Key Theory And Basic Research Of Distributed Cryptographic Protocol

A distributed cryptosystem is a cryptosystem with autonomous computing and multi-party participation.With the large-scale application of cloud computing and big data,one of the distributed cryptography protocols,secret sharing,is more and more favored by researchers in distributed computing systems.The emergence of secret sharing provides a solution for the management,storage of confidential information and the calculation of encrypted data.It is not only an important tool in cryptography,but also used as a component of other secure protocols,such as secure multi-party computation,access control and authentication protocol,and so on.Because the secret sharing is widely used and the distributed computing system are required more and more,the continuous development of secret sharing theory is more and more urgent.This thesis mainly uses linear homogeneous recursive relations,symmetric bivariate polynomial and other mathematical tools to study the theoretical basis of the distributed cryptographic protocol and its application in group authentication.The main research contents include:the ideal hierarchical secret sharing scheme,the ideal compartmented secret sharing scheme,the multi-stage secret sharing scheme based on hierarchical access structure and the group authentication protocol based on secret sharing.In summary,the main contributions of this paper are given as follows:1)As the computational complexity of ideal hierarchical secret sharing is exponential,by using a new mathematical tool,the linear homogeneous recurrence relations,a hierarchical secret sharing scheme is proposed.The linear homogeneous recurrence relation has the properties that the sum of the general terms of two homogeneous linear recurrence relations is still the general term of a homogeneous linear recurrence relation and the order of the newly generated homogeneous linear recurrence relation is the sum of the order of the previous two homogeneous linear recurrence relations.By using the correspondence(The correspondence of the threshold values of the subsets here with the multiplicities of the different roots also show that the participants in the higherlevel subsets can substitute for participants in the lower-level subsets)between the threshold of different subsets in hierarchical access structure and the multiplicities of different roots in the homogeneous linear recurrence relation,this scheme avoids checking the exponential complexity of the matrix nonsingularity and reduces the computational complexity of the hierarchical secret sharing scheme from exponential time to polynomial time in the construction phase.2)Since the existing popular compartmented secret sharing schemes are not ideal and the computational complexity of these schemes is exponential,a compartmented secret sharing scheme is proposed based on the linear homogeneous recurrence relations.First,the subset of the participants in the first compartment is used to initialize the first linear homogeneous recurrence relation and the order of the linear homogeneous recurrence relation corresponds to the threshold of the compartment.Second,the subset of the participants in the second compartment is used to initialize the second linear homogeneous recurrence relation and the order of the linear homogeneous recurrence relation corresponds to the threshold of this compartment,and so on.Finally,the linear recurrence sequences corresponding to these linear homogeneous recurrence relations are added and the secrets are hidden in some items of these additive results.The compartmented secret sharing scheme based on linear homogeneous recurrence relations avoids the check of the non-singularity of the matrix in the compartmented secret sharing schemes.This scheme reduces the computational complexity of compartmented secret sharing scheme from exponential time to polynomial time.The proposed hierarchical secret sharing and compartmented secret sharing solve an open problem:whether there is an efficient multipartite secret sharing scheme to implement the multipartite access structures.3)A new hierarchical access structure is defined by modifying the old hierarchical access structure with existential quantifiers.This modification is meaningful and the original hierarchical access structure is a special form of the new hierarchical access structure.Since different subsets in the hierarchical access structure have different levels,different secrets are given different importances,i.e.,the secrets also have levels.Based on the linear homogeneous recurrence relations,by using the correspondence between the linear homogeneous recurrence relation and the subsets in the hierarchical access structure,a multiple secret sharing scheme for the new hierarchical access structure is proposed.Although this scheme is computationally secure,it enriches the basic research of the multipartite access structure.4)As the secure issues of the popular group authentication based on the secret sharing,the group authentication based on secret sharing is studied.The group manager uses symmetric bivariate polynomial to assign tokens to registered members based on the secret sharing method.As soon as each group member gets a token,every two group menbers immediately establish a secure channel between them.The group manager does not need to participate during the authentication process.In this protocol,two algorithms are presented.The first algorithm involves exchanging data over a secure channel established between two users,based on the secret sharing method.The second algorithm does not need to exchange data in the authentication process,but they use the way of randomizing tokens to generate new tokens,thus changing the threshold from t to m(m≥t).