Conference paper

HUSA Jakub and DOBAI Roland. Designing Bent Boolean Functions With Parallelized Linear Genetic Programming. In: GECCO Companion '17 Proceedings of the Companion Publication of the 2017 on Genetic and Evolutionary Computation Conference. Berlín: Association for Computing Machinery, 2017, pp. 1825-1832. ISBN 978-1-4503-4939-0.
Publication language:english
Original title:Designing Bent Boolean Functions With Parallelized Linear Genetic Programming
Title (cs):Návrh bent boolovských funkcí pomocí pararelizovaného lineárního genetického programování
Pages:1825-1832
Proceedings:GECCO Companion '17 Proceedings of the Companion Publication of the 2017 on Genetic and Evolutionary Computation Conference
Conference:Genetic and Evolutionary Computation Conference 2017
Place:Berlín, DE
Year:2017
ISBN:978-1-4503-4939-0
DOI:10.1145/3067695.3084220
Publisher:Association for Computing Machinery
Keywords
Bent Boolean functions, nonlinearity, parallelization, linear programming.
Annotation
Bent Boolean functions are cryptographic primitives essential for the safety of cryptographic algorithms, providing a degree of non-linearity to otherwise linear systems. The maximum possible non-linearity of a Boolean function is limited by the number of its inputs, and as technology advances, functions with higher number of inputs are required in order to guarantee a level of security demanded in many modern applications. Genetic programming has been successfully used to discover new larger bent Boolean functions in the past. This paper proposes the use of linear genetic programming for this purpose. It shows that this approach is suitable for designing of bent Boolean functions larger than those designed using other approaches, and explores the influence of multiple evolutionary parameters on the evolution runtime. Parallelized implementation of the proposed approach is used to search for new, larger bent functions, and the results are compared with other related work. The results show that linear genetic programming copes better with growing number of function inputs than genetic programming, and is able to create significantly larger bent functions in comparable time.
Abstract
Bent Boolean functions are cryptographic primitives essential to safety of cryptographic algorithms, providing a degree nonlinearity to otherwise linear systems. Maximum possible nonlinearity of a Boolean function is limited by the number of it's inputs, and as technology advances, functions with higher number of inputs are required to guarantee a level of security, demanded in many modern applications. Two of the possible ways to design bent Boolean functions, are genetic programming and Cartesian genetic programming, both of which have been successfully used to discover new larger bent Boolean functions in the past. This paper proposes a new approach using linear genetic programming. It shows that this new approach is suitable for design of bent Boolean functions, and explores the influence of multiple evolutionary parameters on evolution run time. Parallelized implementation of the proposed approach is used to search for new, larger bent functions, and it's results are compared to those obtained in other related works. The results show that linear genetic programming copes better with growing number of function inputs than Cartesian genetic programming, and is able to create significantly larger bent functions in comparable time.
BibTeX:
@INPROCEEDINGS{
   author = {Jakub Husa and Roland Dobai},
   title = {Designing Bent Boolean Functions With Parallelized Linear
	Genetic Programming},
   pages = {1825--1832},
   booktitle = {GECCO Companion '17 Proceedings of the Companion Publication
	of the 2017 on Genetic and Evolutionary Computation
	Conference},
   year = {2017},
   location = {Berl{\'{i}}n, DE},
   publisher = {Association for Computing Machinery},
   ISBN = {978-1-4503-4939-0},
   doi = {10.1145/3067695.3084220},
   language = {english},
   url = {http://www.fit.vutbr.cz/research/view_pub.php?id=11402}
}

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