An evolutionary multiobjective approach to design highly non-linear Boolean functions

Abstract

The proliferation of all kinds of devices with different security requirements and constraints, and the arms-race nature of the security problem are increasingly demanding the development of tools to help on the automatic design of Boolean functions with security application. Nowadays, the design of strong cryptographic Boolean functions is a multiobjective problem. However, so far evolutionary multiobjective algorithms have been largely overlooked and not much is known about this problem from a multiobjective optimization perspective. In this work we focus on non-linearity related criteria and explore a multiobjective evolutionary approach aiming to find several balanced functions of similar characteristics satisfying multiple criteria. We show that the multiobjective approach is an efficient alternative to single objective optimization approaches presented so far. We also argue that it is a better framework for automatic design of cryptographic Boolean functions.