基于向量空间不同访问群体的门限方案

Threshold scheme for different access clusters based on vector space

针对具有不同访问权限的群体的秘密共享是难于处理的问题,在有限域上引入内积向量空间的概念,研究子空间的直和及其正交补结构中基向量的组成形式;利用Gram-Schmidt算法和最近向量定理设计了一个基于向量空间的(s+r,m+n)门限方案,并将此方案推广到有限多个不同访问群体的情形。结果表明,基于向量空间的不同访问群体的门限方案满足秘密共享的重构和安全性要求,是一个完备的秘密共享方案。

Aiming at that the secret sharing of clusters with different access right was difficult problem, the concept of inner product vector space over the finite field was introduced. Then the direct sum of subspaces and the organization lay- out of basis vector for its orthogonal complement space were researched. A （s＋r, m＋n）-threshold scheme based on vector space was designed by using the Gram-Sehmidt algorithm and the closest vector theorem. Furthermore, this seheme was popularized to the situation with finite numbers of different access clusters. The results reveal that this threshold scheme for different access clusters based on vector space is proved to satisfy the requirement of reconstruction and security feature as a perfect secret sharing scheme.