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Member "cryptsetup-2.4.3/lib/verity/rs_decode_char.c" (13 Jan 2022, 5936 Bytes) of package /linux/misc/cryptsetup-2.4.3.tar.xz:
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1 /*
2 * Reed-Solomon decoder, based on libfec
3 *
4 * Copyright (C) 2002, Phil Karn, KA9Q
5 * libcryptsetup modifications
6 * Copyright (C) 2017-2021 Red Hat, Inc. All rights reserved.
7 *
8 * This file is free software; you can redistribute it and/or
9 * modify it under the terms of the GNU Lesser General Public
10 * License as published by the Free Software Foundation; either
11 * version 2.1 of the License, or (at your option) any later version.
12 *
13 * This file is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
16 * Lesser General Public License for more details.
17 *
18 * You should have received a copy of the GNU Lesser General Public
19 * License along with this file; if not, write to the Free Software
20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
21 */
22
23 #include <string.h>
24 #include <stdlib.h>
25
26 #include "rs.h"
27
28 #define MAX_NR_BUF 256
29
30 int decode_rs_char(struct rs* rs, data_t* data)
31 {
32 int deg_lambda, el, deg_omega, syn_error, count;
33 int i, j, r, k;
34 data_t q, tmp, num1, num2, den, discr_r;
35 data_t lambda[MAX_NR_BUF], s[MAX_NR_BUF]; /* Err+Eras Locator poly and syndrome poly */
36 data_t b[MAX_NR_BUF], t[MAX_NR_BUF], omega[MAX_NR_BUF];
37 data_t root[MAX_NR_BUF], reg[MAX_NR_BUF], loc[MAX_NR_BUF];
38
39 if (rs->nroots >= MAX_NR_BUF)
40 return -1;
41
42 memset(s, 0, rs->nroots * sizeof(data_t));
43 memset(b, 0, (rs->nroots + 1) * sizeof(data_t));
44
45 /* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
46 for (i = 0; i < rs->nroots; i++)
47 s[i] = data[0];
48
49 for (j = 1; j < rs->nn - rs->pad; j++) {
50 for (i = 0; i < rs->nroots; i++) {
51 if (s[i] == 0) {
52 s[i] = data[j];
53 } else {
54 s[i] = data[j] ^ rs->alpha_to[modnn(rs, rs->index_of[s[i]] + (rs->fcr + i) * rs->prim)];
55 }
56 }
57 }
58
59 /* Convert syndromes to index form, checking for nonzero condition */
60 syn_error = 0;
61 for (i = 0; i < rs->nroots; i++) {
62 syn_error |= s[i];
63 s[i] = rs->index_of[s[i]];
64 }
65
66 /*
67 * if syndrome is zero, data[] is a codeword and there are no
68 * errors to correct. So return data[] unmodified
69 */
70 if (!syn_error)
71 return 0;
72
73 memset(&lambda[1], 0, rs->nroots * sizeof(lambda[0]));
74 lambda[0] = 1;
75
76 for (i = 0; i < rs->nroots + 1; i++)
77 b[i] = rs->index_of[lambda[i]];
78
79 /*
80 * Begin Berlekamp-Massey algorithm to determine error+erasure
81 * locator polynomial
82 */
83 r = 0;
84 el = 0;
85 while (++r <= rs->nroots) { /* r is the step number */
86 /* Compute discrepancy at the r-th step in poly-form */
87 discr_r = 0;
88 for (i = 0; i < r; i++) {
89 if ((lambda[i] != 0) && (s[r - i - 1] != A0)) {
90 discr_r ^= rs->alpha_to[modnn(rs, rs->index_of[lambda[i]] + s[r - i - 1])];
91 }
92 }
93 discr_r = rs->index_of[discr_r]; /* Index form */
94 if (discr_r == A0) {
95 /* 2 lines below: B(x) <-- x*B(x) */
96 memmove(&b[1], b, rs->nroots * sizeof(b[0]));
