Research Of Secret Sharing Schemes On Vector Space Without Trusted Centers

Since the concept of secret sharing was proposed,secret sharing technique has been deeply studied by some researchers.And secret sharing technique has been widely used in all aspects of the network security.How to ensure the safety of information has become a hot topic in the field of information security.The secret sharing technology is a secrecy fragmentation-reconstruction scheme.It can be prevented from leaking of important information.This paper is devoted to secret sharing schemes on vector space,using vector dot to hide secret.The secret was divided into secret shares and secret shares were sent to each participants.The access structure of secret sharing schemes on vector space was compared with access structure of threshold schemes,the new scheme has the flexibility of access structure.The scheme was not limited to a single equal access structure.In actual life,it is hard to find a trusted center.To solve this problem,schemes of secret sharing without trusted center was proposed.Participants in a dynamic secret sharing scheme can be added and removed dynamically,meantime the secret share can be updated.Because of the insufficient existing secret sharing schemes on vector space without trusted centers,this paper has been proposed.This paper focuses on general access structure,adding or deleting multiple members,updating secret shares.The research results are described as follow.Firstly,this paper is an improvement to existing vector space secret sharing scheme.The new scheme is constructed with a dynamic multi-secret sharing on vector space without trusted centers.The scheme uses the knowledge of vector space,it breaks through the defect of same right in threshold schemes,so all members have a different position in the new scheme.It is reached to add and delete multiple members at the same time in the scheme.It prevents the attacker from stealing secret information effectively by updating the secret share.The scheme is proved to be secure in the random oracle model under the discrete logarithm problem and assumptions of computational Diffie-Hellman problem.Secondly,electronization is the trend on the development of contemporary science and technology.In order to improve the efficiency of all kinds of business activities,two application of secret sharing schemes on vector space that has not trusted center are given,including electronic voting and bank vault doors opening.The new schemes are based on the properties of secert sharing schemes on vector space without trusted centers,it can realize the participants' anonymity and equality.The two new schemes are suitable for large-scale distributed electronic voting and the banking system.Analysis shows the practcality of secret sharing schemes on vector space without trusted centers.Finally,we summarize the research work in this thesis.And the future research direction is suggested.