Oblivious Random Access Machine (ORAM) is a cryptographic tool used to obfuscate the access pattern. In this paper, we focus on perfect security of ORAM. A perfectly secure ORAM is an ORAM that can resist against an adversary with unlimited computing power, and the failure probability of ORAM is zero rather than negligible. Since all existing perfectly secure single-server ORAM solutions require at least sublinear worst-case bandwidth overhead, we pose a natural and open question: can we construct a perfectly secure single-server ORAM with logarithmic worst-case bandwidth overhead? In this paper, we propose the first tree-based perfectly secure ORAM scheme, named LPS-ORAM. To meet the requirements of perfectly secure ORAM, two techniques are presented. One technique is dynamic remapping associated with a mutable scope, and the other is dynamically balanced eviction. Their combined effect allows the root bucket to never fill up while maintaining its statistical security in tree-based ORAM. In the worst case, our solution achieves logarithmic bandwidth overhead. Therefore, our solution answers the open question in the affirmative. In terms of overhead for temporary storage on the client side, compared with the latest perfectly secure ORAM solution, our solution is reduced from sublinear to logarithmic, and even if the server storage overhead scales lightly, it is still at the same level of quantity as the state of the art. Finally, the evaluation results show that our LPS-ORAM has a significant advantage in terms of bandwidth overhead and overhead for temporary storage on the client side.

Oblivious Random Access Machine (ORAM) is a kind of cryptographic primitive that allows a client to access its private data from the server without disclosing the access pattern. To deal with consecutive requested blocks at a time efficiently, range ORAM (rORAM) is presented. In the previous rORAM scheme, the locality, namely, the number of discontinuous seeks to complete a request, is reduced to O(log 2 N), nevertheless, the bandwidth cost is increased to the polylogarithmic level. Hence, there exists an open question, that is, whether rORAM can be constructed with the same bandwidth efficiency as a regular ORAM, that is, O(log N)-block? In this paper, we propose a new rORAM scheme, called L 2 -rORAM. In our scheme, a compatible superblock technique is proposed, and it is combined together with an eviction technique for range blocks, so that it avoids duplication of multiple copies and extra dummy access. As a result, it obtains O(log N)-block bandwidth cost, which affirmatively answers the above open question. Meanwhile, the data locality is reduced to O(log N). In addition, the client storage is maintained at the small level of O(log N)block, and the server storage is maintained at the unexpanded level of O(N)-block. Finally, experimental results show that the average response time of our