雙線性對(duì)的有效計(jì)算

1、中山大學(xué)博士學(xué)位論文雙線性對(duì)的有效計(jì)算姓名：趙昌安申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：計(jì)算機(jī)軟件與理論指導(dǎo)教師：張方國黃繼武20080519英文摘要EmcientComputationsofBilinearPairingsMajor：Name：Supervisor：ComputerSoftwareandTheoryZhaoChan分AnProfZhangFjangguo，ProfHuangJiwuAbstractInrecentyears，many

2、interestingcryptogr印hicprotoeolsbasedonpajringshavebeenproposed，whichcannotbeachievedusingo七h(yuǎn)ermathematicalprimitivesTheemciencyofimpleHlentingtheseprotocolsisdeterminedbythespeedofpairingconlputations、7娓focusonimproving

3、theemciencyofp出ringcomputationsThemainresultsareIistedasfollows：1Usingnontrivialautomorphismsofsomespecialellipticcurves，thenewpairingsareconstructedwhichhaveahalflengthofMillerlooprequiredfortheTa七epairingW色ha鵬!provedth

4、atcomputingthenewpairingsi8moreemcientthancomputingtheori舀nal，Ihtepairing2Newlineev出uationsarepresentedforcomputingthe1、atepairingonsupersingularellipticcurveswithembeddingdegree忌=3，andsomeconjugatetechniquesarepro—posed

5、fbravoidingthedivisioninextensionfieldsE；asedontheseobserVations，arnodifiedMilleralgorithmisproposed，whichisInoreemcientthanthepreViousfastestalgorithm3Millera190rithmbasedondoublebasech缸nsis舀venForpairin分friendlycurvesw

6、ithembeddingdegree尼=6，thenewalgorithmis9％fasterthan七h(yuǎn)epre譏ousfastestrnethod4TheAtepaLiringisoneofthefastestpairingtillnowHo、veVer，theemciencyofcompu七ing七h(yuǎn)eori百nalAtepairingdependsontheValueofFlobeniustraeeofellipticcurVe

7、sW色havegeneralizedtheAtepairingTheMillerloopoftheVariationsoftheAtepairingcouldreachthelowerboundonsomepairin分friendlycurveswithlargenobeniustrauce5Flomanabstractangle，、)lreprovedthataUpairingsareinagroupBaseonthefacts，s