New constructions of even-variable rotation symmetric Boolean functions with maximum algebraic immunity

Rotation symmetric Boolean functions (RSBFs), which are invariant under circular translations, have been used as components of some different cryptosystems. In this paper, we study the constructions of even-variable RSBFs with maximum algebraic immunity (AI). First, we present a new construction class of even-variable RSBFs with maximum AI, which has totally n/2−1n/2−1 different constructions. And then in order to get even-variable RSBFs which achieve both maximum AI and high nonlinearity, an improved construction is proposed.