Provably secure public-key encryption with conjunctive and subset keyword search

Public-key encryption with keyword search (PEKS) schemes enable public key holders to encrypt documents, while the secret key holder is able to generate queries for the encrypted data. In this paper, we present two PEKS schemes with extended functionalities. The first proposed scheme supports conjunctive queries. That is, it enables searching for encrypted documents containing a chosen list of keywords. We prove the computational consistency of our scheme, and we prove security under the asymmetric DBDH assumption. We show that it improves previous related schemes in terms of efficiency and in terms of index and trapdoor size. The second proposed scheme supports subset queries and some more general predicates. We prove the computational consistency of our scheme, and we prove our scheme secure under the p-BDHI assumption. We show that it improves previous related schemes in terms of efficiency and expressiveness. Moreover, unlike previous related schemes, it admits an arbitrary keyword space.