Dynamic Multi-secret Sharing Scheme

The main idea of the threshold secret sharing is that the secret is distributed to a number of members, each member holds a share of the secret which is also called as sub-key or shadow, and only that there is more than certain shares can they reconstruct the secret, when the share is less than a certain number, though cooperation, they can't get any information of the secret. Since Shamir and Blakley have proposed the concept of the (t,n) threshold secret sharing separately in 1979, the scholars studied the theory and the model of the secret sharing in-depth, and a great number of research findings were gained. But most of the secret sharing schemes have the following weaknesses in common:(1) During the process of secret sharing, a secret is shared in many schemes. The capability of application is lower. The secret shadows are distributed by the dealer, which lead to the burder for the dealer and the security of the schemes. If the dealer not honest, it is impossible for participant to detect the cheater.(2) Some schemes are used only once, and when the participants are changed(on the premise that it doesn't need to redistribute the secret shares of the other members, they can't add or delete participants),these schemes are not used. when using these schemes, a security channel must be built between the distributer and the participants, which increases the cost of the system.(3) Every participant is as important as the others, so they have same weights. But in the real life, some people are more important than others. To solve these problems, the article will make the verifiable multi-secret sharing, the secret sharing based on an access structure and the secret sharing among weighted participants to be key point in the research, the research findings of this paper are showed in the following:(1) Based on RSA cryptostystem and discrete logarithm problem, a verifiable multi-secret sharing scheme is proposed. In this paper, secret shadows are selected by participants themselves. This information is not needed to be saved by the dealer,so the burden of saving is mostly reduced. In the sharing process, the information provided by the dealer is checked by participants, at the same time, the information transmitted by participants is verified by the Designated Combine using public information.(2) A dynamical multi-secret sharing scheme in an access structure is proposed, which is based on self-pairing on elliptic curve. A scheme on sharing points on an elliptic curve is devised. The sub-secrets of participants are chosen by themselves. The pseudo shadows are sent, so a security channel is not need between the secret dealer and participants. The shadows do not need to be changed when the secrets are renewed, the access structure is alerted, or participants are deleted(new participant is added). The security of this scheme is examined, which is based on ECDLP problem.(3) A scheme among different weight is proposed that is based on Shamir's secret sharing and Chinese Remainder Theorem. A public-key cryptosystem in elliptic curve is introduced into it, so this scheme does not suffer from any cheating and a secret channel is not needed to build between the dealer D and the participants. During the process, when a participant is joined or deleted freely, the scheme is still useful. It is safe from the viewpoints of attacks without factoring N and multiple attack.