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Polynomial-Time Key-Recovery Attacks Against NTRURe Encrypt from ASIACCS'15

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Journal of Systems Science & Complexity 2024年第3期37卷 1308-1325页

作者： LIU Zhen PAN Yanbin ZHENG Jinwei school of Cyber Science and Technology Hubei Key Laboratory of Applied Mathematics Hubei University Key Laboratory of mathematics Mechanization Academy of Mathematics and Systems Science Chinese Academy of SciencesSchool of Mathematical Sciences University of Chinese Academy of Sciences Key Laboratory of mathematics Mechanization Academy of Mathematics and Systems Science Chinese Academy of Sciences school of Mathematical sciences University of Chinese Academy of Sciences

In ASIACCS 2015, Nu nez, et al. proposed a proxy re-encryption scheme, named NTRURe Encrypt, based on NTRU, which allows a proxy to translate ciphertext under the delegator’s public key into a re-encrypted ciphertext that can be decrypted correctly by delegatee’s private key. Because of the potential resistance to quantum algorithm, high efficiency and various applications in real life,NTRURe Encrypt has drawn lots of attention and its security has been widely discussed and analyzed.In PQCrypto2019, Liu, et al. proposed two key recovery attacks against it. However, their first attack heavily relies on a weaken decryption oracle, and the second attack needs to collect about 260ciphertexts from the same message by theoretical analysis, which makes both of the attacks unrealistic. In this paper, inspired by the broadcast attack against NTRU, the authors find out that for NTRURe Encrypt the delegator and the delegatee can efficiently recover each other’s private key in polynomial time without any unrealistic assumptions. In addition, the authors also show how to fix NTRURe Encrypt to resist the proposed attacks. As a by-product, the authors also show how to commit broadcast attacks against NTRU 2001 with even dg, which was thought infeasible before.

关键词： Broadcast attack key recovery NTRU NTRUReEncrypt

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Approximate Weak Minimal Solutions of Set-Valued Optimization Problems

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Journal of the Operations Research Society of China 2023年第3期11卷 673-692页

作者： S.Khoshkhabar-amiranloo school of mathematics Institute for Research in Fundamental SciencesTehranIran

This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions are investigated.Some topological properties and existence theorems of these solutions are given.It is shown that for set-valued optimization problems with upper(outer)cone-semicontinuous objective values or closed objective maps the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed.By using the polar cone and two scalarization processes,some necessary and sufficient optimality conditions in the sense of vector and set criteria are provided.

关键词： Set-valued optimization Approximate weak minimal solutions Existence theorems Optimality conditions Scalarization functions

2-local unstable homotopy groups of indecomposable A32-complexes

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Science China mathematics 2024年第3期67卷 607-626页

作者： Zhongjian Zhu Jianzhong Pan College of mathematics and Physics Wenzhou University Hua Loo-Keng Key Laboratory of mathematics Institute of MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences school of Mathematical sciences University of Chinese Academy of Sciences

In this paper,we calculate the 2-local unstable homotopy groups of indecomposable A32-complexes.The main technique used is analysing the homotopy property of J(A,X),defined by Gray(1973) for a CW-pair(X,A),which is ho... 详细信息

关键词： homotopy groups A 2 n -complexes fibration sequence relative James construction 55P15

Neighbor Sum Distinguishing Edge Coloring of Subcubic Graphs

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Acta Mathematica Sinica,English Series 2017年第2期33卷 252-262页

作者： Xiao Wei YU Guang Hui WANG Jian Liang WU Gui Ying YAN school of mathematics Shandong University school of mathematics Academy of Mathematics and System SciencesChinese Academy of Sciences

A proper edge-k-coloring of a graph G is a mapping from E（G） to {1, 2,..., k} such that no two adjacent edges receive the same color. A proper edge-k-coloring of G is called neighbor sum distinguishing if for each edge uv ∈ E（G）, the sum of colors taken on the edges incident to u is different from the sum of colors taken on the edges incident to v. Let X（G ） denote the smallest value k in such a ＇ G coloring of G. This parameter makes sense for graphs containing no isolated edges （we call such graphs normal）. The maximum average degree mad（G） of G is the maximum of the average degrees of its non-empty subgraphs. In this paper, we prove that if G is a normal subcubic graph with mad（G）〈 5 then x＇（G） ≤ 5. We also prove that if G is a normal subcubic graph with at least two 2-vertices, 6 colors are enough for a neighbor sum distinguishing edge coloring of G, which holds for the list version as well.

