Evolving S-Boxes with Reduced Differential Power Analysis Susceptibility

Differential power analysis targets S-boxes to break ciphers that resist cryptanalysis. We relax cryptanalytic constraints to lower S-box leakage, as quantified by the transparency order. We apply genetic algorithms to generate 8-bit S-boxes, optimizing transparency order and nonlinearity as in existing work (Picek et al. 2015). We apply multiobjective evolutionary algorithms to generate a Pareto front. We find a tight relationship where nonlinearity drops substantially before transparency order does, suggesting the difficulty of finding S-boxes with high nonlinearity and low transparency order, if they exist. Additionally, we show that the cycle crossover yields more efficient single objective genetic algorithms for generating S-boxes than the existing literature. We demonstrate this in the first side-by-side comparison of the genetic algorithms of Millan et al. 1999, Wang et al. 2012, and Picek et al. 2015. Finally, we propose and compare several methods for avoiding fixed points in S-boxes; repairing a fixed point after evolution in a way that preserves fitness was superior to including a fixed point penalty in the objective function or randomly repairing fixed points during or after evolution.