text: /*
   * Minimal code for RSA support from LibTomMath 0.41
   * http://libtom.org/
   * http://libtom.org/files/ltm-0.41.tar.bz2
   * This library was released in public domain by Tom St Denis.
   *
   * The combination in this file may not use all of the optimized algorithms
   * from LibTomMath and may be considerable slower than the LibTomMath with its
   * default settings. The main purpose of having this version here is to make it
   * easier to build bignum.c wrapper without having to install and build an
   * external library.
   *
   * If CONFIG_INTERNAL_LIBTOMMATH is defined, bignum.c includes this
   * libtommath.c file instead of using the external LibTomMath library.
   */
  //#include "c_types.h"
  #include "os.h"
  #include "stdarg.h"
  
  
  #ifndef CHAR_BIT
  #define CHAR_BIT 8
  #endif
  
  #define BN_MP_INVMOD_C
  #define BN_S_MP_EXPTMOD_C /* Note: #undef in tommath_superclass.h; this would
  			   * require BN_MP_EXPTMOD_FAST_C instead */
  #define BN_S_MP_MUL_DIGS_C
  #define BN_MP_INVMOD_SLOW_C
  #define BN_S_MP_SQR_C
  #define BN_S_MP_MUL_HIGH_DIGS_C /* Note: #undef in tommath_superclass.h; this
  				 * would require other than esp_mp_reduce */
  
  #ifdef LTM_FAST
  
  /* Use faster div at the cost of about 1 kB */
  #define BN_MP_MUL_D_C
  
  /* Include faster exptmod (Montgomery) at the cost of about 2.5 kB in code */
  #define BN_MP_EXPTMOD_FAST_C
  #define BN_MP_MONTGOMERY_SETUP_C
  #define BN_FAST_MP_MONTGOMERY_REDUCE_C
  #define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
  #define BN_MP_MUL_2_C
  
  /* Include faster sqr at the cost of about 0.5 kB in code */
  #define BN_FAST_S_MP_SQR_C
  
  #else /* LTM_FAST */
  
  #define BN_MP_DIV_SMALL
  #define BN_MP_INIT_MULTI_C
  #define BN_MP_CLEAR_MULTI_C
  #define BN_MP_ABS_C
  #endif /* LTM_FAST */
  
  /* Current uses do not require support for negative exponent in exptmod, so we
   * can save about 1.5 kB in leaving out invmod. */
  #define LTM_NO_NEG_EXP
  
  /* from tommath.h */
  
  #ifndef MIN
     #define MIN(x,y) ((x)<(y)?(x):(y))
  #endif
  
  #ifndef MAX
     #define MAX(x,y) ((x)>(y)?(x):(y))
  #endif
  
  #define  OPT_CAST(x) (x *)
  
  typedef unsigned long mp_digit;
  typedef u64 mp_word;
  
  #define DIGIT_BIT          28
  #define MP_28BIT
  
  
  #define XMALLOC  os_malloc
  #define XFREE    os_free
  #define XREALLOC os_realloc
  
  
  #define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
  
  #define MP_LT        -1   /* less than */
  #define MP_EQ         0   /* equal to */
  #define MP_GT         1   /* greater than */
  
  #define MP_ZPOS       0   /* positive integer */
  #define MP_NEG        1   /* negative */
  
  #define MP_OKAY       0   /* ok result */
  #define MP_MEM        -2  /* out of mem */
  #define MP_VAL        -3  /* invalid input */
  
  #define MP_YES        1   /* yes response */
  #define MP_NO         0   /* no response */
  
  typedef int           mp_err;
  
  /* define this to use lower memory usage routines (exptmods mostly) */
  #define MP_LOW_MEM
  
  /* default precision */
  #ifndef MP_PREC
     #ifndef MP_LOW_MEM
        #define MP_PREC                 32     /* default digits of precision */
     #else
        #define MP_PREC                 8      /* default digits of precision */
     #endif   
  #endif
  
  /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
  #define MP_WARRAY               (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
  
  /* the infamous mp_int structure */
  typedef struct  {
      int used, alloc, sign;
      mp_digit *dp;
  } mp_int;
  
  
  /* ---> Basic Manipulations <--- */
  #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
  #define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
  #define mp_isodd(a)  (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
  
  
  /* prototypes for copied functions */
  #define s_mp_mul(a, b, c) esp_s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
  static int esp_s_mp_exptmod(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
  static int esp_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
  static int esp_s_mp_sqr(mp_int * a, mp_int * b);
  static int esp_s_mp_mul_high_digs(mp_int * a, mp_int * b, mp_int * c, int digs);
  
  static int esp_fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
  
  #ifdef BN_MP_INIT_MULTI_C
  static int esp_mp_init_multi(mp_int *mp, ...);
  #endif
  #ifdef BN_MP_CLEAR_MULTI_C
  static void esp_mp_clear_multi(mp_int *mp, ...);
  #endif
  static int esp_mp_lshd(mp_int * a, int b);
  static void esp_mp_set(mp_int * a, mp_digit b);
  static void esp_mp_clamp(mp_int * a);
  static void esp_mp_exch(mp_int * a, mp_int * b);
  static void esp_mp_rshd(mp_int * a, int b);
  static void esp_mp_zero(mp_int * a);
  static int esp_mp_mod_2d(mp_int * a, int b, mp_int * c);
  static int esp_mp_div_2d(mp_int * a, int b, mp_int * c, mp_int * d);
  static int esp_mp_init_copy(mp_int * a, mp_int * b);
  static int esp_mp_mul_2d(mp_int * a, int b, mp_int * c);
  #ifndef LTM_NO_NEG_EXP
  static int mp_div_2(mp_int * a, mp_int * b);
  static int mp_invmod(mp_int * a, mp_int * b, mp_int * c);
  static int mp_invmod_slow(mp_int * a, mp_int * b, mp_int * c);
  #endif /* LTM_NO_NEG_EXP */
  static int esp_mp_copy(mp_int * a, mp_int * b);
  static int esp_mp_count_bits(mp_int * a);
  static int esp_mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
  static int esp_mp_mod(mp_int * a, mp_int * b, mp_int * c);
  static int esp_mp_grow(mp_int * a, int size);
  static int esp_mp_cmp_mag(mp_int * a, mp_int * b);
  #ifdef BN_MP_ABS_C
  static int esp_mp_abs(mp_int * a, mp_int * b);
  #endif
  static int esp_mp_sqr(mp_int * a, mp_int * b);
  static int esp_mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
  static int esp_mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
  static int esp_mp_2expt(mp_int * a, int b);
  static int esp_mp_reduce_setup(mp_int * a, mp_int * b);
  static int esp_mp_reduce(mp_int * x, mp_int * m, mp_int * mu);
  static int esp_mp_init_size(mp_int * a, int size);
  #ifdef BN_MP_EXPTMOD_FAST_C
  static int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
  #endif /* BN_MP_EXPTMOD_FAST_C */
  #ifdef BN_FAST_S_MP_SQR_C
  static int fast_s_mp_sqr (mp_int * a, mp_int * b);
  #endif /* BN_FAST_S_MP_SQR_C */
  #ifdef BN_MP_MUL_D_C
  static int mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
  #endif /* BN_MP_MUL_D_C */
  
  
  
  /* functions from bn_<func name>.c */
  
  
  /* reverse an array, used for radix code */
  static void 
  esp_bn_reverse (unsigned char *s, int len)
  {
    int     ix, iy;
    unsigned char t;
  
    ix = 0;
    iy = len - 1;
    while (ix < iy) {
      t     = s[ix];
      s[ix] = s[iy];
      s[iy] = t;
      ++ix;
      --iy;
    }
  }
  
  
  /* low level addition, based on HAC pp.594, Algorithm 14.7 */
  static int 
  esp_s_mp_add (mp_int * a, mp_int * b, mp_int * c)
  {
    mp_int *x;
    int     olduse, res, min, max;
  
    /* find sizes, we let |a| <= |b| which means we have to sort
     * them.  "x" will point to the input with the most digits
     */
    if (a->used > b->used) {
      min = b->used;
      max = a->used;
      x = a;
    } else {
      min = a->used;
      max = b->used;
      x = b;
    }
  
    /* esp_init result */
    if (c->alloc < max + 1) {
      if ((res = esp_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;
      }
    }
  
    esp_mp_clamp (c);
    return MP_OKAY;
  }
  
  
  /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
  static int 
  esp_s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
  {
    int     olduse, res, min, max;
  
    /* find sizes */
    min = b->used;
    max = a->used;
  
    /* esp_init result */
    if (c->alloc < max) {
      if ((res = esp_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;
      }
    }
  
    esp_mp_clamp (c);
    return MP_OKAY;
  }
  
  
  /* esp_init a new mp_int */
  static int 
  esp_mp_init (mp_int * a)
  {
    int i;
  
    /* allocate memory required and clear it */
    a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
    if (a->dp == NULL) {
      return MP_MEM;
    }
  
    /* set the digits to zero */
    for (i = 0; i < MP_PREC; i++) {
        a->dp[i] = 0;
    }
  
    /* set the used to zero, allocated digits to the default precision
     * and sign to positive */
    a->used  = 0;
    a->alloc = MP_PREC;
    a->sign  = MP_ZPOS;
  
    return MP_OKAY;
  }
  
  
  /* clear one (frees)  */
  static void 
  esp_mp_clear (mp_int * a)
  {
    int i;
  
    /* only do anything if a hasn't been freed previously */
    if (a->dp != NULL) {
      /* first zero the digits */
      for (i = 0; i < a->used; i++) {
          a->dp[i] = 0;
      }
  
      /* free ram */
      XFREE(a->dp);
  
      /* reset members to make debugging easier */
      a->dp    = NULL;
      a->alloc = a->used = 0;
      a->sign  = MP_ZPOS;
    }
  }
  
