Oblivious Parallel RAM and Applications

We initiate the study of cryptography for parallel RAM (PRAM) programs. The PRAM model captures modern multi-core architectures and cluster computing models, where several processors execute in parallel and make accesses to shared memory, and provides the “best of both ” circuit and RAM models, supporting both cheap random access and parallelism. We propose and attain the notion of Oblivious PRAM. We present a compiler taking any PRAM into one whose distribution of memory accesses is statistically independent of the data (with negligible error), while only incurring a polylogarithmic slowdown (in both total and parallel complexity). We discuss applications of such a compiler, building upon recent advances relying on Oblivious (sequential) RAM (Goldreich Ostrovsky JACM’12). In particular, we demonstrate the construction of a garbled PRAM compiler based on an OPRAM compiler and secure identity-based encryption