Improvement of Tzeng et al.'s nonrepudiable threshold proxy signature scheme with known signers

In 2000, Hwang et al. proposed a nonrepudiable threshold proxy signature scheme with known signers. However, Tzeng Hwang, Yang [An improvement of nonrepudiable threshold proxy signature scheme with known signers, Comput. Security 23 (2004) 174-178] showed that Hwang et al.'s scheme was vulnerable to the forgery attack, and a new secure threshold proxy signature scheme was proposed to remedy the weakness of their scheme. Unfortunately, we will show that Tzeng et al.'s scheme is also vulnerable to the forgery attack, the malicious original signer can forge a valid threshold proxy signature for any message with knowing a previously valid threshold proxy signature. Furthermore, we improve the security of the threshold proxy signature scheme that remedies the weakness of Tzeng et al.'s scheme.