International Association for Cryptologic Research

International Association
for Cryptologic Research


Lower Bounds for Multi-Server Oblivious RAMs

Kasper Green Larsen
Mark Simkin
Kevin Yeo
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Abstract: In this work, we consider 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.
Video from TCC 2020
  title={Lower Bounds for Multi-Server Oblivious RAMs},
  booktitle={Theory of Cryptography},
  author={Kasper Green Larsen and Mark Simkin and Kevin Yeo},