SLIDE 1
Quantum Cryptography
Māris Ozols
University of Cambridge
Overview
- What are quantum computers?
- What is quantum cryptography?
- Shor's algorithm for factoring
- Quantum key distribution
- Device-independent quantum cryptography
Quantum Cryptography Mris Ozols University of Cambridge Overview - - PowerPoint PPT Presentation
Quantum Cryptography Mris Ozols University of Cambridge Overview - - PowerPoint PPT Presentation
Quantum Cryptography Mris Ozols University of Cambridge Overview What are quantum computers? What is quantum cryptography? - Shor's algorithm for factoring - Quantum key distribution - Device-independent quantum cryptography What
SLIDE 2
SLIDE 3
What is quantum computing?
Physics Computer Science Mathematics
Quantum Computing
SLIDE 4
Quantum mechanics
SLIDE 5
How to simulate quantum physics?
Simulating quantum systems on a regular computer is very hard... Wouldn't it be easier if the computer itself would
- perate based on the laws
- f quantum physics?
Richard Feynman
SLIDE 6
What is a quantum computer?
Quantum mechanics Quantum computer is a device that processes information by using quantum phenomena
+
Computer
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What quantum computers are not...
SLIDE 8
just
smaller
What quantum computers are not...
SLIDE 9
just
smaller
What quantum computers are not...
just faster
SLIDE 10
just
smaller
What quantum computers are not...
exponentially
faster just faster
SLIDE 11
just
smaller
What quantum computers are not...
exponentially
faster just faster science fiction
SLIDE 12
just
smaller
What quantum computers are not...
exponentially
faster just faster
available for $ale
science fiction
SLIDE 13
Quantum cryptography
- Quantum algorithms for breaking
existing cryptosystems
- Shor's algorithm for factoring
SLIDE 14
Quantum cryptography
- Quantum algorithms for breaking
existing cryptosystems
- Shor's algorithm for factoring
- Enabling secure communication
- Quantum key distribution
SLIDE 15
Quantum cryptography
- Quantum algorithms for breaking
existing cryptosystems
- Shor's algorithm for factoring
- Enabling secure communication
- Quantum key distribution
- Computation with untrusted devices
- Device-independent quantum cryptography
SLIDE 16
Multiplying vs factoring
3 × 5 = 15 11 × 13 = 143 28423087481 × 25162321141 = 715190855015658735821 Multiplying is easy...
SLIDE 17
Multiplying vs factoring
3 × 5 = 15 11 × 13 = 143 28423087481 × 25162321141 = 715190855015658735821 Multiplying is easy...
SLIDE 18
Multiplying vs factoring
12 = 3 × 4 377 = 13 × 29 57249035862524887649 = 2543563837 × 22507410677 3 × 5 = 15 11 × 13 = 143 28423087481 × 25162321141 = 715190855015658735821 Multiplying is easy... Factoring is not...
SLIDE 19
Multiplying vs factoring
12 = 3 × 4 377 = 13 × 29 57249035862524887649 = 2543563837 × 22507410677 3 × 5 = 15 11 × 13 = 143 28423087481 × 25162321141 = 715190855015658735821 Multiplying is easy... Factoring is not...
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Public-key cryptography (RSA)
SLIDE 21
Public-key cryptography (RSA)
Public key
57249035862524887649
Private key
2543563837 22507410677
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Public-key cryptography (RSA)
Public key
57249035862524887649
Private key
2543563837 22507410677
Message Encrypt
SLIDE 23
Public-key cryptography (RSA)
Public key
57249035862524887649
Private key
2543563837 22507410677
Message Encrypt Decrypt Message
SLIDE 24
Shor's algorithm breaks RSA
Peter Shor
- Produces prime factors of a given integer
- Runs in polynomial time
(best known classical algorithm runs in exponential time)
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Shor's algorithm breaks RSA
Peter Shor Fourier transform of Peter Shor
- Produces prime factors of a given integer
- Runs in polynomial time
(best known classical algorithm runs in exponential time)
- Based on quantum Fourier transform
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Quantum key distribution
SLIDE 27
Quantum key distribution
Uncertainty principle Quantum system cannot be
- bserved without disturbing it
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Quantum key distribution
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Device-independent quantum cryptography
untrusted device
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Device-independent quantum cryptography
test test test test compute test test
untrusted device
Strategy 1: Self-testing
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Device-independent quantum cryptography
test test test test compute test test
untrusted device 2
test test test test compute test test
untrusted device 1
Strategy 2: Cross-checking
SLIDE 32
Device-independent quantum cryptography
Device-independent quantum protocols exist for
- quantum key distribution
- randomness expansion
- randomness amplification
test test test test compute test test
untrusted device 2
test test test test compute test test
untrusted device 1
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Long-term implications
Security vs Privacy
SLIDE 34