Heuristic Search by Particle Swarm Optimization of Boolean Functions for Cryptographic Applications

Abstract

We present a Particle Swarm Optimizer for generating boolean functions with good cryptographic properties. The proposed algorithm updates the particles positions while preserving their Hamming weights, to ensure that the generated functions are balanced, and it adopts Hill Climbing to further improve their nonlinearity and correlation immunity. The results of the optimization experiments for n=7 to n=12 variables show that this new PSO algorithm finds boolean functions with good trade-offs of nonlinearity, resiliency and Strict Avalanche Criterion.