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Introduction to Quantum Cryptography and Computation: Concepts and Applications

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Explore the fascinating world of quantum cryptography and computation in this engaging lecture series. Covering essential topics such as the principles of quantum mechanics, superposition, and key exchange protocols, participants will gain a conceptual understanding of quantum systems and their implications for cryptography. This course does not require prior knowledge of physics but some background in cryptography and linear algebra is beneficial. Join us for hands-on problem-solving sessions and utilize resources from Nielsen and Chuang’s acclaimed "Quantum Computation and Quantum Information."

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Introduction to Quantum Cryptography and Computation: Concepts and Applications

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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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