Heuristic methods of gradient search for the cryptographic boolean functions

被引：0
|
作者：
Kuznetsov A.A. [1 ]
Moskovchenko I.V. [2 ]
Prokopovych-Tkachenko D.I. [3 ]
Kuznetsova T.Y. [3 ]
机构：
[1] V. Karazin National University of Kharkiv, 4 Svobody Sq., Kharkiv
[2] University of Customs and Finance, 2/4Volodymyra Vernadskoho St., Dnipro
[3] I. Kozhedub Kharkiv National Air Force University, 77/79 Sumska St., Kharkiv
来源：
Telecommunications and Radio Engineering (English translation of Elektrosvyaz and Radiotekhnika) | 2019年 / 78卷 / 10期
关键词：
Cryptographic Boolean functions; Heuristic methods; Nonlinear substitute blocks; Symmetric cryptography;
D O I：
10.1615/TelecomRadEng.v78.i10.40
中图分类号：
学科分类号：
摘要：
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. © 2019 Begell House Inc.. All rights reserved.
引用
收藏
页码：879 / 899
页数：20
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