New Constructions Of Multi-sender Or Multi-receiver Authentication Codes

Confidentiality and authentication are two main aspects of guaranteeing information security better.However,authentication systems can have the security function or not.In order to prevent the deception attacks between the sender and the receiver,add a completely trusted arbitrator to resolve internal disputes,and then the authentication codes with arbitrator are formed which are also called A~2-codes for short.In this paper,it mainly study that the constructions of A~2-codes with secrecy and multi-receiver authentication codes,and then obtain two kinds of new authentication codes.The main results are as follows: firstly,two constructions of A~2-codes with secrecy from polynomials over finite fields are given.Secondly,it is constructed that the multi-receiver authentication codes with arbitration from symplectic geometry over finite fields.The rationality of them is proved.Then,based on the properties of polynomials,the theory of linear equations and the subspace structure and the counting principle of symplectic geometry,the relevant parameters and the maximum probabilities of successful attacks are computed under the condition that the set of encoding rules,the set of decoding rules and the set of source states are chosen according to a uniform probability distribution.At last,compared with some known A~2-codes,two A~2-codes with secrecy can save more storage spaces,resist attacks from the sender and the receiver better,and they are confidentiality.In the multi-receiver authentication codes,a simulation is made about the impersonation attacks from the sender.The simulation result fully shows that the probability of successful attacks is stable with the increasing number of attacks from the sender,and which is far lower than the theoretical value of maximum probability of successful attacks.