**Constant-Round Rational Secret Sharing with Optimal Coalition Resilience**

*Akinori Kawachi and Yoshio Okamoto and Keisuke Tanaka and Kenji Yasunaga*

**Abstract: **We provide a general construction that
converts any rational secret-sharing protocol to a protocol with a 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 rational secret-sharing protocol
that achieves a strict Nash equilibrium with the optimal coalition resilience
of $\ceil{\frac{n}{2}}-1$,
where $n$ is the number of players.

Although the coalition resilience of $\ceil{\frac{n}{2}}-1$ is known to be optimal for constant-round protocols, we show that the limitation can be circumvented by considering a natural assumption that players avoid reconstructing \emph{fake} secrets. Under this assumption, we give a constant-round protocol that achieves a strict Nash equilibrium with the maximal coalition resilience of $n-1$.

Our construction can be extended to a construction that preserves the \emph{immunity} to unexpectedly behaving players. Then, we obtain a protocol that achieves a Nash equilibrium with the optimal coalition resilience of $\ceil{\frac{n}{2}}-t-1$ in the presence of $t$ unexpectedly behaving players for any constant $t \geq 1$.

**Category / Keywords: **rational secret sharing, game theory

**Date: **received 28 Dec 2013, last revised 9 Feb 2014

**Contact author: **yasunaga at se kanazawa-u ac jp

**Available format(s): **PDF | BibTeX Citation

**Version: **20140210:055056 (All versions of this report)

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