NOTE: This site is obsolete. See book draft (in PDF):

The Laws of Cryptography with Java Code.

Here is the ISBN mod 11 scheme used for book publishing numbers.

// ErrorDetection.java: base class for single-digit error detection
public class ErrorDetection {

   public static void printArray(int[] a) {
      for (int i = 0; i < a.length; i++) {
      	 if (a[i] == 10)
      	    System.out.print("X ");
      	 else
      	    System.out.print(a[i]);
      	 if (i%5 == 0) System.out.print(" ");
      }
      System.out.println();
   }
   
   public static void printUnchecked(int[] a) {
   	  System.out.print("? ");
      for (int i = 1; i < a.length; i++) {
      	 System.out.print(a[i]);
      	 if (i%5 == 0) System.out.print(" ");
      }
      System.out.println();
   }
}

// ISBNErrorDetection.java: Implement the mod 11 check used by ISBN numbers, 
public class ISBNErrorDetection extends ErrorDetection {

   public static int insertCheck(int[] a) {
      int check = 0;
      for (int i = 1; i < a.length; i++)
         check = (check + (i%10 + 1)*a[i])%11;
      if (check == 0) a[0] = 0;
      else a[0] = -check + 11;
      return a[0];
   }
   
   public static boolean doCheck(int[] a) {
      int check = 0;
      for (int i = 0; i < a.length; i++)
         check = (check + (i%10 + 1)*a[i])%11;
      if (check != 0) return false;
      else return true;
   }

   // main function
   public static void main (String[] args) {
      int[] a = new int[9];
      boolean checkFlag = false;
      for (int i = 1; i < a.length; i++)
         a[i] = (int)(Math.random() * 10.0);
      ISBNErrorDetection.printUnchecked(a);
      ISBNErrorDetection.insertCheck(a);
      ISBNErrorDetection.printArray(a);
      System.out.println(ISBNErrorDetection.doCheck(a));
      a[4] = (a[4] + 3)%10;

      ISBNErrorDetection.printArray(a);
      System.out.println(ISBNErrorDetection.doCheck(a));

      // test all adjacent transpositions
      System.out.println("\nISBN error detection scheme");
      System.out.println("\nTest all adjacent transpositions ...");
      for (int pos = 4; pos < 7; pos++)
         for (int p1 = 0; p1 < 10; p1++)
            for (int p2 = 0; p2 < 10; p2++) {
               if (p1 != p2) {
                  a[pos] = p1; a[pos+1] = p2;
                  ISBNErrorDetection.insertCheck(a);
                  // interchange
                  a[pos] ^= a[pos+1];
                  a[pos+1] ^= a[pos];
                  a[pos] ^= a[pos+1];
                  if (ISBNErrorDetection.doCheck(a)) {
                     System.out.println("Warning: Interchange of " + p1 +
                        " and " + p2 + " not detected");
                     checkFlag = true;
                  }
               }
            }
      if (checkFlag)
         System.out.println("At least one transposition undetected");
      else
         System.out.println("All transpositions detected");

   } // end of main
} 

? 11696 554
X  11696 554
true
X  11626 554
false

ISBN error detection scheme

Test all adjacent transpositions ...
All transpositions detected