A Simple Recursive Tree Oblivious RAM

Oblivious RAM (ORAM) has received increasing attention in the past few years. The goal of oblivious RAM is to enable a client, that can locally store only a small (preferably constant) amount of data, to store remotely N data items, and access them while hiding the identities of the items that are being accessed. Most of the earlier ORAM constructions were based on the hierarchical data structure of Goldreich and Ostrovsky [3]. Shi et al. [9] introduced a binary tree ORAM, which is simpler and more efficient than the classical hierarchical ORAM. Gentry et al. [2] have followed them and improved the scheme. In this work, we improve these two constructions. Our scheme asymptotically outperforms all previous tree based ORAM schemes that have constant client memory, with an overhead of O(log N log logN) per operation for a O(N) storage server. Although the best known asymptotic result for ORAM is due to the hierarchical structure of Kushilevitz et al. [6] (O( log N log logN )), tree based ORAM constructions are much simpler.