Boneh, Raghunathan, and Segev (CRYPTO '13) have recently put forward the notion of function privacy and applied it to identity-based encryption, motivated by the need for providing predicate privacy in public-key searchable encryption. Intuitively, their notion asks that decryption keys reveal essentially no information on their corresponding identities, beyond the absolute minimum necessary. While Boneh et al. showed how to construct function-private identity-based encryption (which implies predicate-private encrypted keyword search), searchable encryption typically requires a richer set of predicates.
In this paper we significantly extend the function privacy framework. First, we introduce the new notion of subspace-membership encryption, a generalization of inner-product encryption, and formalize a meaningful and realistic notion for capturing its function privacy. Then, we present a generic construction of a function-private subspace-membership encryption scheme based on any inner-product encryption scheme. Finally, we show that function-private subspace-membership encryption can be used to construct function-private identity-based encryption. These are the first generic constructions of function-private encryption schemes based on non-function-private ones, resolving one of the main open problems posed by Boneh, Raghunathan, and Segev.
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