Oblivious Multi-Way Band Joins: An Efficient Algorithm for Secure Range Queries

Abstract

This thesis introduces the first efficient oblivious algorithm for acyclic multi-way joins with band conditions, extending the classical Yannakakis algorithm to support inequality predicates (>, <, ≥, ≤) without leaking sensitive information through memory access patterns. Band joins, which match tuples over value ranges rather than exact keys, are widely used in temporal, spatial, and proximity-based analytics but present challenges in oblivious computation. Our approach employs a dual-entry technique that transforms range matching into cumulative sum computations, enabling multiplicity computation in an oblivious manner. The algorithm achieves O(N log N + k · OUT log OUT) complexity, where k is the number of tables in the join query, N is the input size, and OUT is the output size, matching state-of-the-art oblivious equality joins up to a factor of k while supporting full band constraints. We implement the method using Intel SGX with batch processing and evaluate it on the TPC-H benchmark dataset, demonstrating practical performance and strong obliviousness guarantees under an honest-but-curious adversary model.