Correlated-Output Differential Privacy and Applications to Dark Pools

Authors James Hsin-yu Chiang , Bernardo David, Mariana Gama , Christian Janos Lebeda

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Author Details

James Hsin-yu Chiang
  • Aarhus University, Denmark
Bernardo David
  • IT University of Copenhagen, Denmark
Mariana Gama
  • COSIC, KU Leuven, Belgium
Christian Janos Lebeda
  • IT University of Copenhagen, Denmark
  • Basic Algorithms Research Copenhagen, Denmark

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James Hsin-yu Chiang, Bernardo David, Mariana Gama, and Christian Janos Lebeda. Correlated-Output Differential Privacy and Applications to Dark Pools. In 5th Conference on Advances in Financial Technologies (AFT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 282, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


In the classical setting of differential privacy, a privacy-preserving query is performed on a private database, after which the query result is released to the analyst; a differentially private query ensures that the presence of a single database entry is protected from the analyst’s view. In this work, we contribute the first definitional framework for differential privacy in the trusted curator setting (Fig. 1); clients submit private inputs to the trusted curator, which then computes individual outputs privately returned to each client. The adversary is more powerful than the standard setting; it can corrupt up to n-1 clients and subsequently decide inputs and learn outputs of corrupted parties. In this setting, the adversary also obtains leakage from the honest output that is correlated with a corrupted output. Standard differentially private mechanisms protect client inputs but do not mitigate output correlation leaking arbitrary client information, which can forfeit client privacy completely. We initiate the investigation of a novel notion of correlated-output differential privacy to bound the leakage from output correlation in the trusted curator setting. We define the satisfaction of both standard and correlated-output differential privacy as round differential privacy and highlight the relevance of this novel privacy notion to all application domains in the trusted curator model. We explore round differential privacy in traditional "dark pool" market venues, which promise privacy-preserving trade execution to mitigate front-running; privately submitted trade orders and trade execution are kept private by the trusted venue operator. We observe that dark pools satisfy neither classic nor correlated-output differential privacy; in markets with low trade activity, the adversary may trivially observe recurring, honest trading patterns, and anticipate and front-run future trades. In response, we present the first round differentially private market mechanisms that formally mitigate information leakage from all trading activity of a user. This is achieved with fuzzy order matching, inspired by the standard randomized response mechanism; however, this also introduces a liquidity mismatch as buy and sell orders are not guaranteed to execute pairwise, thereby weakening output correlation; this mismatch is compensated for by a round differentially private liquidity provider mechanism, which freezes a noisy amount of assets from the liquidity provider for the duration of a privacy epoch, but leaves trader balances unaffected. We propose oblivious algorithms for realizing our proposed market mechanisms with secure multi-party computation (MPC) and implement these in the Scale-Mamba Framework using Shamir Secret Sharing based MPC. We demonstrate practical, round differentially private trading with comparable throughput as prior work implementing (traditional) dark pool algorithms in MPC; our experiments demonstrate practicality for both traditional finance and decentralized finance settings.

Subject Classification

ACM Subject Classification
  • Security and privacy → Privacy-preserving protocols
  • Differential Privacy
  • Secure Multi-party Computation
  • Dark Pools
  • Decentralized Finance


