ABSTRACT
We consider the classical secret sharing problem in the case where all agents are selfish but rational. In recent work, Kol and Naor show that in the non-simultaneous communciation model (i.e. when rushing is possible), there is no Nash equilibrium that ensures all agents learn the secret. However, they describe a mechanism for this problem that is an ε-Nash equilibrium, i.e. it is close to an equilibrium in the sense that no player can gain more than ε utility by deviating from it.
Unfortunately, the Kol and Naor mechanism, and, to the best of our knowledge, all previous mechanisms for this problem require each agent to send O(n) messages in expectation, where n is the number of agents. This may be problematic for some applications of rational secret sharing such as secure multiparty computation and simulation of a mediator.
We address this issue by describing a mechanism for rational n-out-of-n secret sharing that is an ε-Nash equilibrium, and is scalable in the sense that it requires each agent to send only an expected O(1) bits. Moreover, the latency of our mechanism is O(log n) in expectation, compared to O(n) expected latency for the Kol and Naor result. We also design mechanisms for a relaxed variant of rational m-out-of-n secret sharing where m = Θ(n) that require each processor to send O(log n) bits and have O(\log n) latency. Our mechanisms are non-cryptographic, and are not susceptible to backwards induction.
- I. Abraham, D. Dolev, R. Gonen, and J. Halpern. Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation. In Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing, pages 53--62. ACM, 2006. Google ScholarDigital Library
- R. Geambasu, T. Kohno, A. Levy, and H. Levy. Vanish: Increasing data privacy with self-destructing data. In Proceedings of the 18th conference on USENIX security symposium, pages 299--316. USENIX Association, 2009. Google ScholarDigital Library
- O. Goldreich, S. Micali, and A. Wigderson. How to play any mental game. In Proceedings of the nineteenth annual ACM symposium on Theory of computing, pages 218--229. ACM, 1987. Google ScholarDigital Library
- S. Gordon and J. Katz. Rational secret sharing, revisited. Security and Cryptography for Networks, pages 229--241, 2006. Google ScholarDigital Library
- J. Halpern and V. Teague. Rational secret sharing and multiparty computation: extended abstract. In Proceedings of the thirty-sixth annual ACM symposium on Theory of computing, page 632. ACM, 2004. Google ScholarDigital Library
- S. Izmalkov, S. Micali, and M. Lepinski. Rational secure computation and ideal mechanism design. In Foundations of Computer Science, 2005. FOCS 2005. 46th Annual IEEE Symposium on, pages 585--594. IEEE, 2005. Google ScholarDigital Library
- V. King and J. Saia. Breaking the O (n 2) bit barrier: scalable byzantine agreement with an adaptive adversary. In Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing, pages 420--429. ACM, 2010. Google ScholarDigital Library
- G. Kol and M. Naor. Games for exchanging information. In Proceedings of the 40th annual ACM symposium on Theory of computing, pages 423--432. ACM, 2008. Google ScholarDigital Library
- M. Lepinksi, S. Micali, and A. Shelat. Collusion-free protocols. In ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, volume 37, page 543. Citeseer, 2005. Google Scholar
- M. Lepinski, S. Micali, C. Peikert, and A. Shelat. Completely fair SFE and coalition-safe cheap talk. In Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing, pages 1--10. ACM, 2004. Google ScholarDigital Library
- A. Lysyanskaya and N. Triandopoulos. Rationality and adversarial behavior in multi-party computation. Advances in Cryptology-CRYPTO 2006, pages 180--197, 2006. Google ScholarDigital Library
- T. Rabin and M. Ben-Or. Verifiable secret sharing and multiparty protocols with honest majority. In Proceedings of the twenty-first annual ACM symposium on Theory of computing, pages 73--85. ACM, 1989. Google ScholarDigital Library
- M. Wegman and J. Carter. New hash functions and their use in authentication and set equality. Journal of computer and system sciences, 22(3):265--279, 1981.Google ScholarCross Ref
Index Terms
- Scalable rational secret sharing
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