Research Of Verifiable Secret Sharing Scheme

Along with the rapid development of electronic communications and computer network, hot topic has been given to how to ensure the security of the data in the process of storage and transmission in the field of information security. Secret sharing is one of the most commonly useful methods to distribute the secret, store the secret and reconstruct the secret. It can share secret, protect the important privacy and prevent the useful information from being leaked, damaged and tampered. The verifiable secret sharing scheme is one of the secret sharing schemes which can prevent cheating. 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 and secret shares publicly, it will keep important secret information safe in the process of verification.In this thesis, we will research on the secret sharing schemes with the natures of periodically updating, public verificating, and self-selecting sub-secret in depth. The research results are described as follows.Firstly, the mathematical tools of the Elliptic Curve, bilinear pairings and one-way hash chain are used to construct a publicly verifiable and periodically renewable multi-secret sharing scheme while keeping the advantages of the YCH scheme. The secrets can be reconstructed, while the participants holding their secret share in this scheme. The one-way hash chain is used to construct the updating algorithm and it can make the secret shares updated periodically. All of us can verify the correctness of the secret shares and the effectiveness of the public information.The cheating of the participants and distributor can be prevented effectively. Analysis of the correctness and performance of the scheme are given in detail and the scheme is proved to be secure under the assumptions of the Discrete Logarithm problem, bilinear Diffie-Hellman problem and computer Diffie-Hellman problem.Secondly, power of the distributor was abusive in the existing secret sharing schemes. And some secret sharing schemes could not make theirself periodically renewable and publicly verifiable simultaneously. So a publicly verifiable and renewable multi-secret sharing scheme is proposed. The participants select their sub-secrets, and the generated shadow secrets are used in the secrets reconstruction and the true secret shares are protected. The secret shadows are updated periodically to prevent the invaders from intercepting the secret information in the limited time. The public validation of shadow secrets and the public information can prevent the malicious deception. Correctness and the performance of the scheme are given, the security and effectiveness of the scheme are proved in the random oracle model.Finally, we summarize the research work in this thesis. And the next research direction is prospected.