  
  /* high level addition (handles signs) */
  static int 
  esp_mp_add (mp_int * a, mp_int * b, mp_int * c)
  {
    int     sa, sb, res;
  
    /* get sign of both inputs */
    sa = a->sign;
    sb = b->sign;
  
    /* handle two cases, not four */
    if (sa == sb) {
      /* both positive or both negative */
      /* add their magnitudes, copy the sign */
      c->sign = sa;
      res = esp_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 (esp_mp_cmp_mag (a, b) == MP_LT) {
        c->sign = sb;
        res = esp_s_mp_sub (b, a, c);
      } else {
        c->sign = sa;
        res = esp_s_mp_sub (a, b, c);
      }
    }
    return res;
  }
  
  
  /* high level subtraction (handles signs) */
  static int 
  esp_mp_sub (mp_int * a, mp_int * b, mp_int * c)
  {
    int     sa, sb, res;
  
    sa = a->sign;
    sb = b->sign;
  
    if (sa != sb) {
      /* subtract a negative from a positive, OR */
      /* subtract a positive from a negative. */
      /* In either case, ADD their magnitudes, */
      /* and use the sign of the first number. */
      c->sign = sa;
      res = esp_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 (esp_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 = esp_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 = esp_s_mp_sub (b, a, c);
      }
    }
    return res;
  }
  
  
  /* high level multiplication (handles sign) */
  static int 
  esp_mp_mul (mp_int * a, mp_int * b, mp_int * c)
  {
    int     res, neg;
    neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
  
    /* use Toom-Cook? */
  #ifdef BN_MP_TOOM_MUL_C
    if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
      res = mp_toom_mul(a, b, c);
    } else 
  #endif
  #ifdef BN_MP_KARATSUBA_MUL_C
    /* use Karatsuba? */
    if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
      res = mp_karatsuba_mul (a, b, c);
    } else 
  #endif
    {
      /* can we use the fast multiplier?
       *
       * The fast multiplier can be used if the output will 
       * have less than MP_WARRAY digits and the number of 
       * digits won't affect carry propagation
       */
  #ifdef BN_FAST_S_MP_MUL_DIGS_C
      int     digs = a->used + b->used + 1;
  
      if ((digs < MP_WARRAY) &&
          MIN(a->used, b->used) <= 
          (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
        res = esp_fast_s_mp_mul_digs (a, b, c, digs);
      } else 
  #endif
  #ifdef BN_S_MP_MUL_DIGS_C
        res = s_mp_mul (a, b, c); /* uses esp_s_mp_mul_digs */
  #else
  #esp_error mp_mul could fail
        res = MP_VAL;
  #endif
  
    }
    c->sign = (c->used > 0) ? neg : MP_ZPOS;
    return res;
  }
  
  
  /* d = a * b (mod c) */
  static int 
  esp_mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
  {
    int     res;
    mp_int  t;
  
    if ((res = esp_mp_init (&t)) != MP_OKAY) {
      return res;
    }
  
    if ((res = esp_mp_mul (a, b, &t)) != MP_OKAY) {
      esp_mp_clear (&t);
      return res;
    }
    res = esp_mp_mod (&t, c, d);
    esp_mp_clear (&t);
    return res;
  }
  
  
  /* c = a mod b, 0 <= c < b */
  static int 
  esp_mp_mod (mp_int * a, mp_int * b, mp_int * c)
  {
    mp_int  t;
    int     res;
  
    if ((res = esp_mp_init (&t)) != MP_OKAY) {
      return res;
    }
  
    if ((res = esp_mp_div (a, b, NULL, &t)) != MP_OKAY) {
      esp_mp_clear (&t);
      return res;
    }
  
    if (t.sign != b->sign) {
      res = esp_mp_add (b, &t, c);
    } else {
      res = MP_OKAY;
      esp_mp_exch (&t, c);
    }
  
    esp_mp_clear (&t);
    return res;
  }
  
  
  /* this is a shell function that calls either the normal or Montgomery
   * exptmod functions.  Originally the call to the montgomery code was
   * embedded in the normal function but that wasted a lot of stack space
   * for nothing (since 99% of the time the Montgomery code would be called)
   */
  static int 
  esp_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
  {
    int dr;
  
    /* modulus P must be positive */
    if (P->sign == MP_NEG) {
       return MP_VAL;
    }
  
    /* if exponent X is negative we have to recurse */
    if (X->sign == MP_NEG) {
  #ifdef LTM_NO_NEG_EXP
          return MP_VAL;
  #else /* LTM_NO_NEG_EXP */
  #ifdef BN_MP_INVMOD_C
       mp_int tmpG, tmpX;
       int err;
  
       /* first compute 1/G mod P */
       if ((err = esp_mp_init(&tmpG)) != MP_OKAY) {
          return err;
       }
       if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
          esp_mp_clear(&tmpG);
          return err;
       }
  
       /* now get |X| */
       if ((err = esp_mp_init(&tmpX)) != MP_OKAY) {
          esp_mp_clear(&tmpG);
          return err;
       }
       if ((err = esp_mp_abs(X, &tmpX)) != MP_OKAY) {
          esp_mp_clear_multi(&tmpG, &tmpX, NULL);
          return err;
       }
  
       /* and now compute (1/G)**|X| instead of G**X [X < 0] */
       err = esp_mp_exptmod(&tmpG, &tmpX, P, Y);
       esp_mp_clear_multi(&tmpG, &tmpX, NULL);
       return err;
  #else 
  #esp_error mp_exptmod would always fail
       /* no invmod */
       return MP_VAL;
  #endif
  #endif /* LTM_NO_NEG_EXP */
    }
  
  /* modified diminished radix reduction */
  #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
    if (mp_reduce_is_2k_l(P) == MP_YES) {
       return esp_s_mp_exptmod(G, X, P, Y, 1);
    }
  #endif
  
  #ifdef BN_MP_DR_IS_MODULUS_C
    /* is it a DR modulus? */
    dr = mp_dr_is_modulus(P);
  #else
    /* default to no */
    dr = 0;
  #endif
  
  #ifdef BN_MP_REDUCE_IS_2K_C
    /* if not, is it a unrestricted DR modulus? */
    if (dr == 0) {
       dr = mp_reduce_is_2k(P) << 1;
    }
  #endif
      
    /* if the modulus is odd or dr != 0 use the montgomery method */
  #ifdef BN_MP_EXPTMOD_FAST_C
    if (mp_isodd (P) == 1 || dr !=  0) {
      return mp_exptmod_fast (G, X, P, Y, dr);
    } else {
  #endif
  #ifdef BN_S_MP_EXPTMOD_C
      (void) dr;
      /* otherwise use the generic Barrett reduction technique */
      return esp_s_mp_exptmod (G, X, P, Y, 0);
  #else
  #esp_error mp_exptmod could fail
      /* no exptmod for evens */
      return MP_VAL;
  #endif
  #ifdef BN_MP_EXPTMOD_FAST_C
    }
  #endif
  }
  
  
  /* compare two ints (signed)*/
  static int 
  esp_mp_cmp (mp_int * a, mp_int * b)
  {
    /* compare based on sign */
    if (a->sign != b->sign) {
       if (a->sign == MP_NEG) {
          return MP_LT;
       } else {
          return MP_GT;
       }
    }
    
    /* compare digits */
    if (a->sign == MP_NEG) {
       /* if negative compare opposite direction */
       return esp_mp_cmp_mag(b, a);
    } else {
       return esp_mp_cmp_mag(a, b);
    }
  }
  
  
  /* compare a digit */
  static int 
  esp_mp_cmp_d(mp_int * a, mp_digit b)
  {
    /* compare based on sign */
    if (a->sign == MP_NEG) {
      return MP_LT;
    }
  
    /* compare based on magnitude */
    if (a->used > 1) {
      return MP_GT;
    }
  
    /* compare the only digit of a to b */
    if (a->dp[0] > b) {
      return MP_GT;
    } else if (a->dp[0] < b) {
      return MP_LT;
    } else {
      return MP_EQ;
    }
  }
  
  
  #ifndef LTM_NO_NEG_EXP
  /* hac 14.61, pp608 */
  static int 
  mp_invmod (mp_int * a, mp_int * b, mp_int * c)
  {
    /* b cannot be negative */
    if (b->sign == MP_NEG || mp_iszero(b) == 1) {
      return MP_VAL;
    }
  
  #ifdef BN_FAST_MP_INVMOD_C
    /* if the modulus is odd we can use a faster routine instead */
    if (mp_isodd (b) == 1) {
      return fast_mp_invmod (a, b, c);
    }
  #endif
  
  #ifdef BN_MP_INVMOD_SLOW_C
    return mp_invmod_slow(a, b, c);
  #endif
  
  #ifndef BN_FAST_MP_INVMOD_C
  #ifndef BN_MP_INVMOD_SLOW_C
  #esp_error mp_invmod would always fail
  #endif
  #endif
    return MP_VAL;
  }
  #endif /* LTM_NO_NEG_EXP */
  
  
  /* get the size for an unsigned equivalent */
  static int 
  esp_mp_unsigned_bin_size (mp_int * a)
  {
    int     size = esp_mp_count_bits (a);
    return (size / 8 + ((size & 7) != 0 ? 1 : 0));
  }
  
  
  #ifndef LTM_NO_NEG_EXP
  /* hac 14.61, pp608 */
  static int 
  mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
  {
    mp_int  x, y, u, v, A, B, C, D;
    int     res;
  
    /* b cannot be negative */
    if (b->sign == MP_NEG || mp_iszero(b) == 1) {
      return MP_VAL;
    }
  
    /* esp_init temps */
    if ((res = esp_mp_init_multi(&x, &y, &u, &v, 
                             &A, &B, &C, &D, NULL)) != MP_OKAY) {
       return res;
    }
  
    /* x = a, y = b */
    if ((res = esp_mp_mod(a, b, &x)) != MP_OKAY) {
        goto LBL_ERR;
    }
    if ((res = esp_mp_copy (b, &y)) != MP_OKAY) {
      goto LBL_ERR;
    }
  
