Two New Authentication Schemes from Singular Symplectic Geometry over Finite Fields

Two kinds of authentication schemes are constructed using singular symplectic geometry over finite fields in this paper. One is an authentication code with arbitration, another is a multi-receiver authentication code. The parameters of two kinds of codes have been computed. Under the assumption that the encoding rules of the transmitter and the receiver are chosen according to a uniform probability distribution, the maximum probabilities of success of different types of deception attacks are also computed.