|
| Instructor | Dominique Unruh |
| TA | Raul-Martin Rebane (submit homework solutions here) |
| Lecture Period | February 10 - May 26 |
| Lectures | Wednesdays, 16:15-17:45, Zoom (link in Slack chat)
(Dominique; may sometimes be switched with tutorial) |
| Practice sessions |
Tuesdays, 16:15-17:45, Zoom (link in Slack chat) (Raul-Martin) |
| Slack | https://quantumcrypto2021.slack.com/ |
| Course Material | Lecture
notes (old ones), blackboard photos, practice blackboard photos, and exam study guide. |
| Language | English |
| Exam | May 30, 12:00 – 15:00. (Reexam will be scheduled later.) |
| Contact | Dominique Unruh <unruh@ut.ee> |
| Date | Summary | Knowlets covered | Materials |
|---|---|---|---|
| Feb 10 | Quantum systems, quantum states, unitary operations. | QState, UniTrafo, PauliX | Video, Whiteboard |
| Feb 16 | Small exercises with single qubits. Polarization invariant under rotation. | QState, UniTrafo, Hada, Rota | Whiteboard |
| Feb 17 | Measurements in computational basis. Elitzur-Vaidman bomb tester. Complete measurements. | CBMeas, Bomb, ComplMeas, CompBasis | Video, Whiteboard |
| Feb 23 | Light filters as measurements. Improved bomb tester. Quantum Zero effect. | Bomb, ComplMeas | Whiteboard |
| Mar 02 | Initializing using measurements. States from prob. distributions. Equivalent definitions of unitary. | ComplMeas, ConjTrans, Dirac | Whiteboard |
| Mar 03 | Projective measurements. Tensor product. Composition of quantum systems / quantum states / unitaries / measurements. | ProjMeas, ProjMeasVS, ComposQSys, ComposQState, Tensor, ComposUni, ComposMeas | Video, Whiteboard |
| Mar 09 | Using tensor product and proj. measurements. Quantum teleportation. | ProjMeas, Tensor, ComposUni, ComposMeas | Whiteboard |
| Mar 10 | Deutsch's algorithm. Quantum state probability distributions (ensembles). Operations on ensembles. Density operators. | Deutsch, QDistr, PhysInd, QDistrU, QDistrX, QDistrM, Density | Video, Whiteboard |
| Mar 16 | Distinguishing incorrect toy crypto. Density operators. Creating unitaries for boolean functions. | QDistr, QDistrM, Density, DensityPhysInd, Toff | Whiteboard |
| Mar 17 | Operations on density operators. Theorem: Physically indistinsuishable iff same density operator. Toy crypto protocol is secure. Quantum one-time pad. | Density, DensityU, DensityM, DensityX, DensityPhysInd, QOTP | Video, Whiteboard |
| Mar 23 | Unitaries and measurements on density ops. Observables. | Density, DensityU | Whiteboard |
| Mar 24 | Partial trace. Quantum operations. | ParTr, QOper, QOperAlt | Video, Whiteboard |
| Mar 30 | Tracing out buffer qubits in $U_f$. Trace as a quantum op. Replace operation. | ParTr, QOper | Whiteboard |
| Mar 31 | Statistical distance. Trace distance. Short mentions not in notes: Fidelity. Optimal distinguisher | SD, SDSumDef, SDProps, TD, TDMaxDef, TDSD, TDProps | Video, Whiteboard |
| Apr 06 | Trace distance of biased distributions. QOTP without 0-keys. TD between any two states. | SD, SDSumDef, TD, TDProps | Whiteboard |
| Apr 07 | Quantum key distribution: Intro. Security definition. Protocol overview. First step (distributing Bell pairs). | QKDIntro, QKDSecDef, QKDProto, Bell, TildeNotation | Video, Whiteboard |
| Apr 13 | Prob. of measuring key after QKD. Alternate sec def of QKD. SMT from QKD. | QKDSecDef | Whiteboard |
