Balanced $$2^k$$ 2 k -variable rotation symmetric Boolean functions with optimal algebraic immunity

Abstract

Rotation symmetric Boolean functions have been extensive studied because of their importance in cryptography. These functions are invariant under circular translation of indices. In this paper, we propose a new construction of \(2^k\)-variable balanced rotation symmetric Boolean functions with optimal algebraic immunity. The nonlinearity of our new functions is significantly higher than all previously obtained even-variable rotation symmetric Boolean functions with optimal algebraic immunity.