1/*	$NetBSD: bn_mp_jacobi.c,v 1.2 2017/01/28 21:31:47 christos Exp $	*/
2
3#include <tommath.h>
4#ifdef BN_MP_JACOBI_C
5/* LibTomMath, multiple-precision integer library -- Tom St Denis
6 *
7 * LibTomMath is a library that provides multiple-precision
8 * integer arithmetic as well as number theoretic functionality.
9 *
10 * The library was designed directly after the MPI library by
11 * Michael Fromberger but has been written from scratch with
12 * additional optimizations in place.
13 *
14 * The library is free for all purposes without any express
15 * guarantee it works.
16 *
17 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
18 */
19
20/* computes the jacobi c = (a | n) (or Legendre if n is prime)
21 * HAC pp. 73 Algorithm 2.149
22 */
23int mp_jacobi (mp_int * a, mp_int * p, int *c)
24{
25  mp_int  a1, p1;
26  int     k, s, r, res;
27  mp_digit residue;
28
29  /* if p <= 0 return MP_VAL */
30  if (mp_cmp_d(p, 0) != MP_GT) {
31     return MP_VAL;
32  }
33
34  /* step 1.  if a == 0, return 0 */
35  if (mp_iszero (a) == 1) {
36    *c = 0;
37    return MP_OKAY;
38  }
39
40  /* step 2.  if a == 1, return 1 */
41  if (mp_cmp_d (a, 1) == MP_EQ) {
42    *c = 1;
43    return MP_OKAY;
44  }
45
46  /* default */
47  s = 0;
48
49  /* step 3.  write a = a1 * 2**k  */
50  if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
51    return res;
52  }
53
54  if ((res = mp_init (&p1)) != MP_OKAY) {
55    goto LBL_A1;
56  }
57
58  /* divide out larger power of two */
59  k = mp_cnt_lsb(&a1);
60  if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
61     goto LBL_P1;
62  }
63
64  /* step 4.  if e is even set s=1 */
65  if ((k & 1) == 0) {
66    s = 1;
67  } else {
68    /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
69    residue = p->dp[0] & 7;
70
71    if (residue == 1 || residue == 7) {
72      s = 1;
73    } else if (residue == 3 || residue == 5) {
74      s = -1;
75    }
76  }
77
78  /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
79  if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
80    s = -s;
81  }
82
83  /* if a1 == 1 we're done */
84  if (mp_cmp_d (&a1, 1) == MP_EQ) {
85    *c = s;
86  } else {
87    /* n1 = n mod a1 */
88    if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
89      goto LBL_P1;
90    }
91    if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
92      goto LBL_P1;
93    }
94    *c = s * r;
95  }
96
97  /* done */
98  res = MP_OKAY;
99LBL_P1:mp_clear (&p1);
100LBL_A1:mp_clear (&a1);
101  return res;
102}
103#endif
104
105/* Source: /cvs/libtom/libtommath/bn_mp_jacobi.c,v  */
106/* Revision: 1.4  */
107/* Date: 2006/12/28 01:25:13  */
108