Paper 2013/874

General Constructions of Rational Secret Sharing with Expected Constant-Round Reconstruction

Akinori Kawachi, Yoshio Okamoto, Keisuke Tanaka, and 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.