(Post-) Quantum Cryptography, Fall 2022, University of Luxembourg

Table of Content: (Odd sessions may contain discussions about weekly home-works)

Session 1: Mathematics of a single qubit: a single qubit quantum state, measurement and unitary on a single qubit, Elitzur-Vaidman bomb tester

Session 2. Elitzur-Vaidman bomb tester (improvement), inner product, projective measurements

Session 3. Composing quantum systems: tensor product, composing unitary and measurements, Deutsch-Jozsa algorithm

Session 4. Quantum ensembles, density operator, unitary and measurement on density operators, partial trace, trace distance

Session 5. Example for calculating trace distance, quantum teleportation

Session 6. Simon's algorithm, discrete quantum Fourier transform, order finding algorithm assuming phase estimation algorithm

Session 7. Generalization of Deutsch-Jozsa and purification of a density operator (homework questions), continued with order finding algorithm to do the factoring (Shor's algorithm)

Session 8. Quantum key distribution protocol (BB84 protocol)

Session 9. How to implement a classical function on a quantum computer (using controlled swap unitary), attacking 3-round Feistel cipher using Simon's algorithm

Session 10. Interactive proof system, zero-knowledge proof system, quantum rewinding lemma

Session 11. Public-key encryption (PKE) scheme, learning with errors (LWE) assumptions, Regev's LWE-based PKE, key encapsulation mechanism

Session 12. Random oracle model, quantum random oracle model, Zhandry's compressed oracle technique, Fujisaki-Okamoto and OAEP transforms