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At first, your syntax (Setup,GenKey,Encrypt,Query) seems to be the syntax of public-key encryption with keyword-search (PKES). In the case of predicate-based encryption, we use Decrypt rather than Query. The Sahai-Waters Fuzzy IBE I recommend Sahai and Waters: Fuzzy identity-based encryption (EUROCRYPT 2005) as a first step. I assume you know the basic of ...

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