, mp_int *Y)
static int	s_mp_mul_digs (const mp_int *a, const mp_int *b, mp_int *c, int digs)
static int	s_mp_mul_high_digs (const mp_int *a, const mp_int *b, mp_int *c, int digs)
static int	s_mp_sqr (const mp_int *a, mp_int *b)
static int	s_mp_sub (const mp_int *a, const mp_int *b, mp_int *c)
static int	mp_exptmod_fast (const mp_int *G, const mp_int *X, mp_int *P, mp_int *Y, int mode)
static int	mp_invmod_slow (const mp_int *a, mp_int *b, mp_int *c)
static int	mp_karatsuba_mul (const mp_int *a, const mp_int *b, mp_int *c)
static int	mp_karatsuba_sqr (const mp_int *a, mp_int *b)
static int	mp_grow (mp_int *a, int size)
static int	mp_div_2 (const mp_int *a, mp_int *b)
static void	mp_exch (mp_int *a, mp_int *b)
static int	mp_init (mp_int *a)
static int	mp_init_size (mp_int *a, int size)
static void	mp_clear (mp_int *a)
static void	mp_zero (mp_int *a)
static int	mp_abs (const mp_int *a, mp_int *b)
static int	fast_mp_invmod (const mp_int *a, mp_int *b, mp_int *c)
static int	fast_mp_montgomery_reduce (mp_int *x, const mp_int *n, mp_digit rho)
static int	fast_s_mp_mul_digs (const mp_int *a, const mp_int *b, mp_int *c, int digs)
static int	fast_s_mp_mul_high_digs (const mp_int *a, const mp_int *b, mp_int *c, int digs)
static int	fast_s_mp_sqr (const mp_int *a, mp_int *b)
static int	mp_2expt (mp_int *a, int b)
int	mp_add (mp_int *a, mp_int *b, mp_int *c)
static int	mp_add_d (mp_int *a, mp_digit b, mp_int *c)
void	mp_clear_multi (mp_int *mp,...)
int	mp_cmp (const mp_int *a, const mp_int *b)
int	mp_cmp_d (const mp_int *a, mp_digit b)
int	mp_copy (const mp_int *a, mp_int *b)
int	mp_count_bits (const mp_int *a)
static int	mp_mod_2d (const mp_int *a, int b, mp_int *c)
static void	mp_rshd (mp_int *a, int b)
static int	mp_div_2d (const mp_int *a, int b, mp_int *c, mp_int *d)
static int	mp_lshd (mp_int *a, int b)
static int	mp_mul_2d (const mp_int *a, int b, mp_int *c)
static int	mp_mul_d (const mp_int *a, mp_digit b, mp_int *c)
static int	mp_div (const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
static BOOL	s_is_power_of_two (mp_digit b, int *p)
static int	mp_div_d (const mp_int *a, mp_digit b, mp_int *c, mp_digit *d)
static int	mp_dr_reduce (mp_int *x, const mp_int *n, mp_digit k)
static void	mp_dr_setup (const mp_int *a, mp_digit *d)
int	mp_exptmod (const mp_int *G, const mp_int *X, mp_int *P, mp_int *Y)
int	mp_gcd (const mp_int *a, const mp_int *b, mp_int *c)
unsigned long	mp_get_int (const mp_int *a)
int	mp_init_copy (mp_int *a, const mp_int *b)
int	mp_init_multi (mp_int *mp,...)
int	mp_invmod (const mp_int *a, mp_int *b, mp_int *c)
int	mp_lcm (const mp_int *a, const mp_int *b, mp_int *c)
int	mp_mod (const mp_int *a, mp_int *b, mp_int *c)
static int	mp_mod_d (const mp_int *a, mp_digit b, mp_digit *c)
static int	mp_mul_2 (const mp_int *a, mp_int *b)
int	mp_mul (const mp_int *a, const mp_int *b, mp_int *c)
int	mp_mulmod (const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
static int	mp_prime_is_divisible (const mp_int *a, int *result)
static int	mp_prime_miller_rabin (mp_int *a, const mp_int *b, int *result)
static int	mp_prime_is_prime (mp_int *a, int t, int *result)
int	mp_prime_rabin_miller_trials (int size)
int	mp_prime_random_ex (mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
int	mp_read_unsigned_bin (mp_int *a, const unsigned char *b, int c)
int	mp_set_int (mp_int *a, unsigned long b)
int	mp_shrink (mp_int *a)
int	mp_sub (mp_int *a, mp_int *b, mp_int *c)
int	mp_sub_d (mp_int *a, mp_digit b, mp_int *c)
int	mp_to_unsigned_bin (const mp_int *a, unsigned char *b)
int	mp_unsigned_bin_size (const mp_int *a)

Variables
static const int	KARATSUBA_MUL_CUTOFF = 88
static const int	KARATSUBA_SQR_CUTOFF = 128
static const int	lnz [16]
static const mp_digit	__prime_tab []
struct {
int   k
int   t
}	sizes []

Macro Definition Documentation

s_mp_mul

#define s_mp_mul	(		a,
			b,
			c
	)		s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)

Definition at line 95 of file mpi.c.

Function Documentation

bn_reverse()

static void bn_reverse ( unsigned char *  s, int  len  )

static

Definition at line 3907 of file mpi.c.

{
  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;
  }
}

Referenced by mp_to_unsigned_bin().

fast_mp_invmod()

static int fast_mp_invmod ( const mp_int *  a, mp_int *  b, mp_int *  c  )

static

Definition at line 314 of file mpi.c.

{
  mp_int  x, y, u, v, B, D;
  int     res, neg;
 
  /* 2. [modified] b must be odd   */
  if (mp_iseven (b) == 1) {
    return MP_VAL;
  }
 
  /* init all our temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
     return res;
  }
 
  /* x == modulus, y == value to invert */
  if ((res = mp_copy (b, &x)) != MP_OKAY) {
    goto __ERR;
  }
 
  /* we need y = |a| */
  if ((res = mp_abs (a, &y)) != MP_OKAY) {
    goto __ERR;
  }
 
  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
    goto __ERR;
  }
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
    goto __ERR;
  }
  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 __ERR;
    }
    /* 4.2 if B is odd then */
    if (mp_isodd (&B) == 1) {
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
        goto __ERR;
      }
    }
    /* B = B/2 */
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto __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 __ERR;
    }
    /* 5.2 if D is odd then */
    if (mp_isodd (&D) == 1) {
      /* D = (D-x)/2 */
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
        goto __ERR;
      }
    }
    /* D = D/2 */
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
      goto __ERR;
    }
  }
 
  /* 6.  if u >= v then */
  if (mp_cmp (&u, &v) != MP_LT) {
    /* u = u - v, B = B - D */
    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
      goto __ERR;
    }
 
    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
      goto __ERR;
    }
  } else {
    /* v - v - u, D = D - B */
    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
      goto __ERR;
    }
 
    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto __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 __ERR;
  }
 
  /* b is now the inverse */
  neg = a->sign;
  while (D.sign == MP_NEG) {
    if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
      goto __ERR;
    }
  }
  mp_exch (&D, c);
  c->sign = neg;
  res = MP_OKAY;
 
__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
  return res;
}

Referenced by mp_invmod().

fast_mp_montgomery_reduce()

static int fast_mp_montgomery_reduce ( mp_int *  x, const mp_int *  n, mp_digit  rho  )

static

Definition at line 444 of file mpi.c.

{
  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 offsetting 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;
}

Referenced by mp_exptmod_fast(), and mp_montgomery_reduce().

fast_s_mp_mul_digs()

static int fast_s_mp_mul_digs ( const mp_int *  a, const mp_int *  b, mp_int *  c, int  digs  )

static

Definition at line 604 of file mpi.c.

{
  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 iterate, essentially it's
         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 = digs;
 
  {
    register mp_digit *tmpc;
    tmpc = c->dp;
    for (ix = 0; ix < digs; 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;
}

Referenced by mp_mul(), and s_mp_mul_digs().

fast_s_mp_mul_high_digs()

static int fast_s_mp_mul_high_digs ( const mp_int *  a, const mp_int *  b, mp_int *  c, int  digs  )

static

Definition at line 683 of file mpi.c.

{
  int     olduse, res, pa, ix, iz;
  mp_digit W[MP_WARRAY];
  mp_word  _W;
 
  /* grow the destination as required */
  pa = a->used + b->used;
  if (c->alloc < pa) {
    if ((res = mp_grow (c, pa)) != MP_OKAY) {
      return res;
    }
  }
 
  /* number of output digits to produce */
  pa = a->used + b->used;
  _W = 0;
  for (ix = digs; ix <= pa; ix++) { 
      int      tx, ty, 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 iterate, essentially it's
         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 + digs;
    for (ix = digs; ix <= pa; 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;
}

Referenced by s_mp_mul_high_digs().

fast_s_mp_sqr()

static int fast_s_mp_sqr ( const mp_int *  a, mp_int *  b  )

static

Definition at line 780 of file mpi.c.

{
  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 iterate, essentially it's
         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] = _W;
 
      /* 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;
}

Referenced by mp_sqr().

mp_2expt()

static int mp_2expt ( mp_int *  a, int  b  )

static

Definition at line 869 of file mpi.c.

