| Secret Sharing Schemes(SSS)refers to method for distributing a secret amongst a group of participants,each of whom is allocated a share of the secret.The secret can be reconstructed only when an authorized subset of shares are available.Shamir’s(t,n)threshold scheme is one of the most well-known secret sharing schemes which provides a very simple and efficient way to share a secret among any t of the n participants.Sometimes,some shares may be obtained by outside adversaries or maybe one of the participants himself is an adversary.In Shamir’s(t,n)threshold scheme,an adversary without a valid share may obtain the secret when more than t shareholders participate in the secret reconstruction.To address this problem,we 1)put forward the notion and gives the formal definition of(t,m,n)-Group Oriented Secret Sharing((t,m,n)—GOSS);and then 2)proposes a(t,m,n)-GOSS scheme based on Chinese Remainder Theorem,which uses Randomized Components(RC)to protect shares 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.Different from Verifiable SS schemes,the security does not depend on any share verification or user authentication mechanism.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,where m(m>t)is the number of participants in a secret reconstruction group.Moreover,our scheme does not depend on any assumption of hard problems or one way functions. |
