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 2 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 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 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 Dominique Unruh
Organizatorial • Questions? Dominique Unruh
Quantum Mechanics 7 Dominique Unruh
Double Slit Experiment • Light falls through two slits (S2) • Light-dark pattern occurs • Reason: Light is a wave → Interference Quantum Cryptography 8 Dominique Unruh
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 9 Dominique Unruh
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 10 Dominique Unruh
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 11 Dominique Unruh
Quantum Computing 12 Dominique Unruh
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 13 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 14 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 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 Dominique Unruh
Today • No quantum computers (except for toy models) • Cannot execute quantum algorithms • Future will tell 17 Dominique Unruh
Quantum Cryptography 18 Dominique Unruh
Quantum Key Exchange • Bennet, Brassard 1984: – Key exchange using quantum communication • Idea: – Measurement destroys state → Adversary cannot eavesdrop unnoticed 19 Dominique Unruh
Quantum Key Exchange Alice Bob Polarisation: Measures Sends basis Shared key bits 20 Dominique Unruh
Quantum Key Exchange – Attack Alice Bob Caution: This is only the intuition. Polarisation: Security analysis much more involved. Changed by measurement (Took 12 additional years…) Adversary measures → Bit destroyed → Alice+Bob: different keys → Attack detected 21 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 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 Dominique Unruh
End of Intro 24 Dominique Unruh
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