Content distributed by broadcast and multicast services is often encrypted (scrambled) to protect copyrighted material. When any cryptanalysis of the current cryptographic scheme used in such services is found, the scheme must be updated. However, the scheme cannot be updated suddenly because a lot of subscribers have receivers with the current scheme.We have previously proposed two cryptographic scheme updating methods. The two methods have trade-off relationship between security and transmission bit rate. However, our security analysis was insufficient. We revisit the security analysis on the methods. In addition, we show a new strong attack against the methods and we evaluate the security against the new attack. As a result, we show that, even if the new attack is implemented in a pirate receiver (PR), its probability to reconstruct content in real-time is very small and that the proposed methods are secure against such a new attack from the viewpoint of service quality. Totally, we show the update methods are practical and secure.