Singhalese(锡兰人).ppt

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1、EllipticCurveCryptographyJen-ChangLiu,2004AdaptedfromlectureslidesbyLawrieBrownRef:RSASecurity’sOfficialGuidetoCryptographyNoSinghalese(錫蘭人),whethermanorwoman,wouldventureoutofthehousewithoutabunchofkeysinhishand,forwithoutsuchatalisman(護身符)hewouldfearthatsomedevilmighttakeadvantag

2、eofhisweakstatetoslipintohisbody.—TheGoldenBough,SirJamesGeorgeFrazerReview:Requirementforpublic-keycryptographyDiffieandHellman(1976)proposedthepublic-keycryptographyrequirement:ItiscomputationallyeasytogenerateapairofkeysItiscomputationallyeasyforasendertoencryptItiscomputational

3、lyeasyforareceivertodecryptItiscomputationallyinfeasibleforanopponent,knowingthepublickey,todeterminetheprivatekeyItiscomputationallyinfeasibleforanopponent,knowingthepublickeyandciphtertext,torecovertheplaintextbX=DKR(Y)Y=EKU(X)b=>Trap-doorone-wayfunctionReview:one-wayfunction1968

4、,R.M.Needham’ssystem1974,G.Purdypublishedthefirstdetaildescriptionofsuchaone-wayfunctionOne-wayfunctionComputationinZp,A’spasswordOne-waycipherEncryptedpasswordlist……A’sencryptedpasswordHardtoinvert!Review:(trapdoor)one-wayfunctiondomaintargetY=f(X):easyX=f-1(Y):infeasible(>polynom

5、ialtime)X=fK-1(Y):easyiftrap-doorKisknown(~polynomialtime)Thenotionof“computationallyinfeasible”playsanimportantroleAencipheringtransformationthatcansafelyberegardedasa(trapdoor)one-wayfunctionin1994mightloseitsone-wayortrapdoorstatusin2004or2994EllipticCurveCryptography(ECC)majori

6、tyofpublic-keycrypto(RSA,D-H)useeitherintegerorpolynomialarithmeticwithverylargenumbers/polynomialsimposesasignificantloadinstoringandprocessingkeysandmessagesanalternativeistouseellipticcurvesofferssamesecuritywithsmallerbitsizesOutlineOperationsoverabeliangroups(可換群)Ellipticcurve

7、sovertherealsEllipticcurvesoverthefinitefieldsEllipticcurvecryptographyAbeliangroupGroupwithcommunicativepropertyGroup:{G,•}G:asetofelements•:binaryoperationtoeachpair(a,b)inGobeys:closure:a•bisalsoinGassociativelaw:(a•b)•c=a•(b•c)hasidentitye:e•a=a•e=ahasinversesa-1:a•a-1=ePublicc

8、iphersbasedonanabeliangrou