Cartesian Authentication Codes with Arbitration Based on Cross-product

This paper proposes a construction method for Cartesian authentication codes with arbitration based on the cross-product. By calculating the parameters of the authentication code and the probabilities of various successful attacks under the conditions of encoding rules chosen according to a uniform probability distribution for both the receiver and transmitter, it is demonstrated that the constructed authentication code is an optimal arbitration Cartesian authentication code of each order. The performance of the authentication code is analyzed. Furthermore, a class of secret-preserving arbitration authentication codes based on the cross-product and Latin squares is constructed, and the relevant parameters of this code are calculated.