Quantum Cryptography

18h 8mAdvanced2019-02-04

Authors

Thomas Vidick

Stephanie Wehner

Course details

Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution to the key exchange problem.

Skills covered

Cryptography

Concepts

0. A crash course on quantum information

01 - Julia lab exercises installing the weekly sheet
02 - Introduction - Introduction
03 - 0.1 Classical vs. Quantum bits - Classical vs. Quantum bits
04 - 0.1 Classical vs. Quantum bits - More than one qubit
05 - 0.2 Combining qubits using the tensor product - Combining qubits using the tensor product
06 - 0.2 Combining qubits using the tensor product - Examples - combining qubits using the tensor product
07 - 0.3 Measuring quantum bits - Measuring qubits in the standard basis
08 - 0.3 Measuring quantum bits - Measuring qubits in another basis
09 - 0.3 Measuring quantum bits - Examples - measuring qubits
10 - 0.4 Performing operations on qubits - Operations on qubits
11 - 0.4 Performing operations on qubits - Examples - operations on qubits
12 - 0.5 Why we cannot copy qubits - Why we cannot copy qubits
13 - 0.6 The Bloch sphere - The Bloch Sphere representation

1. Quantum tools and a first protocol

14 - Introduction and overview - Introduction and Overview
15 - 1.1 The one time pad (1 Question) - The one time pad
16 - 1.1 The one time pad (1 Question) - Example - the one time pad
17 - 1.2 The density matrix (5 Questions) - The density matrix
18 - 1.2 The density matrix (5 Questions) - Example - the density matrix
19 - 1.2 The density matrix (5 Questions) - The Bloch sphere representation of the density matrix
20 - 1.3 Encrypting quantum bits with the quantum one-time pad (2 Questions) - Encrypting qubits with the quantum one-time pad
21 - 1.3 Encrypting quantum bits with the quantum one-time pad (2 Questions) - Example - The quantum one-time pad
22 - 1.4 Tensor products of mixed states (3 Questions) - Combining multiple qubits - tensor product of density matrices
23 - 1.4 Tensor products of mixed states (3 Questions) - Example - tensor product of density matrices
24 - 1.5 Classical-quantum states (2 Questions) - Classical-quantum states
25 - 1.5 Classical-quantum states (2 Questions) - Example - Classical quantum states
26 - 1.6 Generalized measurements (3 Questions) - Generalized measurements
27 - 1.6 Generalized measurements (3 Questions) - Example - measuring one out of two qubits
28 - 1.7 The partial trace (3 Questions) - The partial trace
29 - 1.7 The partial trace (3 Questions) - Another way to compute the partial trace
30 - 1.7 The partial trace (3 Questions) - Example - tracing out a qubit

2. The power of entanglement

31 - 2.1 Separable states, entangled states (3 Questions) - Separable states, entangled states
32 - 2.1 Separable states, entangled states (3 Questions) - Example - Separable states, entangled states
33 - 2.2 Purification and Uhlmann s theorem (1 Question) - Purification
34 - 2.2 Purification and Uhlmann s theorem (1 Question) - Uhlmann's theorem
35 - 2.2 Purification and Uhlmann s theorem (1 Question) - Example - Applying Uhlmann's theorem
36 - 2.3 Schmidt-Decomposition (3 Questions) - The Schmidt decomposition
37 - 2.3 Schmidt-Decomposition (3 Questions) - Uniqueness of the Schmidt decomposition
38 - 2.4 Sharing a classical secret using quantum states (2 Questions) - Using entanglement to share a classical secret
39 - 2.4 Sharing a classical secret using quantum states (2 Questions) - Sharing a quantum secret
40 - Looking ahead to quantum key distribution - verifying entanglement using a Bell experiment
41 - Example - Looking ahead to quantum key distribution - verifying entanglement using a Bell exp
42 - 2.6 Monogamy of entanglement (2 Questions) - Monogamy of entanglement
43 - 2.6 Monogamy of entanglement (2 Questions) - Playing CHSH with three players

