分布式密码协议及公平性研究
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摘要
分布式密码协议是一种面向多方参与的密码体制,它的目标是将各种关键控制进行分布式安全实现,在现代多用户环境下的安全通信中有着广泛的应用.公平性是分布式密码协议的非常关键的期望目标.在分布式密码协议的实际应用中往往涉及多方,故其公平性就显得尤其重要.由于分布式应用系统的安全需求和公平性问题日益突出,所以分布式密码协议及公平性的研究日趋重要.
论文主要以博弈论、通用可组合理论和双线性对技术为工具,对分布式密码协议及公平性展开研究,研究内容主要涉及可验证秘密共享协议、秘密共享体制的博弈论分析、群组通信的通用可组合机制、安全通信协议的博弈论模型及具有公平性质的秘密共享协议等.具体如下：
(1)在博弈论框架下,基于纳什均衡设计安全通信协议的计算和通信规则.首先,我们提出安全协议的扩展式博弈模型,结合通用可组合安全的思想给出安全通信协议博弈参与者集合、信息集、可行策略、行动序列、参与者函数、效用函数等定义；其次,根据博弈的纳什均衡给出安全通信协议的形式化模型,在该模型下给出协议公平性的新定义,同时通过实例说明模型的有效性；最后,基于该机制给出一个安全通信协议实验,实验数据分析表明该安全通信协议博弈机制的可行性和有效性.
(2)在通用可组合框架下研究群组通信问题.首先,我们在UC框架下分别提出群组通信的理想函数、基于身份签密的理想函数和群密钥分发的理想函数.其次,我们构造了UC安全的基于身份签密协议.同时,我们证明基于身份的签密协议安全实现其理想函数当且仅当相应的基于身份的签密协议IDSC是安全的.最后,利用基于身份的签密协议,提出一种群组通信机制,该机制在混合模型下能安全实现群组通信的理想函数.
(3)在基于椭圆曲线上的双线性对技术,构造一种可验证秘密共享方案.该方案的信息率为2/3,与Pederson的方案(Crypto91)及相关方案相比,该方案在相同的安全级别下具有较高的信息率,从而提高了秘密共享协议的效率.同时,理论上证明该案是信息论安全的.最后,经分析表明,该方案具有更高的安全性和有效性,能更好地满足应用需求.
(4)提出理性第三方的概念,在秘密共享中任何理性的参与者都可以充当“可信中心”来分发秘密信息,这样使秘密共享体制更具普适性.基于博弈论对秘密分发协议进行分析,将其抽象为n个二人博弈.证明在这些博弈中,理性秘密分发者总是选择欺骗各参与者以获得更大的收益,同时提出解决该问题的理性秘密分发机制.最后,基于健忘传输协议提出秘密重构机制,有效解决秘密重构过程中各参与者不合作的问题.
(5)研究秘密共享方案的公平性问题.秘密共享公平性是指在秘密共享的秘密重构阶段,要么每个参加秘密重构的参与者都获得重构的秘密,要么都未得到所重构的秘密.我们利用一种新的方法实现了秘密公平重构.首先从概率的角度给出秘密共享公平性的定义.根据该定义,提出公平秘密共享协议,包括秘密分发协议和秘密重构协议；在三种不同攻击类型下证明协议的公平性和安全性,且协议的安全性不依赖于任何困难性假设.所提方案是Shamir秘密共享方案的扩展,在公平性实现方法上,是Dov Gordon等(STOC2008)公平性方法的扩展.理论分析表明所提公平方案是有效的.
The distributed cryptographic protocol is a cryptosystem of multiparty-oriented par-ticipation. Its goal is to perform various kinds of key controls securely by distribution. Now it is widely used in the multi-user secure communication on Internet. The fairness is one of the key requirements of distributed cryptographic protocol. It is more and more significant to study the distributed cryptographic protocol and fairness, for increasingly urgent secure requirement and fair problem in the distributed application system.
This thesis studies the distributed cryptographic protocol and its fairness based on the game theory, the universally composable security theory and the bilinear pairing, mainly including the verifiable secret sharing, the game-theoretic analysis for the secret shar-ing, the universally composable mechanism for group communication, the game-theoretic mechanism for cryptographic protocol and secret sharing scheme with fairness. The de-tails are as follows:
(1) The rational version of the classical secure communication problem is studied. The goal is to design a general procedure for secure communication among some rational participants. We propose a game theory based formal model for secure communi-cation secure protocols, including the player set, information set, available action, action sequence, player function, and utility function using the idea from universally composable security. Secure protocols can be concurrently run within this rational model. Moreover, the novel notion of fairness is presented according to Nash equi-librium of the communication game and condition of equivalence for fair protocol is given. Analysis shows that our mechanism is effective.