    /* 2. [modified] if x,y are both even then return an esp_error! */
    if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
      res = MP_VAL;
      goto LBL_ERR;
    }
  
    /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
    if ((res = esp_mp_copy (&x, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    if ((res = esp_mp_copy (&y, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    esp_mp_set (&A, 1);
    esp_mp_set (&D, 1);
  
  top:
    /* 4.  while u is even do */
    while (mp_iseven (&u) == 1) {
      /* 4.1 u = u/2 */
      if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
        goto LBL_ERR;
      }
      /* 4.2 if A or B is odd then */
      if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
        /* A = (A+y)/2, B = (B-x)/2 */
        if ((res = esp_mp_add (&A, &y, &A)) != MP_OKAY) {
           goto LBL_ERR;
        }
        if ((res = esp_mp_sub (&B, &x, &B)) != MP_OKAY) {
           goto LBL_ERR;
        }
      }
      /* A = A/2, B = B/2 */
      if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
        goto LBL_ERR;
      }
      if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
  
    /* 5.  while v is even do */
    while (mp_iseven (&v) == 1) {
      /* 5.1 v = v/2 */
      if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
        goto LBL_ERR;
      }
      /* 5.2 if C or D is odd then */
      if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
        /* C = (C+y)/2, D = (D-x)/2 */
        if ((res = esp_mp_add (&C, &y, &C)) != MP_OKAY) {
           goto LBL_ERR;
        }
        if ((res = esp_mp_sub (&D, &x, &D)) != MP_OKAY) {
           goto LBL_ERR;
        }
      }
      /* C = C/2, D = D/2 */
      if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
        goto LBL_ERR;
      }
      if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
  
    /* 6.  if u >= v then */
    if (esp_mp_cmp (&u, &v) != MP_LT) {
      /* u = u - v, A = A - C, B = B - D */
      if ((res = esp_mp_sub (&u, &v, &u)) != MP_OKAY) {
        goto LBL_ERR;
      }
  
      if ((res = esp_mp_sub (&A, &C, &A)) != MP_OKAY) {
        goto LBL_ERR;
      }
  
      if ((res = esp_mp_sub (&B, &D, &B)) != MP_OKAY) {
        goto LBL_ERR;
      }
    } else {
      /* v - v - u, C = C - A, D = D - B */
      if ((res = esp_mp_sub (&v, &u, &v)) != MP_OKAY) {
        goto LBL_ERR;
      }
  
      if ((res = esp_mp_sub (&C, &A, &C)) != MP_OKAY) {
        goto LBL_ERR;
      }
  
      if ((res = esp_mp_sub (&D, &B, &D)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
  
    /* if not zero goto step 4 */
    if (mp_iszero (&u) == 0)
      goto top;
  
    /* now a = C, b = D, gcd == g*v */
  
    /* if v != 1 then there is no inverse */
    if (esp_mp_cmp_d (&v, 1) != MP_EQ) {
      res = MP_VAL;
      goto LBL_ERR;
    }
  
    /* if its too low */
    while (esp_mp_cmp_d(&C, 0) == MP_LT) {
        if ((res = esp_mp_add(&C, b, &C)) != MP_OKAY) {
           goto LBL_ERR;
        }
    }
    
    /* too big */
    while (esp_mp_cmp_mag(&C, b) != MP_LT) {
        if ((res = esp_mp_sub(&C, b, &C)) != MP_OKAY) {
           goto LBL_ERR;
        }
    }
    
    /* C is now the inverse */
    esp_mp_exch (&C, c);
    res = MP_OKAY;
  LBL_ERR:esp_mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
    return res;
  }
  #endif /* LTM_NO_NEG_EXP */
  
  
  /* compare maginitude of two ints (unsigned) */
  static int 
  esp_mp_cmp_mag (mp_int * a, mp_int * b)
  {
    int     n;
    mp_digit *tmpa, *tmpb;
  
    /* compare based on # of non-zero digits */
    if (a->used > b->used) {
      return MP_GT;
    }
    
    if (a->used < b->used) {
      return MP_LT;
    }
  
    /* alias for a */
    tmpa = a->dp + (a->used - 1);
  
    /* alias for b */
    tmpb = b->dp + (a->used - 1);
  
    /* compare based on digits  */
    for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
      if (*tmpa > *tmpb) {
        return MP_GT;
      }
  
      if (*tmpa < *tmpb) {
        return MP_LT;
      }
    }
    return MP_EQ;
  }
  
  
  /* reads a unsigned char array, assumes the msb is stored first [big endian] */
  static int 
  esp_mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
  {
    int     res;
  
    /* make sure there are at least two digits */
    if (a->alloc < 2) {
       if ((res = esp_mp_grow(a, 2)) != MP_OKAY) {
          return res;
       }
    }
  
    /* zero the int */
    esp_mp_zero (a);
  
    /* read the bytes in */
    while (c-- > 0) {
      if ((res = esp_mp_mul_2d (a, 8, a)) != MP_OKAY) {
        return res;
      }
  
  #ifndef MP_8BIT
        a->dp[0] |= *b++;
        a->used += 1;
  #else
        a->dp[0] = (*b & MP_MASK);
        a->dp[1] |= ((*b++ >> 7U) & 1);
        a->used += 2;
  #endif
    }
    esp_mp_clamp (a);
    return MP_OKAY;
  }
  
  
  /* store in unsigned [big endian] format */
  static int 
  esp_mp_to_unsigned_bin (mp_int * a, unsigned char *b)
  {
    int     x, res;
    mp_int  t;
  
    if ((res = esp_mp_init_copy (&t, a)) != MP_OKAY) {
      return res;
    }
  
    x = 0;
    while (mp_iszero (&t) == 0) {
  #ifndef MP_8BIT
        b[x++] = (unsigned char) (t.dp[0] & 255);
  #else
        b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
  #endif
      if ((res = esp_mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
        esp_mp_clear (&t);
        return res;
      }
    }
    esp_bn_reverse (b, x);
    esp_mp_clear (&t);
    return MP_OKAY;
  }
  
  
  /* shift right by a certain bit count (store quotient in c, optional remainder in d) */
  static int 
  esp_mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
  {
    mp_digit D, r, rr;
    int     x, res;
    mp_int  t;
  
  
    /* if the shift count is <= 0 then we do no work */
    if (b <= 0) {
      res = esp_mp_copy (a, c);
      if (d != NULL) {
        esp_mp_zero (d);
      }
      return res;
    }
  
    if ((res = esp_mp_init (&t)) != MP_OKAY) {
      return res;
    }
  
    /* get the remainder */
    if (d != NULL) {
      if ((res = esp_mp_mod_2d (a, b, &t)) != MP_OKAY) {
        esp_mp_clear (&t);
        return res;
      }
    }
  
    /* copy */
    if ((res = esp_mp_copy (a, c)) != MP_OKAY) {
      esp_mp_clear (&t);
      return res;
    }
  
    /* shift by as many digits in the bit count */
    if (b >= (int)DIGIT_BIT) {
      esp_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;
      }
    }
    esp_mp_clamp (c);
    if (d != NULL) {
      esp_mp_exch (&t, d);
    }
    esp_mp_clear (&t);
    return MP_OKAY;
  }
  
  
  static int 
  esp_mp_init_copy (mp_int * a, mp_int * b)
  {
    int     res;
  
    if ((res = esp_mp_init (a)) != MP_OKAY) {
      return res;
    }
    return esp_mp_copy (b, a);
  }
  
  
  /* set to zero */
  static void 
  esp_mp_zero (mp_int * a)
  {
    int       n;
    mp_digit *tmp;
  
    a->sign = MP_ZPOS;
    a->used = 0;
  
    tmp = a->dp;
    for (n = 0; n < a->alloc; n++) {
       *tmp++ = 0;
    }
  }
  
  
  /* copy, b = a */
  static int 
  esp_mp_copy (mp_int * a, mp_int * b)
  {
    int     res, n;
  
    /* if dst == src do nothing */
    if (a == b) {
      return MP_OKAY;
    }
  
    /* grow dest */
    if (b->alloc < a->used) {
       if ((res = esp_mp_grow (b, a->used)) != MP_OKAY) {
          return res;
       }
    }
  
    /* zero b and copy the parameters over */
    {
      register mp_digit *tmpa, *tmpb;
  
      /* pointer aliases */
  
      /* source */
      tmpa = a->dp;
  
      /* destination */
      tmpb = b->dp;
  
      /* copy all the digits */
      for (n = 0; n < a->used; n++) {
        *tmpb++ = *tmpa++;
      }
  
      /* clear high digits */
      for (; n < b->used; n++) {
        *tmpb++ = 0;
      }
    }
  
    /* copy used count and sign */
    b->used = a->used;
    b->sign = a->sign;
    return MP_OKAY;
  }
  
  
  /* shift right a certain amount of digits */
  static void 
  esp_mp_rshd (mp_int * a, int b)
  {
    int     x;
  
    /* if b <= 0 then ignore it */
    if (b <= 0) {
      return;
    }
  
    /* if b > used then simply zero it and return */
    if (a->used <= b) {
      esp_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;
  }
  
  
  /* esp_swap the elements of two integers, for cases where you can't simply esp_swap the 
   * mp_int pointers around
   */
  static void 
  esp_mp_exch (mp_int * a, mp_int * b)
  {
    mp_int  t;
  
    t  = *a;
    *a = *b;
    *b = t;
  }
  
  
  /* trim unused digits 
   *
   * This is used to esp_ensure that leading zero digits are
   * trimed and the leading "used" digit will be non-zero
   * Typically very fast.  Also fixes the sign if there
   * are no more leading digits
   */
  static void 
  esp_mp_clamp (mp_int * a)
  {
    /* decrease used while the most significant digit is
     * zero.
     */
    while (a->used > 0 && a->dp[a->used - 1] == 0) {
      --(a->used);
    }
  
