Rational Secret Sharing over an Asynchronous Broadcast Channel with Information Theoretic Security

William K. Moses, C. Pandu Rangan

We consider the problem of rational secret sharing introduced by Halpern and Teague [1], where the players involved in secret sharing play only if it is to their advantage. This can be characterized in the form of preferences. Players would prefer to get the secret than to not get it and secondly with lesser preference, they would like as few other players to get the secret as possible. Several positive results have already been published to efficiently solve the problem of rational secret sharing but only a handful of papers have touched upon the use of an asynchronous broadcast channel. [2] used cryptographic primitives, [3] used an interactive dealer, and [4] used an honest minority of players in order to handle an asynchronous broadcast channel. In our paper, we propose an m-out-of-n rational secret sharing scheme which can function over an asynchronous broadcast channel without the use of cryptographic primitives and with a non-interactive dealer. This is possible because our scheme uses a small number, k+1, of honest players. The protocol is resilient to coalitions of size up to k and furthermore it is {\epsilon}-resilient to coalitions of size up to and including m-1. The protocol will have a strict Nash equilibrium with probability Pr((k+1)/n) and an {\epsilon}-Nash equilibrium with probability Pr((n-k-1)/n) . Furthermore, our protocol is immune to backward induction. Later on in the paper, we extend our results to include malicious players as well. We also show that our protocol handles the possibility of a player deviating in order to force another player to get a wrong value in what we believe to be a more time efficient manner than was done in Asharov and Lindell [5].

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