基于FPGA的高速椭圆曲线标量乘法结构

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1、万方数据计算机研究与发展ISSN1000—1239[CN11—1777／TPJournalofComputerResearchandDevelopment45(11)：1947-1954，2008基于FPGA的高速椭圆曲线标量乘法结构陈婧1蒋俊洁2王石2邓小铁2汪东升11(清华大学计算机科学与技术系微处理器与片上系统研究中心北京100084)2(香港城市大学计算机系中国香港)(jingchen@cityu．edu．hk)HighPerformanceArchitectureforEllipticCurveScalarMultiplicationBasedonFPGAChe

2、nJin91，JiangJunjie2，DuncanS．Won92，DengXiaotie2，andWangDongshen911(MicroprocessorandSoCTechnologyR&DCenter，DepartmentofComputerScienceandTechnology。TsinghuaUniversity，Beijing100084)2(DepartmentofComputerScience，CityUniversityofHongKong。HongKong，China)AbstractEllipticcurvescalarmultiplicati

3、on(ECSM)isthemostimportantoperationinellipticcurvecryptography(ECC)．ThestudyofitsimplementationperformanceandoptimizationhasattractedgreatinterestsofresearchersduetotherapiddevelopmentanddeploymentofECCrecently．Focusingondesigninghighperformancehardwarearchitectureforthisoperation，firstad

4、igit—serial／parallelfinitefieldmultiplierwithwordwidthDisdeveloped，whichcompletesonemultiplicationoverGF(2“)in胁／D]cycles．Usingthismultiplier，ahardwiredlogicdesignforperformingellipticcurvescalarmultiplicationoverGF(2“)isproposed．Thisarchitecturemaximizestheparallelismthattheprojectivecoor

5、dinatesversionoftheMontgomeryscalarmultiplicationalgorithmcanachieve，andalsoshortensthemaximumdelaypath．ItcompletesonescalarmultiplicationoverGF(2“)inabout(5m一6)陬／D]cycles．WhenimplementedonXilinxVirtex4一LX200FPGA，usingmultiplierswithwordwidth16，itoccupiesabout46％ofallcomputationresourcesa

6、vailable，achievesafrequencyof225MHz，andtakesonly36ⅡstOcompleteoneellipticcurvescalarmultiplicationoperationforarbitraryellipticcurves，arbitrarypointsandintegersoverGF(2163)．ThisresultoutperformsallcomparableFPGA—basedellipticcurvescalarmultipliersintheworld．Ontheotherhand，thisarchitecture

7、canbeeasilyreconfiguredtoadaptdifferentsecuritylevelsandperformancerequirements．Keywordsellipticcurve；scalarmuhiplication；FPGA；finitefield；hardwiredlogic擒要椭圆曲线密码系统是最近十几年来获得迅速发展的一类密码系统．为了提高椭圆曲线密码系统的处理速度，针对其中最关键的运算——椭圆曲线标量乘法设计并实现了一种基于FPGA的硬件结构，完成GF(2”)上的椭圆曲线标量乘法计算．该结构