Efficient Rational Secret Sharing in Standard Communication Networks

We propose a new methodology for rational secret sharing leading to various instantiations (in both the two-party and multi-party settings) that are simple and efficient in terms of computation, share size, and round complexity. Our protocols do not require physical assumptions or simultaneous channels, and can even be run over asynchronous, point-to-point networks. We also propose new equilibrium notions (namely, computational versions of strict Nash equilibrium and stability with respect to trembles) and prove that our protocols satisfy them. These notions guarantee, roughly speaking, that at each point in the protocol there is a unique legal message a party can send. This, in turn, ensures that protocol messages cannot be used as subliminal channels, something achieved in prior work only by making strong assumptions on the communication network.

[1]  Silvio Micali,et al.  Verifiable random functions , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[2]  G. R. Blakley,et al.  Safeguarding cryptographic keys , 1899, 1979 International Workshop on Managing Requirements Knowledge (MARK).

[3]  Yevgeniy Dodis,et al.  A Verifiable Random Function with Short Proofs and Keys , 2005, Public Key Cryptography.

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

[5]  Abhi Shelat,et al.  Collusion-Free Multiparty Computation in the Mediated Model , 2009, CRYPTO.

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

[7]  Danny Dolev,et al.  Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation , 2006, PODC '06.

[8]  Abhi Shelat,et al.  Collusion-Free Protocols in the Mediated Model , 2008, CRYPTO.

[9]  Abhi Shelat.  Collusion-free protocols , 2010, BQGT.

[10]  Yevgeniy Dodis,et al.  Efficient Construction of (Distributed) Verifiable Random Functions , 2003, Public Key Cryptography.

[11]  Anna Lysyanskaya,et al.  Unique Signatures and Verifiable Random Functions from the DH-DDH Separation , 2002, CRYPTO.

[12]  T. Rabin,et al.  Algorithmic Game Theory: Cryptography and Game Theory , 2007 .

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

[14]  Jonathan Katz,et al.  Partial Fairness in Secure Two-Party Computation , 2010, Journal of Cryptology.

[15]  R. Canetti,et al.  Cryptography and Game Theory , 2009 .

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

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

[18]  Abhi Shelat,et al.  Fair-Zero Knowledge , 2005, TCC.

[19]  Moni Naor,et al.  Cryptography and Game Theory: Designing Protocols for Exchanging Information , 2008, TCC.

[20]  Sergei Izmalkov,et al.  Verifiably Secure Devices , 2008, TCC.

[21]  Abhi Shelat,et al.  Purely Rational Secret Sharing (Extended Abstract) , 2009, TCC.

[22]  Moni Naor,et al.  Games for exchanging information , 2008, STOC.

[23]  Yehuda Lindell,et al.  Utility Dependence in Correct and Fair Rational Secret Sharing , 2009, CRYPTO.

[24]  David C. Parkes,et al.  Fairness with an Honest Minority and a Rational Majority , 2009, TCC.

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

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

[27]  Jonathan Katz,et al.  Bridging Game Theory and Cryptography: Recent Results and Future Directions , 2008, TCC.