The Power Of The Balanced Nature Of The Function Of Differential Over Finite Fields And Rings Multi-valued Logic Function Construction

In the first part of this paper we consider the security of DES-like cryptosystems against the differential cryptanalysis and present a criterion defined as num which is minor than the criterion called differentially uniform. With f keeping the same value, the ability of the nonlinear power mapping over finite field to resist against the differential cryptanalysis is stronger when num get smaller. Moreover we discuss the inversion mapping over GF(3n)on this kind of property. On the second part, we investigate a decomposition formula of spectrum of a class of m-valued logical functions. Futhermore,we give a new method for construction of k-dimension generalized Bent functions based on this formula.