3. Quantifying information

44 - 3.1 What it means to be ignorant - ideal case (2 Questions) - Ignorance
45 - 3.1 What it means to be ignorant - ideal case (2 Questions) - Example of ignorance
46 - 3.2 Trace distance and its use in security definitions (3 Questions) - Trace distance and applications
47 - 3.2 Trace distance and its use in security definitions (3 Questions) - Example of trace distance
48 - 3.3 The (min)-entropy including the smooth min-entropy (2 Questions) - Quantifying randomness (min-entropy)
49 - 3.3 The (min)-entropy including the smooth min-entropy (2 Questions) - Conditional min-entropy
50 - 3.3 The (min)-entropy including the smooth min-entropy (2 Questions) - Example of min-entropy
51 - 3.4 Uncertainty principles - simple version BB84 (2 Questions) - Uncertainty principle and security
52 - 3.4 Uncertainty principles - simple version BB84 (2 Questions) - Example of uncertainty principle
53 - 3.5 Extended UR principles - tripartite version (3 Questions) - Tripartite uncertainty game
54 - 3.5 Extended UR principles - tripartite version (3 Questions) - Example of tripartite uncertainty
55 - Meet the TAs - Introducing Glaucia Murta
56 - Meet the TAs - Introducing J r my Ribeiro
57 - Meet the TAs - Introducing Kaushik Chakraborty
58 - Meet the TAs - Introducing Matt Skrzypczyk
59 - Meet the TAs - Introducing Victoria Lipinska

4. From imperfect information to (near) perfect security

60 - 4.1 Introduction to privacy amplification (2 Questions) - Privacy amplification
61 - 4.1 Introduction to privacy amplification (2 Questions) - Amplifying a weak secret by taking parities
62 - 4.2 What s an extractor and why does it achieve that task (1 Question) - Video - Randomness extractors
63 - 4.2 What s an extractor and why does it achieve that task (1 Question) - A strong extractor against bit-fixing sources
64 - 4.3 Randomness extraction using two-universal hashing (3 Questions) - An extractor construction based on two-universal hash functions
65 - 4.3 Randomness extraction using two-universal hashing (3 Questions) -
66 - 4.4 The pretty good measurement (2 Questions) - The pretty good measurement
67 - 4.4 The pretty good measurement (2 Questions) - The PGM in action
68 - 4.5 Extractor and actual privacy amplification - A strong quantum-proof extractor
69 - 4.5 Extractor and actual privacy amplification - The two-universal extractor in action

5. Distributing keys

70 - 5.1 Introduction to key distribution the challenge of being correct and secure (1 Question) - Introduction to key distribution
71 - 5.2 Key distribution with limited Eve (2 Questions) - Key distribution over a special channel
72 - 5.2 Key distribution with limited Eve (2 Questions) - Key distribution with an storage limited eavesdropper
73 - 5.3 The need for information reconciliation (2 Questions) - The need for error correction
74 - 5.4 Practical error correction in key distribution protocols - Introduction to information reconciliation
75 - 5.4 Practical error correction in key distribution protocols - A simple protocol for information reconciliation

6. Quantum key distribution protocols

76 - 6.1 Introduction to Quantum Key Distribution - Video
77 - 6.2 Quantum key distribution - definitions and concepts (1 Question) - Definitions and concepts in QKD
78 - 6.3 BB84 states and Six state protocol states (2 Questions) - BB84 states and the six state protocol
79 - 6.4 The BB84 protocol (3 Questions) - The BB84 protocol
80 - 6.4 The BB84 protocol (3 Questions) - Security in BB84
81 - 6.5 Purifying protocols using entanglement (2 Questions) - Purifying protocols using entanglement
82 - 6.5 Purifying protocols using entanglement (2 Questions) - Locally projecting on a maximally entangled state using classical communication
83 - 6.6 Security from the tripartite uncertainty relation (1 Question) - Security from a guessing game
84 - 6.6 Security from the tripartite uncertainty relation (1 Question) - A concentration inequality
85 - 6.7 Authentication (1 Question) - Authentication
86 - Quantum cryptography in practice - Video

