**Collusion Free Protocol for Rational Secret Sharing**

*Amjed Shareef*

**Abstract: **We consider the \textit{rational secret sharing problem} introduced by Halpern and Teague\cite{ht04}, where players prefer to get the secret rather than not to get the secret and with lower preference, prefer that as few of the other players get the secret. Some positive results have been derived by Kol and Naor\cite{stoc08} by considering that players only prefer to learn. They have proposed an efficient $m$-out-of-$n$ protocol for rational secret sharing without using cryptographic primitives. Their solution considers that players are of two types; one player is the short player and the rest of the players are long players. But their protocol is susceptible to coalitions if the short player colludes with any of the long players. We extend their protocol, and propose a completely collusion free, $\varepsilon$-Nash equilibrium protocol, when $n \geq 2m -1 $, where $n$ is the number of players and $m$ is the number of shares needed to construct the secret.

**Category / Keywords: **foundations / Rational Cryprography

**Publication Info: **Accepted as Brief Announcment in PODC 2010

**Date: **received 30 Apr 2010, last revised 16 May 2010

**Contact author: **amjedshareef at gmail com

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Version: **20100516:071142 (All versions of this report)

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