Paper 2005/130

Results on Rotation Symmetric Boolean Functions on Even Number Variable

pinhui ke, changzhu ling, and wenqiao yan

Abstract

Construction of Boolean functions with cryptographic properties is an important and difficult work. In this paper, we concentrate on rotation symmetric Boolean functions(RSBFs), which are invariant under circular translation of indices. Recent research show that this class of Boolean function is rich in functions of cryptographic signifinance. In this paper, we consider the RSBFs on even number variable. We show that the matrix ${}_n\mathcal{A}$ may result in a better form after rearrange the representative elements. This allows us to improved the search strategy. At last, some combinaatorial results about ${\mathcal{P}}_n^1$ , which only apear in the case $n$ even, are presented in the case $n=2p$, $p$ be odd prime.