Data-Oblivious Graph Algorithms in Outsourced External Memory

TL;DR

This paper develops new data-oblivious algorithms for fundamental graph problems in outsourced external memory, enhancing privacy by hiding data access patterns without relying on random oracles.

Contribution

It introduces efficient data-oblivious algorithms for graph problems in outsourced external memory, addressing privacy concerns in data outsourcing scenarios.

Findings

New algorithms for minimum spanning trees in data-oblivious external memory

Efficient data-oblivious algorithms for tree traversals and LCA queries

Algorithms do not rely on constant-time random oracles

Abstract

Motivated by privacy preservation for outsourced data, data-oblivious external memory is a computational framework where a client performs computations on data stored at a semi-trusted server in a way that does not reveal her data to the server. This approach facilitates collaboration and reliability over traditional frameworks, and it provides privacy protection, even though the server has full access to the data and he can monitor how it is accessed by the client. The challenge is that even if data is encrypted, the server can learn information based on the client data access pattern; hence, access patterns must also be obfuscated. We investigate privacy-preserving algorithms for outsourced external memory that are based on the use of data-oblivious algorithms, that is, algorithms where each possible sequence of data accesses is independent of the data values. We give new efficient data-oblivious algorithms in the outsourced external memory model for a number of fundamental graph problems. Our results include new data-oblivious external-memory methods for constructing minimum spanning trees, performing various traversals on rooted trees, answering least common ancestor queries on trees, computing biconnected components, and forming open ear decompositions. None of our algorithms make use of constant-time random oracles.