Crypanalysis of Kuo and Chen's threshold proxy signature scheme based on the RSA

In a (t, n) threshold proxy signature scheme, an original signer delegates a group of n proxy signers to sign messages on behalf of him or her. When the proxy signature is created, t or more proxy signers cooperate to generate valid proxy signatures and any less than t proxy signers can't cooperatively produce valid proxy signatures. In 2003, Hwang et al. proposed a practical threshold proxy signature scheme (HLL-scheme) which is based on RSA cryptosystem for the first time. In 2004, Wang et al. had provided some comments on HLL-scheme. They showed that some mistakes of equations had made HLL-scheme become insecure. Moreover, in 2005, Kuo and Chen also showed two security weaknesses in Hwang et al.'s scheme: one is similar to RSA reblocking problem and the other is that the value of L_i is not clearly defined. In addition, to overcome the second shortcoming of HLL-scheme, Kuo and Chen also provided a modified threshold proxy signature scheme (KC-scheme) based on HLL-scheme. By observation, we find that KC-scheme cannot still work. In other words, in KC-scheme, the value of L_i cannot still be worked out, as makes KC-scheme not workable. To design a workable threshold proxy signature scheme, based on KC-scheme, an improved scheme is proposed.