# quantam cryptography

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QUANTUM CRYPTOGRAPHY

QUANTUM CRYPTOGRAPHYD.DEEPIKAB.TECH IV YEARCryptography (krypts)hidden+ (grpho)write=Hidden Writing

INTRODUCTIONWhat is Cryptography? Cryptography is the art of devising codes and ciphers. Crypto analysis is the art of breaking them. Cryptology is the combination of the two i. e Cryptography and Crypto analysisWhat is Quantum Cryptography? Quantum Cryptography is an effort to allow two users of a common communication channel to create a body of shared and secret information. This information, which generally takes the form of a random string of bits, can then be used as a conventional secret key for secure communication. The Heisenberg Uncertainty principle and quantum entanglement can be exploited in as system of secure communication often referred to as quantum Cryptography.

History of Quantum CryptographyStephen Wiesner wrote Conjugate Coding in the late sixties

Charles H. Bennett and Gilles Brassard revived the field in 1982 by combining quantum process with public key cryptography

Quantum cryptographyKey distributionEavesdroppingDetecting eavesdroppingNoiseError correctionPrivacy AmplificationEncryption

Key distributionAlice and Bob first agree on two representations for ones and zeroes One for each basis used, {,} and {, }. This agreement can be done in publicDefine1 = 0 = 1 = 0 =

A schedule design for optional periods of time/objectives. 7KEY DISTRIBUTION

Key distribution - BB84Alice sends a sequence of photons to Bob.Each photon in a state with polarization corresponding to 1 or 0, but with randomly chosen basis. Bob measures the state of the photons he receives, with each state measured with respect to randomly chosen basis. 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 discardedEavesdroppingEve has to randomly select basis for her measurementHer basis will be wrong in 50% of the time.Whatever basis Eve chose she will measure 1 or 0When Eve picks the wrong basis, there is 50% chance that she'll measure the right value of the bit 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.

Alicesbasis AlicesbitAlicesphotonEvesbasisCorrectEvesphotonEvesbitCorrect{,}1{,}Yes1Yes{, }No1Yes0No0{,}Yes0Yes{, }No1No0Yes{, }1

{,}

No1Yes0No{, }Yes1Yes0{,}

No1No0Yes{, }yes0YesEves problemEve has to re-send all the photons to Bob Will introduce an error, since Eve don't know the correct basis used by Alice Bob will detect an increased error rateStill 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.

Detecting eavesdroppingWhen Alice and Bob need to test for eavesdroppingBy randomly selecting a number of bits from the key and compute its error rateError rate < Emax assume no eavesdroppingError rate > Emax assume eavesdropping(or the channel is unexpectedly noisy)Alice and Bob should then discard the whole key and start over

NoiseNoise might introduce errorsA detector might detect a photon even though there are no photonsSolution:send the photons according to a time schedule.Then Bob knows when to expect a photon, and can discard those that doesn't fit into the scheme's time window.There also has to be some kind of error correction in the over all process.

Error correctionAlice and Bob agree on a random permutation of the bits in the keyThey split the key into blocks of length kCompare 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 announcedThis is repeated with different permutations and block size, until Alice and Bob fail to find any disagreement in many subsequent comparisons

Privacy amplificationEve might have partial knowledge of the key.

Transform the key into a shorter but secure key

Suppose there are n bits in the key and Eve has knowledge of m bits.

Randomly chose a hash function whereh(x): {0,1\}n {0,1\} n-m-s

Reduces Eve's knowledge of the key to 2 s / ln2 bits

EncryptionKey of same size as the plaintextUsed as a one-time-padEnsures the crypto text to be absolutely unbreakable

ADVANTAGES: The biggest advantage of public key cryptography is the secure nature of the private key. In fact, it never needs to be transmitted or revealed to anyone. It enables the use of digital certificates and digital timestamps, which is a very secure technique of signature authorization.DISADVANTAGES:Transmission time for documents encrypted using public key cryptography are significantly slower then symmetric cryptography. In fact, transmission of very large documents is prohibitive.The key sizes must be significantly larger than symmetric cryptography to achieve the same level of protection. Public key cryptography is susceptible to impersonation attacks.CONCLUSIONQuantum cryptography is a major achievement in security engineering.As it gets implemented, it will allow perfectly secure bank transactions, secret discussions for government officials, and well-guarded trade secrets for industry!

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