{
  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;
}

Referenced by mp_montgomery_calc_normalization(), mp_reduce_2k_setup(), and mp_reduce_setup().

mp_abs()

static int mp_abs ( const mp_int *  a, mp_int *  b  )

static

Definition at line 290 of file mpi.c.

{
  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;
}

Referenced by fast_mp_invmod(), mp_exptmod(), and mp_gcd().

mp_add()

int mp_add	(	mp_int *	a,
		mp_int *	b,
		mp_int *	c
	)

Definition at line 891 of file mpi.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;
}

Referenced by fast_mp_invmod(), mp_div(), mp_invmod_slow(), mp_karatsuba_mul(), mp_karatsuba_sqr(), mp_mod(), mp_reduce(), and rsa_exptmod().

mp_add_d()

static int mp_add_d ( mp_int *  a, mp_digit  b, mp_int *  c  )

static

Definition at line 924 of file mpi.c.

{
  int     res, ix, oldused;
  mp_digit *tmpa, *tmpc, mu;
 
  /* grow c as required */
  if (c->alloc < a->used + 1) {
     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
        return res;
     }
  }
 
  /* if a is negative and |a| >= b, call c = |a| - b */
  if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
     /* temporarily fix sign of a */
     a->sign = MP_ZPOS;
 
     /* c = |a| - b */
     res = mp_sub_d(a, b, c);
 
     /* fix sign  */
     a->sign = c->sign = MP_NEG;
 
     return res;
  }
 
  /* old number of used digits in c */
  oldused = c->used;
 
  /* sign always positive */
  c->sign = MP_ZPOS;
 
  /* source alias */
  tmpa    = a->dp;
 
  /* destination alias */
  tmpc    = c->dp;
 
  /* if a is positive */
  if (a->sign == MP_ZPOS) {
     /* add digit, after this we're propagating
      * the carry.
      */
     *tmpc   = *tmpa++ + b;
     mu      = *tmpc >> DIGIT_BIT;
     *tmpc++ &= MP_MASK;
 
     /* now handle rest of the digits */
     for (ix = 1; ix < a->used; ix++) {
        *tmpc   = *tmpa++ + mu;
        mu      = *tmpc >> DIGIT_BIT;
        *tmpc++ &= MP_MASK;
     }
     /* set final carry */
     ix++;
     *tmpc++  = mu;
 
     /* setup size */
     c->used = a->used + 1;
  } else {
     /* a was negative and |a| < b */
     c->used  = 1;
 
     /* the result is a single digit */
     if (a->used == 1) {
        *tmpc++  =  b - a->dp[0];
     } else {
        *tmpc++  =  b;
     }
 
     /* setup count so the clearing of oldused
      * can fall through correctly
      */
     ix       = 1;
  }
 
  /* now zero to oldused */
  while (ix++ < oldused) {
     *tmpc++ = 0;
  }
  mp_clamp(c);
 
  return MP_OKAY;
}

Referenced by mp_prime_random_ex(), and mp_sub_d().

mp_clamp()

void mp_clamp ( mp_int *  a )

static

Definition at line 1017 of file mpi.c.

{
  /* 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;
  }
}

Referenced by fast_mp_montgomery_reduce(), fast_s_mp_mul_digs(), fast_s_mp_mul_high_digs(), fast_s_mp_sqr(), mp_add_d(), mp_div(), mp_div_2(), mp_div_2d(), mp_div_d(), mp_dr_reduce(), mp_karatsuba_mul(), mp_karatsuba_sqr(), mp_mod_2d(), mp_montgomery_reduce(), mp_mul_2d(), mp_mul_d(), mp_read_unsigned_bin(), mp_set_int(), mp_sub_d(), s_mp_add(), s_mp_mul_digs(), s_mp_mul_high_digs(), s_mp_sqr(), and s_mp_sub().

mp_clear()

static void mp_clear ( mp_int *  a )

static

Definition at line 255 of file mpi.c.

{
  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 */
    HeapFree(GetProcessHeap(), 0, a->dp);
 
    /* reset members to make debugging easier */
    a->dp    = NULL;
    a->alloc = a->used = 0;
    a->sign  = MP_ZPOS;
  }
}

Referenced by mp_clear_multi(), mp_div(), mp_div_2d(), mp_div_d(), mp_exptmod(), mp_exptmod_fast(), mp_gcd(), mp_init_multi(), mp_karatsuba_mul(), mp_karatsuba_sqr(), mp_mod(), mp_mulmod(), mp_prime_is_prime(), mp_prime_miller_rabin(), mp_reduce(), mp_reduce_2k(), mp_reduce_2k_setup(), mp_sqrmod(), mp_to_unsigned_bin(), s_mp_exptmod(), s_mp_mul_digs(), s_mp_mul_high_digs(), and s_mp_sqr().

mp_clear_multi()

void mp_clear_multi	(	mp_int *	mp,
			...
	)

Definition at line 1032 of file mpi.c.

{
    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);
}

Referenced by fast_mp_invmod(), mp_exptmod(), mp_invmod_slow(), mp_lcm(), rsa_exptmod(), rsa_free(), and rsa_make_key().

mp_cmp()

int mp_cmp	(	const mp_int *	a,
		const mp_int *	b
	)

Definition at line 1046 of file mpi.c.

{
  /* 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);
  }
}

Referenced by fast_mp_invmod(), mp_div(), mp_invmod_slow(), mp_prime_miller_rabin(), mp_reduce(), and rsa_exptmod().

mp_cmp_d()

int mp_cmp_d	(	const mp_int *	a,
		mp_digit	b
	)

Definition at line 1067 of file mpi.c.

{
  /* 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;
  }
}

Referenced by fast_mp_invmod(), mp_invmod_slow(), mp_prime_is_prime(), mp_prime_miller_rabin(), mp_reduce(), and rsa_make_key().

mp_cmp_mag()

int mp_cmp_mag ( const mp_int *  a, const mp_int *  b  )

static

Definition at line 1090 of file mpi.c.

{
  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;
}

Referenced by fast_mp_montgomery_reduce(), mp_add(), mp_cmp(), mp_div(), mp_dr_reduce(), mp_gcd(), mp_invmod_slow(), mp_lcm(), mp_montgomery_calc_normalization(), mp_montgomery_reduce(), mp_reduce_2k(), and mp_sub().

mp_cnt_lsb()

int mp_cnt_lsb ( const mp_int *  a )

static

Definition at line 1128 of file mpi.c.

{
   int x;
   mp_digit q, qq;
 
   /* easy out */
   if (mp_iszero(a) == 1) {
      return 0;
   }
 
   /* scan lower digits until non-zero */
   for (x = 0; x < a->used && a->dp[x] == 0; x++);
   q = a->dp[x];
   x *= DIGIT_BIT;
 
   /* now scan this digit until a 1 is found */
   if ((q & 1) == 0) {
      do {
         qq  = q & 15;
         x  += lnz[qq];
         q >>= 4;
      } while (qq == 0);
   }
   return x;
}

Referenced by mp_gcd(), and mp_prime_miller_rabin().

mp_copy()

int mp_copy	(	const mp_int *	a,
		mp_int *	b
	)

Definition at line 1156 of file mpi.c.

{
  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;
}

Referenced by fast_mp_invmod(), mp_abs(), mp_div(), mp_div_2d(), mp_div_d(), mp_exptmod_fast(), mp_init_copy(), mp_invmod_slow(), mp_mod_2d(), mp_mul_2d(), rsa_make_key(), and s_mp_exptmod().

mp_count_bits()

int mp_count_bits

(

const mp_int *

a

)

Definition at line 1203 of file mpi.c.

{
  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 > 0) {
    ++r;
    q >>= ((mp_digit) 1);
  }
  return r;
}

Referenced by encrypt_block_impl(), mp_div(), mp_exptmod_fast(), mp_montgomery_calc_normalization(), mp_reduce_2k(), mp_reduce_2k_setup(), mp_unsigned_bin_size(), and s_mp_exptmod().

mp_div()

static int mp_div ( const mp_int *  a, const mp_int *  b, mp_int *  c, mp_int *  d  )

static

Definition at line 1565 of file mpi.c.

{
  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 __Q;
  }
 
  if ((res = mp_init (&t2)) != MP_OKAY) {
    goto __T1;
  }
 
  if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
    goto __T2;
  }
 
  if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
    goto __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 < DIGIT_BIT-1) {
     norm = (DIGIT_BIT-1) - norm;
     if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
       goto __Y;
     }
     if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
       goto __Y;
     }
  } else {
     norm = 0;
  }
 
  /* note hac does 0 based, so if used==5 then it's 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 __Y;
  }
 
  while (mp_cmp (&x, &y) != MP_LT) {
    ++(q.dp[n - t]);
    if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
      goto __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 __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 __Y;
    }
 
    if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
      goto __Y;
    }
 
    if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
      goto __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 __Y;
      }
      if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
        goto __Y;
      }
      if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
        goto __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;
 
__Y:mp_clear (&y);
__X:mp_clear (&x);
__T2:mp_clear (&t2);
__T1:mp_clear (&t1);
__Q:mp_clear (&q);
  return res;
}

Referenced by mp_lcm(), mp_mod(), and mp_reduce_setup().

mp_div_2()

static int mp_div_2 ( const mp_int *  a, mp_int *  b  )

static

Definition at line 142 of file mpi.c.

