On Relevance of Nonlinearity, Derivative, and E-Derivative for Boolean Functions

Abstract

In this paper, we discuss the impact of weight structure of the derivative and e-derivative on the nonlinearity of Boolean functions, and the relationship among the nonlinearity, derivative, and e-derivative of Boolean functions. And get six kinds of relations among nonlinearity, derivative, and e-derivative of Boolean functions. The methods to solve the nonlinearity are derived based on those relationships, thus solving the problem that it’s difficult to calculate the nonlinearity only in accordance with the definition.