1. Dominique Unruh 3 September 2012 Quantum Cryptography Dominique Unruh

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 2

3. 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 3

4. 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 4

5. 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!!! 5

6. Dominique Unruh Organizatorial Questions?

7. Dominique Unruh Quantum Mechanics 7

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

9. 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 9

10. 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 10

11. 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 11

12. Dominique Unruh Quantum Computing 12

13. 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 efficiently efficient Strong 13

14. 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 probabilistic 14

15. Dominique Unruh 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… 15

16. 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 16

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

18. Dominique Unruh Quantum Cryptography 18

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

20. Dominique Unruh Quantum Key Exchange AliceBob Polarisation: Measures  Sends basis Shared key bits 20

21. Dominique Unruh Quantum Key Exchange – Attack AliceBob Polarisation: measures 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…) 21

22. 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 22

23. 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 23

24. Dominique Unruh End of Intro 24