New construction of A2-model from Symplectic spaces over finite field

Many mathematicians have worked in this erea by using classical groups, normal form of matrices or some known vector spaces and came out some good results. But few of them have used symplectic spaces to construct authentication codes with arbitration. Then in this paper we give a new construction of authentication code with arbitration based on sympletic spaces and also compute parameters and probabilities from this code. The main objective of studying authentication codes with arbitration is to use them for the provision of better security in practical information communications. In the first part of this paper, we present and study the concept of authentication code with arbitration. The historical perspective of the development of authentication code with arbitration is also presented. In the part two of this paper some essential conceptions of symplectic spaces over finite field, which constitute the basic of this paper are introduced. In the same way several theorems are given, then parameters and probabilities of authentication code with arbitration are easily computed. In part three a new construction of authentication code with arbitration from symplectic geometry is presented. In our discussion, we describe the subspaces geometrical characteristics with matrices and use this method to deal with the counting problems in the computation of parameters and probabilities.