Lecture 11: Quantum Cryptography Wayne Patterson SYCS 654 Spring 2009

Quantum Cryptology  Based on the Heisenberg Uncertainty Principle  Polarization of a photon using a vertical filter  Probability(passage through a filter)  angle of filter  p = 1 (0  ), p = 0.5 (45  ), p = 0 (90  )  First model: BB84 (Bennett-Brassard)  A and B are two parties, each have two polarizers  Notation: + (0  or 90  )  (45  or 135  )

Quantum Cryptology (cont’d)  A sends to B, each photon polarized at random 0, 45, 90, 135 degrees  When B receives, chooses a polarizer at random to measure  If A sends | B chooses + correct receipt  If A sends | B chooses  receives either / or \ incorrect  After the sequence of bits, A and B have a public discussion  B tells A which basis for each, A tells whether or not correct  Discard all data for which no match, thus leaving two matched strings

Quantum Cryptology (cont’d)  e.g.: | = \ = 1 - = / = 0  All of this yields a shared key  If E intercepts, measures, resends:  E will corrupt at least 25% of the bits where A and B coincide  A and B can compare, find no discrepancy  E learned nothing A se nd s + X++XX++XX++X A - > B |/|-/\|-\\-|/ B me asu res +XX++X+XX+X+X B res ult |//-|\I\\-\|/ Vali d dat a I/-\|\|/ To Key

Quantum Cryptology (cont’d)  If E can do more than just observe a public channel, above will still work as key expansion  IN REALITY:  Real photon detectors have noise  Current technology can’t reliably generate single photons  Let m = average number of photons per pulse  If m  1, p(splitting the pulse)  m 2 /2  Practicality also determined by distance of transmission

Quantum Factoring  t/299/paper/node18.html t/299/paper/node18.html