Abstract: In order to investigate the security of cryptographic protocols against quantum adversary, researchers have extended various quantum random oracle models beyond the foundation of classical random oracle models, encompassing the realms of post-quantum cryptography and quantum cryptography. This paper summarizes the research progress of different random oracle models, and other weakened quantum random oracle models. By synthesizing the concepts, instantiation methods, and diverse proof techniques of different random oracle models, a comprehensive overview of quantum random oracle models is provided. This paper offers security analyses of cryptographic protocols under different quantum random oracle models. A comparative study of quantum-accessible random oracle model, quantum random oracle model, and classical random oracle model is carried out to clarify the differences and relationships between various random oracle models. Furthermore, this paper points out future research directions with the goal of successfully advancing the investigation of cryptography to address the threat posed by quantum computing.

Key words: Quantum Cryptography, Post-quantum Cryptography, Quantum Random Oracle Model, Quantum-accessible Random Oracle Model, Provable Security