bn_mp_jacobi.c

/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is library that provides for multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library is designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
 */
#include <tommath.h>

/* computes the jacobi c = (a | n) (or Legendre if n is prime)
 * HAC pp. 73 Algorithm 2.149
 */
int
mp_jacobi (mp_int * a, mp_int * n, int *c)
{
  mp_int  a1, n1, e;
  int     s, r, res;
  mp_digit residue;

  /* step 1.  if a == 0, return 0 */
  if (mp_iszero (a) == 1) {
    *c = 0;
    return MP_OKAY;
  }

  /* step 2.  if a == 1, return 1 */
  if (mp_cmp_d (a, 1) == MP_EQ) {
    *c = 1;
    return MP_OKAY;
  }

  /* default */
  s = 0;

  /* step 3.  write a = a1 * 2^e  */
  if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_init (&n1)) != MP_OKAY) {
    goto __A1;
  }

  if ((res = mp_init (&e)) != MP_OKAY) {
    goto __N1;
  }

  while (mp_iseven (&a1) == 1) {
    if ((res = mp_add_d (&e, 1, &e)) != MP_OKAY) {
      goto __E;
    }

    if ((res = mp_div_2 (&a1, &a1)) != MP_OKAY) {
      goto __E;
    }
  }

  /* step 4.  if e is even set s=1 */
  if (mp_iseven (&e) == 1) {
    s = 1;
  } else {
    /* else set s=1 if n = 1/7 (mod 8) or s=-1 if n = 3/5 (mod 8) */
    if ((res = mp_mod_d (n, 8, &residue)) != MP_OKAY) {
      goto __E;
    }

    if (residue == 1 || residue == 7) {
      s = 1;
    } else if (residue == 3 || residue == 5) {
      s = -1;
    }
  }

  /* step 5.  if n == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
  if ((res = mp_mod_d (n, 4, &residue)) != MP_OKAY) {
    goto __E;
  }
  if (residue == 3) {
    if ((res = mp_mod_d (&a1, 4, &residue)) != MP_OKAY) {
      goto __E;
    }
    if (residue == 3) {
      s = -s;
    }
  }

  /* if a1 == 1 we're done */
  if (mp_cmp_d (&a1, 1) == MP_EQ) {
    *c = s;
  } else {
    /* n1 = n mod a1 */
    if ((res = mp_mod (n, &a1, &n1)) != MP_OKAY) {
      goto __E;
    }
    if ((res = mp_jacobi (&n1, &a1, &r)) != MP_OKAY) {
      goto __E;
    }
    *c = s * r;
  }

  /* done */
  res = MP_OKAY;
__E:mp_clear (&e);
__N1:mp_clear (&n1);
__A1:mp_clear (&a1);
  return res;
}