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A PRESENTATION ON QUANTUM CRYPTOGRAPHY,[object Object]
SOUGATO GHOSH ECE 22,[object Object]
What is cryptography?,[object Object],Cryptography (derived from the Greek words kryptos and grapheinmeaning hidden writing) is the science of codes and ciphers. ,[object Object],.,[object Object]
A cipher is essentially a cryptographic,[object Object],    algorithm which is used to convert a message, known as the plaintext, into unreadable,[object Object],    text.,[object Object],[object Object],What is cipher?,[object Object]
The process,[object Object],Plaintext,[object Object],Key,[object Object],Sender ,[object Object],Encryption,[object Object],Cryptotext,[object Object],Secure,[object Object],transmission,[object Object],Decryption,[object Object],Recipient,[object Object],Plaintext,[object Object],Key ready for use,[object Object],Message encryption,[object Object],Secure key distribution,[object Object],Hard Problem for conventional,[object Object],encryption,[object Object]
The classic cryptography,[object Object],Encryption algorithm and related key are kept secret.,[object Object],Breaking the system is hard due to large numbers of possible keys.,[object Object],For example: for a key 128 bits long,[object Object],there are,[object Object],keys to check    using brute force.,[object Object],The fundamental difficulty is key distribution to parties,[object Object], who want to exchange messages.,[object Object]
PKC :the modern cryptography,[object Object],In 1970s the Public Key Cryptography emerged.,[object Object],Each user has two mutually inverse keys,,[object Object],The encryption key is published;,[object Object],The decryption key is kept secret.,[object Object],Anybody can send a message to x,[object Object],    but only xcan read it.,[object Object]
RSA,[object Object],The most widely used PKC is the RSA algorithm based on the difficulty of ,[object Object],factoring a product ot two large primes.,[object Object],Easy ProblemHard Problem,[object Object],Given n ,[object Object],compute p and q.,[object Object],Given two large,[object Object], primes p and q ,[object Object],compute ,[object Object]
Light waves are propagated as discrete quanta called photons.,[object Object],They are massless and have energy,  momentum and angular momentum called spin.,[object Object],Spin carries the polarization.,[object Object],If on its way we put a polarization filter,[object Object],    a photon may pass through it or may not.,[object Object],We can use a detector to check of a photon has passed through  a filter.,[object Object],Elements of the Quantum Theory,[object Object]
Introduction,[object Object],Spawned during the last century,[object Object],Describes properties and interaction between matter at small distance scales,[object Object],Quantum state determined by(among others),[object Object],Positions,[object Object],Velocities,[object Object],Polarizations,[object Object],Spins,[object Object],qubits,[object Object]
Binary information,[object Object],Each photon carries one qubitof information,[object Object],Polarization can be used to represent a 0 or 1.,[object Object],In quantum computation this is called ,[object Object],qubit.,[object Object]
Notation,[object Object],Bra/Ket notation  (pronounced “bracket”),[object Object],From Dirac 1958,[object Object],Each state represented by a vector denoted by a arrow pointing in the direction of the polarization,[object Object]
Notation,[object Object],Simplified Bra/Ket-notation in this presentation,[object Object],Representation of polarized photons:,[object Object],horizontally: ,[object Object],vertically: ,[object Object],diagonally:  and ,[object Object]
Polarized photons,[object Object],Measurement of a state not only measures but actually transforms that state to one of the basis vectors  and ,[object Object],If we chose the basis vectors  and  when measuring the state of the photon, the result will tell us that the photon's polarization is either  or , nothing in between.,[object Object],ψ,[object Object],b,[object Object],,[object Object],a,[object Object],,[object Object]
Experiment,[object Object],Classical experiment,[object Object],Equipment:,[object Object],laser pointer ,[object Object],three polarization filters,[object Object],The beam of light i pointed toward a screen.,[object Object],The three filters are polarized at ,  and  respectively ,[object Object]
Experiment,[object Object],The  filter is put in front of the screen,[object Object],Light on outgoing side of filter is now 50% of original intensity,[object Object],,[object Object],,[object Object],,[object Object]
Experiment,[object Object],Next we insert a  filter whereas no light continue on the output side,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object]
Experiment,[object Object],Here is the puzzling part…,[object Object],We insert a  filter in between,[object Object],This increases the number of photons passing through,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object]
Experiment explained,[object Object],Filter  is hit by photons in random states. It will measure half of the photons polarized as ,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object]
Experiment explained,[object Object],Filter  is perpendicular to that and will measure the photons with respect to   , which none of the incoming photons match,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object]
Experiment explained,[object Object],Filter  measures the state with respect to the basis {, },[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object]
Experiment explained,[object Object],Photons reaching filter  will be measured as   with 50% chance. These photons will be measured by filter  as  with 50% probability and thereby 12,5% of the original light pass through all three filters.,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object],,[object Object]
Key distribution,[object Object],Alice and Bob first agree on two representations for ones and zeroes ,[object Object],One for each basis used, {,}and {, }. ,[object Object],This agreement can be done in public,[object Object],Define1 = 	0 = 1 =  	0 = ,[object Object]
