Error Detection and Correction on the Credit Card Number using Luhn Algorithm

Abstract

The Luhn algorithm is used in credit card number for validation purposes. The algorithm was designed to cater for document storage and retrival in IBM. But later it was improved to cater for error detection purposes in credit cards and IMEI numbers among other applications. The algorithm does not detect jump transposition errors, some twin errors, some adjacent transposition errors and also does not have any error correction capabilities. In this research it is observed modulo 10 is not effective in error detection since it allows errors associated with zero divisors not to be detected. Also, the Luhn algorithm does not detect some twin errors and transposition of digit 09 for 90 due to the reduction of the products to a single digit. Jump transposition errors can only be detected if the weights of the algorithm are changed which ultimately changes the Luhn algorithm. A modulo 13 algorithm is then designed with its error detection capabilities discussed and analyzed and then a convertion tool for existing codes in Luhn algorithm to the new modulo 13 algorithm code is given. It is shown that the modulo 13 algorithm surpasses the Luhn algorithm in as far as error detection is concerned. ix