One of the principal impediments to the achievement of a scalable access control for a large number of subscribers in a public broadcast is to distribute key update messages reliably to all stateless receivers. However, in a public broadcast, the rekeying messages can be dropped or compromised during the transmission over an insecure broadcast channel, or transmitted to the receivers while it was off-line. In this study, we propose a novel group key management scheme that features a mechanism that allows the legitimate receivers to recover the current group key even if they lose key update messages for long-term sessions using short hint messages and member computation. The performance analysis result shows that the proposed scheme has advantages of the scalable and efficient rekeying compared with the previous reliable group key distribution schemes. The proposed key management scheme targets a conditional access system in a media broadcast where there is no feedback channel from receivers to the broadcasting station.