A mix of physics, mathematics, and computer science, the study of quantum information seeks to understand and utilize the information that can be held in the state of a quantum system. Quantum cryptography is then the study of various cryptographic protocols on the information in a quantum system. One of the goals we may have is to verify the integrity of quantum data, a process called quantum message authentication. In this thesis, we consider two quantum message authentication schemes, the Clifford code and the trap code. While both of these codes have been previously proven secure, they have not been proven secure in the simulator model, with an efficient simulation. We offer a new class of simulator that is efficient, so long as the adversary is efficient, and show that both of these codes can be proven secure using the efficient simulator. The efficiency of the simulator is typically a crucial requirement for a composable notion of security. The main results of this thesis have been accepted to appear in the Proceedings of the 9th International Conference on Information Theoretic Security (ICITS 2016).