Presentations for my Bachelor's thesis (ongoing) on the topic of
Cryptographic Proofs in the Quantum World under the guidance of
Prof. Venkata Koppula and
Dr. Mahesh Sreekumar Rajarshee in collaboration with
Shankh Gupta. We focused on the
Quantum Random Oracle Model and
Minimal Assumptions for Quantum Cryptography.
The classical random oracle model has proven to be of immense utility in proving a cryptographic scheme to be secure against generic attacks. However, these proofs stop working if we allow an adversary to have quantum access to the oracles, primarily because they can query it in superposition. Several techniques have been developed to adapt cryptographic proofs to the quantum setting, including history-free reductions
[BDF+11], one-way-to-hiding
[Unr14], and compressed oracles
[Zha19]. In this project, we began by studying these techniques in depth and then applied the one-way-to-hiding lemma to prove the security of Nielsen's non-committing encryption scheme
[Nie02] in the quantum random oracle model.
This investigation into adapting classical techniques for quantum settings naturally raised broader questions about the foundational role of cryptographic primitives in the quantum world. For instance, one-way functions are widely accepted to be the root of classical cryptography, but quantum information reshapes their role. Notably, quantum public-key encryption can be constructed from one-way functions, something that is believed to be impossible for the classical case. Furthermore, evidence suggests that quantum primitives weaker than one-way functions may also exist. Continuing this line of research, we presently investigate whether we can obtain quantum security against chosen ciphertext attacks from one-way functions and possibly weaker assumptions.