Rational Secret Research Articles

RATIONAL MULTI-SECRET SHARING SCHEME IN STANDARD POINT-TO-POINT COMMUNICATION NETWORKS

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.

Fair ( t , n ) threshold secret sharing scheme

In the setting of secret sharing, a group of parties wish to run a protocol for recovering the secret when they input their shares. The security requirement include privacy, correctness and others. One desirable property is fairness, which guarantees that if either party gets the secret, then the other party does too. However, basic secret sharing schemes, verifiable secret sharing schemes and publicly verifiable secret sharing schemes do not satisfy the fairness. Moreover, fairness is a central objective of the rational secret sharing scheme. In this work, the authors study the fairness problem of secret reconstruction in a (t, n) secret sharing scheme. They use a new approach to achieve the fairness of the protocol. They first define the fair notion of secret sharing probabilistically. Using the definition, a fair (t, n) secret sharing scheme is proposed, its security and fairness are shown against three different attack types. The proposed scheme is an extension of basic model of secret sharing (Shamir's scheme) and the approach of fairness of Dov Gordon et al.(STOC2008). Theoretical analysis shows that the proposed scheme is more efficient.

Verifiable rational secret sharing scheme based on Chinese remainder theorem

Verifiable rational secret sharing scheme based on Chinese remainder theorem

An Anti-cheating Rational Secret Sharing Scheme

An Anti-cheating Rational Secret Sharing Scheme

Rational Multi-Secret Sharing Scheme Based On Bit Commitment Protocol

In this paper we mainly focus on the fraud problem among the players and the shortcomings of multi-secret sharing existed in rational secret sharing schemes. Based on the exited schemes and the related knowledge such as bit commitment agreement, we proposed a new rational multi-secret sharing scheme that has high security. In our scheme, we take an identity authentication for the dealer in distribution phase. Players can verify the correctness of the identity of the dealer. In this way, it is feasible to prevent the forger from cheating. Based on the discrete logarithm problem, the player can also verify the correctness of the secret share. At the same time the secret shares are divided into groups so that the distribution phase is well designed for the multi-secret sharing. Additional the game theory model is also adopted to realize the rational multi secret sharing. The Execution efficiency, security and the feasibility has been remarkably improved in this our scheme compared with the traditional secret sharing schemes

Rational secret sharing with semi-rational players

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.

Repeated rational secret sharing, revisited

Rational Secret Sharing Scheme (RSSS) disposes the dilemma that several selfish players come together and willingly pool their shares to reconstruct a secret without a compulsory execution measure, while cooperation is not a strict optimisation. This paper introduces four punishment strategies and expands the perfect conclusions in infinitely repeated RSSS to show that cooperation will recur by means of some strategies. For finitely repeated RSSS, this paper verifies that there is no way for players to cooperate under perfect and complete information for backward induction. To overcome this difficulty, this paper relaxes conditions such as the types of players and the randomised strategies. It is proved that, given the different types and incomplete information, players will insist on cooperation in finitely repeated RSSS. In addition, we discuss repeated games in an extensive form and propose a 2-out-of-2 RSSS.

Rational Secret Sharing Over an Asynchronous Broadcast Channel With Information Theoretic Security

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 {\epsilon}-resilient to coalitions of size up to and including m-1. The protocol will have a strict Nash equilibrium with probability Pr((k+1)/n) and an {\epsilon}-Nash equilibrium with probability Pr((n-k-1)/n) . 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].

Publicly Verifiable Rational Secret Sharing

Publicly Verifiable Rational Secret Sharing

Rational secret sharing as extensive games

The threat that comes from previously used punishment strategies in rational secret sharing is weakened because the punishment somtimes also causes loss to the punisher himself. In this paper, we first model 2-out-of-2 rational secret sharing in an extensive game with imperfect information, and then provide a strategy for achieving secret recovery in this game. Moreover, we prove that the strategy is a sequential equilibrium which means after any history of the game no player can benefit from deviations so long as the other players stick to the strategy. In particular, when a deviation is detected, the punishment executed by the punisher is still his optimal option. Therefor, by considering rational secret sharing as an extensive game, we design punishment strategies that effectively punish the deviants and meanwhile guarantee punishers’ benefit. Hence, these punishments are more credible than previous ones. Except assuming the existence of simultaneous channels, our scheme can have dealer off-line and extend to the t-out-of-n setting, and also satisfies computational equilibria in some sense.

One-time rational secret sharing scheme based on bayesian game

The rational secret sharing cannot be realized in the case of being played only once, and some punishments in the one-time rational secret sharing schemes turn out to be empty threats. In this paper, after modeling 2-out-of-2 rational secret sharing based on Bayesian game and considering different classes of protocol parties, we propose a 2-out-of-2 secret sharing scheme to solve cooperative problem of a rational secret sharing scheme being played only once. Moreover, we prove that the strategy is a perfect Bayesian equilibrium, adopted only by the parties in their decision-making according to their belief system (denoted by the probability distribution) and Bayes rule, without requiring simultaneous channels.

AN EFFICIENT AND INFORMATION THEORETICALLY SECURE RATIONAL SECRET SHARING SCHEME BASED ON SYMMETRIC BIVARIATE POLYNOMIALS

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.

Rational Secret Sharing Scheme Based on Probability Encryption without Trusted Center

Considering the case of players’ deceptions, traditional secret sharing scheme can not resolve the security issues. To address these security issues, the paper proposes a rational secret sharing scheme against cheating based on game theory. Under the conditions of the rational, applying the idea of threshold, the scheme is composed of key generation, share encryption, verification and secret reconstruction. In the process, the scheme firstly utilizes secure multiparty computation function instead of trusted center for key generation and share validation; secondly uses probability encryption which can effectively solve the problem of players keeping silent in the final iteration; thirdly without revealing the secret, employs the commitment to detect the cheat in the scheme; finally, the scheme can reconstruct the secret in the meaningful encryption. In conclusion, the scheme is safe and effective.

Utility Dependence in Correct and Fair Rational Secret Sharing

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 case of two parties, rational secret sharing cannot be achieved without it. On the positive side, we show that in the multiparty case it is possible to construct a single mechanism that works for all (polynomial) utility functions. Our protocol has an expected number of rounds that is constant, and is optimally resilient to coalitions. In addition to the above, we 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 needs to be considered.) We show that this problem is inherent in the non-simultaneous channels model, unless the actual values of the parties’ utilities from this attack are known, in which case it is possible to prevent this from happening.