International Association
for Cryptologic Research

The construction of Boolean functions with good cryptographic properties over subsets of vectors with fixed Hamming weight is significant for lightweight stream ciphers like FLIP. In this article, we propose a general method to construct a class of Weightwise Almost Perfectly Balanced (WAPB) Boolean functions using the action of a cyclic permutation group on $\mathbb{F}_2^n$. This class generalizes the Weightwise Perfectly Balanced (WPB) $2^m$-variable Boolean function construction by Liu and Mesnager to any $n$. We show how to bound the nonlinearity and weightwise nonlinearities of functions from this construction. Additionally, we explore two significant permutation groups, $\langle \psi \rangle$ and $\langle \sigma \rangle$, where $\psi$ is a binary-cycle permutation and $\sigma$ is a rotation. We theoretically analyze the cryptographic properties of the WAPB functions derived from these permutations and experimentally evaluate their nonlinearity parameters for $n$ between 4 and 10.