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  1. Abbas Acar, Z Berkay Celik, Hidayet Aksu, A Selcuk Uluagac, and Patrick McDaniel. Achieving secure and differentially private computations in multiparty settings. In 2017 IEEE Symposium on Privacy-Aware Computing (PAC), pages 49-59. IEEE, 2017. URL:
  2. Mehrdad Aliasgari, Marina Blanton, Yihua Zhang, and Aaron Steele. Secure computation on floating point numbers. 20th Annual Network and Distributed System Security Symposium, NDSS 2013, San Diego, California, USA, 2013. Google Scholar
  3. Abdelrahaman Aly, Kelong Cong, Daniele Cozzo, Marcel Keller, Emmanuela Orsini, Dragos Rotaru, Oliver Scherer, Peter Scholl, Nigel P. Smart, Titouan Tanguy, and Tim Wood. SCALE-MAMBA v1.12: Documentation, 2021. URL:
  4. Carsten Baum, James Hsin-yu Chiang, Bernardo David, and Tore Kasper Frederiksen. Eagle: Efficient Privacy Preserving Smart Contracts. Cryptology ePrint Archive, 2022. URL:
  5. Jonas Böhler and Florian Kerschbaum. Secure multi-party computation of differentially private median. In 29th USENIX Security Symposium (USENIX Security 20), pages 2147-2164. USENIX Association, August 2020. URL:
  6. John Cartlidge, Nigel P Smart, and Younes Talibi Alaoui. MPC joins the dark side. In Proceedings of the 2019 ACM Asia Conference on Computer and Communications Security, pages 148-159, 2019. URL:
  7. John Cartlidge, Nigel P Smart, and Younes Talibi Alaoui. Multi-party computation mechanism for anonymous equity block trading: A secure implementation of turquoise plato uncross. Intelligent Systems in Accounting, Finance and Management, 28(4):239-267, 2021. URL:
  8. David Chaum, Debajyoti Das, Farid Javani, Aniket Kate, Anna Krasnova, Joeri De Ruiter, and Alan T Sherman. cmix: Mixing with minimal real-time asymmetric cryptographic operations. In Applied Cryptography and Network Security: 15th International Conference, ACNS 2017, Kanazawa, Japan, July 10-12, 2017, Proceedings 15, pages 557-578. Springer, 2017. URL:
  9. David L Chaum. Untraceable electronic mail, return addresses, and digital pseudonyms. Communications of the ACM, 24(2):84-90, 1981. URL:
  10. James Hsin-yu Chiang, Bernardo David, Mariana Gama, and Christian Janos Lebeda. Correlated-Output Differential Privacy and Applications to Dark Pools., 2023. Full paper version.
  11. Tarun Chitra, Guillermo Angeris, and Alex Evans. Differential privacy in constant function market makers. Cryptology ePrint Archive, 2021. URL:
  12. Mariana Botelho da Gama, John Cartlidge, Antigoni Polychroniadou, Nigel P Smart, and Younes Talibi Alaoui. Kicking-the-bucket: Fast privacy-preserving trading using buckets. Cryptology ePrint Archive, 2021. To appear at FC'22. URL:
  13. Mariana Botelho da Gama, John Cartlidge, Nigel P. Smart, and Younes Talibi Alaoui. All for one and one for all: Fully decentralised privacy-preserving dark pool trading using multi-party computation. Cryptology ePrint Archive, Paper 2022/923, 2022. URL:
  14. Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith. Calibrating noise to sensitivity in private data analysis. In Theory of cryptography conference, pages 265-284. Springer, 2006. URL:
  15. Cynthia Dwork, Aaron Roth, et al. The algorithmic foundations of differential privacy. Foundations and Trendsregistered in Theoretical Computer Science, 9(3-4):211-407, 2014. URL:
  16. Fabienne Eigner, Aniket Kate, Matteo Maffei, Francesca Pampaloni, and Ivan Pryvalov. Differentially private data aggregation with optimal utility. In Proceedings of the 30th Annual Computer Security Applications Conference, ACSAC 2014, New Orleans, LA, USA, December 8-12, 2014, ACSAC '14, pages 316-325, New York, NY, USA, 2014. Association for Computing Machinery. URL:
  17. Peter Kairouz, Sewoong Oh, and Pramod Viswanath. The composition theorem for differential privacy. In ICML, volume 37 of JMLR Workshop and Conference Proceedings, pages 1376-1385., 2015. Google Scholar
  18. Frank McSherry and Kunal Talwar. Mechanism design via differential privacy. In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07), pages 94-103. IEEE, 2007. URL:
  19. United States of America before the Securities and Exchange Commission. In the matter of itg inc. and alternet securities, inc., exchange act release no. 75672., 12 Aug 2015.
  20. United States of America before the Securities and Exchange Commission. In the matter of pipeline trading systems llc, et al., exchange act release no. 65609., 24 Oct 2011.
  21. United States of America before the Securities and Exchange Commission. In the matter of liquidnet, inc., exchange act release no. 72339., 6 Jun 2014.
  22. Manas Pathak, Shantanu Rane, and Bhiksha Raj. Multiparty differential privacy via aggregation of locally trained classifiers. Advances in neural information processing systems, 23, 2010. URL:
  23. Sikha Pentyala, Davis Railsback, Ricardo Maia, Rafael Dowsley, David Melanson, Anderson Nascimento, and Martine De Cock. Training differentially private models with secure multiparty computation. arXiv preprint arXiv:2202.02625, 2022. URL:
  24. Penumbra. ZSwap documentation., 2023.
  25. Monica Petrescu and Michael Wedow. Dark pools in european equity markets: emergence, competition and implications. ECB Occasional Paper, (193), 2017. URL:
  26. Thomas Steinke. Composition of differential privacy & privacy amplification by subsampling. CoRR, abs/2210.00597, 2022. Google Scholar
  27. Sameer Wagh, Xi He, Ashwin Machanavajjhala, and Prateek Mittal. Dp-cryptography: marrying differential privacy and cryptography in emerging applications. Communications of the ACM, 64(2):84-93, 2021. URL:
  28. Stanley L Warner. Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60(309):63-69, 1965. URL:
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