极小特权数组上的理想多秘密共享方案

如何构造针对一般存取结构的理想的多秘密共享方案是一个比较困难的问题.本文首先解决了Spiez等最近提出的一个公开问题Finite Fields and Their Application,2011,17:329–342],即在特权数组存在的前提下,设计求得任意长度的特权数组的算法.进一步,我们利用特权数组理论,以Pang等和Yang等的方案为例,分析了大多现有的基于Shamir门限体制的多秘密共享方案均不是完善的.最后,基于特权数组的算法,本文提出了一个多秘密共享方案,我们证明了该方案是理想的,并且方案的存取结构中的授权集比门限方案的更加丰富.

An ideal multi-secret sharing scheme based on minimal privileged coalitions

How to construct an ideal multi-secret sharing scheine for general access structures is difficult. In this paper, we solve a public problem proposed by Spiez et al. recently Finite fields and their application, 2011, 17： 329 3,12], namely to design an algorithm of privileged coalitions of any length if such coalitions exist. in terms of privileged coalitions, we show that most of the existing multi-secret sharing schemes based on Shamir threshold secret sharing are not perfect by analyzing Yang et al.＇s scheme and Pang et al.＇s scheme. Finally. based on the algorithm mentioned above, we devise an ideal nmlti-secret sharing scheme for families of access structures, which possesses more vivid qualified sets than that of the threshold scheme.