Analysis of Two Signature Schemes from CIS´2006

In CIS´2006 Li et al proposed a proxy ring signature, which allows proxy signer to sign messages on behalf of the original signer while providing anonymity. At the same conference, Weng et al proposed an ID-based key-insulated signature scheme. In this paper, we point out that the former scheme is not correctly specified. The required hash function H₂ should be a map from an elliptic curve to itself. Thus, the additional cost occurs. The latter scheme is insecure because the defined function f(·) is not collision-free. With the exposed temporary signing key in time period t, an adversary can forge signatures in time period t´ if f(U´_ID,t´) = f(U´_ID,t), where U´_ID,t ¿ {1, 2, ¿, n}. In order to overcome this drawback, it suffices to replace f(·) with a hash function, which maps a string onto an elliptic curve.