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Cryptanalysis of a Key Exchange Protocol Based on Commuting Matrices

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Chinese Journal of Electronics 2017年第5期26卷 947-951页

作者： JIA Jianwei LIU Jinhui ZHANG Huanguo Computer School of Wuhan University Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education

A key exchange protocol is considered *** scheme is based on a set of m commuting square singular matrices of dimension n×n over a finite field,and its security is claimed to rely on the hardness of the matrix version discrete logarithm ***,the proposal’s design allows for a clean attack *** show that the key exchange protocol is vulnerable to a linear algebra attack which only requires polynomial time to obtain the equivalent keys for all given public *** conduct a detailed analysis on the attack method and provide some improved suggestions on the key exchange protocol based on commuting matrices.

关键词： Cryptography Key exchange protocol Cryptanalysis discrete logarithm problem Linear equations

Targeted Fully Homomorphic Encryption Based on a Double Decryption Algorithm for Polynomials

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Tsinghua Science and Technology 2014年第5期19卷 478-485页

作者： Yatao Yang Shuang Zhang Junming Yang Jia Li Zichen Li Beijing Electronic Science and Technology Institute Communication Engineering Institute Xidian University

Several public-key encryption schemes used to solve the problem of ciphertext data processing on the fly are discussed. A new targeted fully homomorphic encryption scheme based on the discrete logarithm problem is presented. Public-key encryption cryptosystems are classified to examine homomorphic encryption. Without employing techniques proposed by Gentry such as somewhat homomorphic and bootstrapping techniques, or relinearization technique proposed by Brakerski et al., a new method called ＂Double Decryption Algorithm＂ is employed in our cryptography to satisfy a fully or targeted fully homomorphic property. Inspired by EIGamal and BGN cryptography, we obtain the desired fully homomorphic property by selecting a new group and adding an extra component to the ciphertext. Proof of semantic security is also demonstrated.

关键词： targeted fully homomorphic encryption discrete logarithm problem exponential function method power function method

New signature scheme based on two cryptographic assumptions

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Journal of Southeast University(English Edition) 2007年第3期23卷 461-464页

作者：郑明辉崔国华华中科技大学计算机科学与技术学院

In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mathematical problems. Combining the E1Gamal scheme based on the discrete logarithm problem and the OSS scheme based on the factoring problem, a digital signature scheme based on these two cryptographic assumptions is proposed. The security of the proposed scheme is based on the difficulties of simultaneously solving the factoring problem and the discrete logarithm problem. So the signature scheme will be still secure under the situation that any one of the two hard-problems is solved. Compared with previous schemes, the proposed scheme is more efficient in terms of space storage, signature length and computation complexities.

关键词： digital signature security factoring problem discrete logarithm problem

A more efficient accountable authority IBE scheme under the DL assumption

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Science China(Information Sciences) 2010年第3期53卷 581-592页

作者： XU Peng, CUI GuoHua, FU Cai & TANG XueMing Laboratory of Information Security, College of Computer Science, Huazhong University of Science and Technology, Wuhan 430074, China Laboratory of Information Security College of Computer Science Huazhong University of Science and Technology Wuhan China

In 2007, Goyal introduced a new and creative approach, called accountable authority identity-based encryption (referred to as A-IBE), to reduce the degree of trust that must be placed in the private-key generator (PKG) in an identity-based encryption (IBE) scheme. Based on his work, a new universal A-IBE scheme is proposed in this paper. Compared with Goyal’s universal scheme, this new universal A-IBE scheme not only optimizes the time requirements for pairing operations, but also achieves a "tighter" security reduction based on a weaker hard problem (the discrete logarithm problem) under a stronger security definition (using an adaptively selected identity). Because there are many fewer pairing operations in this new scheme, the performance of the application can be improved to some degree. In addition, because of the "tighter" security reduction achieved by this new proposed scheme, a less restrictive security parameter can be chosen while achieving the same security as with Goyal’s scheme along with an improvement in performance. In the respect of the time requirement, compared with the Goyal’s universal scheme, this new scheme could be more efficient. Regrettably, these improvements will increase the memory needed for the public parameters and the volume of communications required. Compromise values of the public parameters should therefore be chosen to balance the advantages and drawbacks.

