This paper proposed a new threshold secret sharing scheme based on the Shamir(n,t) threshold secret sharing scheme. Using the characteristic that the characteristic equation of the n-th order matrix had multiple roots, it realized the secret sharing of participants in different sets. The secondary master key corresponding to the same participation set was the same, that was, the eigenvalue were the same. The algorithm firstly used the feature vector corresponding to the same eigenvalue as a subkey, then it distributed the subkey to the participating members of the same participating set. What's more, the members of the same collection could use the black box to verify the authenticity of the sub-keys in their own hands so as to achieve the purpose of fraud prevention. The analysis result shows that this scheme is safe and ideal.

[2019-08-05] Printed Article /doc/2018.01.0167/v2