TWORAM: Efficient Oblivious RAM in Two Rounds with Applications to Searchable Encryption

We present TWORAM, an asymptotically efficient oblivious RAM (ORAM) protocol providing oblivious access (read and write) of a memory index y in exactly two rounds: The client prepares an encrypted query encapsulating y and sends it to the server. The server accesses memory M obliviously and returns encrypted information containing the desired value M[y]. The cost of TWORAM is only a multiplicative factor of security parameter higher than the tree-based ORAM schemes such as the path ORAM scheme of Stefanov et al. (CCS, 2013). TWORAM substantially improves the worst-case asymptotic complexity of existing round-optimal ORAM protocols and gives rise to interesting applications, and in particular to a 4-round searchable encryption scheme where search is sublinear in the worst case and the search pattern is not leaked—the access pattern can also be concealed assuming the documents are stored in the obliviously accessed memory M.