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].
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].
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.
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.
In the problem of rational secret sharing, each player, who prefers to be the only one to learn the secret, acts rationally rather than merely honestly or maliciously in the traditional cryptographic settings. The core issue of rational secret sharing is to construct a mechanism so that all rational participants have incentive to provide their shares in the reconstruction phase. However, lack of enough incentive and how to achieve fairness in asynchronous model are always the hot potatoes for obtaining a deterministic protocol in this field. In this paper, we devote our attention to solving the above two difficulties in asynchronous model and succeed in obtaining a satisfactory result, 1/p-rational secret sharing protocol, in 2-out-of-2 case. Firstly, we apply the repeated interaction method to provide motivation so as to attract the players to participant in the collaboration and make it possible for a deterministic protocol. Secondly, inspired by 1/p-security of partial fairness, we propose a new concept, 1/p-advantage, to reduce the unavoidable probability of unfairness in asynchronous model to a satisfactory level. Besides, in order to perfect our protocol, we bring in the augmented perfect coin-tossing to determine the sending-order at the start of every round. Compared with previous ones, our protocol is applicable to the asynchronous model as well as the traditional synchronous model, which makes our protocol more practical. Furthermore, the new concept, 1/p-advantage, gives us a new perspective on rational secret sharing and makes our solution fresh.
We propose cryptographic rational secret sharing protocols over general networks. In a general network, the dealer may not have direct connections to each player, and players may not have direct connections to each of the other players. We present conditions on the network topology for which our proposed protocols are computational strict Nash equilibria and (k−1)-resilient, along with analysis on their round and communication complexity. We also present new notions of equilibria such as Φ-resilient computational Nash equilibria, whereby a protocol is resilient to coalitions that satisfy conditions in Φ, regardless of the coalition’s size. We also propose (n−1)-key leakage-tolerant equilibria applicable to cryptographic protocols involving secret keys, whereby the equilibrium holds even if some players acquire (n−1) tuples of secret keys.
The design of rational cryptographic protocols is a recently created research area at the intersection of cryptography and game theory. In this paper, we propose a new m-out-of-n rational secret sharing scheme requiring neither the involvement of the dealer (except during the initial share distribution) nor a trusted mediator. Our protocol leads to a Nash equilibrium surviving the iterated deletion of weakly dominated strategies for m ≥ 4. Our construction is information theoretically secure and it is immune against backward induction attacks. Contrary to Kol and Naor who used a specific cryptographic primitive in their TCC'08 paper (namely, meaningful/meaningless encryption), the immunity of our scheme is based on the use of bivariate polynomials and one-time pads. To the best of our knowledge, it is the first time that such polynomials have been used for rational secret sharing. Our scheme is efficient and does not require any physical assumptions such as envelopes or ballot boxes. As most of existing rational protocols, our construction requires simultaneous broadcast channels. However, our proposed scheme does not require any computational assumption and it provides information theoretical security.