Quantum Cryptography

Presