The Studies On Bent Functions

Bent functions are a kind of special Boolean functions, which were first presented by Rothaus in Paper in 1976. The application fields are continually extended these years, and as a result the studies on Bent functions are simultaneously added. Especially after Bent function has been successfully used by J.Olsen to design balance quadriphase sequences with optimum correlation properties, Bent functions have drawn the researchers' recognition. It has been among the important fields of coding and cryptology theory.This paper has gained the results as following:1) In the first Chapter, the developing progress and main results have been summarized.2) How to construct Bent functions with more variables from ones with less variables is quite an important study project. In the second chapter, two sufficient and indispensable conditions have been brought forward to construct Bent functions with m(m>n) variables from ones with n variables in the way of spectrum and some different vector forms of Bent functions have been pointed out.3) Balancedness, nonlinearity and propagation are three of the most essential characters that Boolean functions with high cryptographic specialty have to obey. In the third chapter, some methods of using Bent functions to construct balanced Boolean functions satisfying the highly propagation characteristics with highly nonlinearity have been put forward.