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3 September 2012

Quantum Cryptography. 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. Organizatorial. Black board lecture (except today)

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3 September 2012

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  1. Quantum Cryptography Dominique Unruh 3 September 2012

  2. 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

  3. 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

  4. 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

  5. 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!!!

  6. Organizatorial • Questions?

  7. Quantum Mechanics

  8. Double Slit Experiment • Light falls through two slits (S2) • Light-dark pattern occurs • Reason: Light is a wave → Interference Quantum Cryptography

  9. 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 Quantum Cryptography

  10. 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 Quantum Cryptography

  11. 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 Quantum Cryptography

  12. Quantum Computing

  13. Church-Turing Thesis Strong • Turing: Definition of Turing-machines • Church-Turing thesis: → Turing-Machine characterises physical computability Usually: Efficient = polynomial-time efficiently Any physically computable function can be computed by a Turing machine efficient

  14. 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 probabilistic

  15. 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…

  16. 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

  17. Today • No quantum computers(except for toy models) • Cannot execute quantum algorithms • Future will tell

  18. Quantum Cryptography

  19. Quantum Key Exchange • Bennet, Brassard 1984: • Key exchange using quantum communication • Idea: • Measurement destroys state → Adversary cannot eavesdrop unnoticed

  20. Polarisation:       Quantum Key Exchange Alice Bob Measures Sends basis Shared key bits

  21. Quantum Key Exchange – Attack Alice Bob Adversary measures → Bit destroyed → Alice+Bob: different keys → Attack detected Caution: This is only the intuition. Security analysis much more involved. (Took 12 additional years…) Polarisation: Changed by measurement measures

  22. 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

  23. Quantum Cryptography • Any cryptography using quantum • Key exchange • Bit commitment • Oblivious transfer • Zero knowledge • Signatures • Often: Quantum Crypto = Key Exchange • Other applications often ignored

  24. End of Intro

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