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Inverting Cryptographic Hash Functions via Cube-and-Conquer

Journal of Artificial Intelligence Research 2024年 81卷 359-399页

作者： Zaikin, Oleg Novosibirsk State University Novosibirsk630090 Russia Matrosov Institute for System Dynamics and Control Theory SB RAS Irkutsk664033 Russia

MD4 and MD5 are fundamental cryptographic hash functions proposed in the early 1990s. MD4 consists of 48 steps and produces a 128-bit hash given a message of arbitrary finite size. MD5 is a more secure 64-step extension of MD4. Both MD4 and MD5 are vulnerable to practical collision attacks, yet it is still not realistic to invert them, i.e., to find a message given a hash. In 2007, the 39-step version of MD4 was inverted by reducing to SAT and applying a CDCL solver along with the so-called Dobbertin’s constraints. As for MD5, in 2012 its 28-step version was inverted via a CDCL solver for one specified hash without adding any extra constraints. In this study, Cube-and-Conquer (a combination of CDCL and lookahead) is applied to invert step-reduced versions of MD4 and MD5. For this purpose, two algorithms are proposed. The first one generates inverse problems for MD4 by gradually modifying the Dobbertin’s constraints. The second algorithm tries the cubing phase of Cube-and-Conquer with different cutoff thresholds to find the one with the minimum runtime estimate of the conquer phase. This algorithm operates in two modes: (i) estimating the hardness of a given propositional Boolean formula;(ii) incomplete SAT solving of a given satisfiable propositional Boolean formula. While the first algorithm is focused on inverting step-reduced MD4, the second one is not area-specific and is therefore applicable to a variety of classes of hard SAT instances. In this study, 40-, 41-, 42-, and 43-step MD4 are inverted for the first time via the first algorithm and the estimating mode of the second algorithm. Also, 28-step MD5 is inverted for four hashes via the incomplete SAT solving mode of the second algorithm. For three hashes out of them, it is done for the first time. © 2024 The Authors.

关键词： Geometry

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On a Global Search in Bilevel Optimization Problems with a Bimatrix Game at the Lower Level 23rd

On a Global Search in Bilevel Optimization Problems with ...

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23rd International Conference on Mathematical Optimization theory and Operations Research, MOTOR 2024

作者： Orlov, Andrei V. Matrosov Institute for System Dynamics and Control Theory of SB of RAS Irkutsk Russia

ISBN: (纸本)9783031627910

This paper addresses one class of bilevel optimization problems (BOPs) with an equilibrium at the lower level (in optimistic statement). Namely, we study BOPs with a convex quadratic optimization problem under linear constraints at the upper level and with a parametric non-normalized bimatrix game at the lower one, where we need to find a Nash equilibrium. In order to construct numerical methods for the problem in question, first, we transform the original bilevel problem into a single-level nonconvex optimization problem by replacing the lower level with its optimality conditions. Then we apply the Exact Penalization theory and Global Search theory (GST) to the resulting problem. According to the standard research of nonconvex problems by the GST, we construct the d.c. representations of all nonconvex functions from the original statement (into the differences of two convex functions), formulate the Global Optimality Conditions in terms of reduced penalized problem, and develop local and global search method taking into account the specific of problem in question. The main feature of the developed methods consists in the possibility of varying the penalty parameter within the methods themselves. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

关键词： Numerical methods

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Modeling Agent Behavior in Interacting Microgrids 10

Modeling Agent Behavior in Interacting Microgrids

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10th International Conference on Information Technology and Nanotechnology, ITNT 2024

作者： Bychkov, Igor Feoktistov, Alexander Chekan, Mikhail Matrosov Institute For System Dynamics And Control Theory Of Sb Ras Irkutsk Russia

ISBN: (纸本)9798350372939

We propose the agent-based approach to intellectualize data processing and analysis in modeling the operations of interconnected microgrids. Microgrids are modern energy systems with a large share of environmentally friendly and resource-saving equipment. The modeling of different aspects for the organization and operation of microgrids is relevant for their structural and parametric optimization. The study of these aspects in the interaction of microgrids deserves special attention. In this case, it becomes possible to take into account the synergistic effect in the distribution and consumption of electric power. We implement the modeling process using a multi-agent system. In this regard, we describe the structure of this system, methods of its construction, and goals and processes of agent operations. In addition, we provide a model of agent behavior developed based on the basis of a finite-state control machine. The advantages of the proposed approach are demonstrated on a model example of balancing generation and consumption of electric power. © 2024 IEEE.

