Por favor, use este identificador para citar o enlazar este ítem:
http://cimat.repositorioinstitucional.mx/jspui/handle/1008/1007| Metaheuristics in the Optimization of Cryptographic Boolean Functions | |
| ISAAC LOPEZ LOPEZ | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Funciones booleanas | |
| The aim of the research presented in this thesis is to proof that diversity-based metaheuristics are able to generate Boolean Functions (BFs) with high nonlinearity. The best results known for 10-variable BFs correspond to algebraic constructions and the metaheuristics have never been successful generating such BFs. Metaheuristics have obtained BFs with suboptimal nonlinearity and this thesis shows that by incorporating a proper control of diversity and adequately designed cost function, results are improved further. We have proposed a new cost function to guide the search based on considering more information from the Walsh Hadamard Transform (WHT). Instead of using only one value of the WHT, we employ the two maximum absolute values that appear and their number of appearances. It is also proposed a diversity-based metaheuristic that allows us to explore a large amount of regions in the search space. The thesis focuses on the design of a novel evolutionary memetic algorithm that incorporates a clustering technique coupled with a diversity-based replacement strategy. Typical diversity management techniques force to all the BFs to contribute to the diversity, however, in the technique designed for the thesis is allowed that some BFs form clusters to promote both exploration and exploitation at each phase of the algorithm. We call this algorithm as: Memetic Algorithm with Clusters coupled with a Replacement with Elite based Dynamic Diversity Control with Clustering (MAC-REDDCC). The MAC-REDDCC algorithm is the first of its kind according to the best of our knowledge. The MAC-REDDCC method proposed is able to overcome all the existing results found by traditional metaheuristics and is able to reach the results obtained with algebraic constructions by incorporating a simple algebraic technique such as initialization. This implies that a diversity-based method is able to generate BFs with high nonlinearity. The MAC-REDDCC method is even better than all traditional methods to generate BFs with high nonlinearity and has a successful performance when comparing with algebraic constructions. | |
| 03-04-2019 | |
| Tesis de maestría | |
| CIENCIA DE LOS ORDENADORES | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
Cargar archivos:
| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| TE 731 (2).pdf | 2.08 MB | Adobe PDF | Visualizar/Abrir |