Mercurial > dropbear

annotate libtommath/bn_mp_jacobi.c @ 1646:6d1bbe7d5fa5 DROPBEAR_2019.77

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2019.77
author Matt Johnston <matt@ucc.asn.au>
date Sat, 23 Mar 2019 21:46:29 +0800
parents 8bba51a55704
children f52919ffd3b1
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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diff changeset
1 #include <tommath_private.h>
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2 #ifdef BN_MP_JACOBI_C
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
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4 *
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5 * LibTomMath is a library that provides multiple-precision
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6 * integer arithmetic as well as number theoretic functionality.
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7 *
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8 * The library was designed directly after the MPI library by
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9 * Michael Fromberger but has been written from scratch with
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10 * additional optimizations in place.
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11 *
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12 * The library is free for all purposes without any express
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13 * guarantee it works.
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14 *
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15 * Tom St Denis, [email protected], http://libtom.org
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16 */
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17
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18 /* computes the jacobi c = (a | n) (or Legendre if n is prime)
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19 * HAC pp. 73 Algorithm 2.149
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20 * HAC is wrong here, as the special case of (0 | 1) is not
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21 * handled correctly.
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22 */
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23 int mp_jacobi (mp_int * a, mp_int * n, int *c)
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24 {
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25 mp_int a1, p1;
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26 int k, s, r, res;
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27 mp_digit residue;
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28
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29 /* if a < 0 return MP_VAL */
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30 if (mp_isneg(a) == MP_YES) {
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31 return MP_VAL;
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32 }
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33
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34 /* if n <= 0 return MP_VAL */
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35 if (mp_cmp_d(n, 0) != MP_GT) {
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36 return MP_VAL;
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37 }
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38
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39 /* step 1. handle case of a == 0 */
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40 if (mp_iszero (a) == MP_YES) {
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41 /* special case of a == 0 and n == 1 */
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42 if (mp_cmp_d (n, 1) == MP_EQ) {
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43 *c = 1;
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44 } else {
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45 *c = 0;
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46 }
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47 return MP_OKAY;
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48 }
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49
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50 /* step 2. if a == 1, return 1 */
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51 if (mp_cmp_d (a, 1) == MP_EQ) {
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52 *c = 1;
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53 return MP_OKAY;
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54 }
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55
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56 /* default */
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57 s = 0;
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58
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59 /* step 3. write a = a1 * 2**k */
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60 if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
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61 return res;
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62 }
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63
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64 if ((res = mp_init (&p1)) != MP_OKAY) {
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65 goto LBL_A1;
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66 }
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67
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68 /* divide out larger power of two */
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69 k = mp_cnt_lsb(&a1);
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70 if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
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71 goto LBL_P1;
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72 }
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73
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74 /* step 4. if e is even set s=1 */
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75 if ((k & 1) == 0) {
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76 s = 1;
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77 } else {
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78 /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
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79 residue = n->dp[0] & 7;
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80
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81 if ((residue == 1) || (residue == 7)) {
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82 s = 1;
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83 } else if ((residue == 3) || (residue == 5)) {
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84 s = -1;
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85 }
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86 }
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parents:
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87
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88 /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
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89 if ( ((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
284
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90 s = -s;
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91 }
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parents:
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92
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parents:
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93 /* if a1 == 1 we're done */
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94 if (mp_cmp_d (&a1, 1) == MP_EQ) {
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parents:
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95 *c = s;
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96 } else {
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parents:
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97 /* n1 = n mod a1 */
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98 if ((res = mp_mod (n, &a1, &p1)) != MP_OKAY) {
284
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parents:
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99 goto LBL_P1;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
100 }
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
101 if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
102 goto LBL_P1;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
103 }
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
104 *c = s * r;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
105 }
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
106
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
107 /* done */
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
108 res = MP_OKAY;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
109 LBL_P1:mp_clear (&p1);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
110 LBL_A1:mp_clear (&a1);
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
111 return res;
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
112 }
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
113 #endif
389
5ff8218bcee9 propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 2af95f00ebd5bb7a28b3817db1218442c935388e)
Matt Johnston <matt@ucc.asn.au>
parents: 284
diff changeset
114
1470
8bba51a55704 Update to libtommath v1.0.1
Matt Johnston <matt@ucc.asn.au>
parents: 1436
diff changeset
115 /* ref: $Format:%D$ */
8bba51a55704 Update to libtommath v1.0.1
Matt Johnston <matt@ucc.asn.au>
parents: 1436
diff changeset
116 /* git commit: $Format:%H$ */
8bba51a55704 Update to libtommath v1.0.1
Matt Johnston <matt@ucc.asn.au>
parents: 1436
diff changeset
117 /* commit time: $Format:%ai$ */