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Cryptanalysis of a lattice based key exchange protocol

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Science China(Information Sciences) 2017年第2期60卷 196-198页

作者： shaowu mao Pei ZHANG Houzhen WANG Huanguo ZHANG Wanqing WU Computer School of Wuhan University The Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education Huawei Technoligies Co. Ltd. School of Computer Science and Technology Hebei University

A lattice is a set of points in n-dimensional space with a periodic structure.Lattice-based cryptosystem holds a great promise for post-quantum cryptography[1],as they enjoy very strong security proofs based on the worst-case hardness,relatively efficient implementations,as well as great simplicity.The first lattice-based cryptosystem was proposed by Ajtai and Dwork[2],whose security is based on the lattice problems in the worstcase.After their seminal work,several latticebased cryptosystems have been proposed till now,

关键词： ISIS Bi Cryptanalysis of a lattice based key exchange protocol

Cryptanalysis of an asymmetric cipher protocol using a matrix decomposition problem

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Science China(Information Sciences) 2016年第5期59卷 133-143页

作者： Jinhui LIU Huanguo ZHANG Jianwei JIA Houzhen WANG shaowu mao Wanqing WU Computer School of Wuhan University Key Laboratory of Aerospace Information security and trusted computing Ministry of Education

Advances in quantum computation threaten to break public key cryptosystems such as RSA, ECC,and El Gamal that are based on the difficulty of factorization or taking a discrete logarithm, although up to now,no quantum algorithms have been found to be able to solve certain mathematical problems on non-commutative algebraic structures. Against this background, Raulynaitis et al. have proposed a novel asymmetric cipher protocol using a matrix decomposition problem. Their proposed scheme is vulnerable to a linear algebra attack based on the probable occurrence of weak keys in the generation process. In this paper, we show that the asymmetric cipher of the non-commutative cryptography scheme is vulnerable to a linear algebra attack and that it only requires polynomial time to obtain the equivalent keys for some given public keys. We also propose an improvement to enhance the scheme of Raulynaitis et al.

关键词： cryptography post-quantum computational cryptography asymmetric cipher protocol cryptanalysis matrix decomposition

Cryptanalysis of an MOR cryptosystem based on a finite associative algebra

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Science China(Information Sciences) 2016年第3期59卷 137-145页

作者： Wanqing WU Huanguo ZHANG Houzhen WANG shaowu mao Shuomei WU Haiqing HAN Computer School of Wuhan University Computer Department Shijiazhuang University School of Mathematics and Physics Hubei Polytechnic University

The Shor algorithm is effective for public-key cryptosystems based on an abelian group. At CRYPTO 2001, Paeng（2001） presented a MOR cryptosystem using a non-abelian group, which can be considered as a candidate scheme for post-quantum attack. This paper analyses the security of a MOR cryptosystem based on a finite associative algebra using a quantum algorithm. Specifically, let L be a finite associative algebra over a finite field F. Consider a homomorphism φ : Aut（L） → Aut（H） × Aut（I）, where I is an ideal of L and H ■ L/I.We compute dim Im（φ） and dim Ker（φ）, and combine them by dim Aut（L） = dim Im（φ） + dim Ker（φ）. We prove that Im（φ） = Stab Comp（H,I）(μ + B;（H, I）) and Ker（φ）■ Z;（H, I）. Thus, we can obtain dim Im（φ）, since the algorithm for the stabilizer is a standard algorithm among abelian hidden subgroup algorithms. In addition,Z;（H, I） is equivalent to the solution space of the linear equation group over the Galois fields GF（p）, and it is possible to obtain dim Ker（φ） by the enumeration theorem. Furthermore, we can obtain the dimension of the automorphism group Aut（L）. When the map ? ∈ Aut（L）, it is possible to effectively compute the cyclic group ? and recover the private key a. Therefore, the MOR scheme is insecure when based on a finite associative algebra in quantum computation.

关键词： MOR cryptosystem cryptanalysis quantum algorithm finite associative algebra hidden subgroup problem stabilizer

Cryptanalysis of Public Key Cryptosystems Based on Non-Abelian Factorization Problems

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Tsinghua Science and Technology 2016年第3期21卷 344-351页

作者： Jinhui Liu Aiwan Fan Jianwei Jia Huanguo Zhang Houzhen Wang shaowu mao Computer School of Wuhan University Wuhan 430072China Computer School of Pingdingshan University Pingdingshan 467001China

Advances in quantum computers threaten to break public-key cryptosystems （e.g., RSA, ECC, and EIGamal）, based on the hardness of factoring or taking a discrete logarithm. However, no quantum algorithms have yet been found for solving certain mathematical problems in non-commutative algebraic structures. Recently, two novel public-key encryption schemes, BKT-B cryptosystem and BKT-FO cryptosystem, based on factorization problems have been proposed at Security and Communication Networks in 2013. In this paper we show that these two schemes are vulnerable to structural attacks and linearization equations attacks, and that they only require polynomial time complexity to obtain messages from associated public keys. We conduct a detailed analysis of the two attack methods and show corresponding algorithmic descriptions and efficiency analyses. In addition, we provide some improvement suggestions for the two public-key encryption schemes.

