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. 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
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.
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.
We consider the problem of fair two-party computation, where fairness (informally) means that both parties should learn the correct output. A seminal result of Cleve (STOC 1986) shows that fairness is, in general, impossible to achieve for malicious parties. Here, we treat the parties as rational and seek to understand what can be done. Asharov et al. (Eurocrypt 2011) recently considered this problem and showed impossibility of rational fair computation for a particular function and a particular set of utilities. We observe, however, that in their setting the parties have no incentive to compute the function even in an ideal world where fairness is guaranteed. Revisiting the problem, we show that rational fair computation is possible (for arbitrary functions and utilities) as long as the parties have a strict incentive to compute the function in the ideal world. This gives a new example where game theory can be used to circumvent impossibility results in cryptography.
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.
Existing work on “rational cryptographic protocols ” treats each party (or coalition of parties) running the protocol as a selfish agent trying to maximize its utility. In this work we propose a fundamentally different approach that is better suited to modeling a protocol under attack from an external entity. Specifically, we consider a two-party game between an protocol designer and an external attacker. The goal of the attacker is to break security properties such as correctness or privacy, possibly by corrupting protocol participants; the goal of the protocol designer is to prevent the attacker from succeeding. We lay the theoretical groundwork for a study of cryptographic protocol design in this setting by providing a methodology for defining the problem within the traditional simulation paradigm. Our framework provides ways of reasoning about important cryptographic concepts (e.g., adaptive corruptions or attacks on communication resources) not handled by previous game-theoretic treatments of cryptography. We also prove composition theorems that—for the first time—provide a sound way to design rational protocols assuming “ideal communication resources ” (e.g., broadcast or authenticated channels) and then instantiate these resources using standard cryptographic tools. Finally, we investigate the problem of secure function evaluation in our framework, where the attacker has to pay for each party it corrupts. Our results demonstrate how knowledge of the attacker’s incentives can be used to circumvent known impossibility results in this setting. 1
The field of rational cryptography considers the design of cryptographic protocols in the presence of rational agents seeking to maximize local utility functions. This departs from the standard secure multiparty computation setting, where players are assumed to be either honest or malicious. We detail the construction of both a two-party and a multiparty game theoretic framework for constructing rational cryptographic protocols. Our framework specifies the utility function assumptions necessary to realize the privacy, correctness, and fairness guarantees for protocols. We demonstrate that our framework correctly models cryptographic protocols, such as rational secret sharing, where existing work considers equilibrium concepts that yield unreasonable equilibria. Similarly, we demonstrate that cryptography may be applied to the game theoretic domain, constructing an auction market not realizable in the original formulation. Additionally, we demonstrate that modeling players as rational agents allows us to design a protocol that destabilizes coalitions. Thus, we establish a mutual benefit from combining the two fields, while demonstrating the applicability of our framework to real-world market environments. We also give an application of game theory to adversarial interactions where cryptography is not necessary. Specifically, we consider adversarial machine learning, where the adversary is rational and reacts to the presence of a data miner. We give a general extension to classification algorithms that returns greater expected utility for the data miner than existing classification methods.