Simple and efficient two-server ORAM

Abstract

We show a protocol for two-server oblivious RAM (ORAM) that is simpler and more efficient than the best prior work. Our construction combines any tree-based ORAM with an extension of a two-server private information retrieval scheme by Boyle et al., and is able to avoid recursion and thus use only one round of interaction. In addition, our scheme has a very cheap initialization phase, making it well suited for RAM-based secure computation. Although our scheme requires the servers to perform a linear scan over the entire data, the cryptographic computation involved consists only of block-cipher evaluations. A practical instantiation of our protocol has excellent concrete parameters: for storing an N-element array of arbitrary size data blocks with statistical security parameter ƛ, the servers each store 4N encrypted blocks, the client stores ƛ +2log N blocks, and the total communication per logical access is roughly 10 log N encrypted blocks.