Theory And Application Study On Secret Sharing Based On Game Theory

With the development of the information technology and the polularization of computer applications, the human society's reliance on the network gradually increased, such as the internet banking,E-auction,E-bidding and the transaction of E-cash. Therefore, how to ensure that information in the generation and transmission in the process of security has been more and more attention and become a modern cryptography important research field. Cryptosystem scheme is comprised of algorithm and key. According to Kerckhoff principle, the algorithm is published to public. So the security of cryptosystem scheme fully depends on the security of the key. Therefore, the research of key management and secret sharing occupies a very important position at cryptosystem security research and design.Secret sharing is a technology of sharing secret among a group of participants. Their major function is to protect important information from missing, being destroyed and being changed. Therefore, secret sharing is an important research field and an effective tool in cryptophytic theory. Secret sharing plays an important role in information security. Typical secret sharing scheme has: traditional secret sharing, verifiable secret sharing, multi-secret sharing.In this paper we mainly study rational secret sharing scheme participants in the construction and application. In this paper, the previous theory of secret sharing more in depth research and analysis, combined with the game theory model, give the concept of rational secret sharing and propose a new rational secret sharing scheme, in the applications, we design a rational secret sharing scheme based on special access right, and give proof of its correctness, analyze its application.First of all, This paper introduces in detail the concept of game theory, the typical program and development, explained the definition of Nash equilibrium and the mixed strategy Nash equilibrium, we discuss the existence and multiplicity of Nash equilibrium. we also study the analysis of a typical secret sharing scheme. Secondly, this paper gives a new rational secret sharing scheme. Secret sharing in the past, participants are "honest" or "malicious", but in the game theory model of the participants are rational, which is selfish. In order to build a reality interactive model, we combine these two models. We analyze the HT2004 rational secret sharing scheme, this scheme is a (3,3) rational secret sharing scheme ,and they extended it to a number of rational participants in the secret sharing, and they show that the two participants rational secret sharing can not be successfully resumed. We give a rational definition of secret sharing, analysis of the only two rational secret sharing participants in the feasibility of, and construct a new rational secret sharing scheme. The solution to the only two participants in a rational secret sharing problem, we will extend it to more than rational secret sharing participants, and give a correctness proof.Finally, we have special privileges based on secret sharing scheme in-depth study on the basis of a model and reality is more similar to special privileges based on rational secret sharing scheme. In the past, secret sharing can only satisfy some needs, if the participation of the members have some special identity, the identity of different people have different secret, or access to different participants, then the need to modify the original program so that its to meet these special needs. We analyzes in the study, Li Bin, special privileges based on secret sharing, the combination of rational secret sharing scheme, proposed a new special privileges based on rational secret sharing scheme, the program participants access to different, and are participants are rational. The correctness of the program we have proved, and the application of the program are discussed, and we also give some applications.