Oblivious Parallel RAM

A machine is said to be oblivious if the sequences of memory accesses made by the machine for two inputs with the same running time are identically (or close to identically) distributed. Oblivious RAM (ORAM) compilers—compilers that turn any RAM program Π into a oblivious RAM Π′, while only incurring a “small”, polylogarithmic, slow-down—have been extensively studied since the work of Goldreich and Ostrovsky [GO96] and have numerous fundamental applications. These compilers, however, do not leverage parallelism: even if Π can be heavily parallelized, Π′ will be inherently sequential. In this work, we present the first Oblivious Parallel RAM (OPRAM) compiler, which compiles any PRAM into an oblivious PRAM while only incurring a polylogarithmic slowdown. ∗The research of the first author has received funding from the European Union’s Tenth Framework Programme (FP10/ 2010-2016) under grant agreement no. 259426 ERC-CaC. †Pass is supported in part by a Alfred P. Sloan Fellowship, Microsoft New Faculty Fellowship, NSF Award CNS1217821, 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.