Constructions Of Authentication Codes From Projective Geometry Over Finite Fields

With the development of modern communication technology, the research of message authentication codes becomes very urgent and necessary. At the same time, the projective geometry over finite fields with simple counting theorems and great geometric properties is widely used in computational mathematics, communication theory, coding theory and the theory of certification, etc. In this paper, we concern about the constructions of splitting authentication codes, authentication codes with arbitration and authentication codes with dishonest arbiter from projective geometry over finite fields.Firstly, three splitting authentication codes based on the projective geometry are constructed. The correlative parameters and the maximal successful probabilities are computed. In this way, we get a perfect splitting authentication code. Then a simulation of impersonation attack in the perfect splitting A-code is performed in order to test its correctness.Secondly, a perfect A~2-code is constructed over this space. The parameters and the five maximal successful probabilities are also computed. We obtain a splitting A-code and a perfect A-code without splitting based on the constructed A~2-code.At last, a perfect A~3-code is constructed. In order to verify the security of this construction, not only the parameters and the successful probabilities are compared, but several known constructions are also compared with ours.