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The Laws of Cryptography with Java Code.

The following Java program uses the slow GF(2⁸) multipy function to generate two tables needed for fast multiplication: a table of all powers of the generator 0x03, and the inverse table. (The tables in the main section had a few extra frills inserted by hand.)

// FFMultTables: create the arrays E and L, write html versions of them
public class FFMultTables {
   public byte[] E = new byte[256];
   public byte[] L = new byte[256];
   private String[] dig = {"0","1","2","3","4","5","6","7",
                           "8","9","a","b","c","d","e","f"};
   public byte FFMul(byte a, byte b) {
      byte aa = a, bb = b, r = 0, t;
      while (aa != 0) {
         if ((aa & 1) != 0)
            r = (byte)(r ^ bb);
         t = (byte)(bb & 0x80);
         bb = (byte)(bb << 1);
         if (t != 0)
            bb = (byte)(bb ^ 0x1b);
         aa = (byte)((aa & 0xff) >> 1); 
      }
      return r;
   }

   public String hex(byte a) {
      return dig[(a & 0xff) >> 4] + dig[a & 0x0f];
   }

   public String hex(int a) {
      return dig[a];
   }

   public void loadE() {
      byte x = (byte)0x01;
      int index = 0;
      E[index++] = (byte)0x01;
      for (int i = 0; i < 255; i++) {
         byte y = FFMul(x, (byte)0x03);
         E[index++] = y;
         // System.out.print(hex(y) + " ");
         x = y;
      }
   }

   public void loadL() {
      int index;
      for (int i = 0; i < 255; i++) {
          L[E[i] & 0xff] = (byte)i;
      }
   }

   public void printE() {
      System.out.print("<table border><tr><td></td>");
      for (int i = 0; i < 16; i++)
         System.out.print("<th>" + hex(i) + "</th>");
      System.out.println("</tr>");
      for (int i = 0; i < 256; i++) {
         if (i%16 == 0)
            System.out.print("<tr><th> " + hex(i/16) + " </th>");
         System.out.print("<td> " + hex(E[i]) + " </td>");
         if (i%16 == 15) System.out.println("</tr>");
      }
      System.out.println("</table>");
   }

   public void printL() {
      System.out.print("<table border><tr><td></td>");
      for (int i = 0; i < 16; i++)
         System.out.print("<th>" + hex(i) + "</th>");
      System.out.println("</tr>");
      for (int i = 0; i < 256; i++) {
         if (i%16 == 0)
            System.out.print("<tr><th> " + hex(i/16) + " </th>");
         if (i == 0)
            System.out.print("<td>  </td>");
         else
            System.out.print("<td> " + hex(L[i]) + " </td>");
         if (i%16 == 15) System.out.println("</tr>");
      }
      System.out.println("</table>");
   }

   public static void main(String[] args) {
      FFMultTables ffm = new FFMultTables();
      ffm.loadE();
      ffm.loadL();
      ffm.printL();
      ffm.printE();
   }
}