{
  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;
}

Referenced by fast_mp_invmod(), mp_invmod_slow(), and mp_prime_random_ex().

mp_div_2d()

static int mp_div_2d ( const mp_int *  a, int  b, mp_int *  c, mp_int *  d  )

static

Definition at line 1310 of file mpi.c.

{
  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 >= 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;
}

Referenced by mp_div(), mp_div_d(), mp_gcd(), mp_prime_miller_rabin(), mp_reduce_2k(), and mp_to_unsigned_bin().

mp_div_d()

static int mp_div_d ( const mp_int *  a, mp_digit  b, mp_int *  c, mp_digit *  d  )

static

Definition at line 1762 of file mpi.c.

{
  mp_int  q;
  mp_word w;
  mp_digit t;
  int     res, ix;
 
  /* cannot divide by zero */
  if (b == 0) {
     return MP_VAL;
  }
 
  /* quick outs */
  if (b == 1 || mp_iszero(a) == 1) {
     if (d != NULL) {
        *d = 0;
     }
     if (c != NULL) {
        return mp_copy(a, c);
     }
     return MP_OKAY;
  }
 
  /* power of two ? */
  if (s_is_power_of_two(b, &ix)) {
     if (d != NULL) {
        *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
     }
     if (c != NULL) {
        return mp_div_2d(a, ix, c, NULL);
     }
     return MP_OKAY;
  }
 
  /* no easy answer [c'est la vie].  Just division */
  if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
     return res;
  }
  
  q.used = a->used;
  q.sign = a->sign;
  w = 0;
  for (ix = a->used - 1; ix >= 0; ix--) {
     w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
     
     if (w >= b) {
        t = (mp_digit)(w / b);
        w -= ((mp_word)t) * ((mp_word)b);
      } else {
        t = 0;
      }
      q.dp[ix] = t;
  }
 
  if (d != NULL) {
     *d = (mp_digit)w;
  }
  
  if (c != NULL) {
     mp_clamp(&q);
     mp_exch(&q, c);
  }
  mp_clear(&q);
  
  return res;
}

Referenced by mp_mod_d().

mp_dr_reduce()

static int mp_dr_reduce ( mp_int *  x, const mp_int *  n, mp_digit  k  )

static

Definition at line 1844 of file mpi.c.

{
  int      err, i, m;
  mp_word  r;
  mp_digit mu, *tmpx1, *tmpx2;
 
  /* m = digits in modulus */
  m = n->used;
 
  /* ensure that "x" has at least 2m digits */
  if (x->alloc < m + m) {
    if ((err = mp_grow (x, m + m)) != MP_OKAY) {
      return err;
    }
  }
 
/* top of loop, this is where the code resumes if
 * another reduction pass is required.
 */
top:
  /* aliases for digits */
  /* alias for lower half of x */
  tmpx1 = x->dp;
 
  /* alias for upper half of x, or x/B**m */
  tmpx2 = x->dp + m;
 
  /* set carry to zero */
  mu = 0;
 
  /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
  for (i = 0; i < m; i++) {
      r         = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
      *tmpx1++  = (mp_digit)(r & MP_MASK);
      mu        = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
  }
 
  /* set final carry */
  *tmpx1++ = mu;
 
  /* zero words above m */
  for (i = m + 1; i < x->used; i++) {
      *tmpx1++ = 0;
  }
 
  /* clamp, sub and return */
  mp_clamp (x);
 
  /* if x >= n then subtract and reduce again
   * Each successive "recursion" makes the input smaller and smaller.
   */
  if (mp_cmp_mag (x, n) != MP_LT) {
    s_mp_sub(x, n, x);
    goto top;
  }
  return MP_OKAY;
}

Referenced by mp_exptmod_fast().

mp_dr_setup()

static void mp_dr_setup ( const mp_int *  a, mp_digit *  d  )

static

Definition at line 1903 of file mpi.c.

{
   /* the casts are required if DIGIT_BIT is one less than
    * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
    */
   *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - 
        ((mp_word)a->dp[0]));
}

Referenced by mp_exptmod_fast().

mp_exch()

static void mp_exch ( mp_int *  a, mp_int *  b  )

static

Definition at line 192 of file mpi.c.

{
  mp_int  t;
 
  t  = *a;
  *a = *b;
  *b = t;
}

Referenced by fast_mp_invmod(), mp_div(), mp_div_2d(), mp_div_d(), mp_exptmod_fast(), mp_gcd(), mp_invmod_slow(), mp_mod(), s_mp_exptmod(), s_mp_mul_digs(), s_mp_mul_high_digs(), and s_mp_sqr().

mp_exptmod()

int mp_exptmod	(	const mp_int *	G,
		const mp_int *	X,
		mp_int *	P,
		mp_int *	Y
	)

Definition at line 1917 of file mpi.c.

{
  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) {
     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;
  }
 
  dr = 0;
 
  /* if the modulus is odd use the fast method */
  if (mp_isodd (P) == 1) {
    return mp_exptmod_fast (G, X, P, Y, dr);
  } else {
    /* otherwise use the generic Barrett reduction technique */
    return s_mp_exptmod (G, X, P, Y);
  }
}

Referenced by mp_exptmod(), mp_prime_miller_rabin(), and rsa_exptmod().

mp_exptmod_fast()

int mp_exptmod_fast ( const mp_int *  G, const mp_int *  X, mp_int *  P, mp_int *  Y, int  mode  )

static

Definition at line 1976 of file mpi.c.

{
  mp_int  M[256], 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*,const 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;
  }
 
  /* 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) {
     /* now setup montgomery  */
     if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
        goto __M;
     }
 
     /* automatically pick the comba one if available (saves quite a few calls/ifs) */
     if (((P->used * 2 + 1) < MP_WARRAY) &&
          P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
        redux = fast_mp_montgomery_reduce;
     } else {
        /* use slower baseline Montgomery method */
        redux = mp_montgomery_reduce;
     }
  } else if (redmode == 1) {
     /* setup DR reduction for moduli of the form B**k - b */
     mp_dr_setup(P, &mp);
     redux = mp_dr_reduce;
  } else {
     /* setup DR reduction for moduli of the form 2**k - b */
     if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
        goto __M;
     }
     redux = mp_reduce_2k;
  }
 
  /* setup result */
  if ((err = mp_init (&res)) != MP_OKAY) {
    goto __M;
  }
 
  /* create M table
   *
 
   *
   * The first half of the table is not computed though accept for M[0] and M[1]
   */
 
  if (redmode == 0) {
     /* now we need R mod m */
     if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
       goto __RES;
     }
 
     /* now set M[1] to G * R mod m */
     if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
       goto __RES;
     }
  } else {
     mp_set(&res, 1);
     if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
        goto __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 __RES;
  }
 
  for (x = 0; x < (winsize - 1); x++) {
    if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
      goto __RES;
    }
    if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
      goto __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 __RES;
    }
    if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
      goto __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 = DIGIT_BIT;
    }
 
    /* grab the next msb from the exponent */
    y     = (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 __RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto __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 __RES;
        }
        if ((err = redux (&res, P, mp)) != MP_OKAY) {
          goto __RES;
        }
      }
 
      /* then multiply */
      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
        goto __RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto __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 __RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto __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 __RES;
        }
        if ((err = redux (&res, P, mp)) != MP_OKAY) {
          goto __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 __RES;
     }
  }
 
  /* swap res with Y */
  mp_exch (&res, Y);
  err = MP_OKAY;
__RES:mp_clear (&res);
__M:
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}

Referenced by mp_exptmod().

mp_gcd()

int mp_gcd	(	const mp_int *	a,
		const mp_int *	b,
		mp_int *	c
	)

Definition at line 2228 of file mpi.c.

{
  mp_int  u, v;
  int     k, u_lsb, v_lsb, res;
 
  /* either zero than gcd is the largest */
  if (mp_iszero (a) == 1 && mp_iszero (b) == 0) {
    return mp_abs (b, c);
  }
  if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
    return mp_abs (a, c);
  }
 
  /* optimized.  At this point if a == 0 then
   * b must equal zero too
   */
  if (mp_iszero (a) == 1) {
    mp_zero(c);
    return MP_OKAY;
  }
 
  /* get copies of a and b we can modify */
  if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
    return res;
  }
 
  if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
    goto __U;
  }
 
  /* must be positive for the remainder of the algorithm */
  u.sign = v.sign = MP_ZPOS;
 
  /* B1.  Find the common power of two for u and v */
  u_lsb = mp_cnt_lsb(&u);
  v_lsb = mp_cnt_lsb(&v);
  k     = MIN(u_lsb, v_lsb);
 
  if (k > 0) {
     /* divide the power of two out */
     if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
        goto __V;
     }
 
     if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
        goto __V;
     }
  }
 
  /* divide any remaining factors of two out */
  if (u_lsb != k) {
     if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
        goto __V;
     }
  }
 
  if (v_lsb != k) {
     if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
        goto __V;
     }
  }
 
  while (mp_iszero(&v) == 0) {
     /* make sure v is the largest */
     if (mp_cmp_mag(&u, &v) == MP_GT) {
        /* swap u and v to make sure v is >= u */
        mp_exch(&u, &v);
     }
     
     /* subtract smallest from largest */
     if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
        goto __V;
     }
     
     /* Divide out all factors of two */
     if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
        goto __V;
     } 
  } 
 
  /* multiply by 2**k which we divided out at the beginning */
  if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
     goto __V;
  }
  c->sign = MP_ZPOS;
  res = MP_OKAY;
__V:mp_clear (&u);
__U:mp_clear (&v);
  return res;
}

Referenced by mp_lcm(), and rsa_make_key().

mp_get_int()

unsigned long mp_get_int

(

const mp_int *

a

)

Definition at line 2320 of file mpi.c.

