?
Об эвристическом алгоритме построения подстановок с заданными криптографическими характеристиками с использованием обобщённой конструкции
Прикладная дискретная математика. 2022. № 57. С. 5–21.
М. А. Коврижных, Д. Б. Фомин
In this paper, we study a generalized construction of (2m, 2m)-functions using monomial and arbitrary m-bit permutations as constituent elements. We investigate the possibility of constructing bijective vectorial Boolean functions (permutations) with specified cryptographic properties that ensure the resistance of encryption algorithms to linear and differential methods of cryptographic analysis. We propose a heuristic algorithm for obtaining permutations with the given nonlinearity and differential uniformity based on the generalized construction. For this purpose, we look for auxiliary permutations of a lower dimension using the ideas of the genetic algorithm, spectral-linear, and spectral-difference methods. In the case of m = 4, 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 permutations. We show how to optimize the calculation of cryptographic properties at each iteration of the algorithm. Experimental studies of the most interesting, from a practical point of view, 8-bit permutations have shown that it is possible to construct 6-uniform permutations with nonlinearity 108.
Mylnikov L., Slivnitsin P., Engineering Applications of Artificial Intelligence 2026 Vol. 179 Article 115185
The paper describes a applied artificial intelligence task of recognition-by-components method of real objects based on the recognition of a limited set of primitives or components. The recognition-by-components makes it possible to determine the components, that compose an object, and increase the number of recognizable objects without degrading the recognition quality. Training is performed on ...
Added: May 29, 2026
Gorbounov Vassily, Kazakov A., Data Analytics and Topology 2025 Vol. 1 No. 1 P. 33–45
A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on X which is either observed directly or derived from a data set.
For an electrical network there are two functions on the set of the nodes defined by the resistance matrix and the response ...
Added: May 28, 2026
Mokienko O., Zisman M. A., Bobrov P. et al., American Journal of Physical Medicine and Rehabilitation 2026 Vol. 105 No. 6 P. 555–563
Brain-computer interfaces (BCIs) represent a promising technology for restoring lower limb motor functions and gait after stroke. The application of BCIs in this field is supported by a limited number of studies. The objective of the review was to systematically and critically evaluate the current evidence on the use of BCIs for lower limb function ...
Added: May 28, 2026
М.: Институт проблем управления им. В.А. Трапезникова РАН, 2024.
В сборник вошли материалы VIII Международной научной конференции «Информационные технологии и технические средства управления» (ICCT-2024). На конференции были рассмотрены вопросы, касающиеся перспектив развития научного приборостроения в телекоммуникационных и управляющих системах, биомедицинской информатики, аппаратного и программного обеспечения информационнокоммуникационных систем, надежности, диагностики и неразрушающего контроля, систем управления и автоматизации, цифровых экосистем, управления производством и логистикой, методов математического ...
Added: May 27, 2026
Degtyarev A., Bakhurin S., Yudin N., DSPA 2026 P. 1–6
This paper investigates one possible solution to the problem of self-interference cancellation (SIC) arising in the design of in-band full-duplex (IBFD) communication systems. Self-interference cancellation is performed in the digital domain using multilayer nonlinear models adapted via gradient-based optimization. The presence of local minima and saddle points during the adaptation of multilayer models limits the ...
Added: May 26, 2026
Ilyashenko Y., Shilin I., Stanislav Minkov, Russian Journal of Mathematical Physics 2026 Vol. 33 No. 1 P. 89–106
In this paper, new numerical invariants of structurally unstable vector fields in the plane
are found. One of the main tools is an improved asymptotics of sparkling saddle connections that
occur when a separatrix loop of a hyperbolic saddle breaks. Another main tool is a new topological
invariant of two arithmetic progressions, both perturbed and unperturbed, on the ...
Added: May 26, 2026
Androsov I., Proceedings of the Institute for System Programming of the RAS 2026 Vol. 38 No. 3 P. 87–114
This paper examines echo state networks (ESNs), one of the most prevalent approaches to
implementing reservoir computing. An ESN consists of a recurrent neural network with fixed (untrained)
weights and a readout layer that is typically linear and trainable. This approach enables the creation of energyefficient and computationally efficient neural networks capable of real-time learning. However, since ...
Added: May 26, 2026
Gusev I., Maksaev A., Promyslov V., Journal of Mathematical Sciences 2025 Vol. 299 No. 6
The regular graph of the space of n × m matrices over a field F is defined as the undirected graph whose vertices are matrices of rank min(n, m), and distinct matrices A and B are connected by an edge if and only if rk(A + B) < min(n, m). In this paper, for |F| ...
Added: May 25, 2026
Караваева Е. А., Кулигин Л. А., Rezunik L. et al., Труды Института системного программирования РАН 2026 Т. 38 № 3 С. 67–94
В статье представлен метод рефакторинга исходного кода на основе интеграции большой языковой модели (LLM) и расширенной UML-модели программного кода. Предложенный подход позволяет выявлять проблемные участки кода с использованием функций тревожности и структурных метрик классов, а затем выполнять автоматизированный рефакторинг. Ключевой особенностью метода является использование LLM для генерации формальных спецификаций на языке OCL (Object Constraint Language), ...
