Perfectly Oblivious (Parallel) RAM Revisited, and Improved Constructions.

Abstract

Oblivious RAM (ORAM) is a technique for compiling any RAM program to an oblivious counterpart, i.e., one whose access patterns do not leak information about the secret inputs. Similarly, Oblivious Parallel RAM (OPRAM) compiles a parallel RAM program to an oblivious counterpart. In this paper, we care about ORAM/OPRAM with perfect security, i.e., the access patterns must be identically distributed no matter what the program’s memory request sequence is. In the past, two types of perfect ORAMs/OPRAMs have been considered: constructions whose performance bounds hold in expectation (but may occasionally run more slowly); and constructions whose performance bounds hold deterministically (even though the algorithms themselves are randomized). In this paper, we revisit the performance metrics for perfect ORAM/OPRAM, and show novel constructions that achieve asymptotical improvements for all performance metrics. Our first result is a new perfectly secure OPRAM scheme with O(log³ N/log log N) expected overhead. In comparison, prior literature has been stuck at O(log³ N) for more than a decade. Next, we show how to construct a perfect ORAM with O(log³ N/log log N) deterministic simulation overhead. We further show how to make the scheme parallel, resulting in an perfect OPRAM with O(log⁴ N/log log N) deterministic simulation overhead. For perfect ORAMs/OPRAMs with deterministic performance bounds, our results achieve subexponential improvement over the state-of-the-art. Specifically, the best known prior scheme incurs more than √N deterministic simulation overhead (Raskin and Simkin, Asiacrypt'19); moreover, their scheme works only for the sequential setting and is not amenable to parallelization. Finally, we additionally consider perfect ORAMs/OPRAMs whose performance bounds hold with high probability. For this new performance metric, we show new constructions whose simulation overhead is upper bounded by O(log³ /log log N) except with negligible in N probability, i.e., we prove high-probability performance bounds that match the expected bounds mentioned earlier.