A (t, m, n)‐Group Oriented Secret Sharing Scheme. Issue 1 (1st January 2016) - Miao, Fuyou; Fan, Yuanyuan; Wang, Xingfu; Xiong, Yan; Badawy, Moaman
Abstract : 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.