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

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.