Keyword search meets membership testing: Adaptive security from SXDH

Abstract

Searchable encryption (SE) allows users to securely store sensitive data in encrypted form on cloud and at the same time perform keyword search over the encrypted documents. In this work, we focus on variants of SE schemes that along with keyword search, also support membership testing. The problem can be formulated in two flavors depending on whether the search policy is encoded in the ciphertext or in the trapdoor. The ciphertext-policy variant is called Broadcast Encryption with Keyword Search (BEKS) and allows only privileged users to perform keyword search on an encrypted file. Available dedicated constructions could achieve selective security under parameterized assumption. The key-policy variant, called Key-Aggregate Searchable Encryption (KASE), restricts the keyword search within a particular set of documents. Naive application of existing SE schemes in this scenario leads to inefficient protocols with either variable length trapdoor or exponential blowup of storage requirement in terms of the document set size. This therefore calls for an efficient solution that allows such subset based restricted search with constant trapdoor size. In this work, we have presented adaptively secure solutions for both the above problems. Our BEKS construction achieves constant-size ciphertext whereas the KASE construction achieves constant-size trapdoor. Both the constructions are instantiated in prime-order bilinear groups and are proven anonymous CPA-secure under SXDH assumption by extending Jutla-Roy technique. Our proposed solutions improve upon the only other adaptively secure schemes that can be obtained using the generic technique of Ambrona et al.