The random oracle is a popular heuristic in classical security proofs that allows us to construct simpler and more efficient schemes and get simpler proofs in many situations. (At the expense of some soundness.) In the quantum setting, using the random oracle is, unfortunately, much harder. Many of the classical proof techniques break down, their replacements are considerably more complex, if they even exist. But still, the quantum random oracle is a useful technique, and recent years have seen considerable advances in proof techniques in the quantum random oracle model. This lecture will introduce the model and some of the most important proof techniques.
Syllabus (somewhat tentative):
What is the random-oracle model (ROM) and why is it useful?
What are the problems in the quantum setting?
Elementary proofs in the QROM
Advanced proof techniques:
Oneway-to-hiding (O2H) theorem