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Of all publications in the section: 4
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Article
Гребнев С. В., Лазарева Е. В., Лебедев П. А. и др. Прикладная дискретная математика. Приложение. 2018. № 11. С. 62-65.

We consider implementation of the TLS 1.3 protocol taking into account the experience of Russian researchers and developers, as well as national regulations. We subsequently propose a modification of the protocol which fixes several issues. The changes concern the way of interaction between parties in different modes of connection, cryptographic primitives and the key system of the protocol.  

Added: Dec 12, 2018
Article
Фомин Д. Б., Трифонов Д. И. Прикладная дискретная математика. Приложение. 2019. № 12. С. 134-137.

The paper studies the issues of implementation of one class of S-Boxes on FPGA and ASIC and compares them with the implementation of arbitrary mappings V8 → V8. The way of implementation of arbitrary S-Box is studied. It’s shown that any S-Box over V8 can be implemented using 40 LUTs (812 GE). For one class of S-Boxes over V8 with high cryptographic properties, the possibility of their implementation using 19 LUTs (147 GE) is shown.

Added: Oct 6, 2019
Article
Коврижных М. А., Фомин Д. Б. Прикладная дискретная математика. Приложение. 2021. № 14. С. 181-184.

Bijective vector Boolean functions (permuta- tions) are used as nonlinear primitives of many symmetric ciphers. In this paper, we study a generalized construction of (2m, 2m)-functions using monomial and arbitrary m-bit per- mutations as constituent elements. A heuristic algorithm for obtaining bijective Boolean functions with given nonlinearity and differential uniformity, based on this construction, is proposed. For this, a search is carried out for auxiliary permutations of a lower dimension using the ideas of spectral-linear and spectral-difference methods. The proposed algorithm consists of iterative multiplication of the initial randomly generated 4-bit permutations by transposition, selecting the best ones in nonlinearity, the differential uniformity, and the corresponding values in the linear and differential spectra among the obtained 8-bit permu- tations. The possibility of optimizing the calculation of cryptographic properties at each iteration of the algorithm is investigated; 8-bit 6-uniform permutations with nonlinearity 108 are experimentally obtained.

Added: Sep 22, 2021
Article
Фомин Д. Б. Прикладная дискретная математика. Приложение. 2021. № 14. С. 51-55.

The paper studies new ways of con- structing differentially 2δ-uniform bijections over F_{2^{2m}} , m≥3, that are based on TU-construction. Some well known results on the constructing differentially 4-uniform permutations over F_{2^{2m}} are generalized in this work. The core idea is to use TU-construction and differentially δ-uniform bijections to construct 2^t · δ-uniform permutations. A generalized method for constructing 2m-bit differentially 4-uniform permutations is proposed, and new constructions of differentialy 6 and 8-uniform permutations are introduced.

Added: Sep 22, 2021