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Telecommunications and Radio Engineering

Publicado 12 números por año

ISSN Imprimir: 0040-2508

ISSN En Línea: 1943-6009

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HEURISTIC METHODS OF GRADIENT SEARCH FOR THE CRYPTOGRAPHIC BOOLEAN FUNCTIONS

Volumen 78, Edición 10, 2019, pp. 879-899
DOI: 10.1615/TelecomRadEng.v78.i10.40
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A. A. Kuznetsov
V. Karazin National University of Kharkiv, 4 Svobody Sq., Kharkiv 61022, Ukraine
I. V. Moskovchenko
University of Customs and Finance, 2/4Volodymyra Vernadskoho St., Dnipro 49000, Ukraine
D. I. Prokopovych-Tkachenko
I. Kozhedub Kharkiv National Air Force University, 77/79 Sumska St., Kharkiv 61023, Ukraine
T. Y. Kuznetsova
I. Kozhedub Kharkiv National Air Force University, 77/79 Sumska St., Kharkiv 61023, Ukraine

SINOPSIS

Heuristic methods of gradient search of the cryptographic Boolean functions that satisfy the required properties of balance, nonlinearity, autocorrelation, and other stability indicators are considered. The proposed method of gradient descent is investigated, in particular, estimates of nonlinearity and correlation immunity of the synthesized Boolean functions are given. A method for evaluating the computational efficiency of gradient search methods is proposed, based on the construction of sample (empirical) distribution functions, which characterize the probability of the formation of the Boolean functions with persistence indicators not lower than those required. As an indicator of computational efficiency, we propose the average number of attempts that need to be performed using the heuristic method to form a cryptographic Boolean function with the required properties. It is shown that the proposed gradient descent method allows the formation of cryptographic functions with the required durability indicators in fewer steps. The results of investigations of the cryptographic properties of the formed Boolean functions in comparison with the best known assessments are given.

PALABRAS CLAVE: heuristic methods, cryptographic Boolean functions, symmetric cryptography, nonlinear substitute blocks
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CITADO POR

  1. Potii Oleksandr, Poluyanenko Nikolay, Stelnyk Igor, Revak Iryna, Kavun Sergii, Kuznetsova Tetiana, Nonlinear-Feedback Shift Registers for Stream Ciphers, 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON), 2019. Crossref

  2. Gorbenko Ivan, Kuznetsov Alexandr, Gorbenko Yurii, Pushkar'ov Andriy, Kotukh Yevgen, Kuznetsova Kateryna, Random S-Boxes Generation Methods for Symmetric Cryptography, 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON), 2019. Crossref

  3. Krasnobaev Victor, Dyachenko Andrey, Kuznetsova Tetiana, Panchenko Volodymir, Ulianovska Yuliia, Methods for Monitoring and Diagnosing Data in the Residue Class, 2019 International Conference on Information and Telecommunication Technologies and Radio Electronics (UkrMiCo), 2019. Crossref

  4. Kuznetsov Alexandr, Horkovenko Inna, Maliy Olena, Goncharov Nikita, Kuznetsova Tetiana, Kovalenko Nikolaj, Non-Binary Cryptographic Functions for Symmetric Ciphers, 2020 IEEE International Conference on Problems of Infocommunications. Science and Technology (PIC S&T), 2020. Crossref

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