Weightwise perfectly balanced functions with high weightwise nonlinearity profile

TL;DR

This paper introduces a new class of weightwise perfectly balanced Boolean functions with high weightwise nonlinearity, important for cryptographic applications like the FLIP stream cipher, and provides bounds demonstrating their strong nonlinearity properties.

Contribution

It presents a novel class of WPB functions not affinely equivalent to existing ones, analyzes their nonlinearity profile, and establishes lower bounds showing their high nonlinearity.

Findings

New class of WPB functions with high weightwise nonlinearity

Lower bounds on k-weightwise nonlinearity for powers of 2

Subclass with recursively proven high nonlinearity profile

Abstract

Boolean functions with good cryptographic criteria when restricted to the set of vectors with constant Hamming weight play an important role in the recent FLIP stream cipher. In this paper, we propose a large class of weightwise perfectly balanced (WPB) functions, which is not extended affinely (EA) equivalent to the known constructions. We also discuss the weightwise nonlinearity profile of these functions, and present general lower bounds on $k$-weightwise nonlinearity, where $k$ is a power of $2$. Moreover, we exhibit a subclass of the family. By a recursive lower bound, we show that these subclass of WPB functions have very high weightwise nonlinearity profile.