Construction of authentication codes based on orthogonal array and Latin square

In this paper, the orthogonal array and Latin square are used to construct authentication codes. First, orthogonal arrays are constructed by mutually orthogonal Latin squares. Then, the orthogonal array is used to establish the mapping between authentication tag and the message set, and a non-splitting Cartesian authentication code and a splitting authentication code are constructed. Furthermore, the coding matrix of the non-splitting Cartesian authentication code is used to establish a connection with the Latin square, and a security authentication code is constructed. These construction methods are of universal significance. The probability of successful impersonation attack and substitution attack of these codes, various distribution probabilities, and information entropy are calculated. Finally, the performance of these authentication codes is analyzed, and it is verified that the constructed codes are perfect and optimal.