Till now, few work has been done to analyze the performances of joint fingerprint embedding and decryption schemes. In this paper, the security of the joint fingerprint embedding and decryption scheme proposed by Kundur et al. is analyzed and improved. The analyses include the security against unauthorized customer, the security against authorized customer, the relationship between security and robustness, the relationship between secu-rity and imperceptibility and the perceptual security. Based these analyses, some means are proposed to strengthen the system, such as multi-key encryp-tion and DC coefficient encryption. The method can be used to analyze other JFD schemes. It is expected to provide valuable information to design JFD schemes.