Andreas Brüggemann
ABSTRACT
Privacy-preserving protocols for matchings on general graphs can be used for applications such as online dating, bartering, or kidney donor exchange. In addition, they can act as a building block for more complex protocols. While privacy-preserving protocols for matchings on bipartite graphs are a well-researched topic, the case of general graphs has experienced significantly less attention so far. We address this gap by providing the first privacy-preserving protocol for maximum weight matching on general graphs. To maximize the scalability of our approach, we compute an 1/2-approximation instead of an exact solution. For N nodes, our protocol requires O(N log N) rounds, O(N^3) communication, and runs in only 12.5 minutes for N=400.
- Balamurugan Anandan and Chris Clifton. 2017. Secure Minimum Weighted Bipartite Matching. In 2017 IEEE Conference on Dependable and Secure Computing. 60--67. https://doi.org/10.1109/DESEC.2017.8073798Google Scholar
- Toshinori Araki, Jun Furukawa, Yehuda Lindell, Ariel Nof, and Kazuma Ohara. 2016. High-Throughput Semi-Honest Secure Three-Party Computation with an Honest Majority. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security (CCS '16). 805--817. https://doi.org/10.1145/2976749.2978331Google ScholarDigital Library
- Toshinori Araki, Jun Furukawa, Kazuma Ohara, Benny Pinkas, Hanan Rosemarin, and Hikaru Tsuchida. 2021. Secure Graph Analysis at Scale. In Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security (CCS '21). 610--629. https://doi.org/10.1145/3460120.3484560Google ScholarDigital Library
- David Avis. 1983. A Survey of Heuristics for the Weighted Matching Problem. Networks, Vol. 13, 4 (1983), 475--493. https://doi.org/10.1002/net.3230130404Google ScholarCross Ref
- Marina Blanton and Siddharth Saraph. 2015. Oblivious Maximum Bipartite Matching Size Algorithm with Applications to Secure Fingerprint Identification. In Computer Security -- ESORICS 2015 (Lecture Notes in Computer Science ). 384--406. https://doi.org/10.1007/978--3--319--24174--6_20Google Scholar
- Malte Breuer, Ulrike Meyer, and Susanne Wetzel. 2022. Privacy-Preserving Maximum Matching on General Graphs and its Application to Enable Privacy-Preserving Kidney Exchange. In Proceedings of the Twelfth ACM Conference on Data and Application Security and Privacy (CODASPY '22). 53--64. https://doi.org/10.1145/3508398.3511509Google ScholarDigital Library
- Andreas Brüggemann, Malte Breuer, Andreas Klinger, Thomas Schneider, and Ulrike Meyer. 2022. Secure Maximum Weight Matching Approximation on General Graphs. Cryptology ePrint Archive, Paper 2022/1173. https://eprint.iacr.org/2022/1173.Google Scholar
- Octavian Catrina and Sebastiaan de Hoogh. 2010. Improved Primitives for Secure Multiparty Integer Computation. In Security and Cryptography for Networks (Lecture Notes in Computer Science ). 182--199. https://doi.org/10.1007/978--3--642--15317--4_13Google Scholar
- Ivan Damgård and Jesper Buus Nielsen. 2003. Universally Composable Efficient Multiparty Computation from Threshold Homomorphic Encryption. In Advances in Cryptology - CRYPTO 2003 (Lecture Notes in Computer Science ). Springer, Berlin, Heidelberg, 247--264. https://doi.org/10.1007/978--3--540--45146--4_15Google Scholar
- Jack Doerner, David Evans, and abhi shelat. 2016. Secure Stable Matching at Scale. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security (CCS '16). 1602--1613. https://doi.org/10.1145/2976749.2978373Google ScholarDigital Library
- Doratha E Drake and Stefan Hougardy. 2003. A Simple Approximation Algorithm for the Weighted Matching Problem. Inform. Process. Lett. , Vol. 85, 4 (Feb. 2003), 211--213. https://doi.org/10.1016/S0020-0190(02)00393--9Google ScholarCross Ref
- Doratha E. Drake Vinkemeier and Stefan Hougardy. 2005. A Linear-Time Approximation Algorithm for Weighted Matchings in Graphs. ACM Transactions on Algorithms , Vol. 1, 1 (July 2005), 107--122. https://doi.org/10.1145/1077464.1077472Google ScholarDigital Library
- Ran Duan and Seth Pettie. 2014. Linear-Time Approximation for Maximum Weight Matching. J. ACM, Vol. 61, 1 (Jan. 2014), 1:1--1:23. https://doi.org/10.1145/2529989Google ScholarDigital Library
