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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

A new perturbation to a critical elliptic problem with a variable exponent Dedicated to Professor Daomin Cao on the Occasion of His Sixtieth Birthday

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Science China mathematics 2023年第5期66卷 1021-1040页

作者： Zhongyuan Liu Peng Luo school of mathematics and statistics Henan UniversityKaifeng 475004China School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences Central China Normal UniversityWuhan 430079China

In this paper,we study the following critical elliptic problem with a variable exponent:{-Δu=u^(p+ϵa(x))inΩ,u>0 inΩ,u=0 on∂Ω,where a(x)2∈C^(2)(Ω),p=N+2/N-2,∈>0,andΩis a smooth bounded domain in R^(N)(N>4).We show that for∈small enough,there exists a family of bubble solutions concentrating at the negative stable critical point of the function a(x).This is a new perturbation to the critical elliptic equation in contrast to the usual subcritical or supercritical perturbation,and gives the first existence result for the critical elliptic problem with a variable exponent.

关键词： bubble solution critical elliptic problem variable exponent

On p-rank of even K-groups of rings of integers

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Acta Mathematica Sinica,English Series 2023年

作者： Meng Fai LIM school of mathematics and statistics & hubei key laboratory of mathematical sciences Central China Normal University

Let L/F be finite Galois extension of number fields of degree n and let p be a prime which does not divide n. We shall study the pj-rank of K2i(OL) via its Galois module structure following the approaches of Iwasawa and Komatsu-Nakano. Along the way, we generalize previous observations of Browkin, Wu and Zhou on K2-groups to higher even K-groups. We also give examples to illustrate our results. Finally, we apply our discussion to refine a result of Kitajima pertaining to the p-rank of even K-groups in the cyclotomic Zl-extension, where l≠p.

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ZERO DISSIPATION LIMIT TO A RAREFACTION WAVE WITH A VACUUM FOR A COMPRESSIBLE,HEAT CONDUCTING REACTING MIXTURE

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Acta Mathematica Scientia 2023年第6期43卷 2533-2552页

作者：苌生闯段然 school of mathematics and statistics Hubei Key Laboratory of MathematicalCentral China Normal UniversityWuhan 430079China

In this paper,we study the zero dissipation limit with a vacuum for the reacting mixture Navier-Stokes equations.For proper smooth initial data that the initial density tends to zero as the relevant physical coefficients tend to zero,we demonstrate that the solution tends to a rarefaction wave connected to a vacuum on the left side coupled with a zero mass fraction of reactant.What is more,the uniform convergence rate is obtained.

关键词： zero dissipation limit vacuum reacting mixture Navier-Stokes equations

MAPS PRESERVING THE NORM OF THE POSITIVE SUM IN L_(p) SPACES

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Acta Mathematica Scientia 2022年第2期42卷 789-794页

作者：郝晶晶董云柏李磊 school of mathematical sciences Nankai UniversityTianjin 300071China hubei key laboratory of Applied mathematics Faculty of Mathematics and StatisticsHubei UniversityWuhan 430062China school of mathematical sciences and LPMC Nankai UniversityTianjin 300071China

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关键词： Norm-additive mappings positive cones L_(p)spaces

SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRODINGER-POISSON SYSTEM WITH CRITICAL GROWTH

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数学物理学报:B辑英文版 2023年第5期43卷 2291-2308页

作者：邓引斌帅伟杨小龙 school of mathematics and statistics&hubei key laboratory of mathematical sciences Central China Normal UniversityWuhan 430079China school of mathematics and statistics Central China Normal UniversityWuhan 430079China

In this paper,we study the following Schrodinger-Poisson system with critical growth:■We establish the existence of a positive ground state solution and a least energy sign-changing solution,providing that the nonlin... 详细信息

关键词： Schrodinger-Poisson system ground state solution sign-changing solution critical growth

MINIMIZERS OF L2-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

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Acta Mathematica Scientia 2024年第3期44卷 984-996页

作者：陈彬高永帅郭玉劲吴越 hubei key laboratory of mathematical sciences school of mathematics and statistics Central China Normal University

This paper is concerned with the minimizers of L2-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of RN(N≥1).We prove that the problem admits minimizers for... 详细信息

关键词： decaying nonlinearity L 2 -subcritical minimizers bounded domains mass concentration 35J20 35Q40 46N50

POSITIVE SOLUTIONS FOR A KIRCHHOFF EQUATION WITH PERTURBED SOURCE TERMS

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Acta Mathematica Scientia 2022年第5期42卷 1817-1830页

作者： Narimane AISSAOUI 龙薇 school of mathematics and statistics Hubei Key Laboratory of Mathematical SciencesCentral China Normal UniversityWuhan 430079China College of mathematics and Information Science Jiangci Normal UniversityNanchang 330022China

This paper deals with the existence of positive solutions to the following nonlinear Kirchhoff equation with perturbed external source terms:{−(a+b∫_(R^(3))|∇u|^(2)dx)Δu+V(x)u=Q(x)u^(p)+εf(x),u>0,x∈R^(3),u∈H^(1)(R^(3)).Here a,b are positive constants,V(x),Q(x)are positive radial potentials,10 is a small parameter,f(x)is an external source term in L^(2)(R^(3))∩L^(∞)(R^(3)).

关键词： nonlinear Kirchhoff problem Lyapunov-Schmidt reduction positive solutions level set

Fractional Coloring Planar Graphs under Steinberg-type Conditions

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Acta Mathematica Sinica,English Series 2023年第5期39卷 904-922页

作者： Xiao Lan HU Jia Ao LI school of mathematics and statistics&hubei key laboratory of mathematical sciences Central China Normal UniversityWuhan 430079P.R.China school of mathematical sciences and LPMC Nankai UniversityTianjin 300071P.R.China

A Steinberg-type conjecture on circular coloring is recently proposed that for any prime p≥5,every planar graph of girth p without cycles of length from p+1 to p(p-2)is Cp-colorable(that is,it admits a homomorphism to the odd cycle Cp).The assumption of p≥5 being prime number is necessary,and this conjecture implies a special case of Jaeger’s Conjecture that every planar graph of girth 2p-2 is Cp-colorable for prime p≥5.In this paper,combining our previous results,we show the fractional coloring version of this conjecture is true.Particularly,the p=5 case of our fractional coloring result shows that every planar graph of girth 5 without cycles of length from 6 to 15 admits a homomorphism to the Petersen graph.

关键词： Fractional coloring circular coloring planar graphs girth homomorphism