A new ideal secret sharing scheme based on a tree

Abstract

One of the methods used in order to protect a secret K is a secret sharing scheme. In this method, the secret K is distributed among a finite set of participants P by a special participant called the dealer, assumed to be honest, in such a way that only predefined subsets of participants can recover the secret after collaborating with their secret shares. The construction of secret sharing schemes has received a considerable attention of many researchers whose main goal was to improve the information rate. In this paper, we focused on the hierarchical secret sharing. Related to the previous works, we propose a novel simpler construction of a secret sharing scheme, where the access structure is a tree according to the hierarchical concept of companies illustrated through its organization chart. We prove that the proposed scheme is ideal by showing that the information rate equals 1. In order to show the efficiency of the proposed scheme, we discuss all possible kinds of attacks and prove that the security is ensured. Finally, we include a detailed didactic example of a small company organization chart.

Subject Classification:

• Primary 11T71
• Secondary 94A60

Keywords:

• Hierarchical secret sharing scheme
• Qualified subsets
• Access structure
• Interpolation
• Information rate