I. Moskovchenko, A. Kuznetsov, S. Kavun et al. / International Journal of Computing, 18(3) 2019, 265-277 Print ISSN 1727-6209
[email protected] On-line ISSN 2312-5381 www.computingonline.net International Journal of Computing HEURISTIC METHODS FOR THE DESIGN OF CRYPTOGRAPHIC BOOLEAN FUNCTIONS Illarion Moskovchenko 1,2), Alexandr Kuznetsov 2,3), Sergii Kavun 4), Berik Akhmetov 5), Ivan Bilozertsev 2,3), Serhii Smirnov 6) 1) Ivan Kozhedub Kharkiv National Air Force University, Sumska str., 77/79, Kharkiv, 61023, Ukraine 2) V. N. Karazin Kharkiv National University, Svobody sq., 6, Kharkiv, 61022, Ukraine,
[email protected],
[email protected],
[email protected] 3) JSC “Institute of Information Technologies”, Bakulin St., 12, Kharkiv, 61166, Ukraine 4) Kharkiv University of Technology “STEP”, Malom’yasnitska st. 9/11, 61010, Kharkiv, Ukraine,
[email protected] 5) Yessenov University, 32 microdistricts, 130003, Aktau, The Republic of Kazakhstan,
[email protected] 6) Central Ukrainian National Technical University, University Avenue 8, Kropyvnytskyi, 25006, Ukraine,
[email protected] Paper history: Abstract: In this article, heuristic methods of hill climbing for cryptographic Received 20 November 2018 Boolean functions satisfying the required properties of balance, nonlinearity, Received in revised form 28 June 2019 Accepted 10 September 2019 autocorrelation, and other stability indicators are considered. A technique for Available online 30 September 2019 estimating the computational efficiency of gradient search methods, based on the construction of selective (empirical) distribution functions characterizing the probability of the formation of Boolean functions with indices of stability not lower than required, is proposed. As an indicator of computational efficiency, an average number of attempts is proposed to be performed using a heuristic Keywords: method to form a cryptographic Boolean function with the required properties.