In this paper, we propose a new secure server-aided RSA secret computation protocol which guards against not only the attacks in [1],[2],[15],[18] but also the new powerful active attacks in [3],[4]. The new protocol is also efficient to support high security level.

To improve the efficiency for the threshold schemes, the major problem is that the secret shadows cannot be reused after renewing or recovering 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. Therefore, we introduce an efficient dynamic threshold scheme. In the new scheme, the shadowholders can reuse the secret shadows no matter that the shared secret is renewed or recovered. In addition, the new scheme provides a way by which the dealer can renew the shared secret or reconstruct the secret sharing system, efficiently. Therefore, this scheme is good for maintaining the important secrets.

For the dependent protocols to perform the server-aided RSA secret computation, the damage caused by the active attacks is greater than that by the passive attacks. Though there are two dependent proposed protocols against active attacks, the cost of the two protocols is still high. In this paper, we propose two efficient dependent protocols. Even considering the low cost of these two protocols, they can also guard against the proposed active attacks.