Abstract: The relation between the Cartesian product and authentication codes is studied in this paper. A new idea to use the private keys to carry the information of the authentication symbols is presented, which is based on the character of Cartesian product structure. And the Cartesian productbased optimal authentication codes with equal cheating probabilities of all orders are constructed, which can be easily designed and can be applied well to engineering. In this paper, the secret authentication codes with equal cheating probabilities of all orders are also constructed which are founded on Cartesian product and Latin square. The two construction methods mentioned above need no pre-storing encoder matrix, so that a mass of storage is saved. At the same time, the two schemes can offer an enough security level expected.