Abstract: Based on privileged arrays in Shamir secret sharing schemes, a novel ideal secret sharing scheme is proposed. By researching the new concepts of admissible tracks, non-admissible tracks and privileged arrays on Shamir secret sharing schemes, this paper analyzes non-threshold Shamir schemes. Furthermore, these concepts are extended to Brickell secret sharing scheme based on vector space. This new scheme solves two questions: the difficulty the construction of function in Brickell scheme, and the algorithm to find privileged arrays of any length if such arrays exist. This scheme, on the basis of Brickell scheme, is linear, which has a low computational cost. Meanwhile, the participants can verify their shares with each other, which provids cheat-proof property of the scheme.

Key words: Shamir secret sharing scheme, Brickell secret sharing system, admissible track, non-admissible track, privileged array, cheat-proof

摘要： 基于Shamir秘密共享方案中的特权数组提出一个新的秘密共享方案。研究Shamir秘密共享方案中允许迹、非允许迹及特权数组的概念，分析非门限的Shamir秘密共享方案，并将允许迹、非允许迹和特权数组等概念推广到Brickell向量空间秘密共享体制中。该方案解决了Brickell方案中 函数的构造难题和Spiez S等人提出的公开问题，即任意长度特权数组的求解问题(Finite Fields and Their Applications, 2011, No.4)。分析结果表明，该方案基于向量空间秘密共享体制所构造，具有线性性，因此计算量较小。同时在秘密重构阶段，参与者可以相互验证彼此秘密份额的真实性，具有防欺诈功能。

关键词: Shamir秘密共享方案, Brickell秘密共享体制, 允许迹, 非允许迹, 特权数组, 防欺诈

CLC Number: 

• TP309