Secondary Constructions of Bent Functions and Highly Nonlinear Resilient Functions

TL;DR

This paper introduces new methods for constructing bent and resilient functions with high nonlinearity, expanding the toolkit for cryptographic function design through secondary and generalized constructions.

Contribution

It presents a novel secondary construction for bent functions and a generalized method for resilient functions with high nonlinearity, including concrete examples.

Findings

New secondary construction of bent functions from existing ones

Generalized construction for resilient functions with high nonlinearity

Concrete examples of bent functions derived from specific initial functions

Abstract

In this paper, we first present a new secondary construction of bent functions (building new bent functions from two already defined ones). Furthermore, we apply the construction using as initial functions some specific bent functions and then provide several concrete constructions of bent functions. The second part of the paper is devoted to the constructions of resilient functions. We give a generalization of the indirect sum construction for constructing resilient functions with high nonlinearity. In addition, we modify the generalized construction to ensure a high nonlinearity of the constructed function.