{
  int i;
  unsigned long res;
 
  if (a->used == 0) {
     return 0;
  }
 
  /* get number of digits of the lsb we have to read */
  i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;
 
  /* get most significant digit of result */
  res = DIGIT(a,i);
   
  while (--i >= 0) {
    res = (res << DIGIT_BIT) | DIGIT(a,i);
  }
 
  /* force result to 32-bits always so it is consistent on non 32-bit platforms */
  return res & 0xFFFFFFFFUL;
}

Referenced by export_private_key_impl(), and export_public_key_impl().

mp_grow()

static int mp_grow ( mp_int *  a, int  size  )

static

Definition at line 106 of file mpi.c.

{
  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 = HeapReAlloc(GetProcessHeap(), 0, 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;
}

Referenced by fast_mp_montgomery_reduce(), fast_s_mp_mul_digs(), fast_s_mp_mul_high_digs(), fast_s_mp_sqr(), mp_2expt(), mp_add_d(), mp_copy(), mp_div_2(), mp_dr_reduce(), mp_lshd(), mp_montgomery_reduce(), mp_mul_2(), mp_mul_2d(), mp_mul_d(), mp_read_unsigned_bin(), mp_sub_d(), s_mp_add(), and s_mp_sub().

mp_init()

static int mp_init ( mp_int *  a )

static

Definition at line 202 of file mpi.c.

{
  int i;
 
  /* allocate memory required and clear it */
  a->dp = HeapAlloc(GetProcessHeap(), 0, 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;
}

Referenced by mp_div(), mp_div_2d(), mp_exptmod(), mp_exptmod_fast(), mp_init_copy(), mp_init_multi(), mp_mod(), mp_mulmod(), mp_prime_is_prime(), mp_prime_miller_rabin(), mp_reduce_2k(), mp_reduce_2k_setup(), mp_sqrmod(), and s_mp_exptmod().

mp_init_copy()

int mp_init_copy	(	mp_int *	a,
		const mp_int *	b
	)

Definition at line 2344 of file mpi.c.

{
  int     res;
 
  if ((res = mp_init (a)) != MP_OKAY) {
    return res;
  }
  return mp_copy (b, a);
}

Referenced by duplicate_key_impl(), mp_div(), mp_gcd(), mp_prime_miller_rabin(), mp_reduce(), and mp_to_unsigned_bin().

mp_init_multi()

int mp_init_multi	(	mp_int *	mp,
			...
	)

Definition at line 2354 of file mpi.c.

{
    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. */
}

Referenced by fast_mp_invmod(), import_private_key_impl(), import_public_key_impl(), mp_invmod_slow(), mp_lcm(), rsa_exptmod(), and rsa_make_key().

mp_init_size()

static int mp_init_size ( mp_int *  a, int  size  )

static

Definition at line 227 of file mpi.c.

{
  int x;
 
  /* pad size so there are always extra digits */
  size += (MP_PREC * 2) - (size % MP_PREC);
 
  /* alloc mem */
  a->dp = HeapAlloc(GetProcessHeap(), 0, 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;
}

Referenced by mp_div(), mp_div_d(), mp_karatsuba_mul(), mp_karatsuba_sqr(), s_mp_mul_digs(), s_mp_mul_high_digs(), and s_mp_sqr().

mp_invmod()

int mp_invmod	(	const mp_int *	a,
		mp_int *	b,
		mp_int *	c
	)

Definition at line 2391 of file mpi.c.

{
  /* b cannot be negative */
  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
    return MP_VAL;
  }
 
  /* if the modulus is odd we can use a faster routine instead */
  if (mp_isodd (b) == 1) {
    return fast_mp_invmod (a, b, c);
  }
  
  return mp_invmod_slow(a, b, c);
}

Referenced by mp_exptmod(), and rsa_make_key().

mp_invmod_slow()

int mp_invmod_slow ( const mp_int *  a, mp_int *  b, mp_int *  c  )

static

Definition at line 2407 of file mpi.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_copy (a, &x)) != MP_OKAY) {
    goto __ERR;
  }
  if ((res = mp_copy (b, &y)) != MP_OKAY) {
    goto __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 __ERR;
  }
 
  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
    goto __ERR;
  }
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
    goto __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 __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 __ERR;
      }
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
         goto __ERR;
      }
    }
    /* A = A/2, B = B/2 */
    if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
      goto __ERR;
    }
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto __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 __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 __ERR;
      }
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
         goto __ERR;
      }
    }
    /* C = C/2, D = D/2 */
    if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
      goto __ERR;
    }
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
      goto __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 __ERR;
    }
 
    if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
      goto __ERR;
    }
 
    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
      goto __ERR;
    }
  } else {
    /* v - v - u, C = C - A, D = D - B */
    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
      goto __ERR;
    }
 
    if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
      goto __ERR;
    }
 
    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto __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 __ERR;
  }
 
  /* if it's too low */
  while (mp_cmp_d(&C, 0) == MP_LT) {
      if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
         goto __ERR;
      }
  }
  
  /* too big */
  while (mp_cmp_mag(&C, b) != MP_LT) {
      if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
         goto __ERR;
      }
  }
  
  /* C is now the inverse */
  mp_exch (&C, c);
  res = MP_OKAY;
__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
  return res;
}

Referenced by mp_invmod().

mp_karatsuba_mul()

int mp_karatsuba_mul ( const mp_int *  a, const mp_int *  b, mp_int *  c  )

static

Definition at line 2589 of file mpi.c.

{
  mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
  int     B, err;
 
  /* default the return code to an error */
  err = MP_MEM;
 
  /* min # of digits */
  B = MIN (a->used, b->used);
 
  /* now divide in two */
  B = B >> 1;
 
  /* init copy all the temps */
  if (mp_init_size (&x0, B) != MP_OKAY)
    goto ERR;
  if (mp_init_size (&x1, a->used - B) != MP_OKAY)
    goto X0;
  if (mp_init_size (&y0, B) != MP_OKAY)
    goto X1;
  if (mp_init_size (&y1, b->used - B) != MP_OKAY)
    goto Y0;
 
  /* init temps */
  if (mp_init_size (&t1, B * 2) != MP_OKAY)
    goto Y1;
  if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
    goto T1;
  if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
    goto X0Y0;
 
  /* now shift the digits */
  x0.used = y0.used = B;
  x1.used = a->used - B;
  y1.used = b->used - B;
 
  {
    register int x;
    register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
 
    /* we copy the digits directly instead of using higher level functions
     * since we also need to shift the digits
     */
    tmpa = a->dp;
    tmpb = b->dp;
 
    tmpx = x0.dp;
    tmpy = y0.dp;
    for (x = 0; x < B; x++) {
      *tmpx++ = *tmpa++;
      *tmpy++ = *tmpb++;
    }
 
    tmpx = x1.dp;
    for (x = B; x < a->used; x++) {
      *tmpx++ = *tmpa++;
    }
 
    tmpy = y1.dp;
    for (x = B; x < b->used; x++) {
      *tmpy++ = *tmpb++;
    }
  }
 
  /* only need to clamp the lower words since by definition the 
   * upper words x1/y1 must have a known number of digits
   */
  mp_clamp (&x0);
  mp_clamp (&y0);
 
  /* now calc the products x0y0 and x1y1 */
  /* after this x0 is no longer required, free temp [x0==t2]! */
  if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)  
    goto X1Y1;          /* x0y0 = x0*y0 */
  if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
    goto X1Y1;          /* x1y1 = x1*y1 */
 
  /* now calc x1-x0 and y1-y0 */
  if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
    goto X1Y1;          /* t1 = x1 - x0 */
  if (mp_sub (&y1, &y0, &x0) != MP_OKAY)
    goto X1Y1;          /* t2 = y1 - y0 */
  if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
    goto X1Y1;          /* t1 = (x1 - x0) * (y1 - y0) */
 
  /* add x0y0 */
  if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
    goto X1Y1;          /* t2 = x0y0 + x1y1 */
  if (mp_sub (&x0, &t1, &t1) != MP_OKAY)
    goto X1Y1;          /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
 
  /* shift by B */
  if (mp_lshd (&t1, B) != MP_OKAY)
    goto X1Y1;          /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
  if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
    goto X1Y1;          /* x1y1 = x1y1 << 2*B */
 
  if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
    goto X1Y1;          /* t1 = x0y0 + t1 */
  if (mp_add (&t1, &x1y1, c) != MP_OKAY)
    goto X1Y1;          /* t1 = x0y0 + t1 + x1y1 */
 
  /* Algorithm succeeded set the return code to MP_OKAY */
  err = MP_OKAY;
 
X1Y1:mp_clear (&x1y1);
X0Y0:mp_clear (&x0y0);
T1:mp_clear (&t1);
Y1:mp_clear (&y1);
Y0:mp_clear (&y0);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}

Referenced by mp_mul().

mp_karatsuba_sqr()

int mp_karatsuba_sqr ( const mp_int *  a, mp_int *  b  )

static

Definition at line 2713 of file mpi.c.

