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国际计算机前沿大会会议论文集 2023年第1期 350-360页

作者： Anan Jin Xiang Li Qingzhi Xiong School of Information Engineering East China University of TechnologyNanchang 330013JiangxiChina Jiangxi Engineering Technology Research Center of Nuclear Geoscience Data Science and System East China University of TechnologyNanchang 330013JiangxiChina Jiangxi Key Laboratory of Cybersecurity Intelligent Perception East China University of TechnologyNanchang 330013JiangxiChina

Aiming to address the problems of high costs associated with the storage and transmission of environmental monitoring images,as well as potential security risks,this paper proposes a security compressed sensing image encryption algorithm based on elliptic curve *** algorithm introduces elliptic curve encryption technology within a compressed sensing framework,using elliptic curve cryptography to encrypt the matrix during the compression perception acquisition *** enables secure acquisition of environmental monitoring encrypted ***,this paper presents a security compressed sensing framework to address security gaps in the compression perception reconstruction process and improve the security of environmental monitoring *** results show that the proposed algorithm effectively encrypts and reconstructs environmental monitoring images,with high security and resistance to cracking.

关键词： Compressed Sensing elliptic curve Image Reconstruction Image Encryption Environmental Monitoring

A Generalized MSST Algorithm for Counting Points of elliptic curves over F_(p)^(n)

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Journal of Systems Science & Complexity 2024年第4期37卷 1738-1754页

作者： LI Xiao LV Chang PAN Zhizhong Key Laboratory of Cyberspace Security Defense Institute of Information EngineeringChinese Academy of SciencesBeijing 100085China School of Cyber Security University of Chinese Academy of SciencesBeijing 100085China Huawei Technologies Co. Ltd.Shenzhen 518129China

elliptic curve cryptography is an important part of nowaday's public key *** points of elliptic curves over finite fields is of great significance to the selection of safety *** present,there are many p-adic algorithms,such as SST algorithm,generalized AGM algorithm,Kedlaya algorithm,etc.,which can deal with the situation of finite fields of small *** this paper,the authors generalize the MSST algorithm of characteristic 2 to general fields of odd characteristic,and propose the generalized MSST *** generalized MSST algorithm is achieved by combining the advantages of the SST algorithm and the generalized AGM *** the time complexity of the multiplication of two n-bit numbers is denoted as O((n)^(μ)),then the time complexity of the generalized MSST algorithm is O(n^(2μ+1/1+μ)),which is the same as the improved SST *** practical experiments,the running time of the generalized MSST algorithm is less than that of the improved SST algorithm.

关键词： elliptic curve generalized AGM algorithm generalized MSST algorithm SST algorithm

elliptic curves and their torsion subgroups over number fields of type (2,2,…,2)

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Science China Mathematics 2001年第2期44卷 159-167页

作者：邱德荣张贤科 Department of Mathematical Sciences Tsinghua University Beijing China

Suppose that E：y2=x(x+M)(x+N) is an elliptic curve, where M 详细信息

Suppose that E：y2=x(x+M)(x+N) is an elliptic curve, where Melliptic curve E over any number field F, it is shown that E(L)tors=E(F)tors holds for almost all extensions L/F of degree p(a prime number). These results have remarkably developed the recent results by Kwon about torsion subgroups over quadratic fields.

关键词： elliptic curve Mordell group torsion subgroup number field.

