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Acta Mathematica Sinica,English Series 2013年第3期29卷 515-522页

作者： Ping XI School of Mathematics and Statistics Xi’an Jiaotong University

In this paper, we prove a quantitative version of the statement that every nonempty finite subset of N＋ is a set of quadratic residues for infinitely many primes of the form [nc] with 1 〈 c 〈 243/205. Correspondingly, we can obtain a similar result for the case of quadratic non-residues under reasonable assumptions. These results generalize the previous ones obtained by Wright in certain aspects.

关键词： quadratic residue quadratic non-residue Piatetski-Shapiro prime

Constructions of optimal variable-weight OOCs via quadratic residues

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Frontiers of Mathematics in China 2013年第4期8卷 869-890页

作者： Yah LIU Dianhua WU Department of Mathematics Guangxi Normal University Guilin 541004 China

Variable-weight optical orthogonal code （OOC） was introduced by G. C. Yang [IEEE Trans. Commun., 1996, 44： 47-55] for multimedia optical CDMA systems with multiple quality of service （QoS） requirements. In this p... 详细信息

关键词： Cyclic packing optical orthogonal code (OOC) quadratic residue relative difference family variable-weight OOC

Identity-based signature scheme based on quadratic residues

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Science in China(Series F) 2007年第3期50卷 373-380页

作者： CHAI ZhenChuan CAO ZhenFu DONG XiaoLei Department of Computer Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China

Identity-based （ID-based） cryptography has drawn great concerns in recent years, and most of ID-based schemes are constructed from bilinear parings. Therefore, ID-based scheme without pairing is of great interest in the field of cryptography. Up to now, there still remains a challenge to construct ID-based signature scheme from quadratic residues. Thus, we aim to meet this challenge by proposing a concrete scheme. In this paper, we first introduce the technique of how to calculate a 2^lth root of a quadratic residue, and then give a concrete ID-based signature scheme using such technique. We also prove that our scheme is chosen message and ID secure in the random oracle model, assuming the hardness of factoring.

关键词： ID-based signature quadratic residue factoring random oracle proven security

Identity-based ring signature scheme based on quadratic residues

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High Technology Letters 2009年第1期15卷 94-100页

作者：熊虎 School of Computer Science and Engineering University of Electronic Science and Technology of China

Identity-based （ID-based） ring signature has drawn great concerns in recent years and many ID-based ring signature schemes have been proposed until now. Unfortunately, all of these ID-based ring signatures are constructed from bilinear pairings, a powerful but computationally expensive primitive. Hence, ID-based ring signature without pairing is of great interest in the field of cryptography. In this paper, the authors firstly propose an ID-based ring signature scheme based on quadratic residues. The proposed scheme is proved to be existentially unforgeable against adaptive chosen message-and-identity attack under the random oracle model, assuming the hardness of factoring. The proposed scheme is more efficient than those which are constructed from bilinear pairings.

关键词： identity-based signature ring signature quadratic residue random oracle provable security

Some Remarks on Cocks'Identity-Based Encryption Scheme

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Journal of Donghua University(English Edition) 2024年第4期41卷 447-450页

作者： ZHAO Xiaopeng School of Computer Science and Technology Donghua UniversityShanghai 201620China

The theory of quadratic residues plays an important role in *** 2001,Cocks developed an identity-based encryption(IBE)scheme based on quadratic residues,resolving Shamir’s 17-year-old open ***,a notable drawback of Cocks’scheme is the significant expansion of the ciphertext,and some of its limitations have been addressed in subsequent ***,Cotan and Teşeleanu highlighted that previous studies on Cocks’scheme relied on a trial-and-error method based on Jacobi symbols to generate the necessary parameters for the encryption *** enhanced the encryption speed of Cocks’scheme by eliminating this trialand-error *** on security analysis,this study concludes that the security of Cotan-Teşeleanu’s proposal cannot be directly derived from the security of the original Cocks’***,by adopting the Cotan-Teşeleanu method and introducing an additional variable as a public element,this study develops a similar enhancement scheme that not only accelerates the encryption speed but also provides security equivalent to the original Cocks’scheme.

关键词： identity-based encryption(IBE) quadratic residue security Cocks’IBE scheme

On Diophantine Equation X(X+1)(X+2)(X+3)=14Y(Y+1)(Y+2)(Y+3)

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Journal of Southwest Jiaotong University(English Edition) 2009年第1期17卷 90-93页

作者：段辉明郑继明 College of Mathematics and Physics Chongqing University of Posts and Telecommunications

The Diophantine equation X（ X ＋ 1 ）（ X ＋ 2 ）（ X ＋ 3 ） = 14Y（ Y ＋ 1 ）（ Y ＋ 2 ）（ Y ＋ 3 ） still remains open. Using recurrence sequence, Maple software, Pell equation and quadraric residue, this pap... 详细信息

关键词： Integer solution Diophantine equation Recurrent sequence quadratic residue