Abstract
Private Set Union (PSU) enables two parties to compute the union of their input sets without revealing any additional information. Tu et al. (USENIX Security 2025) introduced the state-of-the-art enhanced PSU (ePSU) framework, which strengthens security by preventing during-execution leakage. However, we observe that directly applying hash-to-bin on input sets within their framework introduces subtle but non-negligible privacy risks. In this work, we address this issue by combining oblivious pseudorandom functions (OPRF) with randomized shuffling, which eliminates the privacy leakage caused by direct hash-to-bin usage. Building on the revised framework, we further optimize the ePSU construction by introducing a bidirectional oblivious key-value store (OKVS), significantly reducing both communication and computational overhead. Experimental results show that, compared with the revised ePSU of Tu et al., our protocol achieves a 1.089–\(3.049\times\) reduction in communication cost and a 1.027–\(1.744\times\) runtime speedup.
Data availability
The datasets used and analyzed during the present study are available from the corresponding author upon reasonable request.
References
Lenstra, A. & Voss, T. Information Security Risk Assessment, Aggregation, and Mitigation. ACISP’04, 391–401 (2004).
Hogan, K. et al. Secure Multiparty Computation for Cooperative Cyber Risk Assessment. SecDev’16, 75–76 (2016).
Chung, H., Kim, M. & Yang, P. C. Multiparty delegated private set union with efficient updates on outsourced datasets. IEEE Trans. Dependable Secur. Comput. https://doi.org/10.1109/TDSC.2024.3419576 (2025).
Burkhart, M., Strasser, M., Many, D. & Dimitropoulos, X. SEPIA: Privacy-Preserving Aggregation of Multi-Domain Network Events and Statistics. USENIX Security’10 (2010).
Freudiger, J., Cristofaro, E.D. & Brito, A.E. Controlled Data Sharing for Collaborative Predictive Blacklisting. DIMVA’15, 327–349 (2015).
Ramanathan, S., Mirkovic, J. & Yu, M. BLAG: improving the accuracy of blacklists. NDSS’20 (2020).
Buddhavarapu, P. et al. Private Matching for Compute. Preprint at https://eprint.iacr.org/2020/599 (2020).
Garimella, G. et al. Private Set Operations from Oblivious Switching. PKC’21, 591–617 (2021).
Yan, J., Wei, L., Qian, X. & Zhang, L. IDPriU: A two-party ID-private data union protocol for privacy-preserving machine learning. J. Inf. Secur. Appl. https://doi.org/10.1016/j.jisa.2024.103913 (2025).
Kolesnikov, V., Rosulek, M., Trieu, N. & Wang, X. Scalable Private Set Union from Symmetric-Key Techniques. ASIACRYPT’19, 636–666 (2019).
Rabin, M.O. How to exchange secrets with oblivious transfer. Preprint at https://eprint.iacr.org/2005/187.pdf (2005).
Jia, Y. et al. Shuffle-based Private Set Union: Faster and More Secure. USENIX Security’22, 2947–2964 (2022).
Zhang, C. et al. Linear Private Set Union from Multi-Query Reverse Private Membership Test. USENIX Security’23, 337–354 (2023).
Chandran, G.R., Schneider, T., Stillger, M., & Weinert, C. Concretely Efficient Private Set Union via Circuit-Based PSI. ASIACCS’25, 149–162 (2025).
Jia, Y., Sun, S., Zhou, H & Gu, D. Scalable Private Set Union, with Stronger Security. USENIX Security’24, 6471–6488 (2024).
Tu, B. et al. Fast Enhanced Private Set Union in the Balanced and Unbalanced Scenarios. USENIX Security’25, 3437–2456 (2025).
Chase, M. & Miao, P. Private Set Intersection in the Internet Setting from Lightweight Oblivious PRF. CRYPTO’20, 34–63 (2020).
Mohassel, P. & Sadeghian, S.S. How to hide circuits in MPC an efficient framework for private function evaluation. EUROCRYPT’13, 557–574 (2013).
Kolesnikov, V., Matania, N., Pinkas, B., Rosulek, M. & Trieu, N. Practical multi-party private set intersection from symmetric-key techniques. ACM CCS’17, 1257–1272 (2017).
Raghuraman, S & Rindal, P. Blazing Fast PSI from Improved OKVS and Subfield VOLE. CCS’22, 2505–2517 (2022).
Tu, B., Chen, Y., Liu, Q., & Zhang, C. Fast Unbalanced Private Set Union from Fully Homomorphic Encryption. ACM CCS’23, 2959–2973 (2023).
Zhang, C. et al. Unbalanced Private Set Union with Reduced Computation and Communication. ACM CCS’24, 1434–1477 (2024).
Dumas, J.G. et al. Optimal Communication Unbalanced Private Set Union. ACNS’25, 107–135 (2025).
Rindal, P. & Schoppmann, P. VOLE-PSI: fast OPRF and circuit-PSI from vector-OLE. EUROCRYPT’21, 901–930 (2021).
Garimella, G. et al. Oblivious Key-Value Stores and Amplification for Private Set Intersection. CRYPTO’21, 395–425 (2021).
Raghuraman, S. & Rindal, P. Blazing Fast PSI from Improved OKVS and Subfield VOLE. ACM CCS’22, 2505–2517 (2022).
Bienstock, A., Patel, S., Seo, J.Y., & Yeo, K. NearOptimal Oblivious Key-Value Stores for Efficient PSI, PSU and Volume-Hiding Multi-Maps. USENIX Security’23, 301–318 (2023).
Pinkas, B., Schneider, T., Segev, G. & Zohner, M. Phasing: Private Set Intersection Using Permutation-based Hashing. USENIX Security’25, 515–530 (2015).
Pinkas, B., Schneider, T. & Zohner, M. Scalable private set intersection based on OT extension. ACM Trans. Priv. Secur. https://doi.org/10.1145/3154794 (2018).
Kolesnikov, V., Kumaresan, R., Rosulek, M. & Trieu, N. Efficient Batched Oblivious PRF with Applications to Private Set Intersection. CCS’16, 818–829 (2016).
Funding
This work was supported by the Institute of Information & Communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (No.RS-2024-00399491, Development of Privacy-Preserving Multiparty Computation Techniques for Secure Multiparty Data Integration)
Author information
Authors and Affiliations
Contributions
Qiang Liu conceived and designed the ePSU scheme, completed the security proofs, set up the experimental environment and conducted the simulations, and wrote the manuscript. JaeYoung Bae was responsible for reviewing and revising the manuscript, validating the experimental results, and checking the security proofs. Joon-Woo Lee supervised the entire study and was responsible for finalizing and submitting the manuscript. All authors have read and approved the final version of the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
About this article
Cite this article
Liu, Q., Bae, J. & Lee, JW. Towards an improved efficient leakage-resilient enhanced private set union. Sci Rep (2026). https://doi.org/10.1038/s41598-026-40531-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41598-026-40531-5
