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Metaheuristics in the Optimization of Cryptographic Boolean Functions

Centro de Investigación en Matemáticas A.C. (CIMAT). Área de Computación, Jalisco S/N, Col. Valenciana, Guanajuato 36023, Mexico
Facultad de Ciencias Económicas y Empresariales, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico
IN3-Computer Science Department, Universitat Oberta de Catalunya, 08860 Castelldefels, Spain
Depto. de Ciencias Computacionales, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara C.P. 44430, Jalisco, Mexico
Author to whom correspondence should be addressed.
Entropy 2020, 22(9), 1052;
Received: 3 September 2020 / Revised: 15 September 2020 / Accepted: 16 September 2020 / Published: 21 September 2020
(This article belongs to the Special Issue Entropy in Soft Computing and Machine Learning Algorithms)
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. View Full-Text
Keywords: boolean function; metaheuristics; nonlinearity; cryptography; hadamard transform; entropy boolean function; metaheuristics; nonlinearity; cryptography; hadamard transform; entropy
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MDPI and ACS Style

López-López, I.; Sosa-Gómez, G.; Segura, C.; Oliva, D.; Rojas, O. Metaheuristics in the Optimization of Cryptographic Boolean Functions. Entropy 2020, 22, 1052.

AMA Style

López-López I, Sosa-Gómez G, Segura C, Oliva D, Rojas O. Metaheuristics in the Optimization of Cryptographic Boolean Functions. Entropy. 2020; 22(9):1052.

Chicago/Turabian Style

López-López, Isaac, Guillermo Sosa-Gómez, Carlos Segura, Diego Oliva, and Omar Rojas. 2020. "Metaheuristics in the Optimization of Cryptographic Boolean Functions" Entropy 22, no. 9: 1052.

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