Cartesian Authentication Codes Obtained By Orthogonal Array And Difference Matrix

Orthogonal arrays can be used not only in statistics but also in coding theory, cryptog-raphy and computer science, etc. Many new methods of constructing orthogonal arrays iscalled up in recent years. This includes: Zhang Ying-shan presented an efcient method forobtaining orthogonal arrays by orthogonal decomposition of projection matrices—MatrixImage Construction (MI Construction). Using this method, a large number of orthogonalarrays are obtained and updated by Zhang Ying-shan and Pang Shan-qi. However, withthe development of the construction theory of orthogonal arrays, the application of orthog-onal arrays has been taken care of. Now this paper gives a further study about the obtainof Cartesian authentication codes by using orthogonal arrays and diference matrix.The details are as follows:Chapter one is to introduce the background and the current research of orthogonalarrays and some necessary basic knowledge of this paper.By using isomorphic transformation of orthogonal arrays, Chapter two introduces ageneral kind of method of constructing perfect Cartesian authentication codes, many ofwhich are optimal. This Chapter also extends the symbol transformation of column oforthogonal arrays to several columns, the Cartesian authentication codes are obtained byusing the the row transformations column transformations the symbol transformationof several columns of isomorphic transformation of orthogonal arrays. And a number ofCartesian authentication codes obtained in Chapter two are more than the existing ones.Some examples are given to illustrate this method.By using diference matrix method, Chapter three introduces a general method forconstructing perfect Cartesian authentication codes, some of which are optimal. We extendthe diference matrix of additive group module n to the diference matrix of Finite Field,a number of sources and messages of the Cartesian authentication codes obtained are morethan the existing ones under the condition of keeping the quantity of encoding rules andauthentication symbols invariable. Some examples are given to illustrate this method. By using the multiplication of orthogonal arrays, Chapter four introduces a generalkind of method of constructing Cartesian authentication codes, and constructs Cartesianauthentication codes with n authentication symbols. This method extends the iterationmethod is based on the orthogonal arrays. A number of sources of the Cartesian authen-tication codes obtained are more than that of the existing Cartesian authentication codesunder the condition of keeping the quantity of encoding rules and authentication symbolsinvariable. And a number of encoding rules of the Cartesian authentication codes obtainedare less than that of the existing Cartesian authentication codes under the condition ofkeeping the quantity of authentication symbols invariable. Some examples are given toillustrate this method.