Hierarchical Threshold Secret Sharing System And Related Research

Secret sharing scheme is a very important branch of modern cryptography and important research field of information security. Especially, participants could be devided into different grades and assigned related power in hierarchy secret sharing system which is of great practical use.Firstly, this thesis reviews the context and advance of hierarchical threshold secret sharing system, and proposes an improved hierarchical threshold secret sharing schemes based on Birkhoff Interpolation, which makes sure the presence of higher level participants must be involved while grant the lower level the right to vote. Secondly, by means of the intractability of discrete logarithm problem and the property of linear equations, three dynamic hierarchical threshold secret sharing schemes with different cheater-detection are proposed. After that, to improve the utilization rate of resources, a hierarchical threshold multi-secret sharing scheme is proposed, with which several secrets of different levels could be shared in a hierarchical system. Moreover, this thesis studies the multiplication of hierarchical scheme and the application to secure multi-parties computation. Finally the thesis gives the necessary conditions and sufficient condition for our improved scheme to be multiplicative and strongly multiplicative, and proves that our improved scheme has better multiplicative properity.