| Apr 14 | Quantum key distribution: Bell test. Measuring the raw key. | BellTest, BellTestAna, RawKey, RawKeyKeyDiff, RawKeyGuess, MinEnt, RawKeyEnt, RawKeyAna | Video, Whiteboard |
| Apr 20 | Alternate sec def for QKD (continued). Measuring key with t errors. | QKDSecDef, RawKeyGuess | Whiteboard |
| Apr 21 | Error correcting codes. Error correction step in QKD. Strong randomness extractors. Universal hash functions. Privacy amplification in QKD. Finished QKD security proof. | ECC, QKDCorr, Chain, QKDCorrAna, PrivAmp, RandExtQ, UHF, LHL, PrivAmpAna, QKDWrapup | Video, Whiteboard |
| Apr 27 | Last bit of key deleted or set 0. Error correction after randomness extraction. Extracting too much from a key. Problems with deterministic randomness extractors. | ECC, RandExtC, UHF | Whiteboard |
| Apr 28 | Shor's algorithm. Period finding. Factoring. Discrete logarithm. | Fact, Period, FactFromPeriod, DFT, DFTAlgo, Shor, DlogAlgo | Video, Whiteboard |
| May 04 | Implementing the Quantum Fourier Transform. The von Neumann extractor. | DFTAlgo | Whiteboard |
| May 05 | LWE problem (computational and decisional). Regev's cryptosystem. IND-CPA security of Regev's cryptosystem. | BinCompLWE, CompLWE, DecLWE, Regev, RegevCPA | Video, Whiteboard |
| May 11 | Example of Regev's cryptosystem. The Short Integer Solutions problem. Collision-Resistant hash functions from SIS. | Regev | Whiteboard |
| May 12 | Classical/quantum zero knowledge. Difficulty with rewinding in the quantum case. | ProofSys, ZK, GIZK, QZK, QZKProblem | Video, Whiteboard |
| May 18 | Aborting simulators - classical and quantum. | ProofSys, ZK, GIZK, QZK | Whiteboard |
| May 19 | Quantum rewinding. Constructing a quantum ZK simulator. | QRewind, QZKAna | Video, Whiteboard |
| May 26 | Schrödinger equation. Particle in an infinite potential well. | Physical | Video, Whiteboard |
| Out | Due | Homework | Solution |
|---|---|---|---|
| 2021-02-21 | 2021-03-01 | Homework 1 | Solution 1 |
| 2021-03-01 | 2021-03-08 | Homework 2 | Solution 2 |
| 2021-03-08 | 2021-03-16 | Homework 3 | Solution 3 |
| 2021-03-15 | 2021-03-23 | Homework 4 | Solution 4 |
| 2021-03-22 | 2021-03-30 | Homework 5 | Solution 5 |
| 2021-03-29 | 2021-04-06 | Homework 6 | Solution 6 |
| 2021-04-05 | 2021-04-13 | Homework 7 | Solution 7 |
| 2021-04-12 | 2021-04-20 | Homework 8 | Solution 8 |
| 2021-04-20 | 2021-04-27 | Homework 9 | Solution 9 |
| 2021-04-26 | 2021-05-04 | Homework 10 | Solution 10 |
| 2021-05-03 | 2021-05-11 | Homework 11 | Solution 11 |
| 2021-05-10 | 2021-05-18 | Homework 12 | Solution 12 |
| 2021-05-18 | 2021-05-25 | Homework 13 | Solution 13 |
In quantum cryptography we use quantum
mechanical effects to construct secure protocols. The paradoxical
nature of quantum mechanics allows for constructions that solve
problems known to be impossible without quantum mechanics. This lecture
gives an introduction into this fascinating area.
Possible topics include:
You need no prior knowledge of quantum mechanics. You should have heard some introductory lecture on cryptography. You should enjoy math and have a sound understanding of linear algebra.
[NC00] Nielsen, Chuang. "Quantum Computation and Quantum Information" Cambridge University Press, 2000. A standard textbook on quantum information and quantum computing. Also contains some quantum cryptography.
Further
reading may be suggested during the
course. See the "further reading" paragraphs in the lecture notes.