Highly nonlinear balanced Boolean functions satisfying high degree propagation criterion
Jennifer Seberry · 1993
Three of the most important nonlinearity criteria for cryptographically strong functions are balancedness, nonlinearity and propagation criterion. In this paper we study systematic methods for constructing highly nonlinear balanced Boolean functions satisfying the high degree propagation criterion. In particular, we present a method for constructing highly nonlinear balanced Boolean functions on V 2k+1 satisfying the propagation criterion with respect to all but one vectors in V 2k+1 , and a method for constructing highly nonlinear balanced Boolean functions on V 2k satisfying the propagation criterion with respect to all but three vectors in V 2k . We then show that the vectors where the propagation criterion is not satisfied can be moved upward in such a way that the functions constructed on V 2k+1 satisfy the propagation criterion of degree 2k, while the function constructed on V 2k satisfy the propagation criterion of degree 4 3 k. The moving technique does not alter the balance...