The Selmer Groups of elliptic curves

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Acta Mathematica Sinica,English Series 2003年第1期19卷 89-96页

作者： FuZhengWANG DepartmentofMathematics PekingUniversityBeijing100871

Let E / K be an elliptic curve with K-rational p-torsion points. The p-Selmer group of E is described by the image of a map uK and hence an upper bound of its order is given in terms of the class numbers of the S-idea... 详细信息

关键词： elliptic curve Selmer group S ideal class group

elliptic curves in Huff's Model

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Wuhan University Journal of Natural Sciences 2012年第6期17卷 473-480页

作者： WU Hongfeng FENG Rongquan College of Sciences North China University of TechnologyBeijing 00China School of Mathematical Sciences/Laboratory of Mathematics and Applied Mathematics(LMAM) Peking UniversityBeijing 100871China

In this paper,we present the generalized Huff curves that contain Huff＇s model as a special ***,it is proved that every elliptic curve with three points of order 2 is isomorphic to a generalized Huff ***,the fast and explicit formulae are derived for generalized Huff curves in projective *** paper also enumerates the number of isomorphism classes of generalized Huff curves over finite ***,the explicit formulae are presented for the doubling step and addition step in Miller＇s algorithm to compute the Tate pairing on generalized Huff elliptic curves.

关键词： elliptic curve Huff curve cryptography scalar multiplication isomorphism classes

Constructing quasi-random subsets of Z_N by using elliptic curves

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Applied Mathematics(A Journal of Chinese Universities) 2012年第1期27卷 105-113页

作者： LIN Zhi-xing CHEN Zhi-xiong Department of Mathematics Putian UniversityPutianFujian 351100China State Key Laboratory of Information Security Institute of SoftwareChinese Academy of SciencesBeijing 100049China

Let ε ： y^2 = x3 ＋ Ax ＋ B be an elliptic curve defined over the finite field Zp（p 〉 3） and G be a rational point of prime order N on ε. Define a subset of ZN, the residue class ring modulo N, asS：={n：n∈ZN,n≠0,（X（nG）/p）=1} where X（nG） denotes the x-axis of the rational points nC and （＊/P） is the Legendre symbol. Some explicit results on quasi-randomness of S are investigated. The construction depends on the intrinsic group structures of elliptic curves and character sums along elliptic curves play an important role in the proofs.

关键词： elliptic curve quasi-random subset quasi-randomness character sum Legendre symbol.

Prüfer Sheaves and Generic Sheaves Over the Weighted Projective Lines and elliptic curves

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Acta Mathematica Sinica,English Series 2017年第5期33卷 705-724页

作者： Jian Min CHEN Jin Jing CHEN Ya Nan LIN School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China

In the present paper, we introduce the concepts of Prüfer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prüfer sheaves and adic sheaves can characterize the category of coherent sheaves. Moreover, we describe the relationship between Prüfer sheaves and generic sheaves, and provide two methods to construct generic sheaves by using coherent sheaves and Prüfer sheaves.

关键词： Weighted projective line elliptic curve quasi-coherent sheaf pure-injective object

Explicit Classification for Torsion Subgroups of Rational Points of elliptic curves

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Acta Mathematica Sinica,English Series 2002年第3期18卷 539-548页

作者： De Rong QIU Center for Advanced Study, Tsinghua University, Beijing 100084. P. R. China Xian Ke ZHANG Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China Center for Advanced Study Tsinghua University Beijing P. R. China Department of Mathematical Sciences Tsinghua University Beijing P. R. China

We study the classification of elliptic curves E over the rationals Q according to the torsion subgroups E_(tors)(Q). More precisely, we classify those elliptic curves with E_(tors)(Q) being cyclic with even orders. We also give explicit formulas for generators of E_(tors)(Q). These results, together with the recent results of K. Ono for the non-cyclic E_(tors)(Q), completely solve the problem of the explicit classification and parameterization when E has a rational point of order 2.

关键词： elliptic curve Rational point Torsion group Mordell group Parameterization

Extreme central L-values of almost prime quadratic twists of elliptic curves

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Science China Mathematics 2023年第12期66卷 2755-2766页

作者： Shenghao Hua Bingrong Huang Data Science Institute and School of Mathematics Shandong UniversityJinan 250100China

In this paper,we prove the extreme values of L-functions at the central point for almost prime quadratic twists of an elliptic *** an application,we get the extreme values for the Tate-Shafarevich groups in the quadra... 详细信息

关键词： extreme value quadratic twist central L-value elliptic curve almost prime