Quantum Cryptography

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