On Plateaued Functions And Their Constructions

Cryptography is the core of information security technology. However, one of the key problems of the Cryptography is the security analysis on cryptographic functions. In this thesis, both the applied background and the studying status on cryptographic functions are introduced. And the security measure indexes on cryptographic functions are analyzed. A class of functions with three-valued spectra are mainly studied, namely the properties and the constructions of Plateaued functions. The main results are as follows:1. Plateaued functions include Bent functions and Partially Bent functions, but are wider than them. At the same time, Plateaued functions are of good tradeoffs among some cryptographic criteria. The further study of the properties and the constructions of Plateaued functions not only have theoretical significance, but also have applicational value. By a method of concatenating Bent functions, Partially-bent functions with balancedness have been constructed. Meanwhile some other properties of the functions are studied.2. In order to better resist against difference analysis and linear analysis, an improved method for the Partially Bent functions is presented. The new functions possess balancedness and no nonzero linear structures. Their degrees are better than the original functions.3. A new method for constructing Bent functions with more variables is proposed by utilizing multi-output Bent functions.