A (t,m,n)-Group Oriented Secret Sharing Scheme

Basic (t,n)-Secret sharing (SS) schemes share a secret among n shareholders by allocating each a share. The secret can be reconstructed only if at least t shares are available. An adversary without a valid share may obtain the secret when more than t shareholders participate in the secret reconstruction. To address this problem, the paper introduces the notion and gives the formal definition of (t,m,n)-Group oriented secret sharing (GOSS); and proposes a (t,m,n)-GOSS scheme based on Chinese remainder theorem. Without any share verification or user authentication, the scheme uses Randomized components (RC) to bind all participants into a tightly coupled group, and ensures that the secret can be recovered only if all m (m≥t) participants in the group have valid shares and release valid RCs honestly. Analysis shows that the proposed scheme can guarantee the security of the secret even though up to m-1 RCs or t-1 shares are available for adversaries. Our scheme does not depend on any assumption of hard problems or one way functions.