A Perfect Ideal Hierarchical Secret Sharing Scheme Based on the CRT for Polynomial Rings

In this paper, for the first time, we propose a new explicit hierarchical threshold secret sharing (HTSS) scheme based on the Chinese Remainder Theorem (CRT) for polynomial rings, where the participant set is divided into disjoint subsets and the threshold of a superior subset is less than the threshold of an inferior subset. In addition, we present a rigorous security analysis to show that our HTSS scheme is both perfect and ideal. Moreover, a toy example of our HTSS scheme is given to enable readers to better understand our construction. By comparison, it appears that our scheme is the first CRT-based HTSS for polynomial rings and also the first ideal and perfect CRT-based HTSS scheme, which is easier to construct than its counterpart for integer rings, where different participants hold shares of different sizes. Besides, our HTSS can also distribute shares of the same size, similar to other HTSS.