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Quantum Cryptography
Dominique Unruh
Dominique Unruh
3 September 2012
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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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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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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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?
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Quantum Mechanics
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Double Slit Experiment
• Light falls through two
slits (S2)
• Light-dark pattern
occurs
• Reason: Light is a wave
→ Interference
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Quantum Cryptography
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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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Quantum Cryptography
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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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Quantum Cryptography
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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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Quantum Cryptography
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Quantum Computing
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Church-Turing Thesis
• Turing: Definition of Turing-machines
• Church-Turing thesis:
Any physically computable function can be
computed by a Turing machine
→ Turing-Machine characterises physical
computability
Usually: Efficient = polynomial-time
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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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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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Quantum Cryptography
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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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

Quantum Key Exchange – Attack
Alice
Bob
Caution: This is only the intuition.
Changed by
measurement
Security analysis much more
involved.
Polarisation:
(Took 12 additional years…)
Adversary measures
→ Bit destroyed
→ Alice+Bob: different keys
→ Attack detected
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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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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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End of Intro
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