Parallel Oblivious Joins using Radix Partitioning

Abstract

We present parallel doubly oblivious algorithms for both non-foreign key and foreign key joins using an oblivious radix partitioning technique. Oblivious query processing enables secure execution over encrypted data when organizations outsource data to the cloud. When the cloud server processes encrypted data within hardware enclaves, the data is vulnerable to side-channel leaks caused by data-dependent memory access patterns and control flow. Our algorithms efficiently defend against these vulnerabilities by combining data partitioning with parallel execution. Specifically, we propose a doubly oblivious radix partitioning approach that divides input arrays into disjoint partitions without leaking the multiplicity of individual elements, unlike vanilla radix partitioning. This is especially important for join operations, where duplicate keys are common. To construct our join algorithm, we apply oblivious radix partitioning independently to each input table, allowing the algorithm to compare tuples only within corresponding partitions. When input tables are presorted, our oblivious join algorithm is the first to avoid combining and obliviously resorting them, yielding performance improvements over the state-of-the-art scheme, Obliviator. Beyond joins, our oblivious radix partitioning technique is a standalone primitive with applications to a broad class of problems, including oblivious aggregation and private set intersection.