{
  mp_int  x0, x1, t1, t2, x0x0, x1x1;
  int     B, err;
 
  err = MP_MEM;
 
  /* min # of digits */
  B = a->used;
 
  /* now divide in two */
  B = B >> 1;
 
  /* init copy all the temps */
  if (mp_init_size (&x0, B) != MP_OKAY)
    goto ERR;
  if (mp_init_size (&x1, a->used - B) != MP_OKAY)
    goto X0;
 
  /* init temps */
  if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
    goto X1;
  if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
    goto T1;
  if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
    goto T2;
  if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
    goto X0X0;
 
  {
    register int x;
    register mp_digit *dst, *src;
 
    src = a->dp;
 
    /* now shift the digits */
    dst = x0.dp;
    for (x = 0; x < B; x++) {
      *dst++ = *src++;
    }
 
    dst = x1.dp;
    for (x = B; x < a->used; x++) {
      *dst++ = *src++;
    }
  }
 
  x0.used = B;
  x1.used = a->used - B;
 
  mp_clamp (&x0);
 
  /* now calc the products x0*x0 and x1*x1 */
  if (mp_sqr (&x0, &x0x0) != MP_OKAY)
    goto X1X1;           /* x0x0 = x0*x0 */
  if (mp_sqr (&x1, &x1x1) != MP_OKAY)
    goto X1X1;           /* x1x1 = x1*x1 */
 
  /* now calc (x1-x0)**2 */
  if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = x1 - x0 */
  if (mp_sqr (&t1, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = (x1 - x0) * (x1 - x0) */
 
  /* add x0y0 */
  if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
    goto X1X1;           /* t2 = x0x0 + x1x1 */
  if (mp_sub (&t2, &t1, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */
 
  /* shift by B */
  if (mp_lshd (&t1, B) != MP_OKAY)
    goto X1X1;           /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
  if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
    goto X1X1;           /* x1x1 = x1x1 << 2*B */
 
  if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = x0x0 + t1 */
  if (mp_add (&t1, &x1x1, b) != MP_OKAY)
    goto X1X1;           /* t1 = x0x0 + t1 + x1x1 */
 
  err = MP_OKAY;
 
X1X1:mp_clear (&x1x1);
X0X0:mp_clear (&x0x0);
T2:mp_clear (&t2);
T1:mp_clear (&t1);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}

Referenced by mp_sqr().

mp_lcm()

int mp_lcm	(	const mp_int *	a,
		const mp_int *	b,
		mp_int *	c
	)

Definition at line 2807 of file mpi.c.

{
  int     res;
  mp_int  t1, t2;
 
 
  if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
    return res;
  }
 
  /* t1 = get the GCD of the two inputs */
  if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
    goto __T;
  }
 
  /* divide the smallest by the GCD */
  if (mp_cmp_mag(a, b) == MP_LT) {
     /* store quotient in t2 so that t2 * b is the LCM */
     if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
        goto __T;
     }
     res = mp_mul(b, &t2, c);
  } else {
     /* store quotient in t2 so that t2 * a is the LCM */
     if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
        goto __T;
     }
     res = mp_mul(a, &t2, c);
  }
 
  /* fix the sign to positive */
  c->sign = MP_ZPOS;
 
__T:
  mp_clear_multi (&t1, &t2, NULL);
  return res;
}

Referenced by rsa_make_key().

mp_lshd()

static int mp_lshd ( mp_int *  a, int  b  )

static

Definition at line 1386 of file mpi.c.

{
  int     x, res;
 
  /* if it's 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 other way 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;
}

Referenced by mp_div(), mp_karatsuba_mul(), mp_karatsuba_sqr(), mp_mul_2d(), and mp_reduce().

mp_mod()

int mp_mod	(	const mp_int *	a,
		mp_int *	b,
		mp_int *	c
	)

Definition at line 2847 of file mpi.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;
}

Referenced by mp_exptmod_fast(), mp_mulmod(), mp_sqrmod(), rsa_make_key(), and s_mp_exptmod().

mp_mod_2d()

static int mp_mod_2d ( const mp_int *  a, int  b, mp_int *  c  )

static

Definition at line 1227 of file mpi.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 > 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] &= (1 << ((mp_digit)b % DIGIT_BIT)) - 1;
  mp_clamp (c);
  return MP_OKAY;
}

Referenced by mp_div_2d(), and mp_reduce().

mp_mod_d()

static int mp_mod_d ( const mp_int *  a, mp_digit  b, mp_digit *  c  )

static

Definition at line 2873 of file mpi.c.

{
  return mp_div_d(a, b, NULL, c);
}

Referenced by mp_prime_is_divisible().

mp_montgomery_calc_normalization()

int mp_montgomery_calc_normalization ( mp_int *  a, const mp_int *  b  )

static

Definition at line 2945 of file mpi.c.

{
  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 < 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;
}

Referenced by mp_exptmod_fast().

mp_montgomery_reduce()

int mp_montgomery_reduce ( mp_int *  a, const mp_int *  m, mp_digit  mp  )

static

Definition at line 2980 of file mpi.c.

{
  int     ix, res, digs;
  mp_digit mu;
 
  /* can the fast reduction [comba] method be used?
   *
   * Note that unlike in mul you're safely allowed *less*
   * than the available columns [255 per default] since carries
   * are fixed up in the inner loop.
   */
  digs = n->used * 2 + 1;
  if ((digs < MP_WARRAY) &&
      n->used <
      (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
    return fast_mp_montgomery_reduce (x, n, rho);
  }
 
  /* grow the input as required */
  if (x->alloc < digs) {
    if ((res = mp_grow (x, digs)) != MP_OKAY) {
      return res;
    }
  }
  x->used = digs;
 
  for (ix = 0; ix < n->used; ix++) {
    /* mu = ai * rho mod b
     *
     * The value of rho must be precalculated via
     * montgomery_setup() such that
     * it equals -1/n0 mod b this allows the
     * following inner loop to reduce the
     * input one digit at a time
     */
    mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
 
    /* a = a + mu * m * b**i */
    {
      register int iy;
      register mp_digit *tmpn, *tmpx, u;
      register mp_word r;
 
      /* alias for digits of the modulus */
      tmpn = n->dp;
 
      /* alias for the digits of x [the input] */
      tmpx = x->dp + ix;
 
      /* set the carry to zero */
      u = 0;
 
      /* Multiply and add in place */
      for (iy = 0; iy < n->used; iy++) {
        /* compute product and sum */
        r       = ((mp_word)mu) * ((mp_word)*tmpn++) +
                  ((mp_word) u) + ((mp_word) * tmpx);
 
        /* get carry */
        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
 
        /* fix digit */
        *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
      }
      /* At this point the ix'th digit of x should be zero */
 
 
      /* propagate carries upwards as required*/
      while (u) {
        *tmpx   += u;
        u        = *tmpx >> DIGIT_BIT;
        *tmpx++ &= MP_MASK;
      }
    }
  }
 
  /* at this point the n.used'th least
   * significant digits of x are all zero
   * which means we can shift x to the
   * right by n.used digits and the
   * residue is unchanged.
   */
 
  /* x = x/b**n.used */
  mp_clamp(x);
  mp_rshd (x, n->used);
 
  /* if x >= n then x = x - n */
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }
 
  return MP_OKAY;
}

Referenced by mp_exptmod_fast().

mp_montgomery_setup()

int mp_montgomery_setup ( const mp_int *  a, mp_digit *  mp  )

static

Definition at line 3077 of file mpi.c.

{
  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 */
  x *= 2 - b * x;               /* here x*a==1 mod 2**16 */
  x *= 2 - b * x;               /* here x*a==1 mod 2**32 */
 
  /* rho = -1/m mod b */
  *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
 
  return MP_OKAY;
}

Referenced by mp_exptmod_fast().

mp_mul()

int mp_mul	(	const mp_int *	a,
		const mp_int *	b,
		mp_int *	c
	)

Definition at line 3107 of file mpi.c.

{
  int     res, neg;
  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
 
  /* use Karatsuba? */
  if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
    res = mp_karatsuba_mul (a, b, c);
  } else 
  {
    /* 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
     */
    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 
      res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
  }
  c->sign = (c->used > 0) ? neg : MP_ZPOS;
  return res;
}

Referenced by mp_exptmod_fast(), mp_karatsuba_mul(), mp_lcm(), mp_mulmod(), mp_reduce(), rsa_exptmod(), rsa_make_key(), and s_mp_exptmod().

mp_mul_2()

static int mp_mul_2 ( const mp_int *  a, mp_int *  b  )

static

Definition at line 2879 of file mpi.c.

