Using Vector Space Over Z/p~kZ To Construct Cartesian Authentication Codes

Let R = Z/p~kZ be a finite local ring where p is a prime and k > 1. In this paper, we use the vector space over finite local ring R to get a construction of Cartesian authentication codes. Moreover, assume that the encoding rules are chosen according to uniform probability distribution, the P_I and P_s, which denote the largest probabilities of a successful impersonation attack and a successful substitution attack respectively, of these codes are also computed.