Security of the redefined Liaw’s broadcasting cryptosystem

Liaw proposed a broadcasting cryptosystem [H.T. Liaw, Broadcasting cryptosystem in computer networks, Computers & Mathematics with Applications 37 (Mar. 1999) 85–87] which claims to involve fewer broadcasting messages, and has attracted quite some research efforts on iterative analysis and improvement [H.M. Sun, Security of broadcasting cryptosystem in computer networks, Electronics Letters 35 (Nov. 1999) 2108–2109; Y.M. Tseng, J.K. Jan, Cryptanalysis of Liaw’s broadcasting cryptosystem, Computers & Mathematics with Applications 41 (Jun. 2001) 1575–1578; J.M. Masque, A. Peinado, Cryptanalysis of improved Liaw’s broadcasting cryptosystem, Journal of Information Science and Engineering 22 (Mar. 2006) 391–399]. We show that the redefined Liaw’s broadcasting cryptosystem recently presented in [J.M. Masque, A. Peinado, Cryptanalysis of improved Liaw’s broadcasting cryptosystem, Journal of Information Science and Engineering 22 (Mar. 2006) 391–399] is still insecure in that an unauthorized user is able to obtain the shared secret, which is only intended for certain privileged users.