Most digital content nowadays is protected by a digital rights management (DRM) framework to prevent piracy. Since much content is distributed throughout the world, modern DRM frameworks must protect the confidentiality and integrity of the data, even from rootkits or physical tampering. Secure processors have been proposed to ensure secure executions by performing memory encryption and integrity verification effectively. However, application start-up takes a considerable time because it requires initial memory hash calculation. In this paper, we propose Promissory Hash, a method to skip the initial hash calculation while maintaining the actual integrity. The processor declares Promissory Hash to the external certifier that should represent the initial memory. While the application is executing, any disagreement from the Promissory Hash halts the execution. A detailed implementation is revealed and additional storage requirement is also estimated: an additional 1,028 KB for the 256 MB main memory greatly reduce the start-up latency.