{
  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;
}

Referenced by mp_montgomery_calc_normalization(), and mp_prime_random_ex().

mp_mul_2d()

static int mp_mul_2d ( const mp_int *  a, int  b, mp_int *  c  )

static

Definition at line 1432 of file mpi.c.

{
  mp_digit d;
  int      res;
 
  /* copy */
  if (a != c) {
     if ((res = mp_copy (a, c)) != MP_OKAY) {
       return res;
     }
  }
 
  if (c->alloc < 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 >= 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;
}

Referenced by mp_div(), mp_gcd(), mp_read_unsigned_bin(), and mp_set_int().

mp_mul_d()

static int mp_mul_d ( const mp_int *  a, mp_digit  b, mp_int *  c  )

static

Definition at line 1497 of file mpi.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] */
  *tmpc++ = u;
 
  /* 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;
}

Referenced by mp_div(), and mp_reduce_2k().

mp_mulmod()

int mp_mulmod	(	const mp_int *	a,
		const mp_int *	b,
		mp_int *	c,
		mp_int *	d
	)

Definition at line 3138 of file mpi.c.

{
  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;
}

Referenced by mp_exptmod_fast(), and rsa_exptmod().

mp_prime_is_divisible()

static int mp_prime_is_divisible ( const mp_int *  a, int *  result  )

static

Definition at line 3200 of file mpi.c.

{
  int     err, ix;
  mp_digit res;
 
  /* default to not */
  *result = MP_NO;
 
  for (ix = 0; ix < PRIME_SIZE; ix++) {
    /* what is a mod __prime_tab[ix] */
    if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) {
      return err;
    }
 
    /* is the residue zero? */
    if (res == 0) {
      *result = MP_YES;
      return MP_OKAY;
    }
  }
 
  return MP_OKAY;
}

Referenced by mp_prime_is_prime().

mp_prime_is_prime()

static int mp_prime_is_prime ( mp_int *  a, int  t, int *  result  )

static

Definition at line 3313 of file mpi.c.

{
  mp_int  b;
  int     ix, err, res;
 
  /* default to no */
  *result = MP_NO;
 
  /* valid value of t? */
  if (t <= 0 || t > PRIME_SIZE) {
    return MP_VAL;
  }
 
  /* is the input equal to one of the primes in the table? */
  for (ix = 0; ix < PRIME_SIZE; ix++) {
      if (mp_cmp_d(a, __prime_tab[ix]) == MP_EQ) {
         *result = 1;
         return MP_OKAY;
      }
  }
 
  /* first perform trial division */
  if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
    return err;
  }
 
  /* return if it was trivially divisible */
  if (res == MP_YES) {
    return MP_OKAY;
  }
 
  /* now perform the miller-rabin rounds */
  if ((err = mp_init (&b)) != MP_OKAY) {
    return err;
  }
 
  for (ix = 0; ix < t; ix++) {
    /* set the prime */
    mp_set (&b, __prime_tab[ix]);
 
    if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
      goto __B;
    }
 
    if (res == MP_NO) {
      goto __B;
    }
  }
 
  /* passed the test */
  *result = MP_YES;
__B:mp_clear (&b);
  return err;
}

Referenced by mp_prime_random_ex().

mp_prime_miller_rabin()

static int mp_prime_miller_rabin ( mp_int *  a, const mp_int *  b, int *  result  )

static

Definition at line 3231 of file mpi.c.

{
  mp_int  n1, y, r;
  int     s, j, err;
 
  /* default */
  *result = MP_NO;
 
  /* ensure b > 1 */
  if (mp_cmp_d(b, 1) != MP_GT) {
     return MP_VAL;
  }     
 
  /* get n1 = a - 1 */
  if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
    return err;
  }
  if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
    goto __N1;
  }
 
  /* set 2**s * r = n1 */
  if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
    goto __N1;
  }
 
  /* count the number of least significant bits
   * which are zero
   */
  s = mp_cnt_lsb(&r);
 
  /* now divide n - 1 by 2**s */
  if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
    goto __R;
  }
 
  /* compute y = b**r mod a */
  if ((err = mp_init (&y)) != MP_OKAY) {
    goto __R;
  }
  if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
    goto __Y;
  }
 
  /* if y != 1 and y != n1 do */
  if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
    j = 1;
    /* while j <= s-1 and y != n1 */
    while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
      if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
         goto __Y;
      }
 
      /* if y == 1 then composite */
      if (mp_cmp_d (&y, 1) == MP_EQ) {
         goto __Y;
      }
 
      ++j;
    }
 
    /* if y != n1 then composite */
    if (mp_cmp (&y, &n1) != MP_EQ) {
      goto __Y;
    }
  }
 
  /* probably prime now */
  *result = MP_YES;
__Y:mp_clear (&y);
__R:mp_clear (&r);
__N1:mp_clear (&n1);
  return err;
}

Referenced by mp_prime_is_prime().

mp_prime_rabin_miller_trials()

int mp_prime_rabin_miller_trials

(

int

size

)

Definition at line 3382 of file mpi.c.

{
   int x;
 
   for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
       if (sizes[x].k == size) {
          return sizes[x].t;
       } else if (sizes[x].k > size) {
          return (x == 0) ? sizes[0].t : sizes[x - 1].t;
       }
   }
   return sizes[x-1].t + 1;
}

Referenced by rand_prime().

mp_prime_random_ex()

int mp_prime_random_ex	(	mp_int *	a,
		int	t,
		int	size,
		int	flags,
		ltm_prime_callback	cb,
		void *	dat
	)

Definition at line 3412 of file mpi.c.

{
   unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
   int res, err, bsize, maskOR_msb_offset;
 
   /* sanity check the input */
   if (size <= 1 || t <= 0) {
      return MP_VAL;
   }
 
   /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
   if (flags & LTM_PRIME_SAFE) {
      flags |= LTM_PRIME_BBS;
   }
 
   /* calc the byte size */
   bsize = (size>>3)+((size&7)?1:0);
 
   /* we need a buffer of bsize bytes */
   tmp = HeapAlloc(GetProcessHeap(), 0, bsize);
   if (tmp == NULL) {
      return MP_MEM;
   }
 
   /* calc the maskAND value for the MSbyte*/
   maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7))); 
 
   /* calc the maskOR_msb */
   maskOR_msb        = 0;
   maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
   if (flags & LTM_PRIME_2MSB_ON) {
      maskOR_msb     |= 1 << ((size - 2) & 7);
   } else if (flags & LTM_PRIME_2MSB_OFF) {
      maskAND        &= ~(1 << ((size - 2) & 7));
   }
 
   /* get the maskOR_lsb */
   maskOR_lsb         = 0;
   if (flags & LTM_PRIME_BBS) {
      maskOR_lsb     |= 3;
   }
 
   do {
      /* read the bytes */
      if (cb(tmp, bsize, dat) != bsize) {
         err = MP_VAL;
         goto error;
      }
 
      /* work over the MSbyte */
      tmp[0]    &= maskAND;
      tmp[0]    |= 1 << ((size - 1) & 7);
 
      /* mix in the maskORs */
      tmp[maskOR_msb_offset]   |= maskOR_msb;
      tmp[bsize-1]             |= maskOR_lsb;
 
      /* read it in */
      if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY)     { goto error; }
 
      /* is it prime? */
      if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)           { goto error; }
      if (res == MP_NO) {  
         continue;
      }
 
      if (flags & LTM_PRIME_SAFE) {
         /* see if (a-1)/2 is prime */
         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY)                    { goto error; }
         if ((err = mp_div_2(a, a)) != MP_OKAY)                       { goto error; }
 
         /* is it prime? */
         if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)        { goto error; }
      }
   } while (res == MP_NO);
 
   if (flags & LTM_PRIME_SAFE) {
      /* restore a to the original value */
      if ((err = mp_mul_2(a, a)) != MP_OKAY)                          { goto error; }
      if ((err = mp_add_d(a, 1, a)) != MP_OKAY)                       { goto error; }
   }
 
   err = MP_OKAY;
error:
   HeapFree(GetProcessHeap(), 0, tmp);
   return err;
}

Referenced by rand_prime().

mp_read_unsigned_bin()

int mp_read_unsigned_bin	(	mp_int *	a,
		const unsigned char *	b,
		int	c
	)

Definition at line 3502 of file mpi.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;
    }
 
    a->dp[0] |= *b++;
    a->used += 1;
  }
  mp_clamp (a);
  return MP_OKAY;
}

Referenced by import_private_key_impl(), import_public_key_impl(), mp_prime_random_ex(), and rsa_exptmod().

mp_reduce()

int mp_reduce ( mp_int *  a, const mp_int *  b, const mp_int *  c  )

static

Definition at line 3534 of file mpi.c.

{
  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 {
    if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
      goto CLEANUP;
    }
  }
 
  /* 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;
}

Referenced by s_mp_exptmod().

mp_reduce_2k()

int mp_reduce_2k ( mp_int *  a, const mp_int *  n, mp_digit  d  )

static

Definition at line 3600 of file mpi.c.

