Study On The Dynamic Multi-Secret Sharing Schemes

Secret sharing technology is an important branch of information security. At first, secret sharing technology is mainly applied in diplomatic, political and military fields. with the development of e-commerce in recent years, commercial value and social value of the technology have been fully affirmed in people's life and work. For the research of dynamic multi-secret sharing scheme, the paper has mainly focused on the dynamic change in members and secret set and dynamic renewing of the secrets. Main contributions are as follows.In order to solve the problems that the existing secrets schemes are based on LUC cryptosystem could not realize dynamic change in members and secret set and could not share multiple secrets one time, this paper proposes a new dynamic multi-secret sharing scheme based on LUC cryptosystem.The scheme does not need to build secure channel between secret dealer and members,and the members and secrets can be dynamically added and deleted. In the recovery phase, cooperative members only need to submit shadow shares to the designated combiner instead of submitting true secret shares and anyone can verify the validity of shadow shares publicly. Thus secret shares do not need to be renewed in sharing multiple secrets and multi-group multi-secret. Finally, the correctness and performance of the scheme are analyzed and the security of the scheme is proved in the random oracle model. Under assumptions of the security of LUC cryptosystem and the Discrete Logarithm, analysis shows that the scheme is safe and effective.In order to resolve the problem that dynamic renewing secret shares and sharing multi-secret one time could not be realized in previous secret sharing schemes, this paper proposes a dynamic renewing multi-secret sharing scheme based on bilinear pairing on elliptic curves and improved signcryption algorithm proposed by Pang Liao-jun etc. The scheme does not need to build secure channel between secret dealer and participants and has forward secrecy when the secret dealer distributes secret. At the same time, anyone can verify the validity of renewed shares and secret shares publicly, and the scheme can share multi-secret when secret is recovered one time. Analysis shows that the scheme which is based on signcryption algorithm, Computational Diffie-Hellman Problem(CDHP), Bilinear Diffie-Hellman Problem(BDHP) and Elliptic Curve Discrete Logarithm Problem(ECDLP) is correct and secure. Finally, we compare the scheme with other schemes on the amount of computation and the overall performance, and obtain advantage of the scheme.