Sub-logarithmic Distributed Oblivious RAM with Small Block Size

TL;DR

This paper introduces new distributed ORAM schemes with sub-logarithmic overhead and small block sizes, leveraging multiple servers and advanced hashing techniques for improved efficiency and privacy.

Contribution

It presents the first distributed ORAM constructions with sub-logarithmic overhead and small block size, utilizing enhanced hierarchical methods and efficient hashing.

Findings

Achieves $O(rac{ ext{log} N}{ ext{log} ext{log} N})$ overhead with $\Omega(\text{log}^2 N)$ block size for any $m\geq 2$ servers.

Develops a 3-server ORAM with near-logarithmic block size and super-logarithmic overhead.

Shows constant overhead is possible with four servers when servers perform light local computations.

Abstract

Oblivious RAM (ORAM) is a cryptographic primitive that allows a client to securely execute RAM programs over data that is stored in an untrusted server. Distributed Oblivious RAM is a variant of ORAM, where the data is stored in $m>1$ servers. Extensive research over the last few decades have succeeded to reduce the bandwidth overhead of ORAM schemes, both in the single-server and the multi-server setting, from $O(\sqrt{N})$ to $O(1)$. However, all known protocols that achieve a sub-logarithmic overhead either require heavy server-side computation (e.g. homomorphic encryption), or a large block size of at least $\Omega(\log^3 N)$. In this paper, we present a family of distributed ORAM constructions that follow the hierarchical approach of Goldreich and Ostrovsky [GO96]. We enhance known techniques, and develop new ones, to take better advantage of the existence of multiple servers. By plugging efficient known hashing schemes in our constructions, we get the following results: 1. For any $m\geq 2$, we show an $m$-server ORAM scheme with $O(\log N/\log\log N)$ overhead, and block size $\Omega(\log^2 N)$. This scheme is private even against an $(m-1)$-server collusion. 2. A 3-server ORAM construction with $O(\omega(1)\log N/\log\log N)$ overhead and a block size almost logarithmic, i.e. $\Omega(\log^{1+\epsilon}N)$. We also investigate a model where the servers are allowed to perform a linear amount of light local computations, and show that constant overhead is achievable in this model, through a simple four-server ORAM protocol.