Finding Boolean functions suitable for cryptographic primitives is a complex combinatorial optimization problem, since they must satisfy several properties to resist cryptanalytic attacks, and the space is very large, which grows super exponentially with the number of input variables. Recent research has focused on the study of Boolean functions that satisfy properties on restricted sets of inputs due to their importance in the development of the FLIP stream cipher. In this paper, we consider one such property, perfect balancedness, and investigate the use of Genetic Programming (GP) and Genetic Algorithms (GA) to construct Boolean functions that satisfy this property along with a good nonlinearity profile. We formulate the related optimization problem and define two encodings for the candidate solutions, namely the truth table and the weightwise balanced representations. Somewhat surprisingly, the results show that GA with the weightwise balanced representation outperforms GP with the classical truth table phenotype in finding highly nonlinear Weightwise Perfectly Balanced (WPB) functions. This is in stark contrast to previous findings on the evolution of balanced Boolean functions, where GP always performs best.

Mariot, L., Picek, S., Jakobovic, D., Djurasevic, M., Leporati, A. (2022). Evolutionary Construction of Perfectly Balanced Boolean Functions. In 2022 IEEE Congress on Evolutionary Computation, CEC 2022 - Conference Proceedings (pp.1-8). IEEE [10.1109/CEC55065.2022.9870427].

Evolutionary Construction of Perfectly Balanced Boolean Functions

Mariot L.;Leporati A.
2022

Abstract

Finding Boolean functions suitable for cryptographic primitives is a complex combinatorial optimization problem, since they must satisfy several properties to resist cryptanalytic attacks, and the space is very large, which grows super exponentially with the number of input variables. Recent research has focused on the study of Boolean functions that satisfy properties on restricted sets of inputs due to their importance in the development of the FLIP stream cipher. In this paper, we consider one such property, perfect balancedness, and investigate the use of Genetic Programming (GP) and Genetic Algorithms (GA) to construct Boolean functions that satisfy this property along with a good nonlinearity profile. We formulate the related optimization problem and define two encodings for the candidate solutions, namely the truth table and the weightwise balanced representations. Somewhat surprisingly, the results show that GA with the weightwise balanced representation outperforms GP with the classical truth table phenotype in finding highly nonlinear Weightwise Perfectly Balanced (WPB) functions. This is in stark contrast to previous findings on the evolution of balanced Boolean functions, where GP always performs best.
paper
balancedness; Boolean functions; genetic algorithms; genetic programming; nonlinearity;
English
2022 IEEE Congress on Evolutionary Computation, CEC 2022 - 18-23 July 2022
2022
2022 IEEE Congress on Evolutionary Computation, CEC 2022 - Conference Proceedings
9781665467087
2022
1
8
reserved
Mariot, L., Picek, S., Jakobovic, D., Djurasevic, M., Leporati, A. (2022). Evolutionary Construction of Perfectly Balanced Boolean Functions. In 2022 IEEE Congress on Evolutionary Computation, CEC 2022 - Conference Proceedings (pp.1-8). IEEE [10.1109/CEC55065.2022.9870427].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/408488
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