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1、Quantum-SecureSymmetric-KeyCryptographyBasedonHiddenShiftsGorjanAlagic1andAlexanderRussell21QMATH,DepartmentofMathematicalSciencesUniversityofCopenhagengalagic@gmail.com2DepartmentofComputerScienceandEngineeringUniversityofConnecticutacr@cse.uconn.eduAbstract.Recentr
2、esultsofKaplanetal.,buildingonworkbyKuwakadoandMorii,haveshownthatawidevarietyofclassically-securesymmetric-keycryptosystemscanbecompletelybrokenbyquantumchosen-plaintextattacks(qCPA).Insuchanattack,thequantumadversaryhastheabilitytoquerythecryptographicfunctionality
3、insuperposition.ThevulnerablecryptosystemsincludetheEven-Mansourblockcipher,thethree-roundFeistelnetwork,theEncrypted-CBC-MAC,andmanyothers.nInthisarticle,westudysimplealgebraicadaptationsofsuchschemesthatreplace(Z/2)additionwithnoperationsoveralternatefinitegroups—su
4、chasZ/2—andprovideevidencethattheseadaptationsareqCPA-secure.Theseadaptationsfurthermoreretaintheclassicalsecuritypropertiesandbasicstructuralfeaturesenjoyedbytheoriginalschemes.Weestablishsecuritybytreatingthe(quantum)hardnessofthewell-studiedHiddenShiftproblemasacr
5、yptographicassumption.Weobservethatthisproblemhasanumberofattractivefeaturesinthiscryptographiccontext,includingrandomself-reducibility,hardnessamplification,and—inmanycasesofinterest—areductionfromthe“searchversion”tothe“decisionalversion.”Wethenestablish,underthisas
6、sumption,theqCPA-securityofseveralsuchHiddenShiftadaptationsofsymmetric-keyconstructions.WeshowthataHiddenShiftversionoftheEven-Mansourblockcipheryieldsaquantum-securepseudorandomfunction,andthataHiddenShiftversionoftheEncryptedCBC-MACyieldsacollision-resistanthashfu
7、nction.Finally,weobservethatsuchadaptationsfrustratethedirectSimon’salgorithm-basedattacksinmoregeneralcircumstances,e.g.,Feistelnetworksandslideattacks.arXiv:1610.01187v2[quant-ph]10Mar20171IntroductionThediscoveryofefficientquantumalgorithmsforalgebraicproblemswithlo
8、ngstandingrolesincryptog-raphy,likefactoringanddiscretelogarithm[30],hasledtoasystematicre-evaluationofcryptographyinthepresenceofq
