Abstract: 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 layout 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-Schmidt algorithm and the closest vector theorem. Furthermore, this scheme 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.

Key words: vector space; direct sum of subspaces; different access clusters; secret sharing; Gram-Schmidt algorithm