Added: May 24, 2026
Tyukin I., Tyukina T., van Helden D. P. et al., Information Sciences 2024 Vol. 678 Article 120856
AI errors pose a significant challenge, hindering real-world applications. This work introduces a novel approach to cope with AI errors using weakly supervised error correctors that guarantee a specific level of error reduction. Our correctors have low computational cost and can be used to decide whether to abstain from making an unsafe classification. We provide ...
Added: May 23, 2026
Zaikin A., Sviridov I., Sosedka A. et al., Technologies 2026 Vol. 14 No. 2 Article 84
High-dimensional tabular data are common in biomedical and clinical research, yet conventional machine learning methods often struggle in such settings due to data scarcity, feature redundancy, and limited generalization. In this study, we systematically evaluate Synolitic Graph Neural Networks (SGNNs), a framework that transforms high-dimensional samples into sample-specific graphs by training ensembles of low-dimensional pairwise ...
Added: May 23, 2026
Chertopolokhov V., Mukhamedov A., Bugriy G. et al., IEEE Access 2026 Vol. 14 P. 14369–14392
This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov–Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization–projection–devectorization implementation suitable for ...
Added: May 22, 2026
Морозов С. В., Calcolo 2026 Vol. 63 No. 2 Article 23
The approximation of tensors in a low-para metric format is a crucial component in many mathematical modelling and data analysis tasks. Among the widely used low-parametric representations, the canonical polyadic (CP) decomposition is known to be very efficient. Nowadays, most algorithms for CP approximation aim to construct the approximation in the Frobenius norm; however, some ...
Added: May 22, 2026
Loshkareva M. E., Matveeva N., Вестник Томского государственного университета. История 2026 № 100 С. 112–118
This research is an endeavor to apply social network analysis (SNA) to the study of a medieval narrative source. The authors suppose that the use of network analysis may offer new possibilities in the study of the history of regions characterized by some political fragmentation. Authors tried to construct networks of historical interactions from 1193 ...
Added: May 22, 2026
Kodaneva N., Lando S., Journal of Geometry and Physics 2025 Vol. 210 Article 105421
Weight systems are functions on chord diagrams satisfying so-called Vassiliev’s 4-term relations. They are closely related to finite type knot invariants, see [31 Certain weight systems can be derived from graph invariants, see a recent account in [19]. Another main source of weight systems are Lie algebras, the construction due to D. Bar-Natan [3] and ...
Added: January 23, 2025
Vasilii A. Gromov, Philip S. Baranov, Complexity 2023 Vol. 2023 Article 6689371
This paper introduces several novel strategies for multi-step-ahead prediction of chaotic time series. Introducing a concept of “generalized z-vectors” (vectors of nonsuccessive time series observations) makes it possible to generate sets of possible prediction values for each point we are trying to predict. +rough examining these sets, uni8ed predictions are calculated, which are in turn ...
Added: September 22, 2023
I. V. Kolokolov, V. V. Lebedev, Tumakova M. M., Journal of Experimental and Theoretical Physics 2023 Vol. 136 No. 6 P. 785–794
We investigate fluctuations of vorticity inside a coherent vortex generated by the inverse energy cascade in two-dimensional turbulence. Temporal and spatial correlations can be characterized by the pair correlation function. The interaction of fluctuations leads to a nonzero third moment of vorticity. We analyze the
pair correlation function and the third moment using a model in ...
Added: June 8, 2023
I. P. Koroleva (Kikot), Kosevich Y. A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2023 Vol. 107 No. 5 Article 054217
The paper is devoted to analytical and numerical studies of the effects of nonlinearity on the two-path phonon
interference in the transmission through two-dimensional arrays of atomic defects embedded in a lattice. The
emergence of transmission antiresonance (transmission node) in the two-path system is demonstrated for the
few-particle nanostructures, which allow us to model both linear and nonlinear ...
Added: May 18, 2023
D. B. Fomin, M. A. Kovrizhnykh, Математические вопросы криптографии 2022 Vol. 13 No. 2 P. 37–52
The work is dedicated to the theoretical substantiation of a directed search for 8-bit permutations with given cryptographic properties: differential uniformity and nonlinearity. The statements on the partition of the set of vectorial Boolean functions derived using generalized construction into equivalence classes are proved. The statements that allow one to reject functions from equivalence classes ...
Added: August 24, 2022
Parfenyev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2022 Vol. 106 No. 2 Article 025102
It is well known that an inverse turbulent cascade in a finite ($2 \pi \times 2 \pi$) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly correlated in time, random ...
Added: August 10, 2022
Teplova T., Gurov S., Annals of Operations Research 2025 Vol. 352 P. 441–469
Using high-frequency transaction-level data for liquid Russian stocks, we empirically reveal a joint nonlinear relationship between the average trade size, log-return variance per transaction, trading volume, and the asset price level described by the Intraday Trading Invariance hypothesis. The relationship is also confirmed during stock market crashes. We show that the invariance principle explains a ...
Added: April 26, 2022
Fomin D., Journal of Computer Virology and Hacking Techniques 2022 Vol. 18 P. 61–67
Currently numerous cryptographic systems are based on SP-networks. These primitives are supposed to be secure but recent investigations show that some attacks are possible. The aim of this work is to study how secure the Russian standardized block cipher Kuznyechik over invariant attacks. We study the already known decompositions of its permutation and show the ...
Added: November 29, 2021
Fomin D., 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 ...
Added: September 22, 2021