{
   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;
   }
   
   if (d != 1) {
      /* q = q * d */
      if ((res = mp_mul_d(&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;
}

Referenced by mp_exptmod_fast().

mp_reduce_2k_setup()

static int mp_reduce_2k_setup ( const mp_int *  a, mp_digit *  d  )

static

Definition at line 3640 of file mpi.c.

{
   int res, p;
   mp_int tmp;
   
   if ((res = mp_init(&tmp)) != MP_OKAY) {
      return res;
   }
   
   p = mp_count_bits(a);
   if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
      mp_clear(&tmp);
      return res;
   }
   
   if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
      mp_clear(&tmp);
      return res;
   }
   
   *d = tmp.dp[0];
   mp_clear(&tmp);
   return MP_OKAY;
}

Referenced by mp_exptmod_fast().

mp_reduce_setup()

int mp_reduce_setup ( mp_int *  a, const mp_int *  b  )

static

Definition at line 3668 of file mpi.c.

{
  int     res;
 
  if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
    return res;
  }
  return mp_div (a, b, a, NULL);
}

Referenced by s_mp_exptmod().

mp_rshd()

static void mp_rshd ( mp_int *  a, int  b  )

static

Definition at line 1259 of file mpi.c.

{
  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;
}

Referenced by mp_div(), mp_div_2d(), mp_montgomery_reduce(), and mp_reduce().

mp_set()

void mp_set ( mp_int *  a, mp_digit  b  )

static

Definition at line 3679 of file mpi.c.

{
  mp_zero (a);
  a->dp[0] = b & MP_MASK;
  a->used  = (a->dp[0] != 0) ? 1 : 0;
}

Referenced by fast_mp_invmod(), mp_exptmod_fast(), mp_invmod_slow(), mp_montgomery_calc_normalization(), mp_prime_is_prime(), mp_reduce(), and s_mp_exptmod().

mp_set_int()

int mp_set_int	(	mp_int *	a,
		unsigned long	b
	)

Definition at line 3687 of file mpi.c.

{
  int     x, res;
 
  mp_zero (a);
  
  /* set four bits at a time */
  for (x = 0; x < 8; x++) {
    /* shift the number up four bits */
    if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) {
      return res;
    }
 
    /* OR in the top four bits of the source */
    a->dp[0] |= (b >> 28) & 15;
 
    /* shift the source up to the next four bits */
    b <<= 4;
 
    /* ensure that digits are not clamped off */
    a->used += 1;
  }
  mp_clamp (a);
  return MP_OKAY;
}

Referenced by import_private_key_impl(), import_public_key_impl(), and rsa_make_key().

mp_shrink()

int mp_shrink

(

mp_int *

a

)

Definition at line 3714 of file mpi.c.

{
  mp_digit *tmp;
  if (a->alloc != a->used && a->used > 0) {
    if ((tmp = HeapReAlloc(GetProcessHeap(), 0, a->dp, sizeof (mp_digit) * a->used)) == NULL) {
      return MP_MEM;
    }
    a->dp    = tmp;
    a->alloc = a->used;
  }
  return MP_OKAY;
}

Referenced by rsa_make_key().

mp_sqr()

int mp_sqr ( const mp_int *  a, mp_int *  b  )

static

Definition at line 3729 of file mpi.c.

{
  int     res;
 
if (a->used >= KARATSUBA_SQR_CUTOFF) {
    res = mp_karatsuba_sqr (a, b);
  } else 
  {
    /* 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
      res = s_mp_sqr (a, b);
  }
  b->sign = MP_ZPOS;
  return res;
}

Referenced by mp_exptmod_fast(), mp_karatsuba_sqr(), mp_sqrmod(), and s_mp_exptmod().

mp_sqrmod()

int mp_sqrmod ( const mp_int *  a, mp_int *  b, mp_int *  c  )

static

Definition at line 3751 of file mpi.c.

{
  int     res;
  mp_int  t;
 
  if ((res = mp_init (&t)) != MP_OKAY) {
    return res;
  }
 
  if ((res = mp_sqr (a, &t)) != MP_OKAY) {
    mp_clear (&t);
    return res;
  }
  res = mp_mod (&t, b, c);
  mp_clear (&t);
  return res;
}

Referenced by mp_prime_miller_rabin().

mp_sub()

int mp_sub	(	mp_int *	a,
		mp_int *	b,
		mp_int *	c
	)

Definition at line 3771 of file mpi.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;
}

Referenced by fast_mp_invmod(), mp_div(), mp_invmod_slow(), mp_karatsuba_mul(), mp_karatsuba_sqr(), mp_reduce(), and rsa_exptmod().

mp_sub_d()

int mp_sub_d	(	mp_int *	a,
		mp_digit	b,
		mp_int *	c
	)

Definition at line 3808 of file mpi.c.

{
  mp_digit *tmpa, *tmpc, mu;
  int       res, ix, oldused;
 
  /* grow c as required */
  if (c->alloc < a->used + 1) {
     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
        return res;
     }
  }
 
  /* if a is negative just do an unsigned
   * addition [with fudged signs]
   */
  if (a->sign == MP_NEG) {
     a->sign = MP_ZPOS;
     res     = mp_add_d(a, b, c);
     a->sign = c->sign = MP_NEG;
     return res;
  }
 
  /* setup regs */
  oldused = c->used;
  tmpa    = a->dp;
  tmpc    = c->dp;
 
  /* if a <= b simply fix the single digit */
  if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
     if (a->used == 1) {
        *tmpc++ = b - *tmpa;
     } else {
        *tmpc++ = b;
     }
     ix      = 1;
 
     /* negative/1digit */
     c->sign = MP_NEG;
     c->used = 1;
  } else {
     /* positive/size */
     c->sign = MP_ZPOS;
     c->used = a->used;
 
     /* subtract first digit */
     *tmpc    = *tmpa++ - b;
     mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
     *tmpc++ &= MP_MASK;
 
     /* handle rest of the digits */
     for (ix = 1; ix < a->used; ix++) {
        *tmpc    = *tmpa++ - mu;
        mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
        *tmpc++ &= MP_MASK;
     }
  }
 
  /* zero excess digits */
  while (ix++ < oldused) {
     *tmpc++ = 0;
  }
  mp_clamp(c);
  return MP_OKAY;
}

Referenced by mp_add_d(), mp_prime_miller_rabin(), mp_prime_random_ex(), and rsa_make_key().

mp_to_unsigned_bin()

int mp_to_unsigned_bin	(	const mp_int *	a,
		unsigned char *	b
	)

Definition at line 3875 of file mpi.c.

{
  int     x, res;
  mp_int  t;
 
  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
    return res;
  }
 
  x = 0;
  while (mp_iszero (&t) == 0) {
    b[x++] = (unsigned char) (t.dp[0] & 255);
    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;
}

Referenced by export_private_key_impl(), export_public_key_impl(), and rsa_exptmod().

mp_unsigned_bin_size()

int mp_unsigned_bin_size

(

const mp_int *

a

)

Definition at line 3899 of file mpi.c.

{
  int     size = mp_count_bits (a);
  return (size / 8 + ((size & 7) != 0 ? 1 : 0));
}

Referenced by export_private_key_impl(), export_public_key_impl(), and rsa_exptmod().

mp_zero()

static void mp_zero ( mp_int *  a )

static

Definition at line 278 of file mpi.c.

{
  a->sign = MP_ZPOS;
  a->used = 0;
  memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
}

Referenced by mp_2expt(), mp_div(), mp_div_2d(), mp_gcd(), mp_mod_2d(), mp_read_unsigned_bin(), mp_rshd(), mp_set(), and mp_set_int().

s_is_power_of_two()

static BOOL s_is_power_of_two ( mp_digit  b, int *  p  )

static

Definition at line 1748 of file mpi.c.

{
   int x;
 
   for (x = 1; x < DIGIT_BIT; x++) {
      if (b == (((mp_digit)1)<<x)) {
         *p = x;
         return TRUE;
      }
   }
   return FALSE;
}

Referenced by mp_div_d().

s_mp_add()

static int s_mp_add ( mp_int *  a, mp_int *  b, mp_int *  c  )

static

Definition at line 3925 of file mpi.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;
}

Referenced by mp_add(), mp_karatsuba_sqr(), mp_reduce_2k(), and mp_sub().

s_mp_exptmod()

static int s_mp_exptmod ( const mp_int *  G, const mp_int *  X, mp_int *  P, mp_int *  Y  )

static

Definition at line 4011 of file mpi.c.

