To improve the efficiency for the threshold schemes, the major problem
is that the secret shadows cannot be reused after renewing or recover
ing the shared secret. However, if the secret shadows cannot be reused
, the established threshold scheme is limited to be used only once. It
is inefficient to reconstruct the whole secret sharing system. Theref
ore, we introduce an efficient dynamic threshold scheme. In the new sc
heme, the shadowholders can reuse the secret shadows no matter that th
e shared secret is renewed or recovered. In addition, the new scheme p
rovides a way by which the dealer can renew the shared secret or recon
struct the secret sharing system, efficiently. Therefore, this scheme
is good for maintaining the important secrets.