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

We demonstrate a simple, statistically secure, ORAM with computational overhead Õ(log n); previous ORAM protocols achieve only computational security (under computational assumptions) or require Ω̃(log 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. ∗Cornell University. {chung,rafael}@cs.cornell.edu Chung is supported in part by NSF Award CCF-1214844 and Pass’ Sloan Fellowship. Pass is supported in part by a Alfred P. Sloan Fellowship, Microsoft New Faculty Fellowship, NSF Award CNS-1217821, NSF CAREER Award CCF-0746990, NSF Award CCF-1214844, AFOSR YIP Award FA9550-10-1-0093, and DARPA and AFRL under contract FA8750-11-20211. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Defense Advanced Research Projects Agency or the US Government. †Princeton University. [email protected] ar X iv :1 30 7. 36 99 v1 [ cs .C R ] 1 4 Ju l 2 01 3