- Jack Edmonds. 1965. Maximum Matching and a Polyhedron With 0,1-Vertices. Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics , Vol. 69B (Jan. 1965), 125. https://doi.org/10.6028/jres.069B.013Google ScholarCross Ref
- Daniel Escudero, Satrajit Ghosh, Marcel Keller, Rahul Rachuri, and Peter Scholl. 2020. Improved Primitives for MPC over Mixed Arithmetic-Binary Circuits. In Advances in Cryptology -- CRYPTO 2020 (Lecture Notes in Computer Science ). 823--852. https://doi.org/10.1007/978--3-030--56880--1_29Google Scholar
- Philippe Golle. 2006. A Private Stable Matching Algorithm. In Financial Cryptography and Data Security (Lecture Notes in Computer Science ). 65--80. https://doi.org/10.1007/11889663_5Google ScholarDigital Library
- P. Hall. 1935. On Representatives of Subsets. Journal of the London Mathematical Society , Vol. s1--10, 1 (1935), 26--30. https://doi.org/10.1112/jlms/s1--10.37.26Google Scholar
- Sven Hanke and Stefan Hougardy. 2010. New Approximation Algorithms for the Weighted Matching Problem. http://www.or.uni-bonn.de/%7Ehougardy/paper.html Report No. 101010, Research Institute for Discrete Mathematics, University Of Bonn.Google Scholar
- Marcel Keller. 2020. MP-SPDZ: A Versatile Framework for Multi-Party Computation. In Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security. 1575--1590. https://doi.org/10.1145/3372297.3417872Google ScholarDigital Library
- John Launchbury, Iavor S. Diatchki, Thomas DuBuisson, and Andy Adams-Moran. 2012. Efficient Lookup-Table Protocol in Secure Multiparty Computation. ACM SIGPLAN Notices, Vol. 47, 9 (Sept. 2012), 189--200. https://doi.org/10.1145/2398856.2364556Google ScholarDigital Library
- Seth Pettie and Peter Sanders. 2004. A Simpler Linear Time $2/3-ε$ Approximation for Maximum Weight Matching. Inform. Process. Lett. , Vol. 91, 6 (Sept. 2004), 271--276. https://doi.org/10.1016/j.ipl.2004.05.007Google ScholarDigital Library
- Robert Preis. 1999. Linear Time 1/2-Approximation Algorithm for Maximum Weighted Matching in General Graphs. In STACS 99 (Lecture Notes in Computer Science ). 259--269. https://doi.org/10.1007/3--540--49116--3_24Google Scholar
- M. Sadegh Riazi, Ebrahim M. Songhori, Ahmad-Reza Sadeghi, Thomas Schneider, and Farinaz Koushanfar. 2017. Toward Practical Secure Stable Matching. Proceedings on Privacy Enhancing Technologies, Vol. 2017, 1 (Jan. 2017), 62--78. https://doi.org/10.1515/popets-2017-0005Google ScholarCross Ref
- Dragos Rotaru and Tim Wood. 2019. MArBled Circuits: Mixing Arithmetic and Boolean Circuits with Active Security. In Progress in Cryptology -- INDOCRYPT 2019 (Lecture Notes in Computer Science ). 227--249. https://doi.org/10.1007/978--3-030--35423--7_12Google Scholar
- Abraham Waksman. 1968. A Permutation Network. J. ACM, Vol. 15, 1 (Jan. 1968), 159--163. https://doi.org/10.1145/321439.321449Google ScholarDigital Library
- Stefan Wüller, Ulrike Meyer, and Susanne Wetzel. 2017a. Privacy-Preserving Multi-Party Bartering Secure Against Active Adversaries. In 2017 15th Annual Conference on Privacy, Security and Trust (PST). 205--20509. https://doi.org/10.1109/PST.2017.00032Google Scholar
- Stefan Wüller, Ulrike Meyer, and Susanne Wetzel. 2017b. Towards Privacy-Preserving Multi-party Bartering. In Financial Cryptography and Data Security (Lecture Notes in Computer Science ). 19--34. https://doi.org/10.1007/978--3--319--70278-0_2Google Scholar
- Stefan Wüller, Michael Vu, Ulrike Meyer, and Susanne Wetzel. 2017c. Using Secure Graph Algorithms for the Privacy-Preserving Identification of Optimal Bartering Opportunities. In Proceedings of the 2017 on Workshop on Privacy in the Electronic Society (WPES '17). 123--132. https://doi.org/10.1145/3139550.3139557Google ScholarDigital Library
- Andrew C. Yao. 1982. Protocols for Secure Computations. In 23rd Annual Symposium on Foundations of Computer Science. 160--164. https://doi.org/10.1109/SFCS.1982.38Google Scholar
- Samee Zahur, Xiao Wang, Mariana Raykova, Adrià Gascón, Jack Doerner, David Evans, and Jonathan Katz. 2016. Revisiting Square-Root ORAM: Efficient Random Access in Multi-party Computation. In 2016 IEEE Symposium on Security and Privacy (S&P). 218--234. https://doi.org/10.1109/SP.2016.21 ioGoogle Scholar
Index Terms
- Secure Maximum Weight Matching Approximation on General Graphs
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