TY - GEN
T1 - Hyper-bent Boolean Functions and Evolutionary Algorithms
AU - Mariot, Luca
AU - Jakobovic, Domagoj
AU - Leporati, Alberto
AU - Picek, Stjepan
PY - 2019
Y1 - 2019
N2 - Bent Boolean functions play an important role in the design of secure symmetric ciphers, since they achieve the maximum distance from affine functions allowed by Parseval’s relation. Hyper-bent functions, in turn, are those bent functions which additionally reach maximum distance from all bijective monomial functions, and provide further security towards approximation attacks. Being characterized by a stricter definition, hyper-bent functions are rarer than bent functions, and much more difficult to construct. In this paper, we employ several evolutionary algorithms in order to evolve hyper-bent Boolean functions of various sizes. Our results show that hyper-bent functions are extremely difficult to evolve, since we manage to find such functions only for the smallest investigated size. Interestingly, we are able to identify this difficulty as not lying in the evolution of hyper-bent functions itself, but rather in evolving some of their components, i.e. bent functions. Finally, we present an additional parameter to evaluate the performance of evolutionary algorithms when evolving Boolean functions: the diversity of the obtained solutions.
AB - Bent Boolean functions play an important role in the design of secure symmetric ciphers, since they achieve the maximum distance from affine functions allowed by Parseval’s relation. Hyper-bent functions, in turn, are those bent functions which additionally reach maximum distance from all bijective monomial functions, and provide further security towards approximation attacks. Being characterized by a stricter definition, hyper-bent functions are rarer than bent functions, and much more difficult to construct. In this paper, we employ several evolutionary algorithms in order to evolve hyper-bent Boolean functions of various sizes. Our results show that hyper-bent functions are extremely difficult to evolve, since we manage to find such functions only for the smallest investigated size. Interestingly, we are able to identify this difficulty as not lying in the evolution of hyper-bent functions itself, but rather in evolving some of their components, i.e. bent functions. Finally, we present an additional parameter to evaluate the performance of evolutionary algorithms when evolving Boolean functions: the diversity of the obtained solutions.
KW - Bent functions
KW - Evolution strategies
KW - Genetic algorithms
KW - Genetic programming
KW - Hyper-bent functions
UR - http://www.scopus.com/inward/record.url?scp=85064943323&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-16670-0_17
DO - 10.1007/978-3-030-16670-0_17
M3 - Conference contribution
AN - SCOPUS:85064943323
SN - 978-3-030-16669-4
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 262
EP - 277
BT - Genetic Programming
A2 - Sekanina, Lukas
A2 - Hu, Ting
A2 - Richter, Hendrik
A2 - García-Sánchez, Pablo
A2 - Lourenço, Nuno
PB - Springer
CY - Cham
T2 - 22nd European Conference on Genetic Programming, EuroGP 2019, held as part of EvoStar 2019
Y2 - 24 April 2019 through 26 April 2019
ER -