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Cryptography on twisted Edwards curves over local fields

Science China(Information Sciences) 2015年第1期58卷 150-164页

作者： TANG ChunMing XU MaoZhi QI YanFeng School of Mathematics and Information China West Normal University Laboratory of Mathematics and Applied Mathematics School of Mathematical SciencesPeking University School of Science Hangzhou Dianzi University

Twisted Edwards curves over finite fields have attracted great interest for their efficient and unified addition formula. In this paper, we consider twisted Edwards curves over local fields and introduce a cryptosystem based on quotient groups of twisted Edwards curves over local fields. From the study of formal groups of twisted Edwards curves and twisted Edwards curves over local fields, we give the choice of cryptographic groups.An element in these groups can be uniformly represented by two n digit p-adic numbers, whereas an element in the elliptic curves in Weierstrass form over local fields is represented by a 3n-2 digit p-adic number and a4n-3 digit p-adic number. In the cryptography on elliptic curves in Weierstrass form over local fields, five cases for different input point pairs in computing points addition have to be considered and sometimes points have to be lifted. In the cryptography on twisted Edwards curves over local fields, the addition formula is simple,unified, and complete, which is efficient, does not need lifting points, and is against the side channel analysis.Finally, a speedy point multiplication algorithm and some concrete instances are given.

关键词： local fields formal groups elliptic curve cryptography twisted Edwards curves addition law

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Strategies for discovery and optimization of thermoelectric materials： Role of real objects and local fields

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Frontiers of physics 2018年第3期13卷 9-16页

作者： Hao Zhu Chong Xiao Hefei National Laboratory for Physical Sciences at the Microscale University of Science & Technology of China Hefei 230026 China

Thermoelectric materials provide a renewable and eco-friendly solution to mitigate energy shortages and to reduce environmental pollution via direct heat-to-electricity conversion. Discovery of the novel thermoelectric materials and optimization of the state-of-the-art material systems lie at the core of the thermoelectric society, the basic concept behind these being comprehension and manipulation of the physical principles and transport properties regarding thermoelectric materials. In this mini-review, certain examples for designing high-performance bulk thermoelectric materials are presented from the perspectives of both real objects and local fields. The highlights of this topic involve the Rashba effect, Peierls distortion, local magnetic field, and local stress field, which cover several aspects in the field of thermoelectric research. We conclude with an overview of future developments in thermoelectricity.

关键词： thermoelectric materials real objects local fields

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Hierarchical Management Scheme by local fields

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Acta Mathematica Sinica,English Series 2011年第1期27卷 155-168页

作者： Zhi Hong YUE Mao Zhi XU School of Mathematical Sciences Peking University Beijing 100871 P. R. China Key Laboratory of Network and Software Security Assurance School of Mathematical Sciences Peking University Beijing 100871 P. R. China

In the present paper we propose a new hierarchical management scheme within suitable extensions of 2-adic numbers, in which the subfields are treated as classes, and the communications are realized by computation on elliptic curves. The security of our system is much stronger than that of the traditional public key cryptographic systems.

关键词： Hierarchical management local fields elliptic curves

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APPROXIMATION OPERATORS AND SELFSIMILARITY OVER P-ADIC FIELD

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数学研究 1994年第1期 9-13页

作者： Zheng Weixing(Dept. of Math,Nanjing Univ.Nanjing 210008)

ＡＰＰＲＯＸＩＭＡＴＩＯＮＯＰＥＲＡＴＯＲＳＡＮＤＳＥＬＦＳＩＭＩＬＡＲＩＴＹＯＶＥＲＰ－ＡＤＩＣＦＩＥＬＤ￥ＺｈｅｎｇＷｅｉｘｉｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ，ＮａｎｊｉｎｇＵｎｉｖ．Ｎａｎｊｉｎｇ２１０００８）Ａｂ... 详细信息

ＡＰＰＲＯＸＩＭＡＴＩＯＮＯＰＥＲＡＴＯＲＳＡＮＤＳＥＬＦＳＩＭＩＬＡＲＩＴＹＯＶＥＲＰ－ＡＤＩＣＦＩＥＬＤ￥ＺｈｅｎｇＷｅｉｘｉｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ，ＮａｎｊｉｎｇＵｎｉｖ．Ｎａｎｊｉｎｇ２１０００８）Ａｂｓｔｒａｃｔ：Ｆｏｕｒｉｅｒａｎａ...

关键词： local fields p-Adic field p-Series field Approximation operator Fractals Self-similarity.

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Preface

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Acta Mechanica Solida Sinica 2017年第3期30卷 223-223页

作者： Wanlin Guo Daining Fang

Mechanical properties of low-dimensional and nanostructured materials have attracted great scientific interests as nanomaterials are distinctly different in both properties and functions from their macroscopic counterparts especially under multifields. At nanoscale, as the local fields of matters consisting of the electronic structure, molecular orbit, charge density and spin states become strongly coupled with the applied mechanical forces or strain, external electric field, magnetic field or optical action, one have to unify the traditional mechanics principles with the quantum mechanics theory to develop physical mechanics.

关键词： nanostructured materials electronic structure quantum mechanics electric field local fields

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