    /* reset the sign flag if used == 0 */
    if (a->used == 0) {
      a->sign = MP_ZPOS;
    }
  }
  
  
  /* grow as required */
  static int 
  esp_mp_grow (mp_int * a, int size)
  {
    int     i;
    mp_digit *tmp;
  
    /* if the alloc size is smaller alloc more ram */
    if (a->alloc < size) {
      /* esp_ensure there are always at least MP_PREC digits extra on top */
      size += (MP_PREC * 2) - (size % MP_PREC);
  
      /* reallocate the array a->dp
       *
       * We store the return in a temporary variable
       * in case the operation failed we don't want
       * to overwrite the dp member of a.
       */
      tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
      if (tmp == NULL) {
        /* reallocation failed but "a" is still valid [can be freed] */
        return MP_MEM;
      }
  
      /* reallocation succeeded so set a->dp */
      a->dp = tmp;
  
      /* zero excess digits */
      i        = a->alloc;
      a->alloc = size;
      for (; i < a->alloc; i++) {
        a->dp[i] = 0;
      }
    }
    return MP_OKAY;
  }
  
  
  #ifdef BN_MP_ABS_C
  /* b = |a| 
   *
   * Simple function copies the input and fixes the sign to positive
   */
  static int 
  esp_mp_abs (mp_int * a, mp_int * b)
  {
    int     res;
  
    /* copy a to b */
    if (a != b) {
       if ((res = esp_mp_copy (a, b)) != MP_OKAY) {
         return res;
       }
    }
  
    /* force the sign of b to positive */
    b->sign = MP_ZPOS;
  
    return MP_OKAY;
  }
  #endif
  
  
  /* set to a digit */
  static void 
  esp_mp_set (mp_int * a, mp_digit b)
  {
    esp_mp_zero (a);
    a->dp[0] = b & MP_MASK;
    a->used  = (a->dp[0] != 0) ? 1 : 0;
  }
  
  
  #ifndef LTM_NO_NEG_EXP
  /* b = a/2 */
  static int 
  mp_div_2(mp_int * a, mp_int * b)
  {
    int     x, res, oldused;
  
    /* copy */
    if (b->alloc < a->used) {
      if ((res = esp_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;
    esp_mp_clamp (b);
    return MP_OKAY;
  }
  #endif /* LTM_NO_NEG_EXP */
  
  
  /* shift left by a certain bit count */
  static int 
  esp_mp_mul_2d (mp_int * a, int b, mp_int * c)
  {
    mp_digit d;
    int      res;
  
    /* copy */
    if (a != c) {
       if ((res = esp_mp_copy (a, c)) != MP_OKAY) {
         return res;
       }
    }
  
    if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
       if ((res = esp_mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
         return res;
       }
    }
  
    /* shift by as many digits in the bit count */
    if (b >= (int)DIGIT_BIT) {
      if ((res = esp_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;
      }
    }
    esp_mp_clamp (c);
    return MP_OKAY;
  }
  
  
  #ifdef BN_MP_INIT_MULTI_C
  static int 
  esp_mp_init_multi(mp_int *mp, ...) 
  {
      mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */
      int n = 0;                 /* Number of ok inits */
      mp_int* cur_arg = mp;
      va_list args;
  
      va_start(args, mp);        /* esp_init args to next argument from caller */
      while (cur_arg != NULL) {
          if (esp_mp_init(cur_arg) != MP_OKAY) {
              /* Oops - esp_error! Back-track and esp_mp_clear what we already
                 succeeded in esp_init-ing, then return esp_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--) {
                  esp_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 esp_error flagged above. */
  }
  #endif
  
  
  #ifdef BN_MP_CLEAR_MULTI_C
  static void 
  esp_mp_clear_multi(mp_int *mp, ...) 
  {
      mp_int* next_mp = mp;
      va_list args;
      va_start(args, mp);
      while (next_mp != NULL) {
          esp_mp_clear(next_mp);
          next_mp = va_arg(args, mp_int*);
      }
      va_end(args);
  }
  #endif
  
  
  /* shift left a certain amount of digits */
  static int 
  esp_mp_lshd (mp_int * a, int b)
  {
    int     x, res;
  
    /* if its less than zero return */
    if (b <= 0) {
      return MP_OKAY;
    }
  
    /* grow to fit the new digits */
    if (a->alloc < a->used + b) {
       if ((res = esp_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 esp_mp_rshd this is implemented using a sliding window
       * except the window goes the otherway around.  Copying from
       * the bottom to the top.  see bn_mp_rshd.c for more info.
       */
      for (x = a->used - 1; x >= b; x--) {
        *top-- = *bottom--;
      }
  
      /* zero the lower digits */
      top = a->dp;
      for (x = 0; x < b; x++) {
        *top++ = 0;
      }
    }
    return MP_OKAY;
  }
  
  
  /* returns the number of bits in an int */
  static int 
  esp_mp_count_bits (mp_int * a)
  {
    int     r;
    mp_digit q;
  
    /* shortcut */
    if (a->used == 0) {
      return 0;
    }
  
    /* get number of digits and add that */
    r = (a->used - 1) * DIGIT_BIT;
    
    /* take the last digit and count the bits in it */
    q = a->dp[a->used - 1];
    while (q > ((mp_digit) 0)) {
      ++r;
      q >>= ((mp_digit) 1);
    }
    return r;
  }
  
  
  /* calc a value mod 2**b */
  static int 
  esp_mp_mod_2d (mp_int * a, int b, mp_int * c)
  {
    int     x, res;
  
    /* if b is <= 0 then zero the int */
    if (b <= 0) {
      esp_mp_zero (c);
      return MP_OKAY;
    }
  
    /* if the modulus is larger than the value than return */
    if (b >= (int) (a->used * DIGIT_BIT)) {
      res = esp_mp_copy (a, c);
      return res;
    }
  
    /* copy */
    if ((res = esp_mp_copy (a, c)) != MP_OKAY) {
      return res;
    }
  
    /* zero digits above the last digit of the modulus */
    for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
      c->dp[x] = 0;
    }
    /* clear the digit that is not completely outside/inside the modulus */
    c->dp[b / DIGIT_BIT] &=
      (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
    esp_mp_clamp (c);
    return MP_OKAY;
  }
  
  
  #ifdef BN_MP_DIV_SMALL
  
  /* slower bit-bang division... also smaller */
  static int 
  esp_mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
  {
     mp_int ta, tb, tq, q;
     int    res, n, n2;
  
    /* is divisor zero ? */
    if (mp_iszero (b) == 1) {
      return MP_VAL;
    }
  
    /* if a < b then q=0, r = a */
    if (esp_mp_cmp_mag (a, b) == MP_LT) {
      if (d != NULL) {
        res = esp_mp_copy (a, d);
      } else {
        res = MP_OKAY;
      }
      if (c != NULL) {
        esp_mp_zero (c);
      }
      return res;
    }
  	
    /* esp_init our temps */
    if ((res = esp_mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
       return res;
    }
  
  
    esp_mp_set(&tq, 1);
    n = esp_mp_count_bits(a) - esp_mp_count_bits(b);
    if (((res = esp_mp_abs(a, &ta)) != MP_OKAY) ||
        ((res = esp_mp_abs(b, &tb)) != MP_OKAY) || 
        ((res = esp_mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
        ((res = esp_mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
        goto LBL_ERR;
    }
  
    while (n-- >= 0) {
       if (esp_mp_cmp(&tb, &ta) != MP_GT) {
          if (((res = esp_mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
              ((res = esp_mp_add(&q, &tq, &q)) != MP_OKAY)) {
             goto LBL_ERR;
          }
       }
       if (((res = esp_mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
           ((res = esp_mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
             goto LBL_ERR;
       }
    }
  
    /* now q == quotient and ta == remainder */
    n  = a->sign;
    n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
    if (c != NULL) {
       esp_mp_exch(c, &q);
       c->sign  = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
    }
    if (d != NULL) {
       esp_mp_exch(d, &ta);
       d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
    }
  LBL_ERR:
     esp_mp_clear_multi(&ta, &tb, &tq, &q, NULL);
     return res;
  }
  
  #else
  
  /* integer signed division. 
   * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
   * HAC pp.598 Algorithm 14.20
   *
   * Note that the description in HAC is horribly 
   * incomplete.  For example, it doesn't consider 
   * the case where digits are removed from 'x' in 
   * the inner loop.  It also doesn't consider the 
   * case that y has fewer than three digits, etc..
   *
   * The overall algorithm is as described as 
   * 14.20 from HAC but fixed to treat these cases.
  */
  static int 
  esp_mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
  {
    mp_int  q, x, y, t1, t2;
    int     res, n, t, i, norm, neg;
  
    /* is divisor zero ? */
    if (mp_iszero (b) == 1) {
      return MP_VAL;
    }
  
    /* if a < b then q=0, r = a */
    if (esp_mp_cmp_mag (a, b) == MP_LT) {
      if (d != NULL) {
        res = esp_mp_copy (a, d);
      } else {
        res = MP_OKAY;
      }
      if (c != NULL) {
        esp_mp_zero (c);
      }
      return res;
    }
  
    if ((res = esp_mp_init_size (&q, a->used + 2)) != MP_OKAY) {
      return res;
    }
    q.used = a->used + 2;
  
    if ((res = esp_mp_init (&t1)) != MP_OKAY) {
      goto LBL_Q;
    }
  
    if ((res = esp_mp_init (&t2)) != MP_OKAY) {
      goto LBL_T1;
    }
  
    if ((res = esp_mp_init_copy (&x, a)) != MP_OKAY) {
      goto LBL_T2;
    }
  
    if ((res = esp_mp_init_copy (&y, b)) != MP_OKAY) {
      goto LBL_X;
    }
  
    /* fix the sign */
    neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
    x.sign = y.sign = MP_ZPOS;
  
