Introduction to Identity-Based Encryption

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1、IntroductiontoIdentity-BasedEncryptionLutherMartinLibraryofCongressCataloging-in-PublicationDataAcatalogrecordforthisbookisavailablefromtheU.S.LibraryofCongress.BritishLibraryCataloguinginPublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.ISBN-13:978-1-59693-238-8Coverdesignb

2、yYekaterinaRatner2008ARTECHHOUSE,INC.685CantonStreetNorwood,MA02062Allrightsreserved.PrintedandboundintheUnitedStatesofAmerica.Nopartofthisbookmaybereproducedorutilizedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recording,orbyanyinformationstorageandretrievalsystem,withoutper

3、missioninwritingfromthepublisher.Alltermsmentionedinthisbookthatareknowntobetrademarksorservicemarkshavebeenappropriatelycapitalized.ArtechHousecannotattesttotheaccuracyofthisinformation.Useofaterminthisbookshouldnotberegardedasaffectingthevalidityofanytrademarkorservicemark.10987654321ContentsPrefa

4、cexiii1Introduction11.1WhatIsIBE?11.2WhyShouldICareAboutIBE?8References132BasicMathematicalConceptsandProperties152.1ConceptsfromNumberTheory152.1.1ComputingtheGCD162.1.2ComputingJacobiSymbols242.2ConceptsfromAbstractAlgebra25References393PropertiesofEllipticCurves413.1EllipticCurves413.2AddingPoint

5、sonEllipticCurves473.2.1AlgorithmforEllipticCurvePointAddition523.2.2ProjectiveCoordinates533.2.3AddingPointsinJacobianProjectiveCoordinates54vviIntroductiontoIdentity-BasedEncryption3.2.4DoublingaPointinJacobianProjectiveCoordinates553.3AlgebraicStructureofEllipticCurves553.3.1HigherDegreeTwists613

6、.3.2ComplexMultiplication65References664DivisorsandtheTatePairing674.1Divisors674.1.1AnIntuitiveIntroductiontoDivisors684.2TheTatePairing764.2.1PropertiesoftheTatePairing814.3Miller’sAlgorithm84References875CryptographyandComputationalComplexity895.1Cryptography915.1.1Definitions915.1.2ProtectionPro

7、videdbyEncryption935.1.3TheFujisaki-OkamotoTransform955.2RunningTimesofUsefulAlgorithms955.2.1FindingCollisionsforaHashFunction965.2.2Pollard’sRhoAlgorithm985.2.3TheGeneralNumberFieldSieve995.2.4TheIn