Key distribution - BB84,[object Object],Alice sends a sequence of photons to Bob.Each photon in a state with polarization corresponding to 1 or 0, but with randomly chosen basis. ,[object Object],Bob measures the state of the photons he receives, with each state measured with respect to randomly chosen basis. ,[object Object],Alice and Bob communicates via an open channel. For each photon, they reveal which basis was used for encoding and decoding respectively. All photons which has been encoded and decoded with the same basis are kept, while all those where the basis don't agree are discarded. ,[object Object]
Eavesdropping,[object Object],Eve has to randomly select basis for her measurement,[object Object],Her basis will be wrong in 50% of the time.,[object Object],Whatever basis Eve chose she will measure 1 or 0,[object Object],When Eve picks the wrong basis, there is 50% chance that she'll measure the right value of the bit,[object Object],E.g. Alice sends a photon with state corresponding to 1 in the {,} basis. Eve picks the {, } basis for her measurement which this time happens to give a 1 as result, which is correct. ,[object Object]
Eavesdropping,[object Object]
Eves problem,[object Object],Eve has to re-send all the photons to Bob ,[object Object],Will introduce an error, since Eve don't know the correct basis used by Alice ,[object Object],Bob will detect an increased error rate,[object Object],Still possible for Eve to eavesdrop just a few photons, and hope that this will not increase the error to an alarming rate. If so, Eve would have at least partial knowledge of the key. ,[object Object]
Detecting eavesdropping,[object Object],When Alice and Bob need to test for eavesdropping,[object Object],By randomly selecting a number of bits from the key and compute its error rate,[object Object],Error rate < Emax  assume no eavesdropping,[object Object],Error rate > Emax  assume eavesdropping(or the channel is unexpectedly noisy)Alice and Bob should then discard the whole key and start over,[object Object]
Noise,[object Object],Noise might introduce errors,[object Object],A detector might detect a photon even though there are no photons,[object Object],Solution:,[object Object],send the photons according to a time schedule.,[object Object],then Bob knows when to expect a photon, and can discard those that doesn't fit into the scheme's time window.,[object Object],There also has to be some kind of error correction in the over all process.,[object Object]
Error correction,[object Object],Suggested by Hoi-Kwong Lo. (Shortened version),[object Object],Alice and Bob agree on a random permutation of the bits in the key,[object Object],They split the key into blocks of length k,[object Object],Compare the parity of each block. If they compute the same parity, the block is considered correct. If their parity is different, they look for the erroneous bit, using a binary search in the block. Alice and Bob discard the last bit of each block whose parity has been announced,[object Object],This is repeated with different permutations and block size, until Alice and Bob fail to find any disagreement in many subsequent comparisons,[object Object]
Privacy amplification,[object Object],Eve might have partial knowledge of the key. ,[object Object],Transform the key into a shorter but secure key,[object Object],Suppose there are n bits in the key and Eve has knowledge of m bits. ,[object Object],Randomly chose a hash function whereh(x): {0,1n  {0,1 n-m-s,[object Object],Reduces Eve's knowledge of the key to 2 –s / ln2 bits,[object Object]
Quantum  Cryptography
Quantum  Cryptography
Binary information,[object Object],A user can suggest a key by sending a stream of randomly polarized photons.,[object Object],This sequence can be converted to a binary key.,[object Object],If the key was intercepted it could be discarded and a new stream of randomly polarized photons sent.,[object Object]
It solved thekey distribution problem.,[object Object],Unconditionally secure key distribution method proposed  by: Charles Bennett and Gilles Brassard in 1984.,[object Object],.,[object Object],The method is called BB84.,[object Object],Once  key is securely received it can be used to encrypt messages transmitted,[object Object],   by conventional channels. ,[object Object],The Main contribution of Quantum Cryptography.,[object Object]
Quantum  cryptography obtains its fundamental security from the fact that each qubit is carried by a single photon, and each photon will be altered  as soon as  it is read.,[object Object],This makes impossible to intercept message without being detected.,[object Object],Security of quantum key distribution,[object Object]
Experimental implementations have existed since 1990.,[object Object],Current (2004) QC is performed over distances of 30-40 kilometers  using ,[object Object],   optical fiber.,[object Object],   In general we need two capabilities.,[object Object],Single photon gun.,[object Object],(2) Being able to measure single photons.,[object Object],State of the Quantum Cryptography technology.,[object Object]
id Quantique, Geneva Switzerland,[object Object],Optical fiber based system,[object Object],Tens of kilometers distances,[object Object],MagiQ Technologies, NY City,[object Object],Optical fiber-glass,[object Object],Up to 100 kilometers distances,[object Object],NEC Tokyo 150 kilometers,[object Object],QinetiQ Farnborough, England,[object Object],Through the air 10 kilometers.,[object Object],Supplied system to BBN in Cambridge Mass.,[object Object],Commercial  QC providers,[object Object]
References,[object Object],[WIK2] Wikipedia -The free encyclopediahttp://www.wikipedia.org/wiki/Interpretation_of_quantum_mechanics,[object Object],[WIK3] Wikipedia -The free encyclopediahttp://www.wikipedia.org/wiki/Copenhagen_interpretation,[object Object],[GIT] Georgia Institute of Technology,The fundamental postulates of quantum mechanicshttp://www.physics.gatech.edu/academics/Classes/spring2002/6107/Resources/The fundamental postulates of quantum mechanics.pdf,[object Object],[HP] Hoi-Kwong Lo, Networked Systems Department,Hewlett Packard, Bristol, December 1997, Quantum Cryptology,[object Object],[SS99] Simon Singh, Code Book, p349-382,Anchor Books, 1999,[object Object],[FoF] Forskning och Framsteg,No. 3, April 2003,[object Object]
THANKS…………………..,[object Object]

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Quantum Cryptography

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