Construction of 1-resilient boolean functions with optimal algebraic immunity and good nonlinearity
Senshan Pan, Xiaotong Fu, Weiguo Zhang · 2011
This paper presents a construction for a class of 1-resilient Boolean functions with optimal algebraic immunity on an even number of variables by dividing them into two correlation classes, i.e. equivalence classes. From which, a nontrivial pair of functions has been found by applying the generating matrix. For n is small (e.g. n = 6), a part of these functions achieve almost optimal nonlinearity. Apart from their good nonlinearity, the functions reach Siegenthaler’s [16] upper bound of algebraic degree. Furthermore, a class of 1-resilient functions on any number n> 2 of variables with at least sub-optimal algebraic immunity is provided.