On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices
In this paper we consider matrices of special form introduced in [11] and used for the constructing of resilient functions with cryptographically optimal parameters. For such matrices we establish lower bound 1/log2(?5+1) = 0.5902... for the important ratio t/t+k of its parameters and point out that there exists a sequence of matrices for which the limit of ratio of these parameters is equal to lower bound. By means of these matrices we construct m-resilient n-variable functions with maximum possible nonlinearity 2n-1-2m+1 for m = 0.5902 . . . n+O (log2 n). This result supersedes the previous record.