This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in assoc...This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler＇s upper bound of algebraic degree. Also a class of l-resilient functions on any number n 〉 2 of variables with at least sub-optimal algebraic immunity is provided.展开更多
基金supported by the National Natural Science Foundations of China under Grant Nos. 60903200,61003299
文摘This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler＇s upper bound of algebraic degree. Also a class of l-resilient functions on any number n 〉 2 of variables with at least sub-optimal algebraic immunity is provided.
