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Rational Secret Sharing, Revisited.

Steven Gordon, Jonathan I. Katz

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

We consider the problem of secret sharing among n rational players. This problem was introduced by Halpern and Teague (STOC 2004), who claim that a solution is impossible for n = 2 but show a solution for the case n >= 3. Contrary to their claim, we show a protocol for rational secret sharing among n = 2 players; our protocol extends to the case n 3, where it is simpler than the Halpern-Teague solution and also o#ers a number of other advantages. We also show how to avoid the continual involvement of the dealer, in either our own protocol or that of Halpern and Teague. Our

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We consider the problem of secret sharing among n rational players. This problem was introduced by Halpern and Teague (STOC 2004), who claim that a solution is impossible for n = 2 but show a solution for the case n >= 3. Contrary to their claim, we show a protocol for rational secret sharing among n = 2 players; our protocol extends to the case n 3, where it is simpler than the Halpern-Teague solution and also o#ers a number of other advantages. We also show how to avoid the continual involvement of the dealer, in either our own protocol or that of Halpern and Teague. Our
We consider the rational secret sharing problem introduced by Halpern and Teague[3], where players prefer to get the secret than not to get the secret and with lower preference, prefer that as few of the other players get the secret. The impossibility of a deterministic protocol for rational secret sharing is proved by Halpern and Teague[3]. The impossibility result is based on the fact that a rational player always chooses a dominating strategy and so there is no incentive for a player to send his secret share. This rational behavior makes secret sharing impossible, but there is an interesting way by which we can force rational players to cooperate for achieving successful secret sharing. A rational player may be deterred from exploiting his short term advantage by the threat of punishment that reduces his long term payoff. This can be captured by the repeated interaction of players. Hence, we study rational secret sharing in a scenario, where players interact repeatedly in several rounds which enables the possibility of secret sharing among rational players. In our model, the dealer, instead of sending shares, forms polynomials of the secret shares and sends points on that polynomial (say subshares) to the players. The dealer constructs polynomials in a manner that the degrees of polynomials used differ by at most one and each player is not aware of the degree of polynomial employed for others. The players distribute shares in terms of subshares. We show a surprising result on the deterministic protocol for rational secret sharing problem in synchronous model. This is the first protocol that achieves rational secret sharing in a reasonable model to the best of our knowledge.
Rational secret sharing was first introduced by Halpern and Teague (STOC, 2004). Since then, a series of works have focused on designing rational secret sharing protocols. However, most existing solutions can share only one secret at one secret sharing process. To share multiple secrets such as m secrets, the dealer must redistribute shares for m times. In addition, previous works assume existence of broadcast channel which is not realistic. Motivated by those problems, this paper proposes a rational multi-secret sharing scheme, which combines the secret sharing scheme with game theory. In the protocol, the problem of sharing multiple secrets is addressed, and there are multiple secrets to be shared during one secret sharing process. Furthermore, this work starts off by constructing a protocol in simultaneous broadcast networks, and then we emulate the broadcast channel over point-to-point networks. Based on a computational assumption, we show that rational players have no incentive to deviate from the protocol and every player can obtain multi-secret fairly.
Rational secret sharing, first introduced by Halpern and Teague, means that whether players send their shares relies on their utilities, whereas in traditional scheme, players are assumed to contribute their shares willingly. This paper introduces a new kind of player and puts forward a 2-out-of-2 rational secret sharing scheme where players run their reconstruction protocol in standard communication networks other than broadcast channels which are often used in previous papers. The 2-out-of-2 rational secret sharing scheme in standard communication networks can achieve fairness.
Abstract. Rational secret sharing was proposed by Halpern and Teague in [12]. The authors show that, in a setting with rational players, secret sharing and multiparty computation are only possible if the actual secret reconstruction round remains unknown to the players. All the subsequent works use a similar approach with different assumptions. We change the direction by bridging cryptography, game theory, and reputation systems, and propose a “social model ” for repeated rational secret sharing. We provide a novel scheme, named socio-rational secret sharing, in which players are invited to each game based on their reputations in the community. The players run secret sharing protocols while founding and sustaining a public trust network. As a result, new concepts such as a rational foresighted player, social game, and social Nash equilibrium are introduced. To motivate our approach, consider a repeated secret sharing game such as “secure auctions”, where the auctioneers receive sealed-bids from the bidders to compute the auction outcome without revealing the losing bids. If we assume each party has a reputation value, we can then penalize (or reward) the players who are selfish (or unselfish) from game to game. We show that this social reinforcement rationally stimulates the players to be cooperative.
Rational secret sharing, first introduced by Halpern and Teague, means that whether players send their shares relies on their utilities, whereas in traditional scheme, players are assumed to contribute their shares willingly. This paper puts forward a rational secret-sharing scheme where players run their reconstruction protocol in point-to-point communication networks other than broadcast channels which are often used in previous papers. Kol and Naor propose an efficient t -out-of- n protocol for rational secret sharing without using cryptographic primitives while it has weak robustness to coalition when short player colludes with any long players. The protocol proposed by Fuchsbauer and Katz runs efficiently in asynchronous or point-to-point networks. Although it achieves strict Nash equilibrium and is stable with respect to trembles, it is susceptible to realise fairness among the whole party. This paper proposes a rational secret-sharing scheme in point-to-point communication networks to achieve fairness and robustness to coalition.