NOTE: This site is obsolete.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

The Laws of Cryptography with Java Code.

Here is the "IBM" scheme used for credit card 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();
   }
}

// IbmErrorDetection.java: Implement the "IBM" decimal error detection method
public class IbmErrorDetection extends ErrorDetection{

   private static int sharp(int d) {
       return (2*d)/10 + (2*d)%10;
   }

   public static int insertCheck(int[] a) {
      int check = 0;
      for (int i = 1; i < a.length; i++)
         if (i%2 == 0)
            check = (check + a[i])%10;
         else
            check = (check + sharp(a[i]))%10;
      if (check == 0) a[0] = 0;
      else a[0] = -check + 10;
      return a[0];
   }
   
   public static boolean doCheck(int[] a) {
      int check = 0;
      for (int i = 0; i < a.length; i++)
         if (i%2 == 0)
            check = (check + a[i])%10;
         else
            check = (check + sharp(a[i]))%10;
      if (check != 0) return false;
      else return true;
   }

   // main function
   public static void main (String[] args) {
      int[] a = new int[15];
      boolean checkFlag = false;
      for (int i = 1; i < a.length; i++)
         a[i] = (int)(Math.random() * 10.0);
      printUnchecked(a);
      IbmErrorDetection.insertCheck(a);
      printArray(a);
      System.out.println(IbmErrorDetection.doCheck(a));
      a[4] = (a[4] + 1)%10;

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

      // test all adjacent transpositions
      System.out.println("\nTest all adjacent transpositions ...");
      for (int p1 = 0; p1 < 10; p1++)
         for (int p2 = 0; p2 < 10; p2++) {
            if (p1 != p2) {
               a[8] = p1; a[9] = p2;
               IbmErrorDetection.insertCheck(a);
               // interchange
               a[8] ^= a[9];
               a[9] ^= a[8];
               a[8] ^= a[9];
               if (IbmErrorDetection.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
} 

? 31623 91033 1003
7 31623 91033 1003
true
7 31633 91033 1003
false

Test all adjacent transpositions ...
Warning: Interchange of 0 and 9 not detected
Warning: Interchange of 9 and 0 not detected
At least one transposition undetected