Construction of Odd-Variable Resilient Boolean Functions with Optimal Degree

摘要

In this paper, we investigate the problem of obtaining new construction methods for resilient Boolean functions. Given n (n odd and n ≥ 35), we firstly provide degree optimized 1-resilient n-variable functions with currently best known nonlinearity. Then we extend our method to obtain m-resilient (m > 1) Boolean functions with degree n-m-1, we show that these Boolean functions also achieve currently best known nonlinearity. Finally, the algebraic immunity and immunity against fast algebraic attack of the obtained Boolean functions are investigated.