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Title:
General Constructions of Rational Secret Sharing with Expected Constant-Round Reconstruction
Authors: Akinori Kawachi, Yoshio Okamoto, Keisuke Tanaka, Kenji Yasunaga
Abstract:We present a general construction of a rational secret-sharing protocol that converts any rational secret-sharing protocol to a protocol with an expected constant-round reconstruction. Our construction can be applied to protocols for synchronous channels, and preserves a strict Nash equilibrium of the original protocol. Combining with an existing protocol, we obtain the first expected constant-round protocol that achieves a strict Nash equilibrium with the optimal coalition resilience \ceil{\frac{n}{2}}-1, where n is the number of players. Our construction can be extended to a construction that preserves the \emph{immunity} to unexpectedly behaving players. Then, for any constant m \geq 1, we obtain an expected constant-round protocol that achieves a Nash equilibrium with the optimal coalition resilience \ceil{\frac{n}{2}}-m-1 in the presence of m unexpectedly behaving players. The same protocol also achieves a strict Nash equilibrium with coalition resilience 1. We show that our protocol with immunity achieves the optimal coalition resilience among constant-round protocols with immunity with respect to both Nash and strict Nash equilibria.
ePrint: https://eprint.iacr.org/2013/874
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