Tightly coupled multi-group threshold secret sharing based on Chinese Remainder Theorem

Abstract

(t,n)-Threshold secret sharing ((t,n)-SS) scheme is a fundamental cryptographic primitive. As a special (t,n)-SS, a Multi-Level threshold Secret Sharing scheme (MLSS) divides shares into different levels. Shares at higher levels can be used at lower ones but shares of lower levels are invalid at higher ones. However, MLSS is limited in applications and vulnerable to Illegal Participant (IP) attack and t-Share Capture (SC) attack. Therefore, the paper first extends the notion of MLSS to multi-group threshold secret sharing (MGSS) to accommodate wider application scenarios. In order to cope with the 2 attacks, the paper then proposes a tightly coupled MGSS scheme based on Chinese Remainder Theorem. In the scheme, a shareholder, with only one private share, is allowed to participate in secret reconstruction of different groups. Moreover, when sufficient shareholders collaborate to recover the secret in a group, they first form a tightly coupled subgroup by constructing a randomized component each so that the secret can be recovered only if each participant has valid share and actually participates in secret reconstruction. Analyses show that the proposed scheme is capable of thwarting IP and SC attacks. Besides, the scheme is more flexible and popular in applications compared with MLSS scheme.