{
  mp_int  M[256], res, mu;
  mp_digit buf;
  int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
 
  /* 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;
  }
 
  /* 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 __M;
  }
  if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
    goto __MU;
  }
 
  /* 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 __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 __MU;
  }
 
  for (x = 0; x < (winsize - 1); x++) {
    if ((err = mp_sqr (&M[1 << (winsize - 1)], 
                       &M[1 << (winsize - 1)])) != MP_OKAY) {
      goto __MU;
    }
    if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
      goto __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 __MU;
    }
    if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) {
      goto __MU;
    }
  }
 
  /* setup result */
  if ((err = mp_init (&res)) != MP_OKAY) {
    goto __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 = 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 __RES;
      }
      if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
        goto __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 __RES;
        }
        if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
          goto __RES;
        }
      }
 
      /* then multiply */
      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
        goto __RES;
      }
      if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
        goto __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 __RES;
      }
      if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
        goto __RES;
      }
 
      bitbuf <<= 1;
      if ((bitbuf & (1 << winsize)) != 0) {
        /* then multiply */
        if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
          goto __RES;
        }
        if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
          goto __RES;
        }
      }
    }
  }
 
  mp_exch (&res, Y);
  err = MP_OKAY;
__RES:mp_clear (&res);
__MU:mp_clear (&mu);
__M:
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}

Referenced by mp_exptmod().

s_mp_mul_digs()

static int s_mp_mul_digs ( const mp_int *  a, const mp_int *  b, mp_int *  c, int  digs  )

static

Definition at line 4223 of file mpi.c.

{
  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;
}

Referenced by mp_reduce().

s_mp_mul_high_digs()

static int s_mp_mul_high_digs ( const mp_int *  a, const mp_int *  b, mp_int *  c, int  digs  )

static

Definition at line 4292 of file mpi.c.

{
  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 (((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);
  }
 
  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;
}

Referenced by mp_reduce().

s_mp_sqr()

static int s_mp_sqr ( const mp_int *  a, mp_int *  b  )

static

Definition at line 4348 of file mpi.c.

{
  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 != 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;
}

Referenced by mp_sqr().

s_mp_sub()

int s_mp_sub ( const mp_int *  a, const mp_int *  b, mp_int *  c  )

static

Definition at line 4412 of file mpi.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;
}

Referenced by fast_mp_montgomery_reduce(), mp_add(), mp_dr_reduce(), mp_gcd(), mp_montgomery_calc_normalization(), mp_montgomery_reduce(), mp_reduce(), mp_reduce_2k(), mp_reduce_2k_setup(), and mp_sub().

Variable Documentation

__prime_tab

const mp_digit __prime_tab[]

static

Definition at line 3157 of file mpi.c.

Referenced by mp_prime_is_divisible(), and mp_prime_is_prime().

k

int k

Definition at line 3369 of file mpi.c.

Referenced by __ieee754_jn(), _getw(), hashtable< _Val, _Key, _HF, _Traits, _ExK, _EqK, _All >::_M_get_key(), AcpiExConvertToAscii(), AcpiUtAllocateOwnerId(), adapt(), AddIpv6HostEntries(), Subdivider::arc_split(), Array_map(), Array_reverse(), Array_sort(), ata_bblk(), Ata_is_dev_listed(), AtapiInterrupt(), AtapiInterrupt__(), AtapiResetController__(), Mapdesc::bbox(), Mapdesc::bboxTooBig(), bezierCurveEval(), bezierCurveEvalDer(), bezierCurveEvalDerGen(), bezierPatchMake2(), bezierPatchMeshDelDeg(), bezierPatchMeshDraw(), bezierPatchMeshEval(), bezierPatchMeshListCollect(), bezierPatchMeshMake(), BIDI_Reorder(), build_tlib_section(), build_wndclass_section(), cache_container_set_size(), calc_sha256(), Mapdesc::calcPartialVelocity(), CC_CheckDigitsInEdit(), CC_PaintPredefColorArray(), CC_PaintUserColorArray(), cert_name_to_str_with_indent(), CertGetValidUsages(), cff_encoding_load(), cfgets(), check_generated_effects_(), CheckAgainstNTFS(), chmc_namelist_create(), cleanupA(), cleanupW(), CmpConvertKcbSharedToExclusive(), CmpSortKcbArray(), CmpTryToConvertKcbSharedToExclusive(), codeview_snarf_linetab(), coff_process_info(), compareCTLInfo(), ComposeConsonants(), compute_text_mesh(), computeIsolatingRunsSet(), convert_to_fos_high_precision(), copypixels_to_24bppBGR(), copypixels_to_32bppBGRA(), crc32_z(), create_arp_response(), CRYPT_ExportKeyTrans(), CRYPT_FormatUserNotice(), CRYPT_ImportKeyTrans(), d3dcompiler_shader_reflection_GetVariableByName(), d3drm_mesh_builder3_CreateMesh(), d3dx9_mesh_GenerateAdjacency(), d3dx_pool_sync_shared_parameter(), D3DXCreateTextW(), D3DXLoadMeshFromXInMemory(), DATETIME_UseFormat(), de_casteljau_surf(), DECLAREContigPutFunc(), decode_mcu(), decode_mcu_AC_first(), decode_mcu_AC_refine(), decode_mcu_sub(), deleteRepeatDiagonals(), DetectSerialPointerPeripheral(), DIB_1BPP_BitBlt(), dictionary_find(), dictionary_find_internal(), dictionary_insert(), dictionary_remove(), DisplayArpEntries(), DoGetAliasPIDLs(), DoTestEntry(), primStream::draw(), rectBlock::draw(), draw_cursor(), draw_cursor_under(), CToolSettingsWindow::drawAirBrush(), drawStrips(), dump_template(), dumpMenu(), empty_image(), emptyImage3D(), encode_mcu(), encode_mcu_AC_first(), encode_mcu_AC_refine(), encode_one_block(), enumerate_mapped_resources(), Slicer::evalRBArray(), Slicer::evalStream(), OpenGLSurfaceEvaluator::evalUStrip(), OpenGLSurfaceEvaluator::evalVStrip(), CShellCommandValue::Execute(), execute_preshader(), ExecuteREBytecode(), Ext2ParseRegistryVolumeParams(), ext4_ext_binsearch(), ext4_ext_binsearch_idx(), ext4_ext_correct_indexes(), ext4_ext_split(), ExtractName(), FatUnpinRepinnedBcbs(), Fbt_Dispatch(), fdi_Ziphuft_build(), fdi_Zipinflate_block(), fdi_Zipinflate_codes(), fdi_Zipinflate_dynamic(), fdi_Zipinflate_stored(), fill_image(), fillImage3D(), MemFunPtrTest::find(), find_dev_alloc(), findBotSeparator(), findDiagonals(), FindTest::findif0(), findLeftGridIndices(), findRightGridIndices(), findTopSeparator(), flush_partial_stripe(), fnt_face_get_dll_font(), BtrfsVolPropSheet::FormatUsage(), FstubTranslateResource(), FT_Outline_EmboldenXY(), get_matrix(), get_valid_pass(), GetLayoutName(), GetPrivateProfileStructW(), gl_color_shade_vertices(), gl_color_shade_vertices_fast(), gl_copy_map_points1d(), gl_copy_map_points1f(), gl_copy_map_points2d(), gl_copy_map_points2f(), gl_display_matches(), gl_index_shade_vertices(), gl_Map1f(), gl_Map2f(), glsl_program_key_compare(), glsl_vertex_pipe_view(), GPOS_apply_ChainContextPos(), GPOS_apply_ContextPos(), GPOS_apply_MarkToLigature(), GPOS_apply_PairAdjustment(), GSUB_apply_ChainContextSubst(), GSUB_apply_ContextSubst(), GSUB_apply_LigatureSubst(), HalpDebugPciDumpBus(), HalpGetPciBridgeConfig(), HalpInitializePciBus(), HalpReportResourceUsage(), halveImage(), halveImage_byte(), halveImage_float(), halveImage_int(), halveImage_short(), halveImage_ubyte(), halveImage_uint(), halveImage_ushort(), help(), HelpCmd(), horner_bezier_curve(), 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KARATSUBA_MUL_CUTOFF

const int KARATSUBA_MUL_CUTOFF = 88

static

Definition at line 42 of file mpi.c.

Referenced by mp_mul().

KARATSUBA_SQR_CUTOFF

const int KARATSUBA_SQR_CUTOFF = 128

static

Definition at line 43 of file mpi.c.

Referenced by mp_sqr().

lnz

const int lnz[16]

static

Initial value:

= { 
   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
}

Definition at line 1123 of file mpi.c.

Referenced by mp_cnt_lsb().

const struct { ... } sizes[]

Initial value:

= {
{   128,    28 },
{   256,    16 },
{   384,    10 },
{   512,     7 },
{   640,     6 },
{   768,     5 },
{   896,     4 },
{  1024,     4 }
}

Referenced by check_height_font_enumproc(), EnumAddress_cb(), EnumAddress_cb2(), InstallEngine_GetSizes(), mp_prime_rabin_miller_trials(), nego_QueryContextAttributesA(), nego_QueryContextAttributesW(), SdbGetTagDataSize(), SetFontSizesToCombo3(), START_TEST(), test_authentication(), test_communication(), and test_merge_colors().

t

int t

Definition at line 3369 of file mpi.c.

Referenced by bn_reverse(), mp_div(), mp_div_2d(), mp_div_d(), mp_exch(), mp_mod(), mp_mulmod(), mp_prime_is_prime(), mp_sqrmod(), mp_to_unsigned_bin(), s_mp_mul_digs(), s_mp_mul_high_digs(), and s_mp_sqr().