Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity

Sen-Shan Pan, Xiao-Tong Fu, Wei-Guo Zhang
2011 Journal of Computer Science and Technology  
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
more » ... c degree. Furthermore, a class of 1-resilient functions on any number n > 2 of variables with at least sub-optimal algebraic immunity is provided.
doi:10.1007/s11390-011-9433-6 fatcat:wixo5sppdrfnjdt77rzyi5gbd4