Construction and Application of Multi-Degree Secrecy System based on Threshold Secret Sharing

Abstract

A multi-degree secrecy system is constructed based on threshold secret sharing. In this system, a tree-like relation among the participators was set up, and by which a tree structure came into being for the secret shares. This scheme can be demarcated into three phases: initial phase, distribution phase and reconstruction phase. In the initial phase, the dealer (or the most privileged person) "divides" his secret key into n pieces by the number of his juniors (some of them can be gathered to renew the secret key ). And for each share, take it as a new secret key and "divide" it into some pieces so that a new share set was got. Repeat this process until a tree of secret key come into being, which is isomorphic to the tree of participators. In the distribution phase, the dealer distributes the keys of the key tree to the participators on the corresponding position of the participator tree. And in the reconstruction phase, the shareholders of each group can renew the shared secret key by the shares they hold, which ensure that this group can renew the prior key if it is lost. In this system, all the secrets are connected with a tree structure, and all of them are dependent on the secret shares lying on the leaves of the tree; by which much cost of computation and communication is saved. And because of the peculiarity of (t, n) secret sharing schemes that any subset with less t-1 shareholders are not capable of renewing the secret shared by them, this system is relatively secure to some extent, and the security of this system depends on the security of Shamir's (t, n) threshold secret sharing scheme. However, the (t, n) threshold scheme in this system is selected just because it is the simplest one of the current secret sharing schemes. But the steps using Shamir's (t, n) threshold secret sharing scheme are dependent and these steps can be replaced with other secret sharing schemes, such as verifiable secret sharing scheme, proactive secret sharing scheme, and so on, by which the secrecy systems with more peculiarities and applications can be constructed, and the most important of which is that it can provide more security. This system can be applied into the fields of relatively high require of security, such as electric, financial and military fields, to get a multi-degree management of secrets. Take the electric field for example, this system allows the leader to assign different power to different junior by the way of distributing secret shares, by which the behavior over his power is prohibited so that some unnecessary loss is avoided. Furthermore, the authorized group of shareholders can reconstruct the secret if it is lost or the shareholder with it "mutinies", by which the process of reconstructing system is avoided once some shareholder loses his secret (key) or "mutinies".