Introduction to QuantumCryptographyDr. Janusz KowalikIEEE talkSeattle,February 9,2005
Cryptography.• Transmitting information with accessrestricted to the intended recipient even ifthe message is intercepted by others.• Cryptography is of increasing importancein our technological age using broadcast,network communications, Internet ,e-mail,cell phones which may transmit sensitiveinformation related to finances, politics,business and private confidential matters.
The process• Sender PlaintextCryptotextDecryptionPlaintextRecipientMessage encryptionKeyKey ready for useSecure key distributionEncryptionSecuretransmissionHard Problem for conventionalencryption
The classic cryptography• Encryption algorithm and related key are keptsecret.• Breaking the system is hard due to largenumbers of possible keys.• For example: for a key 128 bits long• there are38128102 ≈keys to check using brute force.The fundamental difficulty is key distribution to partieswho want to exchange messages.
PKC :the modern cryptography• In 1970s the Public Key Cryptographyemerged.• Each user has two mutually inversekeys,• The encryption key is published;• The decryption key is kept secret.• Anybody can send a message to Bobbut only Bob can read it.
RSA• The most widely used PKC is the RSAalgorithm based on the difficulty of• factoring a product ot two large primes.• Easy Problem Hard ProblemGiven two largeprimes p and qcomputeqpn ×=Given ncompute p and q.
Factoring a product of two largeprimes• The best known conventional algorithmrequires the solution time proportional to:])ln(ln)(lnexp[)( 3/23/1nncnT =For p & q 65 digits long T(n) is approximatelyone month using cluster of workstations.For p&q 200 digits long T(n) is astronomical.
Quantum Computing algorithm forfactoring.• In 1994 Peter Shor from the AT&T BellLaboratory showed that in principle aquantum computer could factor a very longproduct of primes in seconds.• Shor’s algorithm time computationalcomplexity is])[(ln)( 3nOnT =Once a quantum computer is builtthe RSA methodwould not be safe.
Elements of the Quantum Theory• Light waves are propagated as discretequanta called photons.• They are massless and have energy,momentum and angular momentum calledspin.• Spin carries the polarization.• If on its way we put a polarization filtera photon may pass through it or may not.• We can use a detector to check of a photonhas passed through a filter.
Heisenberg Uncertainty Principle• Certain pairs of physical properties are relatedin such a way that measuring one propertyprevents the observer from knowing the valueof the other.When measuring the polarization of a photon,the choice of what direction to measure affectsall subsequent measurements.• If a photon passes through a vertical filterit will have the vertical orientation regardless ofits initial direction of polarization.
Photon PolarizationθVerticalfilterTilted filter atthe angleThe probability of a photon appearing after the secondfilter depends on the angle and becomes 0 at= 90 degrees.The first filter randomizes the measurements of thesecond filter.θθ
Polarization by a filter• A pair of orthogonal filters such asvertical/horizontal is called a basis.• A pair of bases is conjugate if themeasurement in the first basiscompletely randomizes themeasurements in the second basis.• As in the previous slide example for=45deg.θ
Sender-receiver of photons• Suppose Alice uses 0-deg/90-deg polarizersending photons to Bob. But she does notreveal which.• Bob can determine photons by usingfilter aligned to the same basis.• But if he uses 45deg/135 deg polarizer tomeasure the photon he will not be able todetermine any information about the initialpolarization of the photon.• The result of his measurement will be completelyrandom
Eavesdropper Eve• If Eve uses the filter aligned withAlice’s she can recover the originalpolarization of the photon.• If she uses the misaligned filter shewill receive no information about thephoton .• Also she will influence the originalphoton and be unable to retransmit itwith the original polarization.• Bob will be able to deduce Ave’spresence.
Binary information• Each photon carries one qubit of information• Polarization can be used to represent a 0 or 1.• In quantum computation this is calledqubit.To determine photon’s polarization therecipient must measure the polarization by,for example, passing it through a filter.
Binary information• A user can suggest a key by sending astream of randomly polarized photons.• This sequence can be converted to abinary key.• If the key was intercepted it could bediscarded and a new stream ofrandomly polarized photons sent.
The Main contribution of QuantumCryptography.• It solved the key distribution problem.• Unconditionally secure key distributionmethod proposed by:• Charles Bennett and Gilles Brassard in1984.• The method is called BB84.• Once key is securely received it can beused to encrypt messages transmittedby conventional channels.
Quantum key distribution• (a)Alice communicates with Bob via aquantum channel sending him photons.• (b) Then they discuss results using apublic channel.• (c) After getting an encryption key Bob canencrypt his messages and send them byany public channel.
Quantum key distribution• Both Alice and Bob have two polarizerseach.• One with the 0-90 degree basis (+) and onewith 45-135 degree basis ( )• (a) Alice uses her polarizers to sendrandomly photons to Bob in one of the fourpossible polarizations 0,45,90,135 degree.• (b)××××b) Bob uses his polarizers to measure eachpolarization of photons he receives.He can use the( + )basis or the ( ) but not bothsimultaneously.×××
Security of quantum keydistribution• Quantum cryptography obtains itsfundamental security from the fact thateach qubit is carried by a singlephoton, and each photon will be alteredas soon as it is read.• This makes impossible to interceptmessage without being detected.
Noise• The presence of noise can impactdetecting attacks.• Eavesdropper and noise on thequantum channel areindistinguishable.• (1) Malicious eavesdropper canprevent communication.• (2) Detecting eavesdropper in thepresence of noise is hard.
State of the QuantumCryptography technology.• Experimental implementations haveexisted since 1990.• Current (2004) QC is performed overdistances of 30-40 kilometers usingoptical fiber.In general we need two capabilities.(1) Single photon gun.(2) Being able to measure singlephotons.
State of the QC technology.• Efforts are being made to use PulsedLaser Beam with low intensity for firingsingle photons.• Detecting and measuring photons is hard.• The most common method is exploitingAvalanche Photodiodes in the Geigermode where single photon triggers adetectable electron avalanche.
State of the QC technology.• Key transmissions can be achieved forabout 80 km distance ( Univ of Geneva2001).• (2)For longer distances we can userepeaters. But practical repeaters are along way in the future.• Another option is using satellites.• Richard Hughes at LOS ALAMOS NATLAB (USA) works in this direction.• The satellites distance from earth is inhundreds of kilometers.
NIST System• Uses an infrared laser to generatephotons• and telescopes with 8-inch mirrors tosend and receive photons over the air.• Using the quantum transmitted keymessages were encrypted at the rate1 million bits per second.The speed was impressive but the distancebetween two NIST buildings was only 730meters.
Commercial QC providers• id Quantique, Geneva Switzerland• Optical fiber based system• Tens of kilometers distances• MagiQ Technologies, NY City• Optical fiber-glass• Up to 100 kilometers distances• NEC Tokyo 150 kilometers• QinetiQ Farnborough, England• Through the air 10 kilometers.• Supplied system to BBN in Cambridge Mass.