Two Boolean functions with five-valued Walsh spectra and high nonlinearity

TL;DR

This paper introduces two balanced Boolean functions with five-valued Walsh spectra and high nonlinearity, using a novel method for evaluating exponential sums over finite fields, enhancing cryptographic security.

Contribution

The paper presents two new balanced Boolean functions with specific spectral properties and high nonlinearity, along with a novel evaluation method for exponential sums.

Findings

Functions have low Walsh spectra and high nonlinearity.

New method for evaluating exponential sums over finite fields.

Enhances cryptographic security through improved Boolean functions.

Abstract

For cryptographic systems the method of confusion and diffusion is used as a fundamental technique to achieve security. Confusion is reflected in nonlinearity of certain Boolean functions describing the cryptographic transformation. In this paper, we present two balanced boolean functions which have low Walsh spectra and high nonlinearity. In the proof of the nonlinearity, a new method for evaluating some exponential sums over finite fields was provided.