In electronic subscription and pay TV systems, data can be organized and encrypted using symmetric key algorithms according to predefined time periods and user privileges and then broadcast to users. This requires an efficient way of managing the encryption keys. In this scenario, time-bound key management schemes for a hierarchy were proposed by Tzeng and Chien in 2002 and 2005, respectively. Both schemes are insecure against collusion attacks. In this paper, we propose a new key assignment scheme for access control, which is both efficient and secure. Elliptic-curve cryptography is deployed in this scheme. We also provide the analysis of the scheme with respect to security and efficiency issues.