Schoof算法及其實現(xiàn)的一些策略.pdf

1、華中科技大學碩士學位論文Schoof算法及其實現(xiàn)的一些策略姓名：楊文鋒申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：覃中平2002.5.7華中科技大學碩士學位論文=!!!!!!==!=!=!=!=!!!!==!==!=====!===!==!!=!=!!!==AbstractEllipticCurx7eCr)’ptograph3，(ECC)“、1、、asproposedin1985independentl)吣NealKoNitzfIIand

2、VictorMillerSincethena、astamountofresearchhasbeendoneonitssecurit)randimplementationInrecentjearsECChasrecei!、edincl。easingcommercialacceptancease、idencedbjitsinclusioninstandardOlganizatioussuchasANSI(AmericanNationStan

3、dardsInstitute)1EEE(InstitateofElectricalandElectronicsEngineers)，1SO(InternationalStandardsOrganization)，andNIST(NationalInstituteofStandardsandTechnolog))BeforeimplementinganECCs)stem、、eShouldchoosetheellipticcureEo、er

4、thefinitefieldf，Consideringthefactorofthesecurityofthecry’ptos5’stemⅥshouldcalculate#GF(q)thenumberofthepointsonellipticcurvesoverfinitefieldFfTherearetWOschemestosol!!，etheproblemthefirstischoosingEfollow’ingthesuggesti

5、onsofstandardsorganizations(suchasNISTinFIPS186—2∽：thesecondischoosingEb、randornHoweveT，theEllipticCur_，eCryptosystemiseasilyattackedbyPohig—Hellman㈩algorithmifthenumberofthepointsonellipticcur!!’eo、7elfinitefieldCdoesno

6、t11a、，ehugeprimefactoESowemustsatisfythecondition#GF(q、shouldhashugeprilnefactorinordertOgeneratesecureellipticcur!!eSchoofAlgorithm㈨】proposedby’ReneSchooEwasusedtocalculatethenumberofthepointsOllellipticcurveoverfinitef

7、ieldFrThisarticle、firstintroducesSOITleknou’ledgeaboutellipticcurve，andIhendescribesSchoof‘Salgorithmindetailespeciall)prox，idessomesupplementaryprovingofSchoof’SalgorithmBasedonthis，theorems33，1and332areachieved、andsome