Quantum Cryptography
Lecture spring 2020

Instructor Dominique Unruh
TA Raul-Martin Rebane (submit homework solutions here)
Lecture Period February 12 -
Lectures Wednesdays, 16:15-17:45, room 2010 (Delta) (Dominique; may sometimes be switched with tutorial)
Practice sessions
Thursdays, 16:15-17:45, room 2034 (Delta) (Raul-Martin)
Office hours
See Dominique's webpage
Course Material Lecture notes, blackboard photos, practice blackboard photos, videos and exam study guide.
Language English
Mailing list ut-qcrypto@googlegroups.com
Exam TBA
Contact Dominique Unruh <<surname> at ut dot ee>

Topics covered

See also the blackboard photos and the practice blackboard photos.
2020-02-12 (lecture)Introduction and motivation. Polarized photons.[video]
2020-02-13 (lecture)Mathematics of single qubits. Elizur-Vaidman bomb testing.[video]
2020-02-19 (practice)Small exercises with single qubits.
2020-02-20 (practice)Polarization invariant under rotation (circular polarization). Elitzur-Vaidman bomb testing (extended).
2020-02-26 (lecture)Mathematics of higher-dimensional systems. Composing systems. (Measurements to be continued.)[video]
2020-02-27 (practice)Multi-qubit gates. Projective measurements.
2020-03-04 (lecture)Continued: measurements. Deutsch's algorithm.[video]
2020-03-05 (practice)Quantum teleportation.
2020-03-11 (lecture)Toy crypto example. Quantum state probability distributions. Density operators.[video]
2020-03-12 (practice)Constructing unitary boolean functions. Indistinguishability of global phase.
2020-03-18 (lecture)[Online lecture] Quantum one-time pad. Partial trace.[video]
2020-03-19 (practice)Tracing out buffer qubits. Impracticality of Schrödinger's experiment. [lab_density_trace.pdf]
2020-03-24 (lecture)[Online lecture] Purification of density operators. Quantum operations. Statistical distance.[video]
2020-03-25 (lecture)[Online lecture] Trace distance. Quantum key distribution (QKD) - basic idea[video]
2020-03-26 (practice)Purifying arbitrary circuits. Impossibility of FTL communication.
2020-04-01 (lecture)[Online lecture] Quantum key distribution - security definition, proof overview, notation.[video]
2020-04-02 (practice)Explicit computation of trace distance. Trace distance of orthogonal states.
2020-04-09 (practice)Finding purifications of density op. Quantum Operators.
2020-04-15 (lecture)[Online lecture] QKD construction/proof: Bell test.[video]
2020-04-16 (practice)Guessing the key in QKD (if no classical postprocessing used). [qkd_guessing.pdf]
2020-04-22 (lecture)QKD construction/proof: Bell test (ctd.). Min-entropy. Min-entropy of QKD raw key. Error correcting codes (intro).[video]
2020-04-23 (practice)Analysis of an equivalent security definition for QKD protocol. Analysis of the security of a QKD protocol that discards the last bit of the key.
2020-04-29 (lecture)QKD construction/proof: Error correction, privacy amplification.[video]
2020-04-30 (practice)Proving missing claim from QKD proof. Secure message transfer from QKD. [lab_SMT.pdf]
2020-05-06 (lecture)Shor's algorithm (period finding, factoring).[video]
2020-05-07 (practice)Implementing the Quantum Fourier Transform. [lab_QFT.pdf]
2020-05-13 (lecture)Learning with errors (LWE). Regev's cryptosystem[video]
2020-05-14 (practice)The Short Integer Solutions problem. Collision-Resistance from SIS.
2020-05-19 (lecture)Commitment: Definitions. Impossibility of information-theoretically secure commitment.[video]
2020-05-21 (practice)Breaking concrete commitment protocols. [lab_commitments.pdf]
2020-05-27 (lecture)Zero-knowledge proofs[video]

Homework

Your current amount of points in the homework can be accessed here (as soon as the first sheet has been corrected).
Out Due Homework Solution
2020-02-212020-03-07Homework 1Solution 1
2020-03-072020-03-22Homework 2Solution 2
2020-03-152020-03-23Homework 3Solution 3
2020-03-282020-04-05Homework 4Solution 4
2020-04-052020-04-15Homework 5Solution 5
2020-04-102020-04-22Homework 6Solution 6
2020-04-262020-05-04Homework 7Solution 7
2020-05-032020-05-11Homework 8Solution 8
2020-05-202020-05-27Homework 9Solution 9
2020-05-302020-06-02Homework 10 

Description

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:

Requirements

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.

Reading

[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.