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comparison libtommath/bn_mp_jacobi.c @ 1436:60fc6476e044

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Update to libtommath v1.0
author Matt Johnston <matt@ucc.asn.au>
date Sat, 24 Jun 2017 22:37:14 +0800
parents 5ff8218bcee9
children 8bba51a55704
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1435:f849a5ca2efc 1436:60fc6476e044
1 #include <tommath.h> 1 #include <tommath_private.h>
2 #ifdef BN_MP_JACOBI_C 2 #ifdef BN_MP_JACOBI_C
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis 3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
4 * 4 *
5 * LibTomMath is a library that provides multiple-precision 5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality. 6 * integer arithmetic as well as number theoretic functionality.
10 * additional optimizations in place. 10 * additional optimizations in place.
11 * 11 *
12 * The library is free for all purposes without any express 12 * The library is free for all purposes without any express
13 * guarantee it works. 13 * guarantee it works.
14 * 14 *
15 * Tom St Denis, [email protected], http://math.libtomcrypt.com 15 * Tom St Denis, [email protected], http://libtom.org
16 */ 16 */
17 17
18 /* computes the jacobi c = (a | n) (or Legendre if n is prime) 18 /* computes the jacobi c = (a | n) (or Legendre if n is prime)
19 * HAC pp. 73 Algorithm 2.149 19 * HAC pp. 73 Algorithm 2.149
20 * HAC is wrong here, as the special case of (0 | 1) is not
21 * handled correctly.
20 */ 22 */
21 int mp_jacobi (mp_int * a, mp_int * p, int *c) 23 int mp_jacobi (mp_int * a, mp_int * n, int *c)
22 { 24 {
23 mp_int a1, p1; 25 mp_int a1, p1;
24 int k, s, r, res; 26 int k, s, r, res;
25 mp_digit residue; 27 mp_digit residue;
26 28
27 /* if p <= 0 return MP_VAL */ 29 /* if a < 0 return MP_VAL */
28 if (mp_cmp_d(p, 0) != MP_GT) { 30 if (mp_isneg(a) == MP_YES) {
29 return MP_VAL; 31 return MP_VAL;
30 } 32 }
31 33
32 /* step 1. if a == 0, return 0 */ 34 /* if n <= 0 return MP_VAL */
33 if (mp_iszero (a) == 1) { 35 if (mp_cmp_d(n, 0) != MP_GT) {
34 *c = 0; 36 return MP_VAL;
35 return MP_OKAY; 37 }
38
39 /* step 1. handle case of a == 0 */
40 if (mp_iszero (a) == MP_YES) {
41 /* special case of a == 0 and n == 1 */
42 if (mp_cmp_d (n, 1) == MP_EQ) {
43 *c = 1;
44 } else {
45 *c = 0;
46 }
47 return MP_OKAY;
36 } 48 }
37 49
38 /* step 2. if a == 1, return 1 */ 50 /* step 2. if a == 1, return 1 */
39 if (mp_cmp_d (a, 1) == MP_EQ) { 51 if (mp_cmp_d (a, 1) == MP_EQ) {
40 *c = 1; 52 *c = 1;
62 /* step 4. if e is even set s=1 */ 74 /* step 4. if e is even set s=1 */
63 if ((k & 1) == 0) { 75 if ((k & 1) == 0) {
64 s = 1; 76 s = 1;
65 } else { 77 } else {
66 /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */ 78 /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
67 residue = p->dp[0] & 7; 79 residue = n->dp[0] & 7;
68 80
69 if (residue == 1 || residue == 7) { 81 if ((residue == 1) || (residue == 7)) {
70 s = 1; 82 s = 1;
71 } else if (residue == 3 || residue == 5) { 83 } else if ((residue == 3) || (residue == 5)) {
72 s = -1; 84 s = -1;
73 } 85 }
74 } 86 }
75 87
76 /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */ 88 /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
77 if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) { 89 if ( ((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
78 s = -s; 90 s = -s;
79 } 91 }
80 92
81 /* if a1 == 1 we're done */ 93 /* if a1 == 1 we're done */
82 if (mp_cmp_d (&a1, 1) == MP_EQ) { 94 if (mp_cmp_d (&a1, 1) == MP_EQ) {
83 *c = s; 95 *c = s;
84 } else { 96 } else {
85 /* n1 = n mod a1 */ 97 /* n1 = n mod a1 */
86 if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) { 98 if ((res = mp_mod (n, &a1, &p1)) != MP_OKAY) {
87 goto LBL_P1; 99 goto LBL_P1;
88 } 100 }
89 if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) { 101 if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
90 goto LBL_P1; 102 goto LBL_P1;
91 } 103 }
98 LBL_A1:mp_clear (&a1); 110 LBL_A1:mp_clear (&a1);
99 return res; 111 return res;
100 } 112 }
101 #endif 113 #endif
102 114
103 /* $Source: /cvs/libtom/libtommath/bn_mp_jacobi.c,v $ */ 115 /* $Source$ */
104 /* $Revision: 1.3 $ */ 116 /* $Revision$ */
105 /* $Date: 2006/03/31 14:18:44 $ */ 117 /* $Date$ */