# Quantum Cryptography

Lecture fall 2018

 Instructor Dominique Unruh < at ut dot ee> TA Ehsan Ebrahimi < dot math at gmail dot com> (submit homework solutions here) Lecture Period September 3, 2018 - December 21, 2018 Lectures Mondays, 10:15-11:45, room 218 (Paabel) (Dominique; may sometimes be switched with tutorial) Practice sessions Fridays, 10:15-11:45, room 220 (Paabel) (Ehsan) Course Material Lecture notes, blackboard photos, practice blackboard photos, videos and exam study guide. Language English Mailing list ut-qcrypto@googlegroups.com Exam 20 December 2018, 10am-1pm, room 218 (Paabel). (Reexam to be scheduled later.) Contact Dominique Unruh < at ut dot ee>

## Topics covered

 2018-09-07 (lecture) Introduction and motivation. [video] 2018-09-10 (lecture) Mathematics of single qubits. [video] 2018-09-14 (practice) Small exercises with single qubits. 2018-09-17 (practice) Elizur-Veidman bomb tester 2018-09-21 (lecture) Mathematics of multiple qubits (except measurements). [video] 2018-09-24 (lecture) Measurements on multiple qubits. Deutsch's algorithm. [video] 2018-09-28 (practice) Review of homework 1f. States invariant under rotation. Quantum teleportation. 2018-10-01 (lecture) Ensembles. Density operators. [video] 2018-10-05 (practice) Review of homework 2, problem 1 and 2. Implementing classical functions using quantum gates, an exercise of projective measurement 2018-10-08 (lecture) Operations on density operators. Quantum one-time pad. [video] 2018-10-12 (practice) Exercises of density operator: physically indistinguishable states, measure and forget, quantum one-time pad with Y and Z Pauli matrices 2018-10-15 (lecture) Partial trace. Purification of density operators. [video] 2018-10-19 (practice) Purification of quantum circuits. Exercises for computing partial traces. 2018-10-22 (lecture) Quantum operations. Statistical distance. Trace distance. [video] 2018-10-26 (practice) Explicit computation of trace distance. Trace distance of orthogonal states. 2018-10-29 (lecture) Trace distance (ctd). Quantum key distribution (security def. started). [video] 2018-11-02 (practice) Analysis of the QKD protocol when Eve measures some of the qubits. 2018-11-05 (lecture) Quantum key distribution: Security def., first steps of proof [video] 2018-11-09 (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 2018-11-12 (lecture) Quantum key distribution: proof (ctd.) [video] 2018-11-16 (practice) Secure message transmission from QKD 2018-11-19 (lecture) Quantum key distribution: proof (ctd.) [video] 2018-11-23 (practice) Guessing the key in QKD (if no classical postprocessing used) 2018-11-26 (lecture) Quantum key distribution: proof (finished) [video] 2018-11-30 (practice) Proving missing claims from QKD proof. 2018-12-03 (lecture) Shor's algorithm (period finding, factoring) [video] 2018-12-07 (practice) Implementing Quantum Fourier Transform. 2018-12-10 (lecture) Learning with errors (LWE). Regev's cryptosystem [video] 2018-12-14 (practice) Breaking LWE with small error, Short Integer Solution Problem 2018-12-17 (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
2018-09-122018-09-19Homework 1Solution 1
2018-09-202018-09-27Homework 2Solution 2
2018-10-012018-10-08Homework 3Solution 3
2018-10-112018-10-18Homework 4Solution 4
2018-10-192018-10-26Homework 5Solution 5
2018-10-292018-11-05Homework 6Solution 6
2018-11-092018-11-16Homework 7Solution 7
2018-11-202018-11-27Homework 8Solution 8
2018-12-072018-12-13Homework 9Solution 9
2018-12-142018-12-17Homework 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:

• Basics of Quantum Computation
• Breaking Crypto with Quantum Computers
• Quantum Key Exchange
• Quantum Commitments (Possibility/Impossibility)
• Quantum Zero-Knowledge
• Everlasting Security
• Quantum Time Vaults

## 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.