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Information × Registration Number 0219U101714, 0118U005441 , R & D reports Title The study of mathematical methods for the analysis of singularities of Boolean functions and their use for the analysis of cryptographic systems popup.stage_title Head Koniushok Sergii M., Кандидат технічних наук Registration Date 21-10-2019 Organization Institute of Special Communication and Information Protection National Technical University of Ukraine "Igor Sikorsky Kyiv Politechnic Institute" popup.description2  The object of the study is to evaluate and justify the stability of cryptographic algorithms and protocols against cryptanalysis methods. The purpose of the work is research of existing and creation of new mathematical methods of analysis of properties of Boolean functions from the point of view of their use for estimation of stability of cryptographic algorithms and protocols, application of the obtained results in studying of disciplines of special department № 1. Research Methods are methods of Boolean function theory, linear algebra, probability theory, and mathematical statistics. The work is aimed at solving a scientific problem, the essence of which is to develop mathematical methods for analyzing the properties of Boolean functions in terms of their use to evaluate the stability of cryptographic algorithms and protocols, which includes: development of a method of recognition -dimension of Boolean functions (BF), given by oracles; development of polynomial algorithms for estimating the distance between the Boolean function and the multiple-dimensional BF; development of a method for constructing -dimensional BF approximations, given by oracles. As a result of the research work, a method of recognition of the BF dimensions measured by oracles was developed, polynomial algorithms for estimating the distance between the BF and the multidimensional BF, the method for constructing high-dimensional Boolean functions and the method for substantiating the absence of high-probability features. The results obtained in the research work can be used in the educational process of the special department № 1 during lectures and practical training in the disciplines “Fundamentals of cryptography”, “Mathematical methods for constructing and analyzing symmetric cryptosystems”, “Cryptographic Protocols”. Product Description popup.authors Ischenko Anatolii O. Bondarenko Yulia L. Vasylenko Serhii V. Hyrenko Ihor M. Kondakova Anastasiia M. Koniushok Sergii M. Marchenko Andriy O. Mostiuk Dmytro L. Олексійчук Антон Миколайович Puchkov Alexander O. Synytsyna Nataliya G. Stepaniyk Petro P. Tarapata Oleh P. Уваркіна Олена Василівна popup.nrat_date 2020-04-02 Close