Metaheuristics in the Optimization of Cryptographic Boolean Functions
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. Thi...
Main Authors: | , , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2020-09-01
|
Series: | Entropy |
Subjects: | |
Online Access: | https://www.mdpi.com/1099-4300/22/9/1052 |
id |
doaj-588c41e47d1b4b808fffc9a9c4416352 |
---|---|
record_format |
Article |
spelling |
doaj-588c41e47d1b4b808fffc9a9c44163522020-11-25T03:47:02ZengMDPI AGEntropy1099-43002020-09-01221052105210.3390/e22091052Metaheuristics in the Optimization of Cryptographic Boolean FunctionsIsaac López-López0Guillermo Sosa-Gómez1Carlos Segura2Diego Oliva3Omar Rojas4Centro de Investigación en Matemáticas A.C. (CIMAT). Área de Computación, Jalisco S/N, Col. Valenciana, Guanajuato 36023, MexicoFacultad de Ciencias Económicas y Empresariales, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, MexicoCentro de Investigación en Matemáticas A.C. (CIMAT). Área de Computación, Jalisco S/N, Col. Valenciana, Guanajuato 36023, MexicoIN3-Computer Science Department, Universitat Oberta de Catalunya, 08860 Castelldefels, SpainFacultad de Ciencias Económicas y Empresariales, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, MexicoGenerating 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.https://www.mdpi.com/1099-4300/22/9/1052boolean functionmetaheuristicsnonlinearitycryptographyhadamard transformentropy |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Isaac López-López Guillermo Sosa-Gómez Carlos Segura Diego Oliva Omar Rojas |
spellingShingle |
Isaac López-López Guillermo Sosa-Gómez Carlos Segura Diego Oliva Omar Rojas Metaheuristics in the Optimization of Cryptographic Boolean Functions Entropy boolean function metaheuristics nonlinearity cryptography hadamard transform entropy |
author_facet |
Isaac López-López Guillermo Sosa-Gómez Carlos Segura Diego Oliva Omar Rojas |
author_sort |
Isaac López-López |
title |
Metaheuristics in the Optimization of Cryptographic Boolean Functions |
title_short |
Metaheuristics in the Optimization of Cryptographic Boolean Functions |
title_full |
Metaheuristics in the Optimization of Cryptographic Boolean Functions |
title_fullStr |
Metaheuristics in the Optimization of Cryptographic Boolean Functions |
title_full_unstemmed |
Metaheuristics in the Optimization of Cryptographic Boolean Functions |
title_sort |
metaheuristics in the optimization of cryptographic boolean functions |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2020-09-01 |
description |
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. |
topic |
boolean function metaheuristics nonlinearity cryptography hadamard transform entropy |
url |
https://www.mdpi.com/1099-4300/22/9/1052 |
work_keys_str_mv |
AT isaaclopezlopez metaheuristicsintheoptimizationofcryptographicbooleanfunctions AT guillermososagomez metaheuristicsintheoptimizationofcryptographicbooleanfunctions AT carlossegura metaheuristicsintheoptimizationofcryptographicbooleanfunctions AT diegooliva metaheuristicsintheoptimizationofcryptographicbooleanfunctions AT omarrojas metaheuristicsintheoptimizationofcryptographicbooleanfunctions |
_version_ |
1724503819844321280 |