量子密码学

你将学到什么

课程概况

How can you tell a secret when everyone is able to listen in? In this course, you will learn how to use quantum effects, such as quantum entanglement and uncertainty, to implement cryptographic tasks with levels of security that are impossible to achieve classically.

This interdisciplinary course is an introduction to the exciting field of quantum cryptography, developed in collaboration between QuTech at Delft University of Technology and the California Institute of Technology.

By the end of the course you will

Be armed with a fundamental toolbox for understanding, designing and analyzing quantum protocols.
Understand quantum key distribution protocols.
Understand how untrusted quantum devices can be tested.
Be familiar with modern quantum cryptography – beyond quantum key distribution.

This course assumes a solid knowledge of linear algebra and probability at the level of an advanced undergraduate. Basic knowledge of elementary quantum information (qubits and simple measurements) is also assumed, but if you are completely new to quantum information additional videos are provided for you to fill in any gaps.

课程大纲

Optional Background Videos:

Qubits
Quantum gates
Measuring qubits in a basis

Week 1: Quantum tools and a first protocol

Introduction and overview
Fundamental concepts of quantum information: pure and mixed quantum states, the partial trace, classical-quantum states, generalized measurements
Encrypting quantum bits with the quantum one-time pad

Week 2: The power of entanglement

Separable states, entangled states and purification
Sharing a classical secret using quantum states
Looking ahead to quantum key distribution: verifying entanglement using a Bell experiment
Monogamy of entanglement

Week 3: Quantifying information

What it means to be ignorant: trace distance and its use in security definitions
The (min)-entropy
Uncertainty principles as a guessing game

Week 4: From imperfect information to (near) perfect security

Introduction to privacy amplification
Strong randomness extractors
Randomness extraction using two-universal hashing
A construction of two-universal hash functions

Week 5: Distributing keys

Introduction to key distribution: the challenge of being correct and secure
Key distribution over a noisy channel

Guest video: David Elkouss (QuTech, TU Delft) – Practical error correction in key distribution protocols

Week 6: Quantum key distribution protocols

BB84 Protocol
Warmup: Security against a classical eavesdropper
E91 Protocol: purifying protocols using entanglement
Quantum key distribution: definitions and concepts

Guest video: Nicolas Gisin (University of Geneva) – Quantum key distribution in practice

Week 7: Quantum cryptography using untrusted devices

Introduction to device-independent quantum cryptography
Testing devices using a Bell experiment
Security of device-independent quantum key distribution against collective attacks

Guest video: Ronald Hanson (QuTech, TU Delft) – The first loophole free Bell experiment

Week 8: Quantum cryptography beyond key-distribution

Introduction and overview
Two-party cryptography: bit commitment and oblivious transfer
Impossibility of bit commitment
Weak commitments and coin tossing

Week 9: Perfect security from physical assumptions

The noisy storage model
A simple protocol for bit commitment in the noisy-storage model
Security from quantum uncertainty
A universal primitive: weak string erasure

Week 10: Further topics

Position verification from weak string erasure
Sharing a quantum secret
Secure computations on a remote quantum computer

预备知识

Undergraduate linear algebra
Undergraduate probability and statistics
Basic quantum information theory, including qubits, unitaries and measurements (optional videos will provide additional support for those new to quantum information)