Distributed Cryptographic Protocol And Fairness

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.