Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation

We study k-resilient Nash equilibria, joint strategies where no member of a coalition C of size up to k can do better, even if the whole coalition defects. We show that such k-resilient Nash equilibria exist for secret sharing and multiparty computation, provided that players prefer to get the information than not to get it. Our results hold even if there are only 2 players, so we can do multiparty computation with only two rational agents. We extend our results so that they hold even in the presence of up to t players with "unexpected" utilities. Finally, we show that our techniques can be used to simulate games with mediators by games without mediators.

[1]  Joseph Y. Halpern,et al.  Rational secret sharing and multiparty computation: extended abstract , 2004, STOC '04.

[2]  F. Forges.  Published by: The , 2022 .

[3]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[4]  Jørn Justesen,et al.  On the complexity of decoding Reed-Solomon codes (Corresp.) , 1976, IEEE Trans. Inf. Theory.

[5]  Eytan Adar,et al.  Free Riding on Gnutella , 2000, First Monday.

[6]  Benny Pinkas,et al.  Fairplay - Secure Two-Party Computation System , 2004, USENIX Security Symposium.

[7]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[8]  Leslie Lamport,et al.  The Byzantine Generals Problem , 1982, TOPL.

[9]  Abhi Shelat,et al.  Collusion-free protocols , 2005, STOC '05.

[10]  Elchanan Ben-Porath,et al.  Cheap talk in games with incomplete information , 2003, J. Econ. Theory.

[11]  Gil Neiger,et al.  Automatically Increasing the Fault-Tolerance of Distributed Algorithms , 1990, J. Algorithms.

[12]  Andrew Chi-Chih Yao,et al.  Protocols for Secure Computations (Extended Abstract) , 1982, FOCS.

[13]  Sergei Izmalkov,et al.  Rational secure computation and ideal mechanism design , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[14]  Anna Lysyanskaya,et al.  Rationality and Adversarial Behavior in Multi-party Computation , 2006, CRYPTO.

[15]  Moshe Tennenholtz,et al.  Non-cooperative computation: Boolean functions with correctness and exclusivity , 2005, Theor. Comput. Sci..

[16]  Jonathan Katz,et al.  Rational Secret Sharing, Revisited , 2006, SCN.

[17]  Oded Goldreich,et al.  Foundations of Cryptography: Volume 2, Basic Applications , 2004 .

[18]  Abhi Shelat,et al.  Completely fair SFE and coalition-safe cheap talk , 2004, PODC '04.

[19]  J. Wooders,et al.  Coalition-Proof Equilibrium , 1996 .

[20]  J. M. Bilbao,et al.  Contributions to the Theory of Games , 2005 .

[21]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[22]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[23]  Robert J. Aumann,et al.  16. Acceptable Points in General Cooperative n-Person Games , 1959 .

[24]  M. Whinston,et al.  Coalition-Proof Nash Equilibria I. Concepts , 1987 .

[25]  Tal Rabin,et al.  Verifiable secret sharing and multiparty protocols with honest majority , 1989, STOC '89.

[26]  Oded Goldreich.  Foundations of Cryptography: Index , 2001 .