Research Of Multi-secret Sharing Scheme Without Trusted Centers

With the rapid development of computer and communications technology in modern society,the protection of secret information and privacy has become more and more important,and how to ensure security in the process of storage and transmission of information has become a hot topic in the field of information security.Secret sharing is one of the most usually used methods to distribute and reconstruct the secret.It can share secret,protect the important privacy and prevent the useful information from being leaked,damaged and tampered.Because we can not ensure the existence of a trusted center under many circumstances,the secret sharing scheme without trusted centers grew up as the times require.The secret sharing scheme without trusted centers is one kind of the secret sharing schemes which need not trusted centers.It has found important applications in the key escrowing,electronic transfering,electronic voting and other fields.The publicly verified secret sharing scheme can verify the public information publicly,it will keep important secret information safe in the process of verification.Multi-secret sharing scheme can share many secrets in a reconstruction process to increase efficiency.In this thesis,we will research on the secret sharing schemes with the natures of renewing,public verificating,adding or deleting some participants simultaneously,adding or deleting some secrets simultaneously,and self-selecting sub-secret in depth.The research results are described as follows.Firstly,the mathematical tools of the bilinear pairings,discrete logarithm problem and assumptions of computational Diffie-Hellman problem are used to construct a dynamic renewable multi-secret sharing scheme without trusted centers.Everyone can verify the validity of distributed information based on zero-knowledge proof.It need not secure channels.And it can prevent attacker from intercepting the secret information by updating secret shares.Not only some participants can be added or deleted simultaneously,but also some secrets can be added or deleted simultaneously.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,signcryption and message recovery algorithm is used to construct a publicly verifiable and renewable multi-secret sharing scheme with self-selecting sub-secret without trusted centers.It convey secret information by signcryption algorithm and need not secure channels.Everyone can verify the validity and correction of public information.The schemeis proved to be secure by the simulation algorithm.Finally,we summarize the research work in this thesis.And the next research direction is suggested.