A Framework for Achieving KDM-CCA Secure Public-Key .Previous works on KDM-CCA F-KDM-CCA PKE F-KDM-CPA

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Text of A Framework for Achieving KDM-CCA Secure Public-Key .Previous works on KDM-CCA F-KDM-CCA PKE...

AFrameworkforAchievingKDM-CCASecurePublic-KeyEncryption

FuyukiKitagawa (TokyoInstituteofTechnology)KeisukeTanaka(TokyoInstituteofTechnology)

SecuritynotionsforPKE

IthasbeenconsideredIND-CCAsecurity =standardu takesactiveadversariesintoconsiderationu impliesnon-malleability

SecuritynotionsforPKE

IthasbeenconsideredIND-CCAsecurity =standard

Onetypicalexampleisencryptingsecretkeys

u takesactiveadversariesintoconsiderationu impliesnon-malleability

INDsecurityfallsshortifanadversarycanobtainsideinformationofsecretstates

e.g.)Anonymouscredential,hard-diskencryption,FHE

SecuritynotionsforPKE

IthasbeenconsideredIND-CCAsecurity =standard

Onetypicalexampleisencryptingsecretkeys

Keydependentmessage(KDM)security[BRS02]

u takesactiveadversariesintoconsiderationu impliesnon-malleability

INDsecurityfallsshortifanadversarycanobtainsideinformationofsecretstates

e.g.)Anonymouscredential,hard-diskencryption,FHE

KDM securityF-KDMgame(1userver.)

KDMquery:functionfinF

encryptionoff(sk) or0|f(sk)|

accordingtob

F-KDM-CPAsecure

Challenger AdversaryA

b{0,1}

Guess b

A cannot guess b correctlywith prob. greater than 1/2

KDM security

Theadversarycanalsomakeadecryptionquery F-KDM-CCAsecure

F-KDMgame(1userver.)

KDMquery:functionfinF

encryptionoff(sk) or0|f(sk)|

accordingtob

F-KDM-CPAsecure

Challenger AdversaryA

b{0,1}

Guess b

A cannot guess b correctlywith prob. greater than 1/2

Ourfocus

PreviousworksonKDM-CCA

F-KDM-CCAPKE

F-KDM-CPAPKE

1.[CCS09]+NIZK

NYparadigm

F:anyfunctionclass

Concreteinstantiation:Aff-KDM-CCAPKEfromDDHonpairing

PreviousworksonKDM-CCA

F-KDM-CCAPKE

F-KDM-CPAPKE

1.[CCS09]+NIZK

NYparadigm

2.[Hof13]Circ-CCAPKE

Moreefficientthan[CCS09]DCR

+DDHonpairing

F:anyfunctionclass

Concreteinstantiation:Aff-KDM-CCAPKEfromDDHonpairing

PreviousworksonKDM-CCA

F-KDM-CCAPKE

F-KDM-CPAPKE

1.[CCS09]+NIZK

NYparadigm

2.[Hof13]Circ-CCAPKE

Moreefficientthan[CCS09]DCR

+DDHonpairing

3.[HLL16](basedon[LLJ15])

Aff-KDM-CCAPKEDDH+DCR

onaspecificgroup poly-KDM-CCAPKE

w/opairingandefficient

F:anyfunctionclass

Concreteinstantiation:Aff-KDM-CCAPKEfromDDHonpairing

Openproblem

ALLexistingKDM-CCAsecurePKErelyon

NIZKor

pairingor

multipleassumptions(DDH+DCR)

ConstructionbasedonasingleassumptionusingneitherNIZKnorpairing??

???

Especially,allschemesw/oNIZKareproposedunderDDH+DCRonaspecificgroup Removingoneofthemseemstobedifficult

KDM-CCAforallfunctions[App11]showed

All-KDM-CCAPKE

P-KDM-CCAPKE

P-KDM:KDMsecurityw.r.t.projectionfunctions

Only[CCS09]sschemeiscompatiblewiththistransformation NeedNIZKorpairing

All-KDM-CCAsecurePKEusingneitherNIZKnorpairing??

+Garbledcircuit

???

Thiswork

Aff-KDM-CCAPKE

Projectivehashfunctions

1.AframeworkachievingKDM-CCAsecurityin1usersetting

IND-CCAPKE

Homomorphic

+

Thiswork

Aff-KDM-CCAPKE

ProjectivehashfunctionsDDH

1.AframeworkachievingKDM-CCAsecurityin1usersetting

IND-CCAPKE

Homomorphic

+DCR

QR

Thiswork

Aff-KDM-CCAPKE

ProjectivehashfunctionsDDH

All-KDM-CCAPKE

[App14]

1.AframeworkachievingKDM-CCAsecurityin1usersetting

IND-CCAPKE

Homomorphic

+DCR

QR

Thiswork

Aff-KDM-CCAPKE

ProjectivehashfunctionsDDH

All-KDM-CCAPKE

[App14]

1.AframeworkachievingKDM-CCAsecurityin1usersetting

2.KDM-CCAsecurityinmultiusersettingofconcreteinstantiations

IND-CCAPKE

Homomorphic

+DCR

QR

Reducedgoal

KDM-CPA/IND-CCAPKE

KDM-CCAPKE

IND-CCAPKE

+

Reducedgoal

Weessentiallyshow

Reducedgoal

KDM-CPA/IND-CCAPKE

KDM-CCAPKE

IND-CCAPKE

+

Reducedgoal

MucheasiertoconstructthanKDM-CCAPKEJ

Weessentiallyshow

Projectivehashfunctions

Homomorphic

Reducedgoal

KDM-CPA/IND-CCAPKE

KDM-CCAPKE

IND-CCAPKE

+

Reducedgoal

MucheasiertoconstructthanKDM-CCAPKEJ

Weessentiallyshow

Triplemodeproof[MTY11]

E(pk, f(sk))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