关键词： Proper edge coloring neighbor sum distinguishing edge coloring maximum average de-gree subcubic graph planar graph

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Critical observability of partially observed discrete event systems under cyber attacks

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Science China(Information sciences) 2024年第2期67卷 333-334页

作者： Liyun TONG Jinling LIANG Yang LIU Department of mathematics School of SciencesHangzhou Dianzi University school of mathematics Southeast University College of mathematics and Computer Science Zhejiang Normal University

The discrete event system(DES) is a dynamic system driven by asynchronous/sudden events and has been widely used in many critical infrastructures, such as electric transportation networks and intelligent transportatio...

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Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations

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Numerical mathematics(Theory,Methods and Applications) 2022年第1期15卷 165-199页

作者： Dongdong Liang Wei Gong Xiaoping Xie school of mathematics Sichuan UniversityChengdu 610064China LSEC Institute of Computational MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences&School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100190China

In this paper,we consider parabolic distributed control problems with cost functional of pointwise observation type either in space or in time.First,we show the well-posedness of the optimization problems and derive the first order optimality systems,where the adjoint state can be expressed as the linear combination of solutions to two backward parabolic equations that involve the Dirac delta distribution as source either in space or in time.Second,we use a space-time finite element method to discretize the control problems,where the state variable is approximated by piecewise constant functions in time and continuous piecewise linear polynomials in space,and the control variable is discretized by following the variational discretization concept.We obtain a priori error estimates for the control and state variables with order O(k 12+h)up to a logarithmic factor under the L 2-norm.Finally,we perform several numerical experiments to support our theoretical results.

关键词： Parabolic optimal control problem pointwise observation space-time finite element method parabolic PDE with Dirac measure error estimate

A note on exponential convergence of Cesàro weighted Birkhoff average and multimodal weighted approach

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Acta Mathematica Sinica,English Series 2024年

作者： Zhicheng TONG Yong LI school of mathematics Jilin University school of mathematics and Statistics Center for Mathematics and Interdisciplinary Sciences Northeast Normal University

This note concerns the rapid uniform convergence of Cesàro weighted Birkhoff averages via irrational rotations on tori under certain conditions, involving arbitrary polynomial and exponential convergence rate. We discuss both finite dimensional and infinite dimensional cases, and give Diophantine rotations as examples. These provide the universality of rapid convergence for Cesàro weighted type, which is quite different from Lp(p> 1) convergence for the unweighted one. We also show a certain optimality about our convergence rate. Besides, we introduce a multimodal weighted approach to adapt to the data sparsity, which still preserves exponential convergence.

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Finite time blow-up for heat flows of self-induced harmonic maps

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Acta Mathematica Sinica,English Series 2023年

作者： Bo CHEN Youde WANG school of Mathematical sciences University of Chinese Academy of Sciences school of mathematics South China University of Technology Hua Loo-Keng Key Laboratory of mathematics Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences school of mathematics and Information sciences Guangzhou University

Let Mnbe an embedded closed submanifold of Rk+1or a smooth bounded domain in Rn,where n ≥ 3. We show that the local smooth solution to the heat flow of self-induced harmonic map defined in(1.3) or(1.4) will blow up at a finite time, provided that the initial map u0is in a suitable nontrivial homotopy class with energy small enough.

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Study of gravitational sedimentation of flexible, permeable circular and planktonic particle applying the immersed boundary method

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International Journal of Sediment Research 2023年第5期38卷 643-652页

作者： Rekha Panghal Sudeshna Ghosh Department of mathematics Amity School of Applied Sciences Amity University Haryana

The gravitational settling of a flexible, permeable circular and planktonic particle drenched in a fluid which is assumed to be Newtonian and incompressible along with being viscous was studied. A mathematical formulation and numerical simulations of the studied problem were done by applying the Immersed Boundary Method(IBM) in a two-dimensional fluid domain. Parametric studies were done for analyzing the impact of varying flexibilities and permeabilities with reference to settling velocity(terminal velocity) and shape deformation of the particle. The terminal velocity and permeability of the particle are directly proportional. It was observed that for fixed permeability, the terminal velocity increases when increasing the flexibility of the particle.

关键词： Immersed Boundary Method (IBM) Sedimentation Incompressible fluid Flexible particle Permeable particle Settling velocity