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.