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Об эвристическом подходе к построению биективных векторных булевых функций с заданными криптографическими характеристиками
Прикладная дискретная математика. Приложение. 2021. № 14. С. 181–184.
Коврижных М. А., Fomin D.
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.
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
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
Ivanov N., Rubtsov A. A., Vyalyi M., , in: Descriptional Complexity of Formal Systems. 26th IFIP WG 1.02 International Conference, DCFS 2025 Loughborough, UK, July 22–24, 2025. Proceedings.: Springer, 2025. P. 137–150.
Added: August 24, 2025
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
Дехтярь М. И., Dudakov S., Карлов Б. Н., Тверь: Тверской государственный университет, 2021.
Учебное пособие адресовано изучающим курс дискретной математики, прежде всего, студентам младших курсов, обучающимся по направлениям укрупненных групп 01.03.00 "Математика и механика", 02.03.00 "Компьютерные и информационные науки", 09.03.00 "Информатика и вычислительная техника".
Настоящий сборник задач является пособием для практических занятий по некоторым разделам дискретной математики и может быть использован преподавателями и студентами для подготовки к семинарским занятиям и ...
Added: November 12, 2023
Дехтярь М. И., Dudakov S., Карлов Б. Н., Тверь: Тверской государственный университет, 2021.
Учебник содержит лекционный материал по дисциплине "Дискретная математика", а также примеры задач с решениями и задачи для самостоятельной работы. Основные разделы учебника: множества, математическая индукция, комбинаторика, булевы функции, логика высказываний и предикатов, графы, автоматы и формальные языки, алгоритмы.
Учебник адресован, прежде всего, студентам младших курсов, обучающихся по направлениям укрупненных групп 01.03.00 "Математика и механика", 02.03.00 "Компьютерные ...
Added: November 12, 2023
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
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
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