One Construction Of Cartesian Authentication Codes From The Normal Form Of Orthogonal Involution Matrix Over Finite Fields

During the communicated system modes,besides the transmitter and the receiver,there also existes opponent. The opponent can attack the system through some techniques. The receiver must identify and make sure the truth or the fault of the message in order to protect against the opponent's attacks. The authentication codes are used to resolve the messages's authentication problem.G.J.Simmons firstly described and constructed the authentication codes.Wan Zhexian used sym-plectc and unitary groups over finite fields to construct Cartesian authentication codes.ProfesserYou hong and Professer Nan Jizhu first 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 normal form of orthogonal involution matrices over the finite field F_q is presented.Morover,if the encoding rules are chosen according to a uniform probability distribution,the probabilities P_Iand P_S,of a successful impersonation attack and of a successful substitution attack respectively,of these codes are also computed.