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YOGESH KUMAR PALE.C

0808331052

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QuantumCryptography

Quantuman indivisible elementary particle, usually a photon

+Cryptography

the practice and study of hiding information

=Quantum Cryptographythe use of quantum mechanics to guarantee securecommunication.

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What the...?

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QuantumCryptography

Quantum cryptography is the single

most successful application ofQuantum Computing/InformationTheory.

For the first time in history, we canuse the forces of nature toimplement perfectly securecryptosystems.

Quantum cryptography has beentried experimentally: it works!

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QuantumCryptography

Classical Cryptography relies heavily on thecomplexity of factoring integers.

Quantum Computers can use Shors Algorithm toefficiently break todays cryptosystems.

We need a new kind of cryptography!

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State of the Art

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QuantumCryptography

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Todays Talk

Basic Ideas inCryptography

Ideas from theQuantum World

Quantum KeyDistribution (QKD)

BB84 withouteavesdropping

BB84 witheavesdropping

Working PrototypesResearch here at

Warwick

Conclusion

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QuantumCryptography

Basic Ideas in

CryptographyCryptography: the coding and decoding

of secret messages. [Merriam-Webster]Cryptography < + .The basic idea is to modify a message so as

to make it unintelligible to anyone butthe intended recipient.

For message (plaintext)M,

e(M, K) encryption -ciphertextd[e(M, K), K]= M decryption

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QuantumCryptography

Keys and Key

DistributionKis called the key.

The key is known only to sender

and receiver: it is secret.Anyone who knows the key can

decrypt the message.

Key distribution is the problemof exchanging the key betweensender and receiver.

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QuantumCryptography

Perfect Secrecy and the

OTP

There exist perfectcryptosystems.

Example: One-Time Pad (OTP)

The problem of distributingthe keys in the first placeremains.

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QuantumCryptography

Enter QKD QKD: Quantum Key Distribution

Using quantum effects, we can distribute

keys in perfect secrecy!The Result: The Perfect Cryptosystem,

QC = QKD + OTP

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QuantumCryptography

Ideas from the

Quantum WorldMeasurement Observing, or measuring, a quantum system will

alter its state.

Example: the Qubit

When observed, the state of a qubit will collapse toeither a=0 or b=0.

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0 1a b

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QuantumCryptography

PhotonsPhysical qubits

Any subatomic

particle can be usedto represent a qubit,e.g. an electron.

A photon is aconvenient choice.

A photon is anelectromagneticwave.

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QuantumCryptography

A photon has a property called polarization, which

is the plane in which the electric field oscillates.

We can use photons of different polarizations to

represent quantum states:

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Polarization

0 state 0

90 state 1

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QuantumCryptography

A device called a polarizer allows us to place

a photon in a particular polarization. A

Pockels Cell can be used too.The polarization basis is the mapping we

decide to use for a particular state.

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Polarizers and Bases

0 state 0

90 state 1

Rectilinear:

45 state 0

135 state 1

Diagonal:

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QuantumCryptography

A calcite crystal can be used to recover the bits

encoded into a stream of photons.

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Measuring Photons

CaCO3

DIAGONAL axis

1 0 1 0

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QuantumCryptography

What if the crystal has the wrong orientation?

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Uncertainty Principle

CaCO3

RECTILINEAR axis

???50% chance of

getting rightanswer.

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QuantumCryptography

We have to prevent Eve from eavesdroppingon communications between Alice and Bob.

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Meet Alice and Bob

Eve

Alice Bob

Alan J. Learner,Quantum

Cryptographer

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QuantumCryptography

Quantum Key Distribution exploits the effects

discussed in order to thwarteavesdropping.

If an eavesdropper uses the wrong polarizationbasis to measure the channel, the result of themeasurement will be random.

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Quantum Key

Distribution

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QuantumCryptography

A protocol is a set of rules governing the exchange

of messages over a channel.

A security protocol is a special protocol designed to

ensure security properties are met duringcommunications.

There are three main security protocols for QKD:BB84, B92, and Entanglement-Based QKD.

We will only discuss BB84 here.

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QKD Protocols

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QuantumCryptography

BB84 was the first security protocol implementing

Quantum Key Distribution.

It uses the idea of photon polarization.

The key consists of bits that will be transmitted asphotons.

Each bit is encoded with a random polarizationbasis!

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BB84

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QuantumCryptography

Alice is going to send Bob a key.

She begins with a random sequence of bits.

Bits are encoded with a random basis, andthen sent to Bob:

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BB84 with no

eavesdropping

Bit 0 1 0 1 1

Basis + +

Photon

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QuantumCryptography

Bob receives the photons and must decode them

using a random basis.

Some of his measurementsare correct.

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BB84 with no

eavesdropping (2)

Photon

Basis? + + +

Bit? 0 0 0 1 1

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QuantumCryptography

Alice and Bob talk on the telephone:

Alice chooses a subset of the bits (the test bits) andreveals which basis she used to encode them to Bob.

Bob tells Alice which basis he used to decode thesame bits.

Where the same basis was used, Alice tells Bob whatbits he ought to have got.

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BB84 with no

eavesdropping (3)

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QuantumCryptography

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Comparing

measurementsAlices Bit 0 1 0 1 1

Alices

Basis + +

Photon

Bobs

Basis + + +

Bobs Bit 0 0 0 1 1

Test bitsThe test bits allowAlice and Bob totest whether thechannel is secure.

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QuantumCryptography

As long as no errors and/or eavesdropping haveoccurred, the test bits should agree.

Alice and Bob have now made sure that the channelis secure. The test bits are removed.

Alice tells Bob the basis she used for the other bits,and they both have a common set of bits: the final

key!

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The Trick

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QuantumCryptography

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Getting the Final Key

Alices Bit 0 1 0 1 1Alices

Basis + +

Photon

Bobs

Basis + + +

Bobs Bit 0 0 0 1 1

Test bitsdiscarded

Final Key = 01

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QuantumCryptography

If an eavesdropper Eve tries to tap the channel, thiswill automatically show up in Bobs measurements.

In those cases where Alice and Bob have used thesame basis, Bob is likely to obtain an incorrectmeasurement: Eves measurements are bound toaffect the states of the photons.

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In the presence of eavesdropping

Q

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QuantumCryptography

Quantum cryptography is a major achievement insecurity engineering.

As it gets implemented, it will allow perfectly securebank transactions, secret discussions forgovernment officials, and well-guarded trade secretsfor industry!

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Conclusion

Q t

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QuantumCryptography

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