Using Normal Form Of Idempotent Matrices Of Degree Three Over Z_p^k To Construct Cartesian Authentication Codes

Let R = Z_p^k be a finite local ring ,where p is a prime,and p≥3,and k > 1. In this paper using normal form of idempotent matrices of degree three over R to construct a Cartesian authentication code,and compute ites size parameters and the probabilities of successful impersonation P_I and substitution attack P_S under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.