Cryptanalysis of two threshold proxy signature schemes based on RSA cryptosystem

In 2003, M.-S. Hwang et al. proposed a (t, n) threshold proxy scheme on RSA cryptosystem, which was proved insecure by G. Wang. Recently, Y.-F. Chang and X. Cheng proposed two improved RSA-based threshold proxy signature schemes respectively. In this paper, we propose the cryptanalysis of two schemes. Firstly, we point out that any t or more proxy signers can cooperatively recover the original singer´s private key and factor the modulus No = poqo in X. Cheng´s scheme. Secondly, we point out that the original signer or the combiner can forge any valid proxy signature in Y.-F. Chang´s scheme. Therefore, neither of two threshold proxy signature schemes can satisfy the security requirements of threshold proxy signature.