Two Methods Of Constructing Authentication Code With Special Properties

Perfect secure authentication code has many advantages, such as the small probabil-ity of successful attack and the optimal parameters, these advantages make it useful tocomputer science, statistics and cryptography. Ma Wenping, Wang Xinmei, Shen Hao andmany scholars have researched the constructing methods of authentication code in-depth.This paper studies two methods using mixed orthogonal arrays and linear block codesto construct authentication code with special properties such as Cartesian code, secureauthentication code, perfect secure authentication code and so on.Chapter1introduces the development and the current research status of authentica-tion code and orthogonal arrays, contains basic concepts and main lemmas needed in thispaper.Chapter2proposes one kind of methods for constructing perfect secure authenticationcode through mixed orthogonal arrays. We can make cransformation of these arrays bypermutation matrix, delete one column and find a moderate Latin square to get the perfectsecure authentication code. Some examples are given to illustrate the constructing method.At last we give many mixed orthogonal arrays’ parameters that can be used in this paper.In Chapter3, by using Hamming distances we give a simple proof of a existing methodfor constructing cartesian code by linear block code, and find the formulas of the probabilityof successful attack for i time to the constructed Cartesian code. At last we use someexamples to explain the construction method in detail.Chapter4concludes the main content of this paper and puts forward to some sugges-tions on some of valuable and unsolved problems.