Metaheuristics in the Optimization of Cryptographic Boolean Functions

Abstract

Generating Boolean Functions (BFs) with high nonlinearity is a complex task that is usually addresses through algebraic constructions. Metaheuristics have also been applied extensively to this task. However, metaheuristics have not been able to attain so good results as the algebraic techniques. This paper proposes a novel diversity-aware metaheuristic that is able to excel. This proposal includes the design of a novel cost function that combines several information from the Walsh Hadamard Transform (WHT) and a replacement strategy that promotes a gradual change from exploration to exploitation as well as the formation of clusters of solutions with the aim of allowing intensification steps at each iteration. The combination of a high entropy in the population and a lower entropy inside clusters allows a proper balance between exploration and exploitation. This is the first memetic algorithm that is able to generate 10-variable BFs of similar quality than algebraic methods. Experimental results and comparisons provide evidence of the high performance of the proposed optimization mechanism for the generation of high quality BFs.

Evolving Nonlinear S-Boxes With Improved Theoretical Resilience to Power Attacks

“…As a counterpart, algebraic constructions ensure optimal cryptographic properties with respect to linear and differential cryptanalysis. Finally, the heuristic approach to the generation of S-boxes is an attempt to maintain the randomness present in the structure of pseudo-random generated S-boxes, with properties as close as possible to the ones present in algebraic constructions [57]. Moreover, heuristic methods can be used to improve properties related to side-channel attacks in the search for a good trade-off between cryptographic properties.…”

Discovering Non-Linear Boolean Functions by Evolving Walsh Transforms with Genetic Programming

“…In [22], Clark et al optimized good-quality Boolean functions by using a Simulated Annealing algorithm [23]. Lopez et al [24] presented a novel diversity-aware meta-heuristic for non-linearity maximization of Boolean functions that exploits a cost function that adopts the Walsh-Hadamard Transform (WHT) to gather useful information for the task at hand.…”