A Constant Round Write-Only ORAM

Abstract

The write-only oblivious RAM (ORAM) is proposed to efficiently protect the privacy of applications such as cloud storage synchronization and encrypted hidden volumes. For N blocks with size B = Ω(log2N), the most efficient write-only ORAM, DetWoORAM, achieves O(B) communication complexity with O(logN) rounds per logical write. We propose a two-level write-only ORAM and achieve O(B) communication complexity with O(1) rounds. Similar to the traditional bucket-based ORAM schemes, we set a rate for the write operation to further reduce the communication complexity. The top-level stores data blocks in a flat array and the write pattern is protected by writing blocks uniformly at random. The second level employs a binary tree to store the position map of data blocks. To avoid recursive storage, a static position map for blocks in the second level is used. Both the analysis and experiments show that, besides the achieved low communication complexity and rounds, the stash sizes in the top level and the second level are bounded to O(B) and ω(B), respectively.