Counting Theorem Of Symplectic Involution Matrices Over Finite Field Fq And Its Application

Let Sp_n(Fq) be the set of symplectic matrices over finite field Fq, where q is power of a prime. In the present thesis, by the normal form of involution matrices over Sp_n(Fq), we compute the number of involution matrices. At last we construct one class of Cartesian authentication codes, and compute their size parameters. Moreover assuming that the encoding rules are chosen according to a uniform probability distribution, we also compute the probabilities of a successful impersonation attack and of a successful substitution attack respectively.