Circuit OPRAM: A (Somewhat) Tight Oblivious Parallel RAM

An Oblivious Parallel RAM (OPRAM) provides a general method to simulate any Parallel RAM (PRAM) program, such that the resulting memory access patterns leak nothing about secret inputs. OPRAM was originally proposed by Boyle et al. as the natural parallel counterpart of Oblivious RAM (ORAM), which was shown to have broad applications, e.g., in cloud outsourcing, secure processor design, and secure multiparty computation. Since parallelism is common in modern computing architectures such as multi-core processors or cluster computing, OPRAM is naturally a powerful and desirable building block as much as its sequential counterpart ORAM is. Although prior work (in particular, Circuit ORAM) has shown how to construct ORAM schemes that are asymptotically tight under certain parameter ranges, the performance of known OPRAM schemes still do not match their sequential counterparts, leaving open two main questions: (i) whether one can construct an OPRAM scheme whose performance is competitive relative to known sequential counterparts; and (ii) whether one can construct OPRAM schemes that are asymptotically optimal. Our paper answers the first question positively and gives partial answers to the second question. Specifically, we construct Circuit OPRAM, a new OPRAM scheme that makes the following contributions: 1. We achieve asymptotical improvement in terms of both total work and parallel runtime in comparison with known OPRAM schemes. More specifically, we improve the total work by a logarithmic factor and parallel runtime by poly-logarithmic factors. 2. We show that under sufficiently large block sizes, we can construct an OPRAM scheme that is asymptotically optimal both in total work and parallel runtime when the number of CPUs is not too small. 3. Our construction features a combination of novel techniques that enable us to (i) have asymptotically tight stochastic processes that do not suffer from worst-case and average-case discrepancies; and (ii) temporally reallocate work over offline and online stages of the algorithm such that we can achieve small parallel runtime overall. These techniques can be of independent interest in the design of of parallel oblivious algorithms in general. ∗The University of Hong Kong. Email: [email protected] †Cornell University. Email: [email protected]