/* * GRUB -- GRand Unified Bootloader * Copyright (C) 2010 Free Software Foundation, Inc. * * GRUB is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * GRUB is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with GRUB. If not, see . */ #ifdef TEST #include #include #include #define xmalloc malloc #define grub_memset memset #define grub_memcpy memcpy #endif #ifndef STANDALONE #ifdef TEST typedef unsigned int grub_size_t; typedef unsigned char grub_uint8_t; typedef unsigned short grub_uint16_t; #else #include #include #include #include #endif #endif #ifdef STANDALONE #ifdef TEST typedef unsigned int grub_size_t; typedef unsigned char grub_uint8_t; typedef unsigned short grub_uint16_t; #else #include #include #endif void grub_reed_solomon_recover (void *ptr_, grub_size_t s, grub_size_t rs); #endif #define GF_SIZE 8 typedef grub_uint8_t gf_single_t; typedef grub_uint16_t gf_double_t; #define GF_POLYNOMIAL 0x1d #define GF_INVERT2 0x8e #if defined (STANDALONE) && !defined (TEST) static char *gf_invert __attribute__ ((section(".text"))) = (void *) 0x100000; static char *scratch __attribute__ ((section(".text"))) = (void *) 0x100100; #else #if defined (STANDALONE) static char *scratch; #endif static grub_uint8_t gf_invert[256]; #endif #define SECTOR_SIZE 512 #define MAX_BLOCK_SIZE (200 * SECTOR_SIZE) static gf_single_t gf_reduce (gf_double_t a) { int i; for (i = GF_SIZE - 1; i >= 0; i--) if (a & (1ULL << (i + GF_SIZE))) a ^= (((gf_double_t) GF_POLYNOMIAL) << i); return a & ((1ULL << GF_SIZE) - 1); } static gf_single_t gf_mul (gf_single_t a, gf_single_t b) { gf_double_t res = 0; int i; for (i = 0; i < GF_SIZE; i++) if (b & (1 << i)) res ^= ((gf_double_t) a) << i; return gf_reduce (res); } static void init_inverts (void) { gf_single_t a = 1, ai = 1; do { a = gf_mul (a, 2); ai = gf_mul (ai, GF_INVERT2); gf_invert[a] = ai; } while (a != 1); } static gf_single_t pol_evaluate (gf_single_t *pol, grub_size_t degree, gf_single_t x) { int i; gf_single_t xn = 1, s = 0; for (i = degree; i >= 0; i--) { s ^= gf_mul (pol[i], xn); xn = gf_mul (x, xn); } return s; } #if !defined (STANDALONE) static void rs_encode (gf_single_t *data, grub_size_t s, grub_size_t rs) { gf_single_t *rs_polynomial, a = 1; int i, j; gf_single_t *m; m = xmalloc ((s + rs) * sizeof (gf_single_t)); grub_memcpy (m, data, s * sizeof (gf_single_t)); grub_memset (m + s, 0, rs * sizeof (gf_single_t)); rs_polynomial = xmalloc ((rs + 1) * sizeof (gf_single_t)); grub_memset (rs_polynomial, 0, (rs + 1) * sizeof (gf_single_t)); rs_polynomial[rs] = 1; /* Multiply with X - a^r */ for (j = 0; j < rs; j++) { if (a & (1 << (GF_SIZE - 1))) { a <<= 1; a ^= GF_POLYNOMIAL; } else a <<= 1; for (i = 0; i < rs; i++) rs_polynomial[i] = rs_polynomial[i + 1] ^ gf_mul (a, rs_polynomial[i]); rs_polynomial[rs] = gf_mul (a, rs_polynomial[rs]); } for (j = 0; j < s; j++) if (m[j]) { gf_single_t f = m[j]; for (i = 0; i <= rs; i++) m[i+j] ^= gf_mul (rs_polynomial[i], f); } free (rs_polynomial); grub_memcpy (data + s, m + s, rs * sizeof (gf_single_t)); free (m); } #endif static void syndroms (gf_single_t *m, grub_size_t s, grub_size_t rs, gf_single_t *sy) { gf_single_t xn = 1; unsigned i; for (i = 0; i < rs; i++) { if (xn & (1 << (GF_SIZE - 1))) { xn <<= 1; xn ^= GF_POLYNOMIAL; } else xn <<= 1; sy[i] = pol_evaluate (m, s + rs - 1, xn); } } static void gauss_eliminate (gf_single_t *eq, int n, int m, int *chosen) { int i, j; for (i = 0 ; i < n; i++) { int nzidx; int k; gf_single_t r; for (nzidx = 0; nzidx < m && (eq[i * (m + 1) + nzidx] == 0); nzidx++); if (nzidx == m) continue; chosen[i] = nzidx; r = gf_invert [eq[i * (m + 1) + nzidx]]; for (j = 0; j < m + 1; j++) eq[i * (m + 1) + j] = gf_mul (eq[i * (m + 1) + j], r); for (j = i + 1; j < n; j++) { gf_single_t rr = eq[j * (m + 1) + nzidx]; for (k = 0; k < m + 1; k++) eq[j * (m + 1) + k] ^= gf_mul (eq[i * (m + 1) + k], rr); } } } static void gauss_solve (gf_single_t *eq, int n, int m, gf_single_t *sol) { int *chosen; int i, j; #ifndef STANDALONE chosen = xmalloc (n * sizeof (int)); #else chosen = (void *) scratch; scratch += n * sizeof (int); #endif for (i = 0; i < n; i++) chosen[i] = -1; for (i = 0; i < m; i++) sol[i] = 0; gauss_eliminate (eq, n, m, chosen); for (i = n - 1; i >= 0; i--) { gf_single_t s = 0; if (chosen[i] == -1) continue; for (j = 0; j < m; j++) s ^= gf_mul (eq[i * (m + 1) + j], sol[j]); s ^= eq[i * (m + 1) + m]; sol[chosen[i]] = s; } #ifndef STANDALONE free (chosen); #else scratch -= n * sizeof (int); #endif } static void rs_recover (gf_single_t *m, grub_size_t s, grub_size_t rs) { grub_size_t rs2 = rs / 2; gf_single_t *sigma; gf_single_t *errpot; int *errpos; gf_single_t *sy; int errnum = 0; int i, j; #ifndef STANDALONE sigma = xmalloc (rs2 * sizeof (gf_single_t)); errpot = xmalloc (rs2 * sizeof (gf_single_t)); errpos = xmalloc (rs2 * sizeof (int)); sy = xmalloc (rs * sizeof (gf_single_t)); #else sigma = (void *) scratch; scratch += rs2 * sizeof (gf_single_t); errpot = (void *) scratch; scratch += rs2 * sizeof (gf_single_t); errpos = (void *) scratch; scratch += rs2 * sizeof (int); sy = (void *) scratch; scratch += rs * sizeof (gf_single_t); #endif syndroms (m, s, rs, sy); for (i = 0; i < (int) rs; i++) if (sy[i] != 0) break; /* No error detected. */ if (i == (int) rs) { #ifndef STANDALONE free (sigma); free (errpot); free (errpos); free (sy); #else scratch -= rs2 * sizeof (gf_single_t); scratch -= rs2 * sizeof (gf_single_t); scratch -= rs2 * sizeof (int); scratch -= rs * sizeof (gf_single_t); #endif return; } { gf_single_t *eq; #ifndef STANDALONE eq = xmalloc (rs2 * (rs2 + 1) * sizeof (gf_single_t)); #else eq = (void *) scratch; scratch += rs2 * (rs2 + 1) * sizeof (gf_single_t); #endif for (i = 0; i < (int) rs2; i++) for (j = 0; j < (int) rs2 + 1; j++) eq[i * (rs2 + 1) + j] = sy[i+j]; for (i = 0; i < (int) rs2; i++) sigma[i] = 0; gauss_solve (eq, rs2, rs2, sigma); #ifndef STANDALONE free (eq); #else scratch -= rs2 * (rs2 + 1) * sizeof (gf_single_t); #endif } { gf_single_t xn = 1, yn = 1; for (i = 0; i < (int) (rs + s); i++) { gf_single_t ev = (gf_mul (pol_evaluate (sigma, rs2 - 1, xn), xn) ^ 1); if (ev == 0) { errpot[errnum] = yn; errpos[errnum++] = s + rs - i - 1; } yn = gf_mul (yn, 2); xn = gf_mul (xn, GF_INVERT2); } } { gf_single_t *errvals; gf_single_t *eq; #ifndef STANDALONE eq = xmalloc (rs * (errnum + 1) * sizeof (gf_single_t)); errvals = xmalloc (errnum * sizeof (int)); #else eq = (void *) scratch; scratch += rs * (errnum + 1) * sizeof (gf_single_t); errvals = (void *) scratch; scratch += errnum * sizeof (int); #endif for (j = 0; j < errnum; j++) eq[j] = errpot[j]; eq[errnum] = sy[0]; for (i = 1; i < (int) rs; i++) { for (j = 0; j < (int) errnum; j++) eq[(errnum + 1) * i + j] = gf_mul (errpot[j], eq[(errnum + 1) * (i - 1) + j]); eq[(errnum + 1) * i + errnum] = sy[i]; } gauss_solve (eq, rs, errnum, errvals); for (i = 0; i < (int) errnum; i++) m[errpos[i]] ^= errvals[i]; #ifndef STANDALONE free (eq); free (errvals); #else scratch -= rs * (errnum + 1) * sizeof (gf_single_t); scratch -= errnum * sizeof (int); #endif } #ifndef STANDALONE free (sigma); free (errpot); free (errpos); free (sy); #else scratch -= rs2 * sizeof (gf_single_t); scratch -= rs2 * sizeof (gf_single_t); scratch -= rs2 * sizeof (int); scratch -= rs * sizeof (gf_single_t); #endif } static void decode_block (gf_single_t *ptr, grub_size_t s, gf_single_t *rptr, grub_size_t rs) { int i, j; for (i = 0; i < SECTOR_SIZE; i++) { grub_size_t ds = (s + SECTOR_SIZE - 1 - i) / SECTOR_SIZE; grub_size_t rr = (rs + SECTOR_SIZE - 1 - i) / SECTOR_SIZE; gf_single_t m[ds + rr]; /* Nothing to do. */ if (!ds || !rr) continue; for (j = 0; j < (int) ds; j++) m[j] = ptr[SECTOR_SIZE * j + i]; for (j = 0; j < (int) rr; j++) m[j + ds] = rptr[SECTOR_SIZE * j + i]; rs_recover (m, ds, rr); for (j = 0; j < (int) ds; j++) ptr[SECTOR_SIZE * j + i] = m[j]; } } #if !defined (STANDALONE) static void encode_block (gf_single_t *ptr, grub_size_t s, gf_single_t *rptr, grub_size_t rs) { int i, j; for (i = 0; i < SECTOR_SIZE; i++) { grub_size_t ds = (s + SECTOR_SIZE - 1 - i) / SECTOR_SIZE; grub_size_t rr = (rs + SECTOR_SIZE - 1 - i) / SECTOR_SIZE; gf_single_t m[ds + rr]; for (j = 0; j < ds; j++) m[j] = ptr[SECTOR_SIZE * j + i]; rs_encode (m, ds, rr); for (j = 0; j < rr; j++) rptr[SECTOR_SIZE * j + i] = m[j + ds]; } } #endif #if !defined (STANDALONE) void grub_reed_solomon_add_redundancy (void *buffer, grub_size_t data_size, grub_size_t redundancy) { grub_size_t s = data_size; grub_size_t rs = redundancy; gf_single_t *ptr = buffer; gf_single_t *rptr = ptr + s; /* Nothing to do. */ if (!rs) return; while (s > 0) { grub_size_t tt; grub_size_t cs, crs; cs = s; crs = rs; tt = cs + crs; if (tt > MAX_BLOCK_SIZE) { cs = ((cs * (MAX_BLOCK_SIZE / 512)) / tt) * 512; crs = ((crs * (MAX_BLOCK_SIZE / 512)) / tt) * 512; } encode_block (ptr, cs, rptr, crs); ptr += cs; rptr += crs; s -= cs; rs -= crs; } } #endif void grub_reed_solomon_recover (void *ptr_, grub_size_t s, grub_size_t rs) { gf_single_t *ptr = ptr_; gf_single_t *rptr = ptr + s; /* Nothing to do. */ if (!rs) return; #if defined (STANDALONE) init_inverts (); #endif while (s > 0) { grub_size_t tt; grub_size_t cs, crs; cs = s; crs = rs; tt = cs + crs; if (tt > MAX_BLOCK_SIZE) { cs = ((cs * (MAX_BLOCK_SIZE / 512)) / tt) * 512; crs = ((crs * (MAX_BLOCK_SIZE / 512)) / tt) * 512; } decode_block (ptr, cs, rptr, crs); ptr += cs; rptr += crs; s -= cs; rs -= crs; } } #ifdef TEST int main (int argc, char **argv) { FILE *in, *out; grub_size_t s, rs; char *buf; #ifdef STANDALONE scratch = xmalloc (1048576); #endif #ifndef STANDALONE init_inverts (); #endif in = fopen ("tst.bin", "rb"); if (!in) return 1; fseek (in, 0, SEEK_END); s = ftell (in); fseek (in, 0, SEEK_SET); rs = s / 3; buf = xmalloc (s + rs + SECTOR_SIZE); fread (buf, 1, s, in); fclose (in); grub_reed_solomon_add_redundancy (buf, s, rs); out = fopen ("tst_rs.bin", "wb"); fwrite (buf, 1, s + rs, out); fclose (out); grub_memset (buf + 512 * 15, 0, 512); out = fopen ("tst_dam.bin", "wb"); fwrite (buf, 1, s + rs, out); fclose (out); grub_reed_solomon_recover (buf, s, rs); out = fopen ("tst_rec.bin", "wb"); fwrite (buf, 1, s, out); fclose (out); return 0; } #endif