Description of global avalanche characteristics and constructions of Boolean functions

Abstract

Global avalanche characteristics matrix representation method starting from the expression of global avalanche characteristics was proposed and a new tool for research global avalanche characteristics was provided.According to properties of sum-of-square indicator,an odd almost optimal Boolean functions which meet savariety of properties of cryptography was constructed and hold slower sum-of-square indicator via M-M Boolean functions.It is a problem that how to construct a kind of functions satisfying GAC.There is a effecint way that modifying M-M functions with designing new mapping.

Keywords

• Boolean functions;global avalanche characteristics;matrix;construction algorithm;nonlinearity