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Adhaar Card Validation

  • To validate Aadhar Card number, we adopt Verhoeff algorithm.

  • UIDAI (Unique Identification Authority of India) uses Verhoeff algorithm and it handles various data entry errors.

7564   6239   1883

Birendra Pradhan

Father: Babu Pradhan

DOB: 22/07/1995

MALE

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2
1

Aadhar generated number

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Check Digits (Generated by Verhoeff algorithm)

VERHOEFF ALGORITHM

  • It is a checksum algorithm.

  • In 1969, a Dutch mathematician named Verhoeff carried out a study of errors made by humans in handling decimal numbers.

  • It also works for generating and validating the checksum digits of :

  • Credit Card Validation

  • Debit Card

  • ISBN

  • Account Number

  • Most errors happens:

  • Single errors: a changed to b (60 to 95 percent of all errors)

  • Adjacent Transpositions: ab changed to ba(10 to 20 percent)

  • Twin errors: aa changed to bb (0.5 to 1.5 percent)

  • Jump transpositions: acb changed to bca (0.5 to 1.5 percent)

  • Omitting or adding a digit: (10 to 20 percent)

HOW IT WORKS

The Verhoeff algorithm can be implemented using three tables:

Multiplication table d

  • The first table, d, is based on multiplication in the dihedral group D5.

  • Note that this group is not commutative, that is, for some values of j and k, d(j,k) ≠ d(k, j).

Inverse table inv

  • The inverse table inv represents the multiplicative inverse of a digit, that is, the value that satisfies d(j, inv(j)) = 0.

Permutation table p

  • The permutation table p applies a permutation to each digit based on its position in the number.

Multiplication table d

Permutation table p

Inverse table inv

  • Inversion table required for getting checksum.

  • Here is an example of validating a given number using Verhoeff Algorithm.

Validate the check digit 2363:

  • Put index number in i according to Aadhar no.

  • Put your Aadhar number in ni column on the table, taken from right to left.

  • Initialize the checksum c to zero.

  • For each index, i of the array n, starting at zero, replace c with d(c, p(i mod 8, ni)).

  • If c is zero, so the check is correct.

i   = Index number

ni = Given number

(Right to left)

Given

Calculate

(From above table)

c = 0

The number is Valid.

STRENGTH

  • it can detect more transcription errors than Luhn.

  • It is special as it has the property of detecting 95.3% of the phonetic errors.

  • The strengths of the algorithm are that it detects :

  • All transliteration and transposition errors

  • Additionally most twin

  • Twin jump

  • Jump transposition

WEAKNESS

  • The main weakness of the Verhoeff algorithm is its complexity

  • Calculations required cannot readily be performed by hand.

VERHOEFF ALGORITHM IMPLEMENTATION 

  • Here is the JAVA program of Verhoeff algorithm, used for creating the checksum or validate the checksum digit. 

  • Used in client side to validate:

  • Aadhar Card Number

  • Credit Card 

  • Debit Card

  • ISBN (International Standard Book Number)

  • and more

JAVA PROGRAM for validation of Aadhar card

import java.util.*;

public class Verhoeff {

 

public static void main(String [] args){

             Scanner sc=new Scanner(System.in);

             System.out.println("Enter your Aadhar Card no :");

             String s=sc.nextLine();

             System.out.println("Entered card is = " + validateVerhoeff(s));

}

 

// The multiplication table

 

    static int [ ] [ ] d = new int [ ][ ]

 

      { 

          {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},

          {1, 2, 3, 4, 0, 6, 7, 8, 9, 5},

          {2, 3, 4, 0, 1, 7, 8, 9, 5, 6},

          {3, 4, 0, 1, 2, 8, 9, 5, 6, 7},

          {4, 0, 1, 2, 3, 9, 5, 6, 7, 8},

          {5, 9, 8, 7, 6, 0, 4, 3, 2, 1},

          {6, 5, 9, 8, 7, 1, 0, 4, 3, 2},

          {7, 6, 5, 9, 8, 2, 1, 0, 4, 3},

          {8, 7, 6, 5, 9, 3, 2, 1, 0, 4}, 

          {9, 8, 7, 6, 5, 4, 3, 2, 1, 0}

   };

 

// The permutation table

 

    static int [ ] [ ] p = new int [ ] [ ]

     {  

         {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},

         {1, 5, 7, 6, 2, 8, 3, 0, 9, 4},

         {5, 8, 0, 3, 7, 9, 6, 1, 4, 2},

         {8, 9, 1, 6, 0, 4, 3, 5, 2, 7},

         {9, 4, 5, 3, 1, 2, 6, 8, 7, 0},

         {4, 2, 8, 6, 5, 7, 3, 9, 0, 1},

         {2, 7, 9, 3, 8, 0, 6, 4, 1, 5},

         {7, 0, 4, 6, 9, 1, 3, 2, 5, 8}

     };

 

// The inverse table

 

     static int [ ] inv = {0, 4, 3, 2, 1, 5, 6, 7, 8, 9};

 

/* * For a given number generates a Verhoeff digit * */

 

     public static String generateVerhoeff(String num){

               int c = 0;

               int [ ] myArray = stringToReversedIntArray(num);

               for(int i = 0; i < myArray.length; i++)

                           {

                               c = d [c] [p [ ( ( i + 1) % 8)] [myArray [i]] ];

                           }

              return Integer.toString( inv [ c ] );

          }  

 

/* * Validates that an entered number is Verhoeff compliant. * NB: Make sure the check digit is the last one. */

 

        public static boolean validateVerhoeff(String num){

 

               int c = 0; int [ ] myArray = stringToReversedIntArray(num);

               for (int i = 0 ; i < myArray.length ; i++) {

                           c = d [c] [p[(i % 8)] [myArray[i] ] ];

                          }

               return ( c == 0 );

            }

 

/* * Converts a string to a reversed integer array. */

 

      private static int [ ] stringToReversedIntArray(String num){

              int [ ] myArray = new int[num.length()];

              for (int i = 0; i < num.length(); i++) {

                         myArray [ i ] = Integer.parseInt(num.substring(i, i + 1));

                        }

             myArray = reverse(myArray);

             return myArray;

            }

 

/* * Reverses an int array */

 

      private static int [ ] reverse(int[] myArray) {

              int [ ] reversed = new int[myArray.length];

              for ( int i = 0; i < myArray.length ; i++ ) {

                               reversed [ i ] = myArray[myArray.length - (i + 1)];

                              }

              return reversed;

             }

}

  • Screenshot of the Aadhar Card validation program.

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