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格LWE难题下分层的基于身份的签名方案
Introduction
Withtherapiddevelopmentofmoderncommunicationtechnologies,datasecurityhasbecomeamajorconcernforbothindividualsandorganizations.Publickeycryptographyiswidelyadoptedtoprovidesecurecommunicationoverinsecurenetworks.Inrecentyears,lattice-basedcryptographyhasemergedasapromisingalternativetotraditionalcryptographicschemes.Thelearningwitherrors(LWE)problemisoneofthemostwell-studiedhardnessassumptionsinlattice-basedcryptography.Inthispaper,wefocusonlattice-basedidentity-basedsignature(IBS)schemes,whichofferausefultoolforsecurecommunication.
Lattice-basedIdentity-BasedSignature(IBS)
Identity-basedsignature(IBS)isacryptographicprimitivethatenablesasignertosignamessageonbehalfofadesignatedidentitywithoutrevealingthesecretkey.TheconceptofIBSwasfirstintroducedbyShamirin1984.Sincethen,numerousIBSschemeshavebeenproposedintheliterature.However,mostoftheexistingIBSschemesarebasedontraditionalnumber-theoreticassumptions,whicharevulnerabletoattacksbyquantumcomputers.Therefore,thereisagrowinginterestindevelopingIBSschemesbasedonlattice-basedassumptions.
Lattice-basedcryptographyreliesonthehardnessofcertainlatticeproblems,suchastheshortestvectorproblem(SVP)andtheLWEproblem.TheLWEproblemisawell-studiedprobleminlattice-basedcryptography,anditformsthebasisofmanycryptographicschemes,includingIBS.TheLWEproblemcanbestatedasfollows:
Givenasetofnpairs(ai,bi),whereaiisarandomn-dimensionalvectorwithintegerentriesmoduloqandbiisequaltotheinnerproductofaiandsmoduloq,wheresisasecretn-dimensionalvectorwithintegerentries.Thetaskistorecoverthesecretvectors.
Lattice-basedIBScanbeconstructedbycombiningtheLWEproblemwithothercryptographicprimitives,suchastrapdoorone-wayfunctionsandhashfunctions.Oneofthenotablefeaturesoflattice-basedIBSisthatitprovidesanaturalwaytoachievehierarchicalIBS,whichallowsforefficientdelegationofsigningauthority.
HierarchicalIBS
Inmanyapplications,ahierarchicalstructureisneededtomanagesigningauthority.HierarchicalIBSextendsthebasicIBSschemebyallowinga