7. Quantum cryptography using untrusted devices

87 - 7.1 Introduction to device-independent quantum cryptography - Device-independent cryptography
88 - 7.2 Testing devices using a Bell experiment (4 Questions) - Testing entanglement using the CHSH game
89 - 7.2 Testing devices using a Bell experiment (4 Questions) - The GHZ game
90 - 7.3 Device-independent quantum key distribution against collective attacks (2 Questions) - A protocol for device-independent QKD
91 - 7.3 Device-independent quantum key distribution against collective attacks (2 Questions) - The CHSH guessing game
92 - 7.4 Security of DIQKD - collective attacks (2 Questions) - Security against collective attacks
93 - 7.4 Security of DIQKD - collective attacks (2 Questions) - A candidate attack on DIQKD
94 - 7.5 From collective attacks to general attacks (2 Questions) - Security against general attacks
95 - 7.5 From collective attacks to general attacks (2 Questions) - Playing games in parallel
96 - Guest lecture experimental bell test ronald hanson video

8. Quantum cryptography beyond key-distribution

97 - 8.1 Introduction and Overview (2 Questions) - Secure Function Evaluation
98 - 8.2 Oblivious transfer - the universal gate of crypto - Oblivious transfer
99 - 8.2 Oblivious transfer - the universal gate of crypto - A quantum protocol for OT
100 - 8.3 Two-party cryptography - bit commitment - Bit commitment
101 - 8.4 Impossibility of bit commitment (2 Questions) - Impossibility of bit commitment
102 - 8.4 Impossibility of bit commitment (2 Questions) - Computationally secure commitments
103 - 8.5 Weak commitments and coin tossing (1 Question) - Coin flipping
104 - 8.5 Weak commitments and coin tossing (1 Question) - Coin flipping over the phone

9. Perfect security from physical assumptions

105 - 9.1 Evading impossibility (3 Questions) - 9.1 How to evade impossibility
106 - 9.1 Evading impossibility (3 Questions) - Video
107 - 9.2 The noisy storage model (2 Questions) - Video
108 - 9.2 The noisy storage model (2 Questions) - Video
109 - 9.3 A simple protocol for 1-2 oblivious transfer in the noisy-storage model (1 Question) - Video
110 - 9.3 A simple protocol for 1-2 oblivious transfer in the noisy-storage model (1 Question) - Video
111 - 9.3 A simple protocol for 1-2 oblivious transfer in the noisy-storage model (1 Question) - Video
112 - 9.4 Security from quantum uncertainty (1 Question) - Video
113 - 9.5 A universal primitive - weak string erasure (2 Questions) - Video
114 - 9.5 A universal primitive - weak string erasure (2 Questions) - Video
115 - 9.5 A universal primitive - weak string erasure (2 Questions) - Video

10. Further topics

116 - 10.1 Position verification (3 Questions) - Position based crypthography
117 - 10.1 Position verification (3 Questions) - A protocol for position verification
118 - 10.2 Security of position verification (3 Questions) - Quantum teleportation
119 - 10.2 Security of position verification (3 Questions) - Example of quantum teleportation
120 - 10.2 Security of position verification (3 Questions) - Attack using entanglement
121 - 10.2 Security of position verification (3 Questions) - Security of position verification
122 - 10.3 Quantum computing in the cloud - Computing in the cloud
123 - 10.4 Secure computations on a remote quantum computer - Delegating quantum computations
124 - 10.4 Secure computations on a remote quantum computer - Magic states
125 - 10.5 Delegation in the Measurement-based Quantum Computation model - Delegation of measurements
126 - 10.5 Delegation in the Measurement-based Quantum Computation model - Hiding a Hadamard
127 - 10.6 Delegating to two provers as a classical user - Delegation to multiple provers

Conclusion

128 - Conclusion end of course