Efficient Rational Secret Sharing in Standard Communication Networks

Abstract

Abstract. We propose a new methodology for rational secret sharing leading to various instantiations (in both the two-party and multi-party settings) that are simple and efficient in terms of computation, share size, and round complexity. Our protocols do not require physical assumptions or simultaneous channels, and can even be run over asynchronous, pointto-point networks.We also propose new equilibrium notions (namely, computational versions of strict Nash equilibrium and stability with respect to trembles) and prove that our protocols satisfy them. These notions guarantee, roughly speaking, that at each point in the protocol there is a unique legal message a party can send. This, in turn, ensures that protocol messages cannot be used as subliminal channels, something achieved in prior work only by making strong assumptions on the communication network.

Rational Secret Sharing with Honest Players over an Asynchronous Channel

“…These include Maleka et al's result [10] and Fuchsbauer et al's result [3], and Ong et al's result [13]. However, we contest that we can remove the interactive dealer [10] and cryptographic primitives [3] at the cost of assuming that a few of the participating players must be honest, but we believe that this is a reasonable assumption when the number is small, as in our scheme. This idea of assuming a small minority of honest players with a rational majority was first introduced by Ong et al [13] and enabled them to obtain very strong results in rational secret sharing.…”

“…Work has already been done in the area of asynchronous broadcast by [10], [3], and [13]. In [10], the authors suggested that by modifying their protocol and using repeated games with an interactive dealer, it was possible to have a working protocol for asynchronous broadcast.…”

“…Our protocol makes use of repeated games, however it does not require an interactive dealer. In [3], the authors proposed a working protocol for synchronous broadcast using cryptographic primitives and also extended their results to asynchronous broadcast as well by modifying their protocol. Our protocol does not require any cryptographic primitives but is instead information theoretically secure.…”

“…Several protocols have been devised to solve this problem [5,4,1,10,9,8,7,6,11,13,2,3], but only a handful have actually dealt with rational secret sharing using an asynchronous broadcast channel. These include Maleka et al's result [10] and Fuchsbauer et al's result [3], and Ong et al's result [13]. However, we contest that we can remove the interactive dealer [10] and cryptographic primitives [3] at the cost of assuming that a few of the participating players must be honest, but we believe that this is a reasonable assumption when the number is small, as in our scheme.…”

“…Several positive results have already been published to efficiently solve the problem of rational secret sharing. However, only a handful of papers have touched upon the use of an asynchronous broadcast channel, and in those papers, either the protocol involved cryptographic primitives [3] or else the protocol required the dealer to be interactively involved [10]. However, [13] did handle such a case through the use of an honest minority of players, but in their paper, they had placed a restriction on the number of honest players that could take part in relation to the total number number of players active in the protocol.…”