The traditional quantum secret sharing does not succeed in the presence of rational participants. A rational participant's motivation is to maximize his utility, and will try to get the secret alone. Therefore, in the reconstruction, no rational participant will send his share to others. To tackle with this problem, we propose a rational quantum secret sharing scheme in this paper. We adopt the game theory to analyze the behavior of rational participants and design a protocol to prevent them from deviating from the protocol. As proved, the rational participants can gain their maximal utilities when they perform the protocol faithfully, and the Nash equilibrium of the protocol is achieved. Compared to the traditional quantum secret sharing schemes, our scheme is fairer and more robust in practice.
The traditional quantum secret sharing does not succeed in the presence of rational participants. A rational participant's motivation is to maximize his utility, and will try to get the secret alone. Therefore, in the reconstruction, no rational participant will send his share to others. To tackle with this problem, we propose a rational quantum secret sharing scheme in this paper. We adopt the game theory to analyze the behavior of rational participants and design a protocol to prevent them from deviating from the protocol. As proved, the rational participants can gain their maximal utilities when they perform the protocol faithfully, and the Nash equilibrium of the protocol is achieved. Compared to the traditional quantum secret sharing schemes, our scheme is fairer and more robust in practice.
A rational secret sharing scheme is a game in which each party responsible for reconstructing a secret tries to maximize his or her utility by obtaining the secret alone. Quantum secret sharing schemes, derived either from quantum teleportation or from quantum error correcting code, do not succeed when we assume rational participants. This is because all existing quantum secret sharing schemes consider that the secret is reconstructed by a party chosen by the dealer. In this paper, for the first time, we propose a quantum secret sharing scheme which is resistant to rational parties. The proposed scheme is fair (everyone gets the secret), is correct, and achieves strict Nash equilibrium.
ABSTRACT Quantum secret sharing (QSS) holds a significant place in quantum cryptography. Unlike traditional QSS schemes, which often simplistically model participants as either completely honest or fully malicious, rational QSS introduces a more realistic framework by modeling participants as rational entities who strategically act to maximize their own utility. In this paper, for the first time, a rational quantum multi‐secret sharing scheme designed to share a classical bit string by configuring multiple effective reconstruction rounds is proposed. Further, a novel method is proposed to facilitate equilibrium achievement—deception deterrence. In terms of efficiency, the scheme achieves, for the first time, an effective reconstruction round ratio and a communication efficiency are independent of the total number of reconstruction rounds configured in the scheme, overcoming the communication efficiency limitation inherent in existing schemes. In terms of equilibrium achievement, the proposed new method not only returns to the essence of strategic interaction among rational participants themselves but also avoids the substantial verification cost.
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.
Abstract. The problem of carrying out cryptographic computations when the participating parties are rational in a game-theoretic sense has recently gained much attention. One problem that has been studied considerably is that of rational secret sharing. In this setting, the aim is to construct a mechanism (protocol) so that parties behaving rationally have incentive to cooperate and provide their shares in the reconstruction phase, even if each party prefers to be the only one to learn the secret. Although this question was only recently asked by Halpern and Teague (STOC 2004), a number of works with beautiful ideas have been presented to solve this problem. However, they all have the property that the protocols constructed need to know the actual utility values of the parties (or at least a bound on them). This assumption is very problematic because the utilities of parties are not public knowledge. We ask whether this dependence on the actual utility values is really necessary and prove that in the basic setting, rational secret sharing cannot be achieved without it. On the positive side, we show that by somewhat relaxing the standard assumptions on the utility functions, it is possible to achieve utility independence. In addition to the above, observe that the known protocols for rational secret sharing that do not assume simultaneous channels all suffer from the problem that one of the parties can cause the others to output an incorrect value. (This problem arises when a party gains higher utility by having another output an incorrect value than by learning the secret itself; we argue that such a scenario is not at all unlikely.) We show that this problem is inherent in the non-simultaneous channels model, unless the actual values of the parties ’ utilities from this attack is known, in which case it is possible to prevent this from happening. 1
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.
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.