GOMSS: A Simple Group Oriented ( t, m, n ) Multi‐secret Sharing Scheme
Fuyou Miao, Li Wang, Yangyang Ji, Yan Xiong · Chinese Journal of Electronics · 2017
In most (t, n)-Multi-secret sharing ((t, n)MSS) schemes, an illegal participant, even without any valid share, may recover secrets when there are over t participants in secret reconstructions. To address this problem, the paper presents the notion of Group oriented (t, m, n)-multi-secret sharing (or (t, m, n)-GOMSS), in which recovering each secret requires all m (n≥m≥t) participants to have valid shares and actually participate in secret reconstruction. As an example, the paper then proposes a simple (t, m, n)-GOMSS scheme. In the scheme, every shareholder has only one share; to recover a secret, m shareholders construct a Polynomial-based randomized component (PRC) each with the share to form a tightly coupled group, which forces the secret to be recovered only with all m valid PRCs. As a result, the scheme can thwart the above illegal participant attack. The scheme is simple as well as flexible and does not depend on conventional hard problems or one way functions.