Cartesian Authentication Code Using The Finite Field Idempotent Matrix Of Standard Form Construction

During the communicated system modes, besides the transmitter and the receiver, there also exists opponent. In order to protect against the opponent's attacks the system, G.J.Simmons firstly described and constructed the authentication codes. Wan Zexian used symplectc and unitary groups over finite fields to construct Cartesian authentication codes. You Hong and Nan Jizhu used the method of matrix to construct a Cartesian authentication codes, it is simpler and better in some way.One construction of Cartesian authentication codes from the normalform of Idempotent matrices over the field Fq is presented. Moreover,if the encoding rules are chosen according to a uniform probability distribution, the probabilities P, and Ps, of a successful impersonationattack and of a successful substitution attack respectively, of these codes are also computed.