With the increasing wealth of digital information stored on computer systems today, security issues have become increasingly important. In addition to attacks targeting the software stack of a system, hardware attacks have become equally likely. Researchers have proposed Secure Processor Architectures which utilize hardware mechanisms for memory encryption and integrity verification to protect the confidentiality and integrity of data and computation, even from sophisticated hardware attacks. While there have been many works addressing performance and other system level issues in secure processor design, power issues have largely been ignored. In this paper, we first analyze the sources of power (energy) increase in different secure processor architectures. We then present a power analysis of various secure processor architectures in terms of their increase in power consumption over a base system with no protection and then provide recommendations for designs that offer the best balanc...