(2) The group communication is analyzed within the universally composable security framework. We first propose the group communication model, identity-based sign-cry tion model and group key distribution model in the UC framework by design-ing the secure authenticated group communication ideal functionality, the identity-based signcryption ideal functionality and the group key distribution ideal func-tionality, respectively. Then, we construct a UC secure identity-based signcryption protocol. Moreover, we shows that the identity-based signcryption securely realizes the ideal functionality if and only if the corresponding protocol IDSC is secure. Finally, based on the identity-based protocol, we propose a group communication scheme, which can securely realize its ideal functionality in the hybrid model.
(3) Based on the bilinear pairing on elliptic curves, a verifiable secret sharing (VSS) is constructed. The information rate of our scheme is2/3. Compared with Pederson's scheme (Crypto91) and the related schemes, our scheme is more efficient under the same security level. At the same time, the security of the scheme is proved theo-retically. The result indicates that the scheme is information-theoretically secure. Finally, the analysis shows that our scheme is more secure and effective than others, and it can be more applicable in practical situations.
(4) The concept of rational trusted party is proposed. Any rational party can play the role of the TTP to distribute the shares in the secret sharing such that it is more suitable for use. As far as we know, it is for the first time to analyze the distribution of shares with game theory in secret sharing scheme. It is formalized as n two-person games. It is proven that rational dealer always selects cheating all players to get more payoffs in these games. Simultaneously, a rational secret distribution mechanism is proposed to solve this problem. Moreover, we construct a mechanism of reconstruction of secret based on oblivious transfer protocol, which solve the problem of players' non-cooperation in the reconstruction phase.
(5) The fairness problem of secret reconstruction in a secret sharing scheme is studied. In the setting of secret sharing, one desirable property is fairness, which guarantees that if there is a player getting the secret in the recovery phase, then each player participating in the reconstruction process does too. We propose a new approach to achieve the fairness of secret sharing. We first define the fairness of secret sharing probabilistically. Based on this definition, a fair secret sharing scheme is proposed, its security and fairness are shown against three different attack types and do not depend upon any unproven intractability assumption. Our scheme is an extension of Shamir's secret sharing scheme and the approach of fairness of Dov Gordon et al.(STOC2008). Theoretical analysis shows that our proposed scheme is more efficient.
论文主要以博弈论、通用可组合理论和双线性对技术为工具,对分布式密码协议及公平性展开研究,研究内容主要涉及可验证秘密共享协议、秘密共享体制的博弈论分析、群组通信的通用可组合机制、安全通信协议的博弈论模型及具有公平性质的秘密共享协议等.具体如下：
(1)在博弈论框架下,基于纳什均衡设计安全通信协议的计算和通信规则.首先,我们提出安全协议的扩展式博弈模型,结合通用可组合安全的思想给出安全通信协议博弈参与者集合、信息集、可行策略、行动序列、参与者函数、效用函数等定义；其次,根据博弈的纳什均衡给出安全通信协议的形式化模型,在该模型下给出协议公平性的新定义,同时通过实例说明模型的有效性；最后,基于该机制给出一个安全通信协议实验,实验数据分析表明该安全通信协议博弈机制的可行性和有效性.
(2)在通用可组合框架下研究群组通信问题.首先,我们在UC框架下分别提出群组通信的理想函数、基于身份签密的理想函数和群密钥分发的理想函数.其次,我们构造了UC安全的基于身份签密协议.同时,我们证明基于身份的签密协议安全实现其理想函数当且仅当相应的基于身份的签密协议IDSC是安全的.最后,利用基于身份的签密协议,提出一种群组通信机制,该机制在混合模型下能安全实现群组通信的理想函数.
(3)在基于椭圆曲线上的双线性对技术,构造一种可验证秘密共享方案.该方案的信息率为2/3,与Pederson的方案(Crypto91)及相关方案相比,该方案在相同的安全级别下具有较高的信息率,从而提高了秘密共享协议的效率.同时,理论上证明该案是信息论安全的.最后,经分析表明,该方案具有更高的安全性和有效性,能更好地满足应用需求.
