A TWOOAs Construction For Multi-Receiver Multi-Message Authentication Codes

The paper is divided into four parts. In chapter one the background of authentication code is introduced. In chapter two we discuss the Multi-Receiver Multi-Message Authentication Codes based on the TWOOAs. In chapter three we discuss the upper bounds of the m and n of the TWOOAs and give two constructions of the TWOOAs. In chapter four some further research problems are presented.The notion of a conventional authentication code (A-code) was introduced by Gilbert, MacWilliams and Sloane. This model had been studied extensively. Lower bounds on the cheating probabilities and the size of keys had been given. Optimal A-codes are obtained by using combinatorial designs theory.The notion of a conventional A-code can be easily generalized to the case where a key can be used to authenticate consecutive distinct source states. The notion of a Multi-receiver A-code (MRA-codes) was introduced by Desmedt, Frankel and Yung as another generalization of that of a conventional A-code. They also had gaven two constructions for MRA-codes based on polynomials over finite fields and finite geometries. Then Kurosawa and Obana derived combinatorial lower bounds on the probability of success in impersonation and substitution attacks. They showed that DFY polynomial construction is in fact an optimal construction. The notion of a TWOOAs was introduced by Kurosawa and Obana and used to construct a unconditional secure Multi-receiver single-message A-code. Savavi-Naini and Wang gave a formal definition of an MRA–codes and used it to derive information-theoretic bounds on the probability of success in impersonation and substitution attacks. These bounds are used to obtain lower bounds on the number of keys of transmitter and receivers and also lower bound on the length of the transmitted codewords. They also reviewed of the known constructions of MRA-codes, pointed out their shortcomings and gave constructions to overcome these shortcomings.In this paper, we start by giving a formal definition of a Multi-Receiver Multi- Message Authentication Codes, then we generalize the strength of the second...