Hierarchical threshold multi-secret sharing scheme based on Birkhoff interpolation and cellular automata

Secret sharing is one of the main components of many security protocols that are designed to provide secure communications. In secret sharing schemes, a secret is divided into some pieces, called secret shadows and then, these shadows are shared among a group of participants. Later, authorized subsets of participants can use their shadows and reconstruct the secret. A hierarchical threshold secret sharing (HTSS) scheme is a method to share a secret among a group of participants with different levels of authority. The authorized subsets of HTSS schemes are those satisfying a sequence of threshold requirements. In 2007, Tassa proposed an HTSS scheme based on Birkhoff interpolation. This scheme is not secure for sharing arbitrary number of secrets during a single sharing process. In this paper, we employ cellular automata to improve Tassa's approach and propose a hierarchical threshold multi-secret sharing scheme. We then prove the security of the proposed scheme.