Statistically-secure ORAM with $\tilde{O}(\log^2 n)$ Overhead
This work provides a more efficient and secure ORAM solution for applications requiring data privacy, such as cloud storage or secure computation, though it builds incrementally on prior constructions.
The paper tackles the problem of constructing a statistically secure Oblivious RAM (ORAM) with lower computational overhead, achieving $ ilde{O}(\log^2 n)$ overhead compared to previous protocols that either offered only computational security or required $ ilde{\Omega}(\log^3 n)$ overhead.
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 $\tildeΩ(\log^3 n)$ 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.