Further construction of even-variable balanced rotation symmetric Boolean functions with optimal algebraic immunity

Abstract

The field of cryptography has given a lot of attention to rotation symmetric Boolean functions (RSBFs) because they possess special structures and include many functions with good cryptographic properties. It is difficult to construct even-variable balanced RSBFs with optimal algebraic immunity in the study on RSBFs. Recently, Mesnager et al. proposed the first and only construction of balanced RSBFs with optimal algebraic immunity for arbitrary even variables(Des. Codes Cryptogr. 89(1) (2021) 1-17). The nonlinearity of their functions is not high. In this paper, we develop further research based on their construction and present a fresh design of n-variable balanced RSBFs with optimal algebraic immunity for arbitrary even n. Our functions have higher nonlinearity compared to their functions. Furthermore, the algebraic degree and fast algebraic immunity of our functions are not less than n−2 for n not bigger than 16.