秘密交换的博弈模型及应用研究

发布时间：2019-06-21 08:18

【摘要】：随着云计算和大数据技术的迅速发展,用户之间频繁的数据交流和共享使得分布式计算得到了广泛应用,但是由于分布式环境下平台开放及资源共享的特点,导致用户之间的数据交换面临着很多安全性挑战,而传统秘密交换由于没有考虑参与者的行动动机,暴露出一些固有的缺陷,如只能发现欺骗而不能事先预防。针对秘密交换建立博弈模型属于密码学和博弈论的交叉研究领域,它将所有参与者看作是理性的,根据效用函数来决定是否遵守协议,能更好地解决协议的安全性问题。研究了秘密交换的发展现状,讨论了现有理性秘密交换协议的安全性及存在的问题,通过分析参与者的策略和效用,建立了参与者合作博弈模型、抵抗合谋博弈模型、公平两方计算博弈模型,最后将博弈模型应用到协议设计中,通过惩罚策略控制效用函数来激励所有参与者遵守协议,使得参与者虽然倾向于自己是唯一得到秘密的人,他们也愿意为了各自的利益而选择遵守协议。本文的主要研究成果如下:(1)针对传统秘密共享协议中存在的只能发现参与者欺骗而无法阻止其行为的问题,基于触发策略构建了参与者合作博弈模型。模型中将参与者收益函数和惩罚策略相结合,使得参与者在执行过程中如果偏离协议将导致其收益函数减小,由于理性参与者希望得到最终的秘密,只能选择合作,达到了预防欺骗的目的。(2)针对秘密共享中普遍存在的参与者合谋的问题,基于声誉机制构建了预防参与者合谋的博弈模型。模型中详细分析了理性参与者的合谋动机和行为,通过参数设置使得参与者合谋时的收益只能增加可忽略的效用值,同时引入声誉机制对背离协议的参与者进行惩罚,因此模型可达到可计算防合谋均衡,保证了理性参与者具有遵守协议的动机。(3)针对传统安全两方计算协议中存在的公平性问题,基于激励相容机制构建了公平的两方计算理想世界和现实世界博弈模型。根据模型中的公平性定义,给出了理性安全两方计算的理想函数和理性安全两方计算协议,通过对参与者的策略和效用函数设置,使得发送正确数据是参与者的占优策略,保证了双方能公平地得到计算结果,最后利用理想/现实范式证明了理性安全两方计算协议能安全实现理想函数,并分析了协议的纳什均衡结果。(4)将秘密交换博弈模型应用到协议中,设计了参与者具有合作动机的理性秘密共享协议、可抵抗合谋的理性秘密共享协议和具有公平性的理性安全两方计算协议,并首次将理性参与者的概念应用到门限签名中,针对签名密钥分发阶段密钥分发者不愿意分发正确子密钥,以及签名合成阶段参与者的不合作行为,提出了理性门限签名协议。将签名看作是理性参与者的一种“权利”,同时又需要承担相应“责任”的角度出发,运用讨价还价机制解决理性签名密钥分发问题,采用随机均匀分组方法构造理性门限签名合成机制,保证了各参与者能得到正确的子密钥,同时有动机完成对消息的签名。
[Abstract]:With the rapid development of cloud computing and large-scale data technology, frequent data exchange and sharing among users make the distributed computing to be widely used, but due to the open and resource sharing of the platform under the distributed environment, The data exchange between users is faced with many security challenges, and the traditional secret exchange exposes some of the inherent defects due to the fact that the action motive of the participants is not taken into account, such as only finding fraud and not in advance. The establishment of game model for secret exchange belongs to the cross-research field of cryptography and game theory. It regards all the participants as rational, determines whether to comply with the protocol according to the utility function, and can better solve the security problem of the protocol. In this paper, the development status of the secret exchange is studied, the security and the existing problems of the existing rational secret exchange protocol are discussed. By analyzing the strategy and utility of the participants, the cooperative game model of the participants is established, the game model of the collusion game is resisted, and the game model is calculated on both sides. Finally, the game model is applied to the protocol design, and the utility function is controlled by the penalty strategy to encourage all the participants to abide by the agreement, so that the participants, while inclined to be the only person who is the only secret, are willing to choose to abide by the agreement for their own interests. The main research results of this paper are as follows: (1) A participant cooperation game model is built on the basis of the trigger strategy, aiming at the problem that only the participants can be cheated by the traditional secret sharing agreement and the behavior cannot be prevented. In the model, the participant income function and the penalty strategy are combined, so that the participants can only choose the cooperation if the deviation agreement will lead to the reduction of the gain function in the course of the execution, because the rational participant wants to get the final secret, only the cooperation can be selected, and the purpose of preventing and cheating is achieved. (2) The game model for preventing participants' collusion is constructed based on the reputation mechanism, aiming at the problem of the collusion of the participants in the secret sharing. In the model, the complicit motivation and behavior of the rational participant are analyzed in detail. By setting the parameter, the gain of the participant's collusion can only increase the negligible utility value, and the reputation mechanism is introduced to punish the participants departing from the agreement, so that the model can be used to calculate the anti-collusion equilibrium, The motivation of the rational participant to abide by the agreement is ensured. (3) In view of the fairness problem existing in the traditional security two-party computing agreement, a fair and two-party computing ideal world and a real world game model are constructed based on the incentive compatible mechanism. according to the definition of the fairness in the model, the ideal function and the rational safety two-party calculation protocol of the two-way calculation of the rational safety are given, and the strategy and utility function of the participants are set, so that the sending right data is the dominant strategy of the participants, It is ensured that both parties can obtain the results fairly, and finally, the ideal/ realistic paradigm is used to prove the safe and ideal function of the two-party calculation protocol of the rational safety, and the Nash equilibrium result of the protocol is analyzed. (4) the secret exchange game model is applied to the protocol, the rational secret sharing protocol with the cooperative motivation of the participants is designed, And the concept of the rational participant is applied to the threshold signature for the first time, the key distributor in the signing key distribution stage is unwilling to distribute the correct sub-key and the non-cooperative behavior of the participants in the signature synthesis stage, and a rational threshold signature protocol is proposed. taking the signature as a "rights" of the rational participant, and at the same time, taking the angle of the corresponding "RESPONSIBILITY", using the bargaining mechanism to solve the problem of the distribution of the rational signature key, and adopting a random uniform grouping method to construct a rational threshold signature synthesis mechanism, Ensures that each participant can obtain the correct sub-key, and simultaneously has the motivation to complete the signature of the message.
【学位授予单位】：北京工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP309

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