Optimal Oblivious Algorithms for Multi-way Joins

TL;DR

This paper introduces a new sorting-based, oblivious multi-way join algorithm that achieves optimal time and cache complexity without relying on expensive ORAM techniques, enhancing data privacy in cloud databases.

Contribution

It presents a novel, provably oblivious multi-way join algorithm that matches insecure optimal complexities, avoiding reliance on ORAM or other security assumptions.

Findings

Achieves time complexity matching insecure optimal join algorithms.

Matches cache complexity lower bounds up to logarithmic factors.

Operates without ORAM or trusted computing assumptions.

Abstract

In cloud databases, cloud computation over sensitive data uploaded by clients inevitably causes concern about data security and privacy. Even when encryption primitives and trusted computing environments are integrated into query processing to safeguard the actual contents of the data, access patterns of algorithms can still leak private information about the data. Oblivious Random Access Memory (ORAM) and circuits are two generic approaches to address this issue, ensuring that access patterns of algorithms remain oblivious to the data. However, deploying these methods on insecure algorithms, particularly for multi-way join processing, is computationally expensive and inherently challenging. In this paper, we propose a novel sorting-based algorithm for multi-way join processing that operates without relying on ORAM simulations or other security assumptions. Our algorithm is a non-trivial, provably oblivious composition of basic primitives, with time complexity matching the insecure worst-case optimal join algorithm, up to a logarithmic factor. Furthermore, it is cache-agnostic, with cache complexity matching the insecure lower bound, also up to a logarithmic factor. This clean and straightforward approach has the potential to be extended to other security settings and implemented in practical database systems.