QUANTUM CRYPTOGRAPHY Narayana D Kashyap Security through Uncertainty CS 265 Spring 2003

Classic Cryptography Keys by Transposition and Substitution Strength mainly on Long Keys KDC Mathematical Concepts Allows the eavesdropper in principle to measure physical properties without disturbing them.

Quantum vs. Classic Physics instead of Math Exchange of information – very secure in a strong sense. Laws of physics guarantee (probabilistically) that the secret key exchange will be secure. The ACT OF MEASUREMENT is an integral part of quantum mechanics, not just a passive, external process as in Classic Crypto.

Fundamental Concepts Quantum Channel along with Quantum theory Heisenberg Uncertainty Principle – certain pairs of physical properties are complementary. Any effort to monitor the channel necessarily disturbs the signal in some detectable way. The uncertainty principle is used to build secure channel based on Quantum properties of light. Photons & Polarization

How it works? Bob, informed about polarization being either 0 or 90 (rectilinear), can find out by his photomultiplier as to how it was sent. Such an apparatus is useless for distinguishing 45 or 135 (diagonal) photons - unless the apparatus is turned 45 degrees. Rectilinear and Diagonal polarizations are complementary properties.

BB84 Bennett and Brassard proposed in 1984 Quantum channel – Polarized Photons Public channel – Normal Messages Alice = Sender & Bob = receiver Agreed before hand that 90 and 45 are 1’s 0 and 135 are 0’s

Alice Bob Alice Bob Quantum Key Distribution

Verification of QC Alice and Bob to compare the "parity"- evenness or oddness of a publicly agreed on random subset containing about half the bits in their data. Alice could tell Bob, "I looked at the 1st, 3rd, 4th, 9th,...996th and 999th of my 1,000 bits of data, and they include an even number of l's." It suffices to repeat the test 20 times, with 20 different random subsets, to reduce the chance of an undetected error to less than one in a million.

References Quantum Cryptography ypto/quantum1.htm Quantum Cryptography Tutorial Oxford Quantum Computation Group