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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(&reg[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 }