Dominique Unruh 3 September 2012 Quantum Cryptography Dominique Unruh
Dominique Unruh 3 September 2012
Quantum Cryptography
Dominique Unruh
Dominique Unruh
Organization
• Lecture: Tuesday 10.15am
• Practice: Wednesday 10.15am
– Problem solving as a group
• (sometimes switched)
• Homework: Due after approx. one week
• 50% needed for exam
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Dominique Unruh
Organizatorial
• Black board lecture (except today)
• Material:
– Board photos
– Lecture notes (short)
– Book: Nielsen, Chuang, “Quantum Computation and Quantum Information” (not required)
• Deregistering: Not after deadline
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Dominique Unruh
Scope of the lecture
• No physics (almost)
– Do you need electrodynamics to understand Turing-machines?
– Mathematical abstraction of quantum computation/communication
• Intro to Quantum computation/communication
• Selected topics in quantum crypto
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Dominique Unruh
Requirements
• No physics needed
• Some crypto background recommended
– (To have a context / the big picture)
• Some linear algebra will be used
– You should not be afraid of math
– Can do recap during tutorial ask!!!
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Organizatorial
• Questions?
Dominique Unruh
Quantum Mechanics
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Dominique Unruh Quantum Cryptography
Double Slit Experiment
• Light falls through two slits (S2)
• Light-dark pattern occurs
• Reason: Light is a wave → Interference
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Dominique Unruh Quantum Cryptography
Double Slit Experiment
• Send a single photon at a time
• Photon either goes through left or right path
• After a while, interference pattern occurs
• Each photon “interferes with itself”
→ Physicists puzzled
• Solution: Quantum mechanics:
– Photon takes both ways in superposition
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Dominique Unruh Quantum Cryptography
Superposition
• If two situations are possible, nature “does not always decide”
– Both situations happen “in superposition”
– (Doesn’t need to make sense now)
• Only when we look, “nature decides”
• Schrödinger’s cat
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Dominique Unruh Quantum Cryptography
Quantum Mechanics
• Superposition: Several things happen “at once”
• Our intuition is classical, we cannot understand this
• Mathematical notions allow to handle QM, even if we do not understand it
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Dominique Unruh
Quantum Computing
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Dominique Unruh
Church-Turing Thesis
• Turing: Definition of Turing-machines
• Church-Turing thesis:
→ Turing-Machine characterises physical computability
Usually: Efficient = polynomial-time
Any physically computable function can be computed by a Turing machine
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Dominique Unruh
Randomized algorithms
• 1970s: Solovay-Strassen primality test
• No deterministic test known (at that time)
• Polynomial identity: No deterministic test today
Any efficiently physically computable function can be computed by an efficient
Turing machine
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Enters: The Quantum Computer
• Strong Church-Turing extended once
– Perhaps has to be extended again
• Feynman 1982:
– Simulating quantum systems difficult for TMs
– Quantum system can simulate quantum system
• Probabilistic Church-Turing thesis wrong?
– Unknown so far… But seems so…
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Dominique Unruh
Quantum Algorithms
• Deutsch-Jozsa 1992: – Testing whether function is balanced or constant
– No practical relevance
– Shows: Quantum Computers more powerful than classical
• Shor 1994: – Factorization of integers
• Grover 1996: – Quadratic speed-up of brute-force search
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Today
• No quantum computers (except for toy models)
• Cannot execute quantum algorithms
• Future will tell
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Dominique Unruh
Quantum Cryptography
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Dominique Unruh
Quantum Key Exchange
• Bennet, Brassard 1984:
– Key exchange using quantum communication
• Idea:
– Measurement destroys state
→ Adversary cannot eavesdrop unnoticed
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Quantum Key Exchange Alice Bob
Polarisation:
Measures
Sends basis
Shared key bits
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Dominique Unruh
Quantum Key Exchange – Attack Alice Bob
Polarisation:
Adversary measures
→ Bit destroyed
→ Alice+Bob: different keys
→ Attack detected
Changed by measurement
Caution: This is only the intuition. Security analysis much more involved.
(Took 12 additional years…)
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Dominique Unruh
Quantum Key Exchange
• Idea proposed 1984
• First security proof: Mayers 1996
• Possible with today’s technology
– Single photon sources
– Polarisation filters
• No complexity assumptions
– Impossible classically
• Details later in lecture
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Dominique Unruh
Quantum Cryptography
• Any cryptography using quantum – Key exchange
– Bit commitment
– Oblivious transfer
– Zero knowledge
– Signatures
• Often: Quantum Crypto = Key Exchange – Other applications often ignored
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Dominique Unruh
End of Intro
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