A New Efficient Hierarchical Multi-secret Sharing Scheme Based on Linear Homogeneous Recurrence Relations.

Hierarchical secret sharing is an important key management technique since it is specially customized for hierarchical organizations with different departments allocated with different privileges, such as the government agencies or companies. Hierarchical access structures have been widely adopted in secret sharing schemes, where efficiency is the primary consideration for various applications. How to design an efficient hierarchical secret sharing scheme is an important issue. A famous hierarchical secret sharing (HSS) scheme was proposed by Tassa based on Birkhoff interpolation. Later, based on the same method, many other HSS schemes were proposed. However, these schemes all depend on Polya’s condition, which is a necessary condition, not a sufficient condition. It cannot guarantee that Tassa’s HSS scheme always exists. Furthermore, this condition needs to check the non-singularity of many matrices.