Several Construction Of Authentication Codes

In information system, information security is a very important measurement. Generally speaking, the security of information system mainly refers to the confidentiality, integrity and authentication. Authentication of information in the system, i.e., the recipient being able to identify and confirm the authenticity of the information, so as to prevent information from being deletion, tampering and counterfeiting, is one of the methods to solve this problem in the information system. In this paper we consider the information security form the angel of authentication. This paper is dedicated to the construction of authentication codes using linear codes. Furthermore, we determine the relevant parameters P1and Ps. The linear codes employed in this dissertation are cyclic codes whose duals have three or four zeros. Since the codewords of cyclic code have trace representation, the Hamming weight of the codeword can be expressed as exponential sum on finite field. Using quadratic theory on finite fields, the estimation of the exponential sums on finite field can be reduced to the number of solutions of linearized polynomials. Since these linearized polynomials have a relatively small number of solutions, we can decide all the possible Hamming weights of the corresponding cyclic code. Moreover, we can calculate the maximum frequency of any letter in the alphabet set occurring in all nonzero codewords. Using these results, we can estimate the probability of success of the impersonation attack P1and substitution attack Ps. These authentication codes can attach or asymptotically attach the lower bound. For some fixed parameters, our authentication codes have asymptotically optimal property in the security sense. Comparing with some known constructions, our authentication codes have larger source space.The dissertation is organized as follows.In Chapter1we introduce the background, recent results, the origination of the problem and the main research topic of this dissertation.In Chapter2we introduce the basic knowledge on finite fields, linear codes, cycle codes and authentication codes. In Chapter3We employ linear code to construct authentication code.In chapter4we will construct the first kind of new authentication code, mainly by using the trace formula on the weight of linear codes and analyze the performance of this authentication codes.In Chapter5we construct the second kind of authentication codes, mainly by using the results of the weight distribution of linear code and analyze the safety performance of the authentication code. Furthermore we compare our constructions with the previous ones.Finally we make the conclusion and propose future work.