    /* normalize both x and y, esp_ensure that y >= b/2, [b == 2**DIGIT_BIT] */
    norm = esp_mp_count_bits(&y) % DIGIT_BIT;
    if (norm < (int)(DIGIT_BIT-1)) {
       norm = (DIGIT_BIT-1) - norm;
       if ((res = esp_mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
         goto LBL_Y;
       }
       if ((res = esp_mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
         goto LBL_Y;
       }
    } else {
       norm = 0;
    }
  
    /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
    n = x.used - 1;
    t = y.used - 1;
  
    /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
    if ((res = esp_mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
      goto LBL_Y;
    }
  
    while (esp_mp_cmp (&x, &y) != MP_LT) {
      ++(q.dp[n - t]);
      if ((res = esp_mp_sub (&x, &y, &x)) != MP_OKAY) {
        goto LBL_Y;
      }
    }
  
    /* reset y by shifting it back down */
    esp_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 */
        esp_mp_zero (&t1);
        t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
        t1.dp[1] = y.dp[t];
        t1.used = 2;
        if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
          goto LBL_Y;
        }
  
        /* find right hand */
        t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
        t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
        t2.dp[2] = x.dp[i];
        t2.used = 3;
      } while (esp_mp_cmp_mag(&t1, &t2) == MP_GT);
  
      /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
      if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
        goto LBL_Y;
      }
  
      if ((res = esp_mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
        goto LBL_Y;
      }
  
      if ((res = esp_mp_sub (&x, &t1, &x)) != MP_OKAY) {
        goto LBL_Y;
      }
  
      /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
      if (x.sign == MP_NEG) {
        if ((res = esp_mp_copy (&y, &t1)) != MP_OKAY) {
          goto LBL_Y;
        }
        if ((res = esp_mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
          goto LBL_Y;
        }
        if ((res = esp_mp_add (&x, &t1, &x)) != MP_OKAY) {
          goto LBL_Y;
        }
  
        q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
      }
    }
  
    /* now q is the quotient and x is the remainder 
     * [which we have to normalize] 
     */
    
    /* get sign before writing to c */
    x.sign = x.used == 0 ? MP_ZPOS : a->sign;
  
    if (c != NULL) {
      esp_mp_clamp (&q);
      esp_mp_exch (&q, c);
      c->sign = neg;
    }
  
    if (d != NULL) {
      esp_mp_div_2d (&x, norm, &x, NULL);
      esp_mp_exch (&x, d);
    }
  
    res = MP_OKAY;
  
  LBL_Y:esp_mp_clear (&y);
  LBL_X:esp_mp_clear (&x);
  LBL_T2:esp_mp_clear (&t2);
  LBL_T1:esp_mp_clear (&t1);
  LBL_Q:esp_mp_clear (&q);
    return res;
  }
  
  #endif
  
  
  #ifdef MP_LOW_MEM
     #define TAB_SIZE 32
  #else
     #define TAB_SIZE 256
  #endif
  
  static int 
  esp_s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
  {
    mp_int  M[TAB_SIZE], res, mu;
    mp_digit buf;
    int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
    int (*redux)(mp_int*,mp_int*,mp_int*);
  
    /* find window size */
    x = esp_mp_count_bits (X);
    if (x <= 7) {
      winsize = 2;
    } else if (x <= 36) {
      winsize = 3;
    } else if (x <= 140) {
      winsize = 4;
    } else if (x <= 450) {
      winsize = 5;
    } else if (x <= 1303) {
      winsize = 6;
    } else if (x <= 3529) {
      winsize = 7;
    } else {
      winsize = 8;
    }
  
  #ifdef MP_LOW_MEM
      if (winsize > 5) {
         winsize = 5;
      }
  #endif
  
    /* esp_init M array */
    /* esp_init first cell */
    if ((err = esp_mp_init(&M[1])) != MP_OKAY) {
       return err; 
    }
  
    /* now esp_init the second half of the array */
    for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
      if ((err = esp_mp_init(&M[x])) != MP_OKAY) {
        for (y = 1<<(winsize-1); y < x; y++) {
          esp_mp_clear (&M[y]);
        }
        esp_mp_clear(&M[1]);
        return err;
      }
    }
  
    /* create mu, used for Barrett reduction */
    if ((err = esp_mp_init (&mu)) != MP_OKAY) {
      goto LBL_M;
    }
    
    if (redmode == 0) {
       if ((err = esp_mp_reduce_setup (&mu, P)) != MP_OKAY) {
          goto LBL_MU;
       }
       redux = esp_mp_reduce;
    } else {
       if ((err = esp_mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
          goto LBL_MU;
       }
       redux = esp_mp_reduce_2k_l;
    }    
  
    /* create M table
     *
     * The M table contains powers of the base, 
     * e.g. M[x] = G**x mod P
     *
     * The first half of the table is not 
     * computed though accept for M[0] and M[1]
     */
    if ((err = esp_mp_mod (G, P, &M[1])) != MP_OKAY) {
      goto LBL_MU;
    }
  
    /* compute the value at M[1<<(winsize-1)] by squaring 
     * M[1] (winsize-1) times 
     */
    if ((err = esp_mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
      goto LBL_MU;
    }
  
    for (x = 0; x < (winsize - 1); x++) {
      /* square it */
      if ((err = esp_mp_sqr (&M[1 << (winsize - 1)], 
                         &M[1 << (winsize - 1)])) != MP_OKAY) {
        goto LBL_MU;
      }
  
      /* reduce modulo P */
      if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
        goto LBL_MU;
      }
    }
  
    /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
     * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
     */
    for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
      if ((err = esp_mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
        goto LBL_MU;
      }
      if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
        goto LBL_MU;
      }
    }
  
    /* setup result */
    if ((err = esp_mp_init (&res)) != MP_OKAY) {
      goto LBL_MU;
    }
    esp_mp_set (&res, 1);
  
    /* set initial mode and bit cnt */
    mode   = 0;
    bitcnt = 1;
    buf    = 0;
    digidx = X->used - 1;
    bitcpy = 0;
    bitbuf = 0;
  
    for (;;) {
      /* grab next digit as required */
      if (--bitcnt == 0) {
        /* if digidx == -1 we are out of digits */
        if (digidx == -1) {
          break;
        }
        /* read next digit and reset the bitcnt */
        buf    = X->dp[digidx--];
        bitcnt = (int) DIGIT_BIT;
      }
  
      /* grab the next msb from the exponent */
      y     = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
      buf <<= (mp_digit)1;
  
      /* if the bit is zero and mode == 0 then we ignore it
       * These represent the leading zero bits before the first 1 bit
       * in the exponent.  Technically this opt is not required but it
       * does lower the # of trivial squaring/reductions used
       */
      if (mode == 0 && y == 0) {
        continue;
      }
  
      /* if the bit is zero and mode == 1 then we square */
      if (mode == 1 && y == 0) {
        if ((err = esp_mp_sqr (&res, &res)) != MP_OKAY) {
          goto LBL_RES;
        }
        if ((err = redux (&res, P, &mu)) != MP_OKAY) {
          goto LBL_RES;
        }
        continue;
      }
  
      /* else we add it to the window */
      bitbuf |= (y << (winsize - ++bitcpy));
      mode    = 2;
  
      if (bitcpy == winsize) {
        /* ok window is filled so square as required and multiply  */
        /* square first */
        for (x = 0; x < winsize; x++) {
          if ((err = esp_mp_sqr (&res, &res)) != MP_OKAY) {
            goto LBL_RES;
          }
          if ((err = redux (&res, P, &mu)) != MP_OKAY) {
            goto LBL_RES;
          }
        }
  
        /* then multiply */
        if ((err = esp_mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
          goto LBL_RES;
        }
        if ((err = redux (&res, P, &mu)) != MP_OKAY) {
          goto LBL_RES;
        }
  
        /* empty window and reset */
        bitcpy = 0;
        bitbuf = 0;
        mode   = 1;
      }
    }
  
    /* if bits remain then square/multiply */
    if (mode == 2 && bitcpy > 0) {
      /* square then multiply if the bit is set */
      for (x = 0; x < bitcpy; x++) {
        if ((err = esp_mp_sqr (&res, &res)) != MP_OKAY) {
          goto LBL_RES;
        }
        if ((err = redux (&res, P, &mu)) != MP_OKAY) {
          goto LBL_RES;
        }
  
        bitbuf <<= 1;
        if ((bitbuf & (1 << winsize)) != 0) {
          /* then multiply */
          if ((err = esp_mp_mul (&res, &M[1], &res)) != MP_OKAY) {
            goto LBL_RES;
          }
          if ((err = redux (&res, P, &mu)) != MP_OKAY) {
            goto LBL_RES;
          }
        }
      }
    }
  
    esp_mp_exch (&res, Y);
    err = MP_OKAY;
  LBL_RES:esp_mp_clear (&res);
  LBL_MU:esp_mp_clear (&mu);
  LBL_M:
    esp_mp_clear(&M[1]);
    for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
      esp_mp_clear (&M[x]);
    }
    return err;
  }
  
  
  /* computes b = a*a */
  static int 
  esp_mp_sqr (mp_int * a, mp_int * b)
  {
    int     res;
  
  #ifdef BN_MP_TOOM_SQR_C
    /* use Toom-Cook? */
    if (a->used >= TOOM_SQR_CUTOFF) {
      res = mp_toom_sqr(a, b);
    /* Karatsuba? */
    } else 
  #endif
  #ifdef BN_MP_KARATSUBA_SQR_C
  if (a->used >= KARATSUBA_SQR_CUTOFF) {
      res = mp_karatsuba_sqr (a, b);
    } else 
  #endif
    {
  #ifdef BN_FAST_S_MP_SQR_C
      /* can we use the fast comba multiplier? */
      if ((a->used * 2 + 1) < MP_WARRAY && 
           a->used < 
           (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
        res = fast_s_mp_sqr (a, b);
      } else
  #endif
  #ifdef BN_S_MP_SQR_C
        res = esp_s_mp_sqr (a, b);
  #else
  #esp_error mp_sqr could fail
        res = MP_VAL;
  #endif
    }
    b->sign = MP_ZPOS;
    return res;
  }
  
