Lightweight Symmetric-Key Hidden Vector Encryption without Pairings

Hidden vector encryption (HVE), introduced by Boneh and Waters in TCC’07, is an expressive sub-class of predicate encryption, that allows conjunctive, subset, range and comparison queries over encrypted data. All existing HVE constructions in the cryptographic literature use bilinear pairings over either composite order or prime order groups. In this paper, we address the open problem of constructing a lightweight symmetric-key HVE scheme that does not use bilinear pairings, but only efficient cryptographic primitives such as pseudo-random functions (PRFs) and block ciphers. The relevance of this problem stems from the implementation and performance overheads for bilinear pairings over composite/prime order groups, which are significantly larger than that for PRFs and block ciphers, in both software and hardware. While lightweight symmetric-key constructions exist for keyword search on encrypted data, we aim to expand the scope of such constructions to support a richer set of query predicates. In this direction, we present the first lightweight symmetric-key HVE construction that does not use bilinear pairings. Our construction only uses a PRF and a PCPA-secure symmetrickey encryption algorithm, making it amenable to both hardware and software implementations in real-life resource-constrained environments. We prove the selective-simulation-security and adaptive-simulation-security of our construction in the standard model and ideal cipher model, respectively, against probabilistic polynomial-time adversaries that can make an unrestricted number of ciphertext generation and secret-key generation queries.