Heuristic design of cryptographically strong balanced boolean functions

Abstract

Advances in the design of Boolean functions using heuristic techniques are reported. A genetic algorithm capable of generating highly nonlinear balanced Boolean functions is presented. Hill climbing techniques are adapted to locate balanced, highly nonlinear Boolean functions that also almost satisfy correlation immunity. The definitions for some cryptographic properties are generalised, providing a measure suitable for use as a fitness function in a genetic algorithm seeking balanced Boolean functions that satisfy both correlation immunity and the strict avalanche criterion. Results are presented demonstrating the effectiveness of the methods.