Maximum correlation analysis of nonlinear combining functions in stream ciphers

Abstract

The maximum correlation of a Boolean function to all Boolean functions of a subset of its input variables is investigated. A relationship is derived between the maximum correlation and the mutual information between the output of a balanced Boolean function and a subset of its random input variables. For bent functions (which are never balanced), both the mutual information and the maximum correlation are bounded and shown to be small in a strong sense. © 2000 International Association for Cryplologic Research.