### view libtommath/bn_mp_jacobi.c @ 1470:8bba51a55704

Update to libtommath v1.0.1
author Matt Johnston Thu, 08 Feb 2018 23:11:40 +0800 60fc6476e044 f52919ffd3b1
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```#include <tommath_private.h>
#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, [email protected], http://libtom.org
*/

/* computes the jacobi c = (a | n) (or Legendre if n is prime)
* HAC pp. 73 Algorithm 2.149
* HAC is wrong here, as the special case of (0 | 1) is not
* handled correctly.
*/
int mp_jacobi (mp_int * a, mp_int * n, int *c)
{
mp_int  a1, p1;
int     k, s, r, res;
mp_digit residue;

/* if a < 0 return MP_VAL */
if (mp_isneg(a) == MP_YES) {
return MP_VAL;
}

/* if n <= 0 return MP_VAL */
if (mp_cmp_d(n, 0) != MP_GT) {
return MP_VAL;
}

/* step 1. handle case of a == 0 */
if (mp_iszero (a) == MP_YES) {
/* special case of a == 0 and n == 1 */
if (mp_cmp_d (n, 1) == MP_EQ) {
*c = 1;
} else {
*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**k  */
if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
return res;
}

if ((res = mp_init (&p1)) != MP_OKAY) {
goto LBL_A1;
}

/* divide out larger power of two */
k = mp_cnt_lsb(&a1);
if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
goto LBL_P1;
}

/* step 4.  if e is even set s=1 */
if ((k & 1) == 0) {
s = 1;
} else {
/* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
residue = n->dp[0] & 7;

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

/* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
if ( ((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 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, &p1)) != MP_OKAY) {
goto LBL_P1;
}
if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
goto LBL_P1;
}
*c = s * r;
}

/* done */
res = MP_OKAY;
LBL_P1:mp_clear (&p1);
LBL_A1:mp_clear (&a1);
return res;
}
#endif

/* ref:         \$Format:%D\$ */
/* git commit:  \$Format:%H\$ */
/* commit time: \$Format:%ai\$ */
```