基于koblitz椭圆曲线的公钥密码体制实现技术研究

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1、Abstractb弱is，wemayuseFrobeniusmapintegerktoTNAFrepresentationofit，andthenusingittocomputescalarmultiplication．Therehasnodoublingpointsoperation．Therefore，thekeytoimproVescalarmultiplicationishowtoreducethelen垂hofTNAFofk．711lisaniclehasdeeplyresearchedtheimplementat

2、ionofellipticcurvecryptosystem，andmainlydiscussedthefastgeneratiOnofhmbdaofno咖albasisrepresentation，锄dfinitefieldmultiplicationalgorithm锄dscalarmultiplicati咖ofKoblitzcun，e．Firstly；thisarticlehasdiscussedthetheory；anddeeplyanalyzingthegenefationalgorithmofLambda，and

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5、％bycomparisonwithNing-Yinalgorithm．Amdthen，theaniclehasanalyzedthepropeniesofKoblitzcuⅣe，anddiscussedtheinfluenceofoptionalnonnalbasisonscalarmultiplication，andalsodiscussedthe№蟠algorithmandTNAFalgorithm．Itimplementsanimpro、，eda190rithmof1NAFalgorithm，andimproVesth

6、eperfo咖anceofECCby50％．Finally，thearticlehasappliedtoECDSA．IthasbeenprovedthefeasibilityofaboVeimproVedalgorithmandimplementation．Onthewhole，itcanimproVethee蜀ficiencywith68％comparedwithRosing’simplementation．Theresearchf

7、uitsinthispaperhaVereferencedValueandengineer

8、ingpracticalValueinapplicationsofellipticcuⅣecryptosystem．Keywords：EllipticCurveCrypto黟aphy0ptimalNo珊alBasisFiniteFieldMultiplicationScalarMultiplicationV独创性声明本人声明所呈交的学位论文是本人在导师指导下进行的研究工作及取得的研究成果。据我所知，除了文中特别加以标注和致谢的地方外，论文中不包含其他人已经发表或撰写过的研究成果，也不包含为获得盛都堡王丕堂或其他教育机构的学位

9、或证书而使用过的材料。与我一同工作的同志对本研究所做的任何贡献均已在论文中作了明确的说明并表示谢意。籼姗躲王域如多年多月学位论文版权使用授权书本学位论文作者完全了解盛壑堡王太堂有关保留、使用学位论文的规定，有权保留并向国家有关部门或机构送交论文的复印件和磁盘，允许论文被查阅和借阅。本人授权