/***************************** * Copyright Henry Minsky (hqm@alum.mit.edu) 1991-2009 * * This software library is licensed under terms of the GNU GENERAL * PUBLIC LICENSE * * RSCODE 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. * RSCODE 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 Rscode. If not, see . * Commercial licensing is available under a separate license, please * contact author for details. * * Source code is available at http://rscode.sourceforge.net * * * Multiplication and Arithmetic on Galois Field GF(256) * * From Mee, Daniel, "Magnetic Recording, Volume III", Ch. 5 by Patel. * * ******************************/ #include #include #include "ecc.h" /* This is one of 14 irreducible polynomials * of degree 8 and cycle length 255. (Ch 5, pp. 275, Magnetic Recording) * The high order 1 bit is implicit */ /* x^8 + x^4 + x^3 + x^2 + 1 */ #define PPOLY 0x1D int gexp[512]; int glog[256]; static void init_exp_table (void); void init_galois_tables (void) { /* initialize the table of powers of alpha */ init_exp_table(); } static void init_exp_table (void) { int i, z; int pinit,p1,p2,p3,p4,p5,p6,p7,p8; pinit = p2 = p3 = p4 = p5 = p6 = p7 = p8 = 0; p1 = 1; gexp[0] = 1; gexp[255] = gexp[0]; glog[0] = 0; /* shouldn't log[0] be an error? */ // Private pp8() As Integer = {1, 0, 1, 1, 1, 0, 0, 0, 1} 'specify irreducible polynomial coeffts */ for (i = 1; i < 256; i++) { pinit = p8; p8 = p7; p7 = p6; p6 = p5; p5 = p4 ^ pinit; p4 = p3 ^ pinit; p3 = p2 ^ pinit; p2 = p1; p1 = pinit; gexp[i] = p1 + p2*2 + p3*4 + p4*8 + p5*16 + p6*32 + p7*64 + p8*128; gexp[i+255] = gexp[i]; } for (i = 1; i < 256; i++) { for (z = 0; z < 256; z++) { if (gexp[z] == i) { glog[i] = z; break; } } } } /* multiplication using logarithms */ int gmult(int a, int b) { int i,j; if (a==0 || b == 0) return (0); i = glog[a]; j = glog[b]; return (gexp[i+j]); } int ginv (int elt) { return (gexp[255-glog[elt]]); }