关键词： Balancing

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dynamics of Bipartite Logical Networks 47

Dynamics of Bipartite Logical Networks

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47th ICT and Electronics Convention, MIPRO 2024

作者： Oparin, G.A. Bogdanova, V.G. Pashinin, A.A. Matrosov Institute For System Dynamics And Control Theory Of Sb Ras Irkutsk Russia

ISBN: (纸本)9798350382495

Based on the Boolean constraints method several problems of qualitative analysis of bipartite logical networks are solved. The dynamics of the trajectories behavior of these networks is studied over a finite time interval. A method is proposed for splitting a bipartite trajectory into two independent trajectories based on deterministic block-sequential updating of the state vectors of each part. Conditions for the existence, isolation and attraction of cyclic trajectories of a given length are obtained as Boolean constraints. The solvability of such equations reduces to the well-known Boolean satisfiability problem, effectual algorithms for solving which provide dynamic analysis for systems with high dimensionality of the state vector over large discrete time intervals. The program modules implementation for building Boolean constraints and checking their feasibility in the form of microservices ensures their reuse, simplification of deployment, updating, and high scalability in the cloud environment. Multi-agent computation management in an applied microservices package provides the non-procedural problem formulation on a distributed model of the subject area, forms and executes a scheme for solving it, and automates the additional resources provision. The practical significance of the obtained results consists in providing the opportunity for a more detailed study of dynamics of the molecular features of gene regulation networks. © 2024 IEEE.

关键词： Trajectories

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Solvability of Quasilinear Integral–Algebraic Equations

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Journal of Mathematical Sciences (United States) 2024年第6期279卷 756-762页

作者： Bulatov, Mikhail Solovarova, Liubov Matrosov Institute for System Dynamics and Control Theory SB RAS 134 Lermontova St Irkutsk 664033 Russian Federation

We study quasilinear systems of integral equations that are linear with respect to the principal part and nonlinear with respect to the integral term. We formulate sufficient conditions for the local existence of a unique smooth solution to such a system in terms of matrix pencils and provide some examples. We study quasilinear systems of integral equations that are linear with respect to the principal part and nonlinear with respect to the integral term. We formulate sufficient conditions for the local existence of a unique smooth solution to such a system in terms of matrix pencils and provide some examples. © Springer Nature Switzerland AG 2024.

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On some properties of the Fredholm-type integral algebraic equations

On some properties of the Fredholm-type integral algebraic e...

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作者： Chistyakov, Viktor F. Chistyakova, Elena V. Laboratory for Differential Equations and Control Systems Institute for System Dynamics and Control Theory SB RAS Irkutsk Russia

In this paper, we study systems of Fredholm integral equations with a singular matrix multiplying the leading part. We address the solvability issues of such systems with separable kernels and, similarly to differenti... 详细信息

关键词： Fredholm integral equations

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Binary Dynamic Models of Structural Synthesis of Programs 46

Binary Dynamic Models of Structural Synthesis of Programs

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46th ICT and Electronics Convention, MIPRO 2023

作者： Oparin, G.A. Bogdanova, V.G. Pashinin, A.A. Matrosov Institute for System Dynamics and Control Theory of SB RAS Irkutsk Russia

ISBN: (纸本)9789532331042

In this paper, we propose a matrix-vector Boolean differential model for constructing plans of computational actions in solving non-procedural problems on a computational model of a modular software system. The conditions of the problem of structural synthesis of a program from pre-implemented modules are formulated as a system of Boolean differential equations, the solutions of which, under given initial conditions (consistent with the non-procedural formulation of the problem), determine the solvability of the problem and give constructive plans for its solution (including parallel ones). The proposed method of structural synthesis is focused on high-dimensional models. It allows highly efficient software implementation due to the high parallelism of performing vector-matrix operations on binary vectors at the level of machine instructions. The developed model is used for planning computations in packages of applied microservices based on the HPCSOMAS-MSC platform. © 2023 MIPRO Croatian Society.

