New Constructions Of Authentication Codes With Arbitration

Modern information technology makes people’s information communication and sharing to be more convenient and quick,but also brings safety problems such as information disclosure or information fraud.Therefore,information security has become one of the key research fields in information science.Authentication is one of the important means to ensure information security,and the message authentication codes are a kind of unconditional security authentication system.Assume that the transmitter and the receiver trust each other,the authentication codes are called A-codes.In the case of the transmitter and the receiver distrust each other,the authentication codes with trust arbitrations are called A2-codes,the authentication codes with distrust arbitrations are called A3-codes.An A3-code,in which the receiver,the transmitter,and the arbitration are dishonest,is an extension of an A2-code,which is more suitable for modern communication authentication system.This paper is mainly to explore the new construction method of A3-codes and gain two aspects of research results.On the one hand,a class of A3-codes is constructed based on the theories of polynomials and linear equations over finite fields.In particular,the code is perfect when the parameters are special values.On the other hand,based on the unitary geometry over finite fields,a class of A3-codes is constructed by making full use of subspace structure and unitary space counting principles.At the same time,the parameters of two types of codes and all kinds of cheating attacks the maximum probability of success are calculated.Finally,compared with some known A3-codes,the constructed codes save the storage space,have high security capability,and have a certain advantage.