Lower Bounds for Multi-Server Oblivious RAMs.

In this work, we consider the construction of oblivious RAMs (ORAM) in a setting with multiple servers and the adversary may corrupt a subset of the servers. We present an Omega(log n) overhead lower bound for any k-server ORAM that limits any PPT adversary to distinguishing advantage at most 1/4k when only one server is corrupted. In other words, if one insists on negligible distinguishing advantage, then multi-server ORAMs cannot be faster than single-server ORAMs even with polynomially many servers of which only one unknown server is corrupted. Our results apply to ORAMs that may err with probability at most 1/128 as well as scenarios where the adversary corrupts larger subsets of servers. We also extend our lower bounds to other important data structures including oblivious stacks, queues, deques, priority queues and search trees.