Quantum Cryptography Dominique Unruh Dominique Unruh 3 September - - PowerPoint PPT Presentation

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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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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Dominique Unruh

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
• ccurs
• 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
• nce”
• 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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Dominique Unruh

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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Dominique Unruh

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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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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Dominique Unruh

End of Intro

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