S3ORAM: A Computation-Efficient and Constant Client Bandwidth Blowup ORAM with Shamir Secret Sharing

Oblivious Random Access Machine (ORAM) enables a client to access her data without leaking her access patterns. Existing client-efficient ORAMs either achieve O(log N) client-server communication blowup without heavy computation, or O(1) blowup but with expensive homomorphic encryptions. It has been shown that O(log N) bandwidth blowup might not be practical for certain applications, while schemes with O(1) communication blowup incur even more delay due to costly homomorphic operations. In this paper, we propose a new distributed ORAM scheme referred to as Shamir Secret Sharing ORAM (S(3)ORAM), which achieves O(1) client-server bandwidth blowup and O(1) blocks of client storage without relying on costly partial homomorphic encryptions. S(3)ORAM harnesses Shamir Secret Sharing, tree-based ORAM structure and a secure multi-party multiplication protocol to eliminate costly homomorphic operations and, therefore, achieves O(1) client-server bandwidth blowup with a high computational efficiency. We conducted comprehensive experiments to assess the performance of S(3)ORAM and its counterparts on actual cloud environments, and showed that S(3)ORAM achieves three orders of magnitude lower end-to-end delay compared to alternatives with O(1) client communication blowup (Onion-ORAM), while it is one order of magnitude faster than Path-ORAM for a network with a moderate bandwidth quality. We have released the implementation of S(3)ORAM for further improvement and adaptation.