秘密分享方案的一般结构

The General Structure of Secret Sharing Scheme

通过分析现有的典型秘密分享方案,特别是(t-n)门限秘密分享,指出大部分秘密分享方案都可归结为向量空间中的秘密分享方案,并且这些方案有一个本质的共同点,都蕴含着一个(t×n)矩阵,只要这个矩阵满足任意t列线性无关即可。通过对此类矩阵的分析指出了向量空间中秘密分享方案的一般构造方法。本文给出了此类矩阵的简单构造方法,并利用这样的矩阵构造了一个多秘密分享方案。

After analysising some typical secret sharing schemes, especially the （t-n） threshold secret sharing scheme ,we find that the majority of secret sharing scheme can be attributed to vector space secret sharing scheme, and these schemes have a common feature that all of them contains a matrix of （txn） with any t columns is linearly independent. This paper gives the general method to design secret sharing scheme in vector space through the analysis of the matrix. Then a simple method is proposed to construct the matrix, we design a scheme for multi-secret sharing with such matrix.