  
  /* reduces a modulo n where n is of the form 2**p - d 
     This differs from reduce_2k since "d" can be larger
     than a single digit.
  */
  static int 
  esp_mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
  {
     mp_int q;
     int    p, res;
     
     if ((res = esp_mp_init(&q)) != MP_OKAY) {
        return res;
     }
     
     p = esp_mp_count_bits(n);    
  top:
     /* q = a/2**p, a = a mod 2**p */
     if ((res = esp_mp_div_2d(a, p, &q, a)) != MP_OKAY) {
        goto ERR;
     }
     
     /* q = q * d */
     if ((res = esp_mp_mul(&q, d, &q)) != MP_OKAY) { 
        goto ERR;
     }
     
     /* a = a + q */
     if ((res = esp_s_mp_add(a, &q, a)) != MP_OKAY) {
        goto ERR;
     }
     
     if (esp_mp_cmp_mag(a, n) != MP_LT) {
        esp_s_mp_sub(a, n, a);
        goto top;
     }
     
  ERR:
     esp_mp_clear(&q);
     return res;
  }
  
  
  /* determines the setup value */
  static int 
  esp_mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
  {
     int    res;
     mp_int tmp;
     
     if ((res = esp_mp_init(&tmp)) != MP_OKAY) {
        return res;
     }
     
     if ((res = esp_mp_2expt(&tmp, esp_mp_count_bits(a))) != MP_OKAY) {
        goto ERR;
     }
     
     if ((res = esp_s_mp_sub(&tmp, a, d)) != MP_OKAY) {
        goto ERR;
     }
     
  ERR:
     esp_mp_clear(&tmp);
     return res;
  }
  
  
  /* computes a = 2**b 
   *
   * Simple algorithm which zeroes the int, grows it then just sets one bit
   * as required.
   */
  static int 
  esp_mp_2expt (mp_int * a, int b)
  {
    int     res;
  
    /* zero a as per default */
    esp_mp_zero (a);
  
    /* grow a to accommodate the single bit */
    if ((res = esp_mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
      return res;
    }
  
    /* set the used count of where the bit will go */
    a->used = b / DIGIT_BIT + 1;
  
    /* put the single bit in its place */
    a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
  
    return MP_OKAY;
  }
  
  
  /* pre-calculate the value required for Barrett reduction
   * For a given modulus "b" it calulates the value required in "a"
   */
  static int 
  esp_mp_reduce_setup (mp_int * a, mp_int * b)
  {
    int     res;
    
    if ((res = esp_mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
      return res;
    }
    return esp_mp_div (a, b, a, NULL);
  }
  
  
  /* reduces x mod m, assumes 0 < x < m**2, mu is 
   * precomputed via esp_mp_reduce_setup.
   * From HAC pp.604 Algorithm 14.42
   */
  static int 
  esp_mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
  {
    mp_int  q;
    int     res, um = m->used;
  
    /* q = x */
    if ((res = esp_mp_init_copy (&q, x)) != MP_OKAY) {
      return res;
    }
  
    /* q1 = x / b**(k-1)  */
    esp_mp_rshd (&q, um - 1);         
  
    /* according to HAC this optimization is ok */
    if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
      if ((res = esp_mp_mul (&q, mu, &q)) != MP_OKAY) {
        goto CLEANUP;
      }
    } else {
  #ifdef BN_S_MP_MUL_HIGH_DIGS_C
      if ((res = esp_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
        goto CLEANUP;
      }
  #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
      if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
        goto CLEANUP;
      }
  #else 
      { 
  #esp_error mp_reduce would always fail
        res = MP_VAL;
        goto CLEANUP;
      }
  #endif
    }
  
    /* q3 = q2 / b**(k+1) */
    esp_mp_rshd (&q, um + 1);         
  
    /* x = x mod b**(k+1), quick (no division) */
    if ((res = esp_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 = esp_s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
      goto CLEANUP;
    }
  
    /* x = x - q */
    if ((res = esp_mp_sub (x, &q, x)) != MP_OKAY) {
      goto CLEANUP;
    }
  
    /* If x < 0, add b**(k+1) to it */
    if (esp_mp_cmp_d (x, 0) == MP_LT) {
      esp_mp_set (&q, 1);
      if ((res = esp_mp_lshd (&q, um + 1)) != MP_OKAY) {
        goto CLEANUP;
      }
      if ((res = esp_mp_add (x, &q, x)) != MP_OKAY) {
        goto CLEANUP;
      }
    }
  
    /* Back off if it's too big */
    while (esp_mp_cmp (x, m) != MP_LT) {
      if ((res = esp_s_mp_sub (x, m, x)) != MP_OKAY) {
        goto CLEANUP;
      }
    }
    
  CLEANUP:
    esp_mp_clear (&q);
  
    return res;
  }
  
  
  /* multiplies |a| * |b| and only computes up to digs digits of result
   * HAC pp. 595, Algorithm 14.12  Modified so you can control how 
   * many digits of output are created.
   */
  static int 
  esp_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
  {
    mp_int  t;
    int     res, pa, pb, ix, iy;
    mp_digit u;
    mp_word r;
    mp_digit tmpx, *tmpt, *tmpy;
  
    /* can we use the fast multiplier? */
    if (((digs) < MP_WARRAY) &&
        MIN (a->used, b->used) < 
            (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
      return esp_fast_s_mp_mul_digs (a, b, c, digs);
    }
  
    if ((res = esp_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;
      }
    }
  
    esp_mp_clamp (&t);
    esp_mp_exch (&t, c);
  
    esp_mp_clear (&t);
    return MP_OKAY;
  }
  
  
  /* Fast (comba) multiplier
   *
   * This is the fast column-array [comba] multiplier.  It is 
   * designed to compute the columns of the product first 
   * then handle the carries afterwards.  This has the effect 
   * of making the nested loops that compute the columns very
   * simple and schedulable on super-scalar processors.
   *
   * This has been modified to produce a variable number of 
   * digits of output so if say only a half-product is required 
   * you don't have to compute the upper half (a feature 
   * required for fast Barrett reduction).
   *
   * Based on Algorithm 14.12 on pp.595 of HAC.
   *
   */
  static int 
  esp_fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
  {
    int     olduse, res, pa, ix, iz;
    mp_digit W[MP_WARRAY];
    register mp_word  _W;
  
    /* grow the destination as required */
    if (c->alloc < digs) {
      if ((res = esp_mp_grow (c, digs)) != MP_OKAY) {
        return res;
      }
    }
  
    /* number of output digits to produce */
    pa = MIN(digs, a->used + b->used);
  
    /* clear the carry */
    _W = 0;
    for (ix = 0; ix < pa; ix++) { 
        int      tx, ty;
        int      iy;
        mp_digit *tmpx, *tmpy;
  
        /* get offsets into the two bignums */
        ty = MIN(b->used-1, ix);
        tx = ix - ty;
  
        /* setup temp aliases */
        tmpx = a->dp + tx;
        tmpy = b->dp + ty;
  
        /* this is the number of times the loop will iterrate, essentially 
           while (tx++ < a->used && ty-- >= 0) { ... }
         */
        iy = MIN(a->used-tx, ty+1);
  
        /* execute loop */
        for (iz = 0; iz < iy; ++iz) {
           _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
  
        }
  
        /* store term */
        W[ix] = ((mp_digit)_W) & MP_MASK;
  
        /* make next carry */
        _W = _W >> ((mp_word)DIGIT_BIT);
   }
  
    /* setup dest */
    olduse  = c->used;
    c->used = pa;
  
    {
      register mp_digit *tmpc;
      tmpc = c->dp;
      for (ix = 0; ix < pa+1; ix++) {
        /* now extract the previous digit [below the carry] */
        *tmpc++ = W[ix];
      }
  
      /* clear unused digits [that existed in the old copy of c] */
      for (; ix < olduse; ix++) {
        *tmpc++ = 0;
      }
    }
    esp_mp_clamp (c);
    return MP_OKAY;
  }
  
  
  /* esp_init an esp_mp_init for a given size */
  static int 
  esp_mp_init_size (mp_int * a, int size)
  {
    int x;
  
    /* pad size so there are always extra digits */
    size += (MP_PREC * 2) - (size % MP_PREC);	
    
    /* alloc mem */
    a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
    if (a->dp == NULL) {
      return MP_MEM;
    }
  
    /* set the members */
    a->used  = 0;
    a->alloc = size;
    a->sign  = MP_ZPOS;
  
    /* zero the digits */
    for (x = 0; x < size; x++) {
        a->dp[x] = 0;
    }
  
    return MP_OKAY;
  }
  
  
  /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
  static int 
  esp_s_mp_sqr (mp_int * a, mp_int * b)
  {
    mp_int  t;
    int     res, ix, iy, pa;
    mp_word r;
    mp_digit u, tmpx, *tmpt;
  
    pa = a->used;
    if ((res = esp_mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
      return res;
    }
  
    /* default used is maximum possible size */
    t.used = 2*pa + 1;
  
    for (ix = 0; ix < pa; ix++) {
      /* first calculate the digit at 2*ix */
      /* calculate double precision result */
      r = ((mp_word) t.dp[2*ix]) +
          ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
  
      /* store lower part in result */
      t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
  
      /* get the carry */
      u           = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
  
      /* left hand side of A[ix] * A[iy] */
      tmpx        = a->dp[ix];
  
      /* alias for where to store the results */
      tmpt        = t.dp + (2*ix + 1);
      
      for (iy = ix + 1; iy < pa; iy++) {
        /* first calculate the product */
        r       = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
  
