Identity-basedhashproofsystemisabasicandimportantprimitive.Ittographicschemesandprotocolsthataresecureagainstkey-leakageattacks.Inthisupdatableidentity-basedhashproofsystem,inwhichtherelatedmastersecretkeyiswidelyutilizedtoconstructcryp-paper,weintroducetheconceptofandtheidentitysecretkeycanbeupdatedsecurely.Then,weinstantiatethisprimitivebasedonlatticesinthestandardmodel.Moreover,weintroduceanapplicationofthisnewprimitivebygivingagenericconstructionofleakage-resilientpublic-keyencryptionschemeswithanonymity.Thisconstructioncanbeconsideredastheintegrationofthebounded-retrievalmodelandthecontinualleakagemodel.Comparedwiththeexistingleakage-resilientschemes,ourconstructionnotonlyismoreefficientbutalsocanresistmuchmorekeyleakage.