97 b[0] = A0;
98 } else {
99 /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
100 t[0] = lambda[0];
101 for (i = 0; i < rs->nroots; i++) {
102 if (b[i] != A0)
103 t[i + 1] = lambda[i + 1] ^ rs->alpha_to[modnn(rs, discr_r + b[i])];
104 else
105 t[i + 1] = lambda[i + 1];
106 }
107 if (2 * el <= r - 1) {
108 el = r - el;
109 /*
110 * 2 lines below: B(x) <-- inv(discr_r) *
111 * lambda(x)
112 */
113 for (i = 0; i <= rs->nroots; i++)
114 b[i] = (lambda[i] == 0) ? A0 : modnn(rs, rs->index_of[lambda[i]] - discr_r + rs->nn);
115 } else {
116 /* 2 lines below: B(x) <-- x*B(x) */
117 memmove(&b[1], b, rs->nroots * sizeof(b[0]));
118 b[0] = A0;
119 }
120 memcpy(lambda, t, (rs->nroots + 1) * sizeof(t[0]));
121 }
122 }
123
124 /* Convert lambda to index form and compute deg(lambda(x)) */
125 deg_lambda = 0;
126 for (i = 0; i < rs->nroots + 1; i++) {
127 lambda[i] = rs->index_of[lambda[i]];
128 if (lambda[i] != A0)
129 deg_lambda = i;
130 }
131 /* Find roots of the error+erasure locator polynomial by Chien search */
132 memcpy(®[1], &lambda[1], rs->nroots * sizeof(reg[0]));
133 count = 0; /* Number of roots of lambda(x) */
134 for (i = 1, k = rs->iprim - 1; i <= rs->nn; i++, k = modnn(rs, k + rs->iprim)) {
135 q = 1; /* lambda[0] is always 0 */
136 for (j = deg_lambda; j > 0; j--) {
137 if (reg[j] != A0) {
138 reg[j] = modnn(rs, reg[j] + j);
139 q ^= rs->alpha_to[reg[j]];
140 }
141 }
142 if (q != 0)
143 continue; /* Not a root */
144
145 /* store root (index-form) and error location number */
146 root[count] = i;
147 loc[count] = k;
148 /* If we've already found max possible roots, abort the search to save time */
149 if (++count == deg_lambda)
150 break;
151 }
152
153 /*
154 * deg(lambda) unequal to number of roots => uncorrectable
155 * error detected
156 */
157 if (deg_lambda != count)
158 return -1;
159
160 /*
161 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
162 * x**rs->nroots). in index form. Also find deg(omega).
163 */
164 deg_omega = deg_lambda - 1;
165 for (i = 0; i <= deg_omega; i++) {
166 tmp = 0;
167 for (j = i; j >= 0; j--) {
168 if ((s[i - j] != A0) && (lambda[j] != A0))
169 tmp ^= rs->alpha_to[modnn(rs, s[i - j] + lambda[j])];
170 }
171 omega[i] = rs->index_of[tmp];
172 }
173
174 /*
175 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
176 * inv(X(l))**(rs->fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
177 */
178 for (j = count - 1; j >= 0; j--) {
179 num1 = 0;
180 for (i = deg_omega; i >= 0; i--) {
181 if (omega[i] != A0)
182 num1 ^= rs->alpha_to[modnn(rs, omega[i] + i * root[j])];
183 }
184 num2 = rs->alpha_to[modnn(rs, root[j] * (rs->fcr - 1) + rs->nn)];
185 den = 0;
186
187 /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
188 for (i = RS_MIN(deg_lambda, rs->nroots - 1) & ~1; i >= 0; i -= 2) {
189 if (lambda[i + 1] != A0)
190 den ^= rs->alpha_to[modnn(rs, lambda[i + 1] + i * root[j])];
191 }
192
193 /* Apply error to data */
194 if (num1 != 0 && loc[j] >= rs->pad) {
195 data[loc[j] - rs->pad] ^= rs->alpha_to[modnn(rs, rs->index_of[num1] +
196 rs->index_of[num2] + rs->nn - rs->index_of[den])];
197 }
198 }
199
200 return count;
201 }