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On the impossibility of an invariant attack on Kuznyechik
Journal of Computer Virology and Hacking Techniques. 2022. Vol. 18. P. 61–67.
Fomin D.
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 ways of constructing invariant subsets. A new approach to invariant attacks is presented and it proves that there are no subsets based on S-Box properties that are invariant under round functions of Kuznyechik.
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
Added: August 30, 2026
Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
Added: August 29, 2026
Avdoshin S.M., Patrushev K. A., Proceedings of the Institute for System Programming of the RAS 2026 No. 4 часть 2 P. 245–256
The cardinality-constrained Markowitz problem is NP-hard and traditionally solved with commercial MIQP solvers. Following the 2022 export restrictions that rendered both commercial MIQP software and cloud quantum platforms (IBM Quantum, D-Wave Leap) inaccessible from the Russian Federation, practitioners require open-source alternatives. This paper systematically compares three solver families for the discrete mean-variance problem: two open-source ...
Added: August 27, 2026
Zaikin A., Vlasenko D., Zakharov D. et al., Diagnostics 2026 Vol. 16 No. 17 P. 1–15
Background/Objectives: Synolitic graphs (SGs) were developed for task-based fMRI, where
edge weights encode the discriminative power of pairwise regional features; whether similar
information can be recovered from resting-state data was untested. We benchmarked
SGs for autism spectrum disorder (ASD) classification using the multisite ABIDE-I dataset
(871 subjects: 403 subjects with ASD, 468 typical controls; 17 sites; CC200 atlas). Methods:
Using ...
Added: August 27, 2026
Melnikov I., Pelinovsky E., Nonlinear Dynamics 2026 No. 114 Article 934
Pyramidal solitons (solitons with more than two inflection points) of the generalized Korteweg–de Vries (KdV) equation are investigated. Necessary and sufficient conditions for the existence of such structures are presented. Within the framework of the generalized Gardner equation — the simplest model that admits pyramidal solitons as solutions — it is shown that these solutions ...
Added: August 27, 2026
Тула: Тульский государственный педагогический университет им. Л.Н. Толстого, 2025.
Сборник содержит материалы, представленные на XXIV Международной конференции «Алгебра, теория чисел, дискретная геометрия и многомасштабное моделирование: современные проблемы, приложения и проблемы истории», посвящённой 110-летию со дня рождения академика Юрия Владимировича Линника и 110-летию со дня рождения профессора Андрея Борисовича Шидловского и 80-летию со дня рождения профессора Геннадия Ивановича Архипова. Материалы конференции будут полезны научным работникам, ...
Added: August 27, 2026
Nesterenko A., Чирский В. Г., Матвеев В. Ю., Чебышевский сборник 2026 Т. 27 № 2 С. 118–127
The article presents the results of a practical study of the statistical properties of some sequences that are values of functions of a special type. ...
Added: August 26, 2026
Eduard Sopin, Nazarin A., Begishev V. et al., IEEE Transactions on Vehicular Technology 2026 Vol. 75 No. 6 P. 10995–11007
Aimed at rate-greedy applications having extreme requirements for the data rate at the air interface, 5G New Radio (NR) systems may experience problems when the number of user equipment (UE) in the coverage of the cell increases due to limited capacity of the physical downlink control channel (PDCCH).The aim of this study is to explore ...
Added: August 26, 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
Chukhno A., Курочкин А. В., Фомичев В. М., Прикладная дискретная математика. Приложение 2022 Т. 15 С. 73–77
In this paper, new results of the analysis of the KB 256-3 block cipher algorithm are outlined. We set up a difference relation with probability 1 for the six-round algorithm under study and propose a key recovery method using this difference relation for the nine-round KB 256-3 algorithm. We construct an impossible differential for the ...
Added: May 6, 2024
М. А. Коврижных, Д. Б. Фомин, Прикладная дискретная математика 2022 № 57 С. 5–21
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 ...
Added: October 8, 2022
Маршалко Г. Б., Денисенко Д. В., Рудской В. И. et al., Journal of Experimental and Theoretical Physics 2019 Vol. 128 No. 4 P. 552–559
Following the approach proposed in [3], we estimate resources of a quantum computer required for solving the key search problem of block cipher algorithms Kuznechik and Magma, defined by the national standard GOST R 34.12-2015, with the use of Grover’s quantum algorithm. ...
Added: October 7, 2022
G. B. Marshalko, Rudskoy V. I., Математические вопросы криптографии 2020 Vol. 11 No. 2 P. 99–110
We study the possibility of applying related key attacks to cryptographic devices with hybrid key systems, when a session key is generated from a long-term «classical» key and a key generated via quantum key distribution (QKD). For the simplest system that XORes quantum key and long-term key we study the impact of compromising the «quantum» ...
Added: October 7, 2022
Karakaya E., Sarı E., Alatas S., Resources Policy 2021 Vol. 70 Article 101904
This study investigates the main driving forces behind material use of the EU in the case of heterogeneity between member states with paying special attention to the comparison of domestic material consumption (DMC) with material footprint (MF). To this end, we first classify countries into several clubs based on time-varying behavior of two material use indicators and ...
Added: September 23, 2022
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
Perov A., Инновации в жизнь 2016 № 2(17) С. 89–97
The statistical analysis of iterative block ciphers is carried out for detection of dependences of statistical properties of output sequence depending on number of rounds. It is reasonable to utilize source codes available in the Internet, but their integration into own programs is impeded by at least the following reasons. Firstly, different implementations have different ...
Added: November 1, 2021
Perov A., Вестник НГУЭУ 2016 № 3 С. 290–298
A survey of some important scientic directions in the sphere of symmetric cryptography is presented. We emphasize problems connected with weak keys, with statistical analysis of symmetric algorithms and with investigation of iterative constructions. Some problems, specic to stream ciphers, iterative block ciphers and cryptographic hash-functions, are considered. We also advocate practical significance of scientic ...
Added: November 1, 2021
Perov A., Пестунов А. И., Прикладная дискретная математика 2020 № 3 С. 46–56
The paper explores possibility of applying convolutional neural networks to the security analysis of iterative block ciphers. A new approach for constructing distinguishing
attacks based on a convolutional neural network is proposed. The approach is based
on distinguishing between graphic equivalents of ciphertexts received by the CTR
(counter) encryption mode after different number of rounds, including the number
of ...
Added: November 1, 2021