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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.
How to construct an ideal multi-secret sharing scheme for general access structure is a difficult problem.This paper first solves a recently proposed open question by Spiez et al [Finite Fields and Their Application, 2011, 17: 329-342], that is, We design the algorithm of obtaining an array of privilege of any length under the premise of the privilege array.Furthermore, taking the scheme of Pang et al. And Yang et al. As an example, we use the privilege array theory as an example to analyze the existing algorithms based on Shamir threshold The secret sharing scheme is not perfect.Finally, based on the algorithm of the privilege array, we propose a multi-secret sharing scheme, and we prove that the scheme is ideal and the authorization set in the scheme’s access structure is more abundant than the threshold scheme .