The Propagation Property Of Multi-valued Logical Functions

The design and analysis of some cryptography systems cancontribute to the design and analysis of the multi-valued logical functionfrom the point of view of root. P.V.Kumar popularized the propagationproperty of Boolean function to the multi-valued logical domain in 1985,and studied the multi-valued Bent functions emphatically. Becausepropagation property has an important application in cryptography,especially on the block cipher, the study on the property and constructionof the multi-valued Bent function and the multi-valued logical functionssatisfying SAC(m) , PC(k) , and PC(k)/m respectively, becomes animportant subject in the study of cryptography. The design andconstruction of multi-valued logical functions have made someachievements, but there are relatively less studies on the multi-valuedlogical functions satisfyingSAC(m),PC(k), and PC(k)/m separately. The propagation property and Bent functions on the multi-valuedlogical domain are studied in this paper, and some work has been done asfollows: 1,Main research results about propagation property and Bentfunctions on the multi-valued logical domain both at home and abroadwere surveyed systematically in the first and second chapter. 2,The research results achieved by the author are listed in thechapter 3, these are as follows: 1) The sufficient and necessary conditions which p -valued logicalfunctions meet PC(k) , PC(k)/m ,and EPC(k)/m respectively wereproved by the means of spectrum analysis method. 2) The high order multi-valued logical functions satisfyingPC(2n)(i.e. , Bent function) and PC(k) respectively were constructed 3) By improving the result of the reference [80], the sufficient andnecessary condition of joint function meeting k order propagationcriterion was proved again. 4) The sufficient and necessary conditions of quadric multi-valuedlogical function satisfying PC(k)/m and EPC(k)/m were givenrespectively. 5) Some multi-valued logical functions which meetSAC(m),SAC(n - 2), and SAC(n -1) respectively were given. 6) Present a sufficient and necessary condition according to whichmulti-valued functions are perfect nonlinear functions, and constructedsome multi-valued functions satisfying(n,m,k)SAC .