关键词： identity-based encryption accountable authority identity-based encryption pairing operation discrete logarithm problem

A kind of signature scheme based on class groups of quadratic fields

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Journal of Harbin Institute of Technology(New Series) 2004年第6期11卷 583-587页

作者：董晓蕾曹珍富 Dept. of Computer Science and Engineering Shanghai Jiaotong University Shanghai 200030 China

Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic fields remained open, because of the difficulty of computing class numbers of quadratic fields. In this paper, according to our researches on quadratic fields, we construct the first digital signature scheme in ideal class groups of quadratic fields, using q as modulus, which denotes the prime divisors of ideal class numbers of quadratic fields. Security of the new signature scheme is based fully on CL-DLP. This paper also investigates realization of the scheme, and proposes the concrete technique. In addition, the technique introduced in the paper can be utilized to realize signature schemes of other kinds.

关键词： quadratic-field cryptosystem digital signature ideal class groups discrete logarithm problem

Attack on an Efficient Certificateless Aggregate Signature without Pairing

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Wuhan University Journal of Natural Sciences 2020年第2期25卷 139-145页

作者： LI Huimin LIANG Hongmei WANG Haimin ZHANG Jinhui School of Mathematics and Finance Putian UniversityPutian 351100FujianChina Key Laboratory of Applied Mathematics Fujian Province University(Putian University)Putian 351100FujianChina School of Mathematics and Statistics Minnan Normal UniversityZhangzhou 363000FujianChina

A Certificateless Aggregate Signature(CLAS) scheme was proposed by Qu and Mu recently, which was published in "Int J. Electronic Security and Digital Forensics, 2018, 10(2)". They used discrete logarithm to ensure the scheme's security. However,we show by formulating an attack that their CLAS scheme cannot defend against Type I adversary. Furthermore, we point out an error that exists in the signature simulation of their security *** that we give a correct signature simulation for the security proof. Finally, to resist the Type I attack, we present two methods for improving Qu et al's CLAS scheme. Moreover, the second improving method can elevate the trust level of Qu et al's CLAS scheme to the highest trust level: Level 3.

关键词： certificateless aggregate signature attack security random oracle model discrete logarithm problem

A Proxy Blind Signature Scheme Based on DLP

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Wuhan University Journal of Natural Sciences 2007年第1期12卷 83-86页

作者： YU Baozheng XU Congwei School of Management Hefei University of TechnologyHefei 230009 Anhui China

A proxy signature scheme allows an original signer to delegate his signing capability to a proxy signer who can sign on behalf of the original signer. A blind signature is the concept with a salient feature that the signer can not make a linkage between the blind signature and the identity of the requester. Proxy signature and blind signature are used widely in electronic commerce. With satisfying the security properties of both two signatures, a new proxy blind signature scheme based on discrete logarithm problem is proposed.

关键词： discrete logarithm problem proxy signature blind signature electronic commerce

A novel group signature with one time secret key

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第6期6卷 560-564页

作者：谢琪于秀源 Department of Mathematics Zhejiang University Hangzhou 310027 China School of Information and Engineering Hangzhou Teachers College Hangzhou 310012 China Department of Mathematics Hangzhou Teachers College Hangzhou 310012 China Department of Mathematics and Physics Quzhou College Quzhou 324000 China

A new group signature with one time secret key is proposed. The main merits are that it only needs the trusted center issuing the partial secret key one time for each group member; and that the group member can generate his different secret key each time when he wants to sign a message. The group public key is constant and the size of the signature is independent of the number of group members. The total computation cost of signature and verification requires only 8 modular exponentiations.

关键词： Cryptography Group signature discrete logarithm problem Factoring problem

Cryptanalysis of a Digital Signature Scheme based on Factoring and discrete logarithms

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Cryptanalysis of a Digital Signature Scheme based on Factori...