Research On Several Models Of Rational Information Exchange Cryptographic Protocols And Applications

Rational information exchange cryptographic protocols, combined cryptographyand game theory, were developed to address the problems that classical secret sharingand secure multiparty computation protocols can not take precautions against cheating.These protocols provide a new ideal for solving the defect of classical cryptography,and have become a research focus of cryptography. At present the research aboutrational information exchange cryptographic protocols is in the ascendant, and someproblems need to be resolved urgently as follows: the demand of the on-line dealer orhonest parties, the threatening of the participants’ conspiracy, the demand of thestandard point-to-point communication networks, the unfairness of the calculations,and the lack of strict proof of security, etc.To address the above problems, we study the models of rational informationexchange cryptographic protocols and applications in this dissertation. First andforemost, the game strategies, utilities, and motivations that participants deviate fromor abide by the protocol are analyzed. Besides, the fraud prevention model, thecoalition-proof model, the standard point-to-point communication model, and therational circuit computation model are designed. Last but not least, the models andmethods are applied to specific secret sharing protocols and secure multipartycomputation protocols. These protocols can prevent cheating and collusion of parties,and every party can learn the result of the computation fairly in point-to-pointcommunication networks. Furthermore, the security of these protocols has beenanalyzed and proved.Specifically, the contributions and innovations of this dissertation are as follows.(1) Design methods of strategies and probabilistic payoffs for preventingparticipants’ fraud are proposed, and the game model of fraud prevention is developed.In this model, cheaters will be punished, and every participant has no incentive tocheat, so that the purpose of preventing cheating is achieved. Moreover, the problemof the on-line dealer is addressed. Without the participation of the trusted party orhonest parties, this model, also makes up the defect of the fixed finite round gamemodel that is sensitive to reverse induction.(2) Design methods of computational coalition-proof Nash equilibrium areproposed, and the game model of coalition-proof is developed. The coalition behaviorof participants and the countermeasures have been analyzed. The strategies of participants satisfy the computational coalition-proof Nash equilibrium, and themembers of coalition do not know whether the current round is a real round or a fakeround to test participants’ honesty. The payoff of abiding by the protocol is more thanthe expected payoff of conspiring to deviate from the protocol. As a result, rationalparticipants have no incentive to deviate from the protocol. Therefore, the problem ofcollusion is resolved.(3) The game models of rational information exchange cryptographic protocolsare proposed in the standard point-to-point communication networks. With betterrobustness and concurrent processing capability, the models not only get rid of theshackles of broadcast communication but also simulate the effect of the broadcastcommunication. In addition, the models are easy to be implemented, and do notcollapse to a single point. Thus, the problem that the game models in the broadcastnetworks can not be implemented on the Internet is addressed, which makes theporposed models more practical and realistic.(4) One integrated approach of circuit evaluation model and game theory isproposed，and the rational circuit calculation model is designed. In the model, thepremise that a majority of participants are honest does not need to be concerned, andthe participants have an incentive to send the correct data according to their ownpayoffs. Complying with every step of the circuit evaluation is to maximize theirbenefits. Therefore, the issue of the unfairness in traditional circuit evaluation modelis solved.(5) The correctness of the models is investigated by applying these models to thesecret sharing and secure multiparty computation protocols. Firstly, a provably secureprotocol for rational multi-secret sharing in the standard point-to-pointcommunication networks is proposed, which is coalition-proof and avoids theinefficiency of the rational single secret sharing protocol. In addition, the defect of thesimultaneous broadcast communication mode has been successfully addressed. Then,a rational protocol to millionaire problem is proposed, and the problem that traditionalmillionaire protocols are designed in the semi-honest model has been resolved. Finally,based on circuit evaluation, a rational secure sum protocol is proposed, the problem ofcoalition is addressed and the purpose of fairness is achieved.