关键词： Differential equations

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Efficient Heuristics for a Partial Set Covering Problem with Mutually Exclusive Pairs of Facilities 1

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7th International Conference on Optimization, Simulation and control, COSC 2022

作者： Belykh, Aleksander Gruzdeva, Tatyana Ushakov, Anton Vasilyev, Igor Matrosov Institute for System Dynamics and Control Theory of SB RAS Irkutsk Russia

ISBN: (数字)9783031412295

ISBN: (纸本)9783031412288

Set cover problems are among the most popular and well-studied models in facility location. In this paper, we address an extension of the set covering and partial set covering problems. We suppose that a set of customers to be served is divided into two non-overlapped subsets: "mandatory" customers who must always be covered and "optional" customers who do not require obligatory coverage. To avoid a trivial solution that covers only customers from H, we suppose that the number of covered optional customers must be at least larger than a pre-defined threshold In the real world, local laws may prohibit location of a large number of facilities in some places to reduce harm to people and/or nature. To reflect that fact our problem involves pairs of facilities that are mutually exclusive, hence if a facility from such a pair is located, another one is prohibited. We formulate this problem as an integer linear program and develop and implement several fast heuristic approaches capable of finding high-quality solutions of large-scale problem instances arisen in real-life settings. In particular, we develop a hybrid heuristic involving a greedy algorithm and local search embedded into a variable neighborhood framework. We test our algorithms in a series of intensive computational experiments on both real-life problems and synthetically generated instances. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

关键词： Location

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A Three-Stage Numerical Approach to the Study of Extra-Large Atomic-Molecular Clusters 15th

A Three-Stage Numerical Approach to the Study of Extra-La...

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15th International Conference on Optimization and Applications, OPTIMA 2024

作者： Gornov, Alexander Anikin, Anton Sorokovikov, Pavel Zarodnyuk, Tatiana Matrosov Institute for System Dynamics and Control Theory of SB RAS Lermontov Str. 134 Irkutsk664033 Russia

ISBN: (纸本)9783031791185

The article discusses a novel approach for optimizing atomic-molecular structures in extra-large clusters, focusing on reducing computational complexity and applying parallel computing techniques. A three-stage computation process is outlined, offering benefits over traditional algorithms by efficiently navigating through multi-extremal optimization challenges. The software, based on this methodology, demonstrated high efficacy in solving complex molecular dynamics problems. When comparing the outcomes with experimental data, no significant deviations from the expected patterns in potential values were detected. The developed three-stage numerical approach proved instrumental in solving optimization tasks for extra-large atomic-molecular systems. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Molecular dynamics

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Reversible integer approximation of color space transforms for lossless compression of big color raster data

Computer Optics

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Computer Optics 2022年第3期46卷 492-505页

作者： Hmelnov, A.E. ISDCT SB RAS – Matrisov Institute for System Dynamics and Control Theory of Siberian Branch of RAS Lermontova 134 Irkutsk664033 Russia

Reversible integer transforms are or great importance for lossless compression algorithms. To perform reversible decorrelation of color channels we propose an algorithm for calculating parameters of a reversible integer transform, which approximates such continuous mappings as a discrete Karunen-Loeve transform. We propose a method for estimating the approximation errors, which makes it possible to choose an optimal approximation of the original transform that minimizes these errors. Using the MRG file format, intended for storing large amounts of integer raster data, as an example, we show that after applying decorrelation, it is possible to increase the compression ratio of multichannel raster images using lossless compression algorithms. © 2022, Institution of Russian Academy of Sciences. All rights reserved.

关键词： Color

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