Maliciously Secure Multi-Client ORAM

Abstract

Oblivious RAM (ORAM) has emerged as an enabling technology to secure cloud-based storage services. The goal of this cryptographic primitive is to conceal not only the data but also the access patterns from the server. While the early constructions focused on a single client scenario, a few recent works have focused on a setting where multiple clients may access the same data, which is crucial to support data sharing applications. All these works, however, either do not consider malicious clients or they significantly constrain the definition of obliviousness and the system´s practicality. It is thus an open question whether a natural definition of obliviousness can be enforced in a malicious multi-client setting and, if so, what the communication and computational lower bounds are. In this work, we formalize the notion of maliciously secure multi-client ORAM, we prove that the server-side computational complexity of any secure realization has to be Ω(n), and we present a cryptographic instantiation of this primitive based on private information retrieval techniques, which achieves an O(√N) communication complexity. We further devise an efficient access control mechanism, built upon a novel and generally applicable realization of plaintext equivalence proofs for ciphertext vectors. Finally, we demonstrate how our lower bound can be bypassed by leveraging a trusted proxy, obtaining logarithmic communication and server-side computational complexity. We implemented our scheme and conducted an experimental evaluation, demonstrating the feasibility of our approach.