Security of Chien´s efficient time-bound hierarchical key assignment scheme

Recently, Chien proposed a time-bound hierarchical key assignment scheme based on tamper-resistant devices. Without public key cryptography, Chien´s scheme greatly reduces computation load and implementation cost. In this paper, we show that Chien´s scheme is insecure against a collusion attack whereby three users conspire to access some secret class keys that they should not know according to Chien´s scheme.