In internet protocol television (IPTV) broadcasting, service providers charge subscribing fee by scrambling the program with conditional access system (CAS) using control words (CWs). A smart card is used to decrypt the CWs and transfer them back to set-top box (STB) to descramble the scrambled program. Secure communication between STB and the smart card is closely related with the benefit of service providers and the legal rights of users. In addition, secure key exchange with mutual authentication in the communication between STB and the smart card is an essential part of secure communication that will significantly improve the security of the system. To provide secure communication with mutual authentication in IPTV broadcasting, there are several schemes. The schemes proposed a secure and efficient method for the communication between STB and the smart card. Unfortunately, the schemes still have some security flaws. In this paper, we review that the previous schemes are vulnerable to several attacks. Further, we recommend some modifications to the schemes to correct these security flaws and present a formal analysis about our improved protocol using a logic based formal method.