Constructions of 1-Resilient Boolean Functions with High Nonlinearity and Good Algebraic Degree

摘要

Three of the most essential criteria for cryptographically strong Boolean functions are resiliency,high nonlinearity and high algebraic degree.We give a technique for constructing 1-resilient Boolean functions with high nonlinearity via modifying PS-class bent functions.The main technique is to extend the support of bent functions in PS-class by additionally defining two different plateaued functions on two suitably chosen subspaces.A large class of highly nonlinear 1-resilient functions which were not known earlier are obtained.