A novel application on mutually orthogonal graph squares and graph-orthogonal arrays

Security of personal information has become a major concern due to the increasing use of the Internet by individuals in the digital world. The main purpose here is to prevent an unauthorized person from gaining access to confidential information. The solution to such a problem is by authentication of users. Authentication has a very important role in achieving security. Mutually orthogonal graph squares (MOGS) are considered the generalization of mutually orthogonal Latin squares (MOLS). Also, MOGS are generated from edge decompositions of complete bipartite graphs by isomorphic graphs. Graph-orthogonal arrays can be constructed by MOGS. In this paper, graph-orthogonal arrays are used for constructing authentication codes. These arrays are the encoding matrices of authentication tags. We introduce the concepts and basic theorems of MOGS, graph-orthogonal arrays, and authentication codes. After constructing graph-orthogonal arrays by MOGS, then there is an established mapping between graph-orthogonal arrays and message set. This manages us to construct perfect non-splitting and splitting Cartesian authentication codes. In both cases, we calculate the probabilities of successful impersonation attacks and substitution attacks. Besides that, the performance of constructed non-splitting and splitting authentication codes is analyzed. In the end, optimal authentication codes and secure authentication codes are constructed.