Differentially Oblivious Two-Party Pattern Matching With Sublinear Round Complexity

Abstract

Privacy-preserving pattern matching enables a user to find all occurrences of a pattern in a text without revealing any sensitive information. However, many previous works designed on homomorphic encryption suffer from expensive computational overhead and a simple way to use it can lead to potential input leakage via access pattern during the matching process. In this article, we propose a differentially oblivious pattern matching algorithm, called DOPM. It is deployed on two servers by taking a series of lightweight secret-sharing-based protocols as building blocks. In DOPM, we utilize a witness array and the single instruction multiple data (SIMD) technique to parallelize the algorithm, which achieves sublinear round complexity in performing two-party computation. Additionally, we formally define a new access pattern privacy in the context of differential privacy, named $(\epsilon,\delta)$(ε,δ)-differentially oblivious privacy ($(\epsilon,\delta)$(ε,δ)-DOP), and present a pair of differentially oblivious algorithms to read and write elements in an array without using oblivious shuffle. Detailed security analysis demonstrates that the proposed DOPM achieves the goal of protecting confidentiality and access pattern during the matching process. Finally, we benchmark our scheme on a real-world human genome dataset, and experimental results show that DOPM is $10.9\times$10.9× faster than the brute-force matching, $3.4-7.1\times$3.4-7.1× faster than two state-of-the-art approaches.