Statistically-secure ORAM with $\tilde{O}(\log^2 n)$ Overhead

TL;DR

This paper presents a simple, statistically secure ORAM with an improved overhead of approximately log-squared n, surpassing previous protocols that either relied on computational assumptions or had higher overhead.

Contribution

The authors introduce a new ORAM construction that is both statistically secure and simpler to implement, with a novel analysis based on a supermarket problem model.

Findings

Achieves $ ilde{O}( ext{log}^2 n)$ overhead for statistically secure ORAM.

Simplifies previous ORAM constructions, making implementation easier.

Provides a new analysis technique using the supermarket problem model.

Abstract

We demonstrate a simple, statistically secure, ORAM with computational overhead $\tilde{O}(\log^2 n)$; previous ORAM protocols achieve only computational security (under computational assumptions) or require $\tilde{\Omega}(\log^3 n)$ overheard. An additional benefit of our ORAM is its conceptual simplicity, which makes it easy to implement in both software and (commercially available) hardware. Our construction is based on recent ORAM constructions due to Shi, Chan, Stefanov, and Li (Asiacrypt 2011) and Stefanov and Shi (ArXiv 2012), but with some crucial modifications in the algorithm that simplifies the ORAM and enable our analysis. A central component in our analysis is reducing the analysis of our algorithm to a "supermarket" problem; of independent interest (and of importance to our analysis,) we provide an upper bound on the rate of "upset" customers in the "supermarket" problem.