Some Studies On Threshold Secret Sharing Schemes

Since A.Shamir and G.Blakley respectively proposed (k, n)-threshold secret sharing scheme in 1979, the study of the secret sharing scheme has been widely paid attention to. A special circumstance considered the status of participants has been widely promoted. In real life, the special status of the participants must be taken into consideration. For example, certain players of the participants must participate in certain activities; the sub-secret share held by participants is different in certain activities. Taking the special status of the participants into account, We need to modify the (k,n)-threshold scheme to meet specific needs. This topic studied three kinds of new threshold secret sharing schemes:(t,k,n)-threshold secret sharing scheme, (m+n,t+1)-threshold secret sharing scheme, and (m+ ni+n2+…N_l,t+t1+t2+cdots+tl)-threshold secret sharing scheme. Research focuses on the dynamic properties, sub-key optional properties, verifiable properties, scheme with the right weights and properties on other aspects. the main realization method of (t,k,n)secret sharing scheme with anti-fraud features is to use the Chinese Remainder Theorem. It's security. The key to realize(m+n, t+1)梥ecret sharing scheme is to construct a (m+n, t+1)-Secret sharing matrix. It reflects the nature interrelation of the secret sharing scheme and the matrix. We make a promotion of the (m+n1+n2+…+n+l,t+t1+t2+…+tl)-secret sharing scheme. The weight of each participant in this scheme can be different. This scheme is a dynamic, optional sub-key and verifiable scheme.In these kinds of secret sharing schemes, the status of participants are special. Considering the status of participants is a very important topic in Secret sharing scheme. It has been applied in the circumstance of social division and participants with different rights. These studies of secret sharing schemes have both signification theoretic and practical values.