Proof of a Conjecture about Rotation Symmetric Functions

TL;DR

This paper proves a conjecture about rotation symmetric Boolean functions of degree 3, establishing their nonlinearity, which is crucial for cryptographic applications.

Contribution

The paper provides a proof for Cusik and Stnic's conjecture on degree 3 rotation symmetric Boolean functions, determining their nonlinearity.

Findings

Conjecture about degree 3 RSBFs is proven.

Nonlinearity of degree 3 RSBFs is explicitly determined.

Results enhance understanding of cryptographic properties of RSBFs.

Abstract

Rotation symmetric Boolean functions have important applications in the design of cryptographic algorithms. In this paper, the Conjecture about rotation symmetric Boolean functions (RSBFs) of degree 3 proposed by Cusik and St\u{a}nic\u{a} is proved. As a result, the nonlinearity of such kind of functions is determined.