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On the Impossibility of Surviving (Iterated) Deletion of Weakly Dominated Strategies in Rational MPC

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Theory of Cryptography (TCC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14369))

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Abstract

Rational multiparty computation (rational MPC) provides a framework for analyzing MPC protocols through the lens of game theory. One way to judge whether an MPC protocol is rational is through weak domination: Rational players would not adhere to an MPC protocol if deviating never decreases their utility, but sometimes increases it.

Secret reconstruction protocols are of particular importance in this setting because they represent the last phase of most (rational) MPC protocols. We show that most secret reconstruction protocols from the literature are not, in fact, stable with respect to weak domination. Furthermore, we formally prove that (under certain assumptions) it is impossible to design a secret reconstruction protocol which is a Nash equilibrium but not weakly dominated if (1) shares are authenticated or (2) half of all players may form a coalition.

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing“ under the project number 160364472 – SFB 901/3.

J. Bobolz—Work done while at Paderborn University.

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Acknowledgements

We would like to thank the anonymous reviewers for their valuable feedback and constructive comments.

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Authors and Affiliations

  1. Paderborn University, Paderborn, Germany

    Johannes Blömer & Henrik Bröcher

  2. University of Edinburgh, Edinburgh, UK

    Jan Bobolz

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  1. Johannes Blömer
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  2. Jan Bobolz
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Correspondence to Henrik Bröcher .

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Editors and Affiliations

  1. Apple, Cupertino, CA, USA

    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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Blömer, J., Bobolz, J., Bröcher, H. (2023). On the Impossibility of Surviving (Iterated) Deletion of Weakly Dominated Strategies in Rational MPC. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14369. Springer, Cham. https://doi.org/10.1007/978-3-031-48615-9_14

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  • DOI: https://doi.org/10.1007/978-3-031-48615-9_14

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  • Online ISBN: 978-3-031-48615-9

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