        /* now calculate the double precision result, note we use
         * addition instead of *2 since it's easier to optimize
         */
        r       = ((mp_word) *tmpt) + r + r + ((mp_word) u);
  
        /* store lower part */
        *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
  
        /* get carry */
        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
      }
      /* propagate upwards */
      while (u != ((mp_digit) 0)) {
        r       = ((mp_word) *tmpt) + ((mp_word) u);
        *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
      }
    }
  
    esp_mp_clamp (&t);
    esp_mp_exch (&t, b);
    esp_mp_clear (&t);
    return MP_OKAY;
  }
  
  
  /* multiplies |a| * |b| and does not compute the lower digs digits
   * [meant to get the higher part of the product]
   */
  static int 
  esp_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
  {
    mp_int  t;
    int     res, pa, pb, ix, iy;
    mp_digit u;
    mp_word r;
    mp_digit tmpx, *tmpt, *tmpy;
  
    /* can we use the fast multiplier? */
  #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
    if (((a->used + b->used + 1) < MP_WARRAY)
        && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
      return fast_s_mp_mul_high_digs (a, b, c, digs);
    }
  #endif
  
    if ((res = esp_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;
    }
    esp_mp_clamp (&t);
    esp_mp_exch (&t, c);
    esp_mp_clear (&t);
    return MP_OKAY;
  }
  
  
  #ifdef BN_MP_MONTGOMERY_SETUP_C
  /* setups the montgomery reduction stuff */
  static int 
  mp_montgomery_setup (mp_int * n, mp_digit * rho)
  {
    mp_digit x, b;
  
  /* fast inversion mod 2**k
   *
   * Based on the fact that
   *
   * XA = 1 (mod 2**n)  =>  (X(2-XA)) A = 1 (mod 2**2n)
   *                    =>  2*X*A - X*X*A*A = 1
   *                    =>  2*(1) - (1)     = 1
   */
    b = n->dp[0];
  
    if ((b & 1) == 0) {
      return MP_VAL;
    }
  
    x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
    x *= 2 - b * x;               /* here x*a==1 mod 2**8 */
  #if !defined(MP_8BIT)
    x *= 2 - b * x;               /* here x*a==1 mod 2**16 */
  #endif
  #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
    x *= 2 - b * x;               /* here x*a==1 mod 2**32 */
  #endif
  #ifdef MP_64BIT
    x *= 2 - b * x;               /* here x*a==1 mod 2**64 */
  #endif
  
    /* rho = -1/m mod b */
    *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
  
    return MP_OKAY;
  }
  #endif
  
  
  #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
  /* computes xR**-1 == x (mod N) via Montgomery Reduction
   *
   * This is an optimized implementation of montgomery_reduce
   * which uses the comba method to quickly calculate the columns of the
   * reduction.
   *
   * Based on Algorithm 14.32 on pp.601 of HAC.
  */
  int 
  fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
  {
    int     ix, res, olduse;
    mp_word W[MP_WARRAY];
  
    /* get old used count */
    olduse = x->used;
  
    /* grow a as required */
    if (x->alloc < n->used + 1) {
      if ((res = esp_mp_grow (x, n->used + 1)) != MP_OKAY) {
        return res;
      }
    }
  
    /* first we have to get the digits of the input into
     * an array of double precision words W[...]
     */
    {
      register mp_word *_W;
      register mp_digit *tmpx;
  
      /* alias for the W[] array */
      _W   = W;
  
      /* alias for the digits of  x*/
      tmpx = x->dp;
  
      /* copy the digits of a into W[0..a->used-1] */
      for (ix = 0; ix < x->used; ix++) {
        *_W++ = *tmpx++;
      }
  
      /* zero the high words of W[a->used..m->used*2] */
      for (; ix < n->used * 2 + 1; ix++) {
        *_W++ = 0;
      }
    }
  
    /* now we proceed to zero successive digits
     * from the least significant upwards
     */
    for (ix = 0; ix < n->used; ix++) {
      /* mu = ai * m' mod b
       *
       * We avoid a double precision multiplication (which isn't required)
       * by casting the value down to a mp_digit.  Note this requires
       * that W[ix-1] have  the carry cleared (see after the inner loop)
       */
      register mp_digit mu;
      mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
  
      /* a = a + mu * m * b**i
       *
       * This is computed in place and on the fly.  The multiplication
       * by b**i is handled by offseting which columns the results
       * are added to.
       *
       * Note the comba method normally doesn't handle carries in the
       * inner loop In this case we fix the carry from the previous
       * column since the Montgomery reduction requires digits of the
       * result (so far) [see above] to work.  This is
       * handled by fixing up one carry after the inner loop.  The
       * carry fixups are done in order so after these loops the
       * first m->used words of W[] have the carries fixed
       */
      {
        register int iy;
        register mp_digit *tmpn;
        register mp_word *_W;
  
        /* alias for the digits of the modulus */
        tmpn = n->dp;
  
        /* Alias for the columns set by an offset of ix */
        _W = W + ix;
  
        /* inner loop */
        for (iy = 0; iy < n->used; iy++) {
            *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
        }
      }
  
      /* now fix carry for next digit, W[ix+1] */
      W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
    }
  
    /* now we have to propagate the carries and
     * shift the words downward [all those least
     * significant digits we zeroed].
     */
    {
      register mp_digit *tmpx;
      register mp_word *_W, *_W1;
  
      /* nox fix rest of carries */
  
      /* alias for current word */
      _W1 = W + ix;
  
      /* alias for next word, where the carry goes */
      _W = W + ++ix;
  
      for (; ix <= n->used * 2 + 1; ix++) {
        *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
      }
  
      /* copy out, A = A/b**n
       *
       * The result is A/b**n but instead of converting from an
       * array of mp_word to mp_digit than calling esp_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;
    esp_mp_clamp (x);
  
    /* if A >= m then A = A - m */
    if (esp_mp_cmp_mag (x, n) != MP_LT) {
      return esp_s_mp_sub (x, n, x);
    }
    return MP_OKAY;
  }
  #endif
  
  
  #ifdef BN_MP_MUL_2_C
  /* b = a*2 */
  static int 
  mp_mul_2(mp_int * a, mp_int * b)
  {
    int     x, res, oldused;
  
    /* grow to accommodate result */
    if (b->alloc < a->used + 1) {
      if ((res = esp_mp_grow (b, a->used + 1)) != MP_OKAY) {
        return res;
      }
    }
  
    oldused = b->used;
    b->used = a->used;
  
    {
      register mp_digit r, rr, *tmpa, *tmpb;
  
      /* alias for source */
      tmpa = a->dp;
      
      /* alias for dest */
      tmpb = b->dp;
  
      /* carry */
      r = 0;
      for (x = 0; x < a->used; x++) {
      
        /* get what will be the *next* carry bit from the 
         * MSB of the current digit 
         */
        rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
        
        /* now shift up this digit, add in the carry [from the previous] */
        *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
        
        /* copy the carry that would be from the source 
         * digit into the next iteration 
         */
        r = rr;
      }
  
      /* new leading digit? */
      if (r != 0) {
        /* add a MSB which is always 1 at this point */
        *tmpb = 1;
        ++(b->used);
      }
  
      /* now zero any excess digits on the destination 
       * that we didn't write to 
       */
      tmpb = b->dp + b->used;
      for (x = b->used; x < oldused; x++) {
        *tmpb++ = 0;
      }
    }
    b->sign = a->sign;
    return MP_OKAY;
  }
  #endif
  
  
  #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
  /*
   * shifts with subtractions when the result is greater than b.
   *
   * The method is slightly modified to shift B unconditionally up to just under
   * the leading bit of b.  This saves a lot of multiple precision shifting.
   */
  static int 
  mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
  {
    int     x, bits, res;
  
    /* how many bits of last digit does b use */
    bits = esp_mp_count_bits (b) % DIGIT_BIT;
  
    if (b->used > 1) {
       if ((res = esp_mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
          return res;
       }
    } else {
       esp_mp_set(a, 1);
       bits = 1;
    }
  
  
    /* now compute C = A * B mod b */
    for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
      if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
        return res;
      }
      if (esp_mp_cmp_mag (a, b) != MP_LT) {
        if ((res = esp_s_mp_sub (a, b, a)) != MP_OKAY) {
          return res;
        }
      }
    }
  
    return MP_OKAY;
  }
  #endif
  
  
  #ifdef BN_MP_EXPTMOD_FAST_C
  /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
   *
   * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
   * The value of k changes based on the size of the exponent.
   *
   * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
   */
  
  static int 
  mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
  {
    mp_int  M[TAB_SIZE], res;
    mp_digit buf, mp;
    int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
  
    /* use a pointer to the reduction algorithm.  This allows us to use
     * one of many reduction algorithms without modding the guts of
     * the code with if statements everywhere.
     */
    int     (*redux)(mp_int*,mp_int*,mp_digit);
  
    /* find window size */
    x = esp_mp_count_bits (X);
    if (x <= 7) {
      winsize = 2;
    } else if (x <= 36) {
      winsize = 3;
    } else if (x <= 140) {
      winsize = 4;
    } else if (x <= 450) {
      winsize = 5;
    } else if (x <= 1303) {
      winsize = 6;
    } else if (x <= 3529) {
      winsize = 7;
    } else {
      winsize = 8;
    }
  
  #ifdef MP_LOW_MEM
    if (winsize > 5) {
       winsize = 5;
    }
  #endif
  
    /* esp_init M array */
    /* esp_init first cell */
    if ((err = esp_mp_init(&M[1])) != MP_OKAY) {
       return err;
    }
  
    /* now esp_init the second half of the array */
    for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
      if ((err = esp_mp_init(&M[x])) != MP_OKAY) {
        for (y = 1<<(winsize-1); y < x; y++) {
          esp_mp_clear (&M[y]);
        }
        esp_mp_clear(&M[1]);
        return err;
      }
    }
  