关键词： cryptography post-quantum cryptography public key encryption cryptanalysis linear equations

A public key cryptosystem based on data complexity under quantum environment

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Science China(Information Sciences) 2015年第11期58卷 48-58页

作者： WU WanQing ZHANG HuanGuo WANG HouZhen mao shaowu JIA JianWei LIU JinHui Computer School Wuhan University

Since the Shor algorithm showed that a quantum algorithm can efficiently calculate discrete logarithms and factorize integers, it has been used to break the RSA, EIGamal, and ECC classical public key cryptosystems. This is therefore a significant issue in the context of ensuring communication security over insecure channels. In this paper, we prove that there are no polynomial-size quantum circuits that can compute all Boolean functions(of which there are 22ncases) in the standard quantum oracle model. Based on this,we propose the notion of data complexity under a quantum environment and suggest that it can be used as a condition for post-quantum computation. It is generally believed that NP-complete problems cannot be solved in polynomial time even with quantum computers. Therefore, a public key cryptosystem and signature scheme based on the difficulty of NP-complete problems and the notion of data complexity are presented here. Finally,we analyze the security of the proposed encryption and signature schemes.

关键词： public key cryptography information security NP-complete problem complexity theory quantum computation

Key Exchange Protocol Based on Tensor Decomposition Problem

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China Communications 2016年第3期13卷 174-183页

作者： mao shaowu ZHANG Huanguo WU Wanqing ZHANG Pei SONG Jun LIU Jinhui Computer School of Wuhan University The Key Laboratory of Aerospace Information Security and Trusted ComputingMinistry of EducationWuhan 430072Hubei ProvinceChina China University of Geosciences Wuhan 430074Hubei ProvinceChina Hebei University School of Computer Science and TechnologyHebei UniversityBaoding 071002China

The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing. In this paper, we firstly proposed a new variant of tensor decomposition problem, then two one-way functions are proposed based on the hard problem. Secondly we propose a key exchange protocol based on the one-way functions, then the security analysis, efficiency, recommended parameters and etc. are also given. The analyses show that our scheme has the following characteristics: easy to implement in software and hardware, security can be reduced to hard problems, and it has the potential to resist quantum computing.Besides the new key exchange can be as an alternative comparing with other classical key protocols.

关键词：密钥交换协议张量分解安全性分析量子计算单向函数分解问题密钥协议密码学

A Resistant Quantum Key Exchange Protocol and Its Corresponding Encryption Scheme

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China Communications 2014年第9期11卷 124-134页

作者： mao shaowu ZHANG Huanguo WU Wanqing LIU Jinhui LI Shuanbao Wang Houzhen Computer School of Wuhan University The Key Laboratory of Aerospace Information Security and Trusted Computing Ministry ofEducation Wuhan 430072 Hubei Province P. R. China

The emergence of quantum computer will threaten the security of existing public-key cryptosystems,including the Diffie Hellman key exchange protocol,encryption scheme and etc,and it makes the study of resistant quantum cryptography very urgent.This motivate us to design a new key exchange protocol and encryption scheme in this paper.Firstly,some acknowledged mathematical problems was introduced,such as ergodic matrix problem and tensor decomposition problem,the two problems have been proved to NPC hard.From the computational complexity prospective,NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them.From the algebraic structures prospective,non-commutative cryptography has been considered to resist quantum.The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures,so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures.Secondly,a new problem was constructed based on the introduced problems in this paper,then a key exchange protocol and a public key encryption scheme were proposed based on it.Finally the security analysis,efficiency,recommended parameters,performance evaluation and etc.were also been given.The two schemes has the following characteristics,provable security,security bits can be scalable,to achieve high efficiency,quantum resistance,and etc.

关键词：密钥交换协议量子计算机加密方案可证明安全性公钥密码体制计算复杂性理论抗性代数结构

Software Watermarking Scheme Based on Multivariate Public Key Cryptosystem

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Wuhan University Journal of Natural Sciences 2016年第3期21卷 257-261页

作者： SUN Xiaoyan ZHANG maosheng mao shaowu REN Zhengwei ZHANG Huanguo Guangxi Universities Key Laboratory of Complex SystemOptimization and Big Data Processing Yulin Normal UniversityYulin 537000 Guangxi China School of Computer Wuhan University Wuhan 430072Hubei China Wuhan Digital and Engineering Institute Wuhan 430205Hubei China

Software watermarking is an efficient tool to verify the copyright of software. Public key cryptosystem-based watermarking is widely researched. However, the popular public key cryptosystem is not secure under quantum algorithm. This paper proposes a novel soft-ware watermarking scheme based on multivariate public key cryptosystem. The copyright information generated by copyright holder is transformed into copyright numbers using multivariate quadratic polynomial equations inspired by multivariate public key cryptosystem （MPKC）. Every polynomial is embedded into the host program independently. Based on the security performance of MPKC, the robustness and invisibility of the proposed scheme is significantly improved in comparison with the RSA-based watermarking method.

关键词： software watermarking multivariate cryptosystem copyright

Numerical Modeling of Floating Oil Boom Motions in Wave-Current Coupling Conditions

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Journal of Ocean University of China 2017年第4期16卷 602-608页

作者： SHI Yang LI shaowu ZHANG Huaqin PENG Shitao CHEN Hanbao ZHOU Ran mao Tianyu State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University Tianjin Research Institute for Water Transport Engineering Ministry of Transport

Containment booms are commonly used in collecting and containing spilled oil on the sea surface and in protecting specific sea areas against oil slick spreading.In the present study,a numerical model is proposed based on the N-S equations in a mesh frame.The proposed model tracks the outline of the floating boom in motion by using the fractional area/volume obstacle representation technique.The boom motion is then simulated by the technique of general moving object.The simulated results of the rigid oil boom motions are validated against the experimental results.Then,the failure mechanism of the boom is investigated through numerical experiments.Based on the numerical results,the effects of boom parameters and dynamic factors on the oil containment performance are also assessed.

关键词：运动目标数值模拟耦合条件石油流动波流模拟技术 N-S方程