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

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 ⌈n2 ⌉ − 1, where n is the number of players. Our construction can be extended to a construction that preserves the immunity to unexpectedly behaving players. Then, for any constantm ≥ 1, we obtain an expected constant-round protocol that achieves a Nash equilibrium with the optimal coalition resilience ⌈n2 ⌉ −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.