    /* determine and setup reduction code */
    if (redmode == 0) {
  #ifdef BN_MP_MONTGOMERY_SETUP_C     
       /* now setup montgomery  */
       if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
          goto LBL_M;
       }
  #else
       err = MP_VAL;
       goto LBL_M;
  #endif
  
       /* automatically pick the comba one if available (saves quite a few calls/ifs) */
  #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
       if (((P->used * 2 + 1) < MP_WARRAY) &&
            P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
          redux = fast_mp_montgomery_reduce;
       } else 
  #endif
       {
  #ifdef BN_MP_MONTGOMERY_REDUCE_C
          /* use slower baseline Montgomery method */
          redux = mp_montgomery_reduce;
  #else
          err = MP_VAL;
          goto LBL_M;
  #endif
       }
    } else if (redmode == 1) {
  #if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
       /* setup DR reduction for moduli of the form B**k - b */
       mp_dr_setup(P, &mp);
       redux = mp_dr_reduce;
  #else
       err = MP_VAL;
       goto LBL_M;
  #endif
    } else {
  #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
       /* setup DR reduction for moduli of the form 2**k - b */
       if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
          goto LBL_M;
       }
       redux = mp_reduce_2k;
  #else
       err = MP_VAL;
       goto LBL_M;
  #endif
    }
  
    /* setup result */
    if ((err = esp_mp_init (&res)) != MP_OKAY) {
      goto LBL_M;
    }
  
    /* create M table
     *
  
     *
     * The first half of the table is not computed though accept for M[0] and M[1]
     */
  
    if (redmode == 0) {
  #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
       /* now we need R mod m */
       if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
         goto LBL_RES;
       }
  #else 
       err = MP_VAL;
       goto LBL_RES;
  #endif
  
       /* now set M[1] to G * R mod m */
       if ((err = esp_mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
         goto LBL_RES;
       }
    } else {
       esp_mp_set(&res, 1);
       if ((err = esp_mp_mod(G, P, &M[1])) != MP_OKAY) {
          goto LBL_RES;
       }
    }
  
    /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
    if ((err = esp_mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
      goto LBL_RES;
    }
  
    for (x = 0; x < (winsize - 1); x++) {
      if ((err = esp_mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
        goto LBL_RES;
      }
    }
  
    /* create upper table */
    for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
      if ((err = esp_mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
        goto LBL_RES;
      }
    }
  
    /* set initial mode and bit cnt */
    mode   = 0;
    bitcnt = 1;
    buf    = 0;
    digidx = X->used - 1;
    bitcpy = 0;
    bitbuf = 0;
  
    for (;;) {
      /* grab next digit as required */
      if (--bitcnt == 0) {
        /* if digidx == -1 we are out of digits so break */
        if (digidx == -1) {
          break;
        }
        /* read next digit and reset bitcnt */
        buf    = X->dp[digidx--];
        bitcnt = (int)DIGIT_BIT;
      }
  
      /* grab the next msb from the exponent */
      y     = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
      buf <<= (mp_digit)1;
  
      /* if the bit is zero and mode == 0 then we ignore it
       * These represent the leading zero bits before the first 1 bit
       * in the exponent.  Technically this opt is not required but it
       * does lower the # of trivial squaring/reductions used
       */
      if (mode == 0 && y == 0) {
        continue;
      }
  
      /* if the bit is zero and mode == 1 then we square */
      if (mode == 1 && y == 0) {
        if ((err = esp_mp_sqr (&res, &res)) != MP_OKAY) {
          goto LBL_RES;
        }
        if ((err = redux (&res, P, mp)) != MP_OKAY) {
          goto LBL_RES;
        }
        continue;
      }
  
      /* else we add it to the window */
      bitbuf |= (y << (winsize - ++bitcpy));
      mode    = 2;
  
      if (bitcpy == winsize) {
        /* ok window is filled so square as required and multiply  */
        /* square first */
        for (x = 0; x < winsize; x++) {
          if ((err = esp_mp_sqr (&res, &res)) != MP_OKAY) {
            goto LBL_RES;
          }
          if ((err = redux (&res, P, mp)) != MP_OKAY) {
            goto LBL_RES;
          }
        }
  
        /* then multiply */
        if ((err = esp_mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
          goto LBL_RES;
        }
        if ((err = redux (&res, P, mp)) != MP_OKAY) {
          goto LBL_RES;
        }
  
        /* empty window and reset */
        bitcpy = 0;
        bitbuf = 0;
        mode   = 1;
      }
    }
  
    /* if bits remain then square/multiply */
    if (mode == 2 && bitcpy > 0) {
      /* square then multiply if the bit is set */
      for (x = 0; x < bitcpy; x++) {
        if ((err = esp_mp_sqr (&res, &res)) != MP_OKAY) {
          goto LBL_RES;
        }
        if ((err = redux (&res, P, mp)) != MP_OKAY) {
          goto LBL_RES;
        }
  
        /* get next bit of the window */
        bitbuf <<= 1;
        if ((bitbuf & (1 << winsize)) != 0) {
          /* then multiply */
          if ((err = esp_mp_mul (&res, &M[1], &res)) != MP_OKAY) {
            goto LBL_RES;
          }
          if ((err = redux (&res, P, mp)) != MP_OKAY) {
            goto LBL_RES;
          }
        }
      }
    }
  
    if (redmode == 0) {
       /* fixup result if Montgomery reduction is used
        * recall that any value in a Montgomery system is
        * actually multiplied by R mod n.  So we have
        * to reduce one more time to cancel out the factor
        * of R.
        */
       if ((err = redux(&res, P, mp)) != MP_OKAY) {
         goto LBL_RES;
       }
    }
  
    /* esp_swap res with Y */
    esp_mp_exch (&res, Y);
    err = MP_OKAY;
  LBL_RES:esp_mp_clear (&res);
  LBL_M:
    esp_mp_clear(&M[1]);
    for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
      esp_mp_clear (&M[x]);
    }
    return err;
  }
  #endif
  
  
  #ifdef BN_FAST_S_MP_SQR_C
  /* the jist of squaring...
   * you do like mult except the offset of the tmpx [one that 
   * starts closer to zero] can't equal the offset of tmpy.  
   * So basically you set up iy like before then you min it with
   * (ty-tx) so that it never happens.  You double all those 
   * you add in the inner loop
  
  After that loop you do the squares and add them in.
  */
  
  static int 
  fast_s_mp_sqr (mp_int * a, mp_int * b)
  {
    int       olduse, res, pa, ix, iz;
    mp_digit   W[MP_WARRAY], *tmpx;
    mp_word   W1;
  
    /* grow the destination as required */
    pa = a->used + a->used;
    if (b->alloc < pa) {
      if ((res = esp_mp_grow (b, pa)) != MP_OKAY) {
        return res;
      }
    }
  
    /* number of output digits to produce */
    W1 = 0;
    for (ix = 0; ix < pa; ix++) { 
        int      tx, ty, iy;
        mp_word  _W;
        mp_digit *tmpy;
  
        /* clear counter */
        _W = 0;
  
        /* get offsets into the two bignums */
        ty = MIN(a->used-1, ix);
        tx = ix - ty;
  
        /* setup temp aliases */
        tmpx = a->dp + tx;
        tmpy = a->dp + ty;
  
        /* this is the number of times the loop will iterrate, essentially
           while (tx++ < a->used && ty-- >= 0) { ... }
         */
        iy = MIN(a->used-tx, ty+1);
  
        /* now for squaring tx can never equal ty 
         * we halve the distance since they approach at a rate of 2x
         * and we have to round because odd cases need to be executed
         */
        iy = MIN(iy, (ty-tx+1)>>1);
  
        /* execute loop */
        for (iz = 0; iz < iy; iz++) {
           _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
        }
  
        /* double the inner product and add carry */
        _W = _W + _W + W1;
  
        /* even columns have the square term in them */
        if ((ix&1) == 0) {
           _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
        }
  
        /* store it */
        W[ix] = (mp_digit)(_W & MP_MASK);
  
        /* make next carry */
        W1 = _W >> ((mp_word)DIGIT_BIT);
    }
  
    /* setup dest */
    olduse  = b->used;
    b->used = a->used+a->used;
  
    {
      mp_digit *tmpb;
      tmpb = b->dp;
      for (ix = 0; ix < pa; ix++) {
        *tmpb++ = W[ix] & MP_MASK;
      }
  
      /* clear unused digits [that existed in the old copy of c] */
      for (; ix < olduse; ix++) {
        *tmpb++ = 0;
      }
    }
    esp_mp_clamp (b);
    return MP_OKAY;
  }
  #endif
  
  
  #ifdef BN_MP_MUL_D_C
  /* multiply by a digit */
  static int 
  mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
  {
    mp_digit u, *tmpa, *tmpc;
    mp_word  r;
    int      ix, res, olduse;
  
    /* make sure c is big enough to hold a*b */
    if (c->alloc < a->used + 1) {
      if ((res = esp_mp_grow (c, a->used + 1)) != MP_OKAY) {
        return res;
      }
    }
  
    /* get the original destinations used count */
    olduse = c->used;
  
    /* set the sign */
    c->sign = a->sign;
  
    /* alias for a->dp [source] */
    tmpa = a->dp;
  
    /* alias for c->dp [dest] */
    tmpc = c->dp;
  
    /* zero carry */
    u = 0;
  
    /* compute columns */
    for (ix = 0; ix < a->used; ix++) {
      /* compute product and carry sum for this term */
      r       = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
  
      /* mask off higher bits to get a single digit */
      *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
  
      /* send carry into next iteration */
      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
    }
  
    /* store final carry [if any] and increment ix offset  */
    *tmpc++ = u;
    ++ix;
  
    /* now zero digits above the top */
    while (ix++ < olduse) {
       *tmpc++ = 0;
    }
  
    /* set used count */
    c->used = a->used + 1;
    esp_mp_clamp(c);
  
    return MP_OKAY;
  }
  #endif
  