Public key encryption with equality test in the standard model

Abstract

Public key encryption with equality test (PKEET) is a cryptosystem that allows a tester who has trapdoors issued by one or more users U-i to perform equality tests on ciphertexts encrypted using public key(s) of U-i. Since this feature has a lot of practical applications including search on encrypted data, several PKEET schemes have been proposed so far. However, to the best of our knowledge, all the existing proposals are proven secure only under the hardness of number-theoretic problems and/or the random oracle heuristics. In this paper, we show that this primitive can be achieved not only generically from well-established other primitives but also even without relying on the random oracle heuristics. More precisely, our generic construction for PKEET employs a two-level hierarchical identity-based encryption scheme, which is selectively secure against chosen plaintext at-tacks, a strongly unforgeable one-time signature scheme and a cryptographic hash function. Our generic approach toward PKEET has several advantages over all the previous works; it directly leads the first standard model construction and also directly implies the first lattice-based construction. Finally, we show how to extend our approach to the identity-based setting.