(4)提出理性第三方的概念,在秘密共享中任何理性的参与者都可以充当“可信中心”来分发秘密信息,这样使秘密共享体制更具普适性.基于博弈论对秘密分发协议进行分析,将其抽象为n个二人博弈.证明在这些博弈中,理性秘密分发者总是选择欺骗各参与者以获得更大的收益,同时提出解决该问题的理性秘密分发机制.最后,基于健忘传输协议提出秘密重构机制,有效解决秘密重构过程中各参与者不合作的问题.
(5)研究秘密共享方案的公平性问题.秘密共享公平性是指在秘密共享的秘密重构阶段,要么每个参加秘密重构的参与者都获得重构的秘密,要么都未得到所重构的秘密.我们利用一种新的方法实现了秘密公平重构.首先从概率的角度给出秘密共享公平性的定义.根据该定义,提出公平秘密共享协议,包括秘密分发协议和秘密重构协议；在三种不同攻击类型下证明协议的公平性和安全性,且协议的安全性不依赖于任何困难性假设.所提方案是Shamir秘密共享方案的扩展,在公平性实现方法上,是Dov Gordon等(STOC2008)公平性方法的扩展.理论分析表明所提公平方案是有效的.
The distributed cryptographic protocol is a cryptosystem of multiparty-oriented par-ticipation. Its goal is to perform various kinds of key controls securely by distribution. Now it is widely used in the multi-user secure communication on Internet. The fairness is one of the key requirements of distributed cryptographic protocol. It is more and more significant to study the distributed cryptographic protocol and fairness, for increasingly urgent secure requirement and fair problem in the distributed application system.
This thesis studies the distributed cryptographic protocol and its fairness based on the game theory, the universally composable security theory and the bilinear pairing, mainly including the verifiable secret sharing, the game-theoretic analysis for the secret shar-ing, the universally composable mechanism for group communication, the game-theoretic mechanism for cryptographic protocol and secret sharing scheme with fairness. The de-tails are as follows:
(1) The rational version of the classical secure communication problem is studied. The goal is to design a general procedure for secure communication among some rational participants. We propose a game theory based formal model for secure communi-cation secure protocols, including the player set, information set, available action, action sequence, player function, and utility function using the idea from universally composable security. Secure protocols can be concurrently run within this rational model. Moreover, the novel notion of fairness is presented according to Nash equi-librium of the communication game and condition of equivalence for fair protocol is given. Analysis shows that our mechanism is effective.
(2) The group communication is analyzed within the universally composable security framework. We first propose the group communication model, identity-based sign-cry tion model and group key distribution model in the UC framework by design-ing the secure authenticated group communication ideal functionality, the identity-based signcryption ideal functionality and the group key distribution ideal func-tionality, respectively. Then, we construct a UC secure identity-based signcryption protocol. Moreover, we shows that the identity-based signcryption securely realizes the ideal functionality if and only if the corresponding protocol IDSC is secure. Finally, based on the identity-based protocol, we propose a group communication scheme, which can securely realize its ideal functionality in the hybrid model.
(3) Based on the bilinear pairing on elliptic curves, a verifiable secret sharing (VSS) is constructed. The information rate of our scheme is2/3. Compared with Pederson's scheme (Crypto91) and the related schemes, our scheme is more efficient under the same security level. At the same time, the security of the scheme is proved theo-retically. The result indicates that the scheme is information-theoretically secure. Finally, the analysis shows that our scheme is more secure and effective than others, and it can be more applicable in practical situations.
(4) The concept of rational trusted party is proposed. Any rational party can play the role of the TTP to distribute the shares in the secret sharing such that it is more suitable for use. As far as we know, it is for the first time to analyze the distribution of shares with game theory in secret sharing scheme. It is formalized as n two-person games. It is proven that rational dealer always selects cheating all players to get more payoffs in these games. Simultaneously, a rational secret distribution mechanism is proposed to solve this problem. Moreover, we construct a mechanism of reconstruction of secret based on oblivious transfer protocol, which solve the problem of players' non-cooperation in the reconstruction phase.
(5) The fairness problem of secret reconstruction in a secret sharing scheme is studied. In the setting of secret sharing, one desirable property is fairness, which guarantees that if there is a player getting the secret in the recovery phase, then each player participating in the reconstruction process does too. We propose a new approach to achieve the fairness of secret sharing. We first define the fairness of secret sharing probabilistically. Based on this definition, a fair secret sharing scheme is proposed, its security and fairness are shown against three different attack types and do not depend upon any unproven intractability assumption. Our scheme is an extension of Shamir's secret sharing scheme and the approach of fairness of Dov Gordon et al.(STOC2008). Theoretical analysis shows that our proposed scheme is more efficient.
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