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Lecture notes in computer science

An Efficient Rational Secret Sharing Protocol Resisting against Malicious Adversaries over Synchronous Channels

Yang Yu, Zhanfei Zhou

Published Jan 1, 2013• 1 citation
Publisher
DOI
10.1007/978-3-642-38519-3_6

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Most rational secret sharing protocols aim to achieve a more appealing equilibrium or resist adversaries. However, all previous protocols achieve resilience against irrational adversaries at the cost of inducing a weak guarantee of Nash equilibrium surviving iterated deletion, which has been proved weaker than strict Nash equilibrium. Moreover, they achieve equilibrium in a computational way based on the computational limitations of adversaries. In this paper, we design two unconditionally secure rational (t, n) secret sharing protocols. Contrary to prior works, our protocols induce an enhanced notion of strict equilibrium with respect to adversary structure A, and resist the computationally unbounded and adaptive adversary without using cryptographic primitives. Our protocols achieve stronger stability, since rational players have an incentive not to deviate no matter how the adversary behaves, and they are immune to the backward induction. Our protocols are secure against the adversary corrupting less than [n/3] players and the adversary corrupting less than [n/2]-1 players respectively. Both of them achieve utility independence.

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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 ε-resilient to coalitions of size up to and including m-1.The protocol will have a strict Nash equilibrium with probability Pr ( ାଵ ) and an ε-Nash equilibrium with probability Pr ( ିିଵ ) .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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Efficient Rational Secret Sharing in Standard Communication Networks

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Lecture notes in computer science•Jan 1, 2010•119 citations
Most rational secret sharing protocols aim to achieve a more appealing equilibrium or resist adversaries. However, all previous protocols achieve resilience against irrational adversaries at the cost of inducing a weak guarantee of Nash equilibrium surviving iterated deletion, which has been proved weaker than strict Nash equilibrium. Moreover, they achieve equilibrium in a computational way based on the computational limitations of adversaries. In this paper, we design two unconditionally secure rational (t, n) secret sharing protocols. Contrary to prior works, our protocols induce an enhanced notion of strict equilibrium with respect to adversary structure A, and resist the computationally unbounded and adaptive adversary without using cryptographic primitives. Our protocols achieve stronger stability, since rational players have an incentive not to deviate no matter how the adversary behaves, and they are immune to the backward induction. Our protocols are secure against the adversary corrupting less than [n/3] players and the adversary corrupting less than [n/2]-1 players respectively. Both of them achieve utility independence.
Secure Message Transmission (SMT) is a two-party cryptographic protocol by which the sender can securely and reliably transmit messages to the receiver using multiple channels. An adversary for SMT can corrupt a subset of the channels and make eavesdropping and tampering over the channels. In this work, we introduce a game-theoretic security model for SMT in which adversaries have some preferences for the protocol execution. We define rational timid adversaries who prefer to violate the security requirements, but do not prefer the tampering to be detected. Such adversaries could arise since they may fear losing their corrupted channels for which they needed some cost or risks. First, we consider the basic setting in which a single adversary attacks the protocol. We show that, even if all but one of the channels are corrupted, we can construct perfect SMT protocols against rational adversaries. In the traditional cryptographic setting, perfect SMT can be constructed only when the adversary corrupts a minority of the channels. Our results demonstrate a way of circumventing the cryptographic impossibility results by a game-theoretic approach. Next, we study the setting in which all the channels can be corrupted by multiple adversaries who do not cooperate. Since we cannot hope for any security if a single adversary corrupts all the channels or multiple adversaries cooperate maliciously, the scenario can arise from a game-theoretic model. We present several perfect SMT protocols, including a non-interactive protocol based on the idea of cheater-identifiable secret sharing. We also study the scenario in which both malicious and rational adversaries exist.
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 ε-resilient to coalitions of size up to and including m-1.The protocol will have a strict Nash equilibrium with probability Pr ( ାଵ ) and an ε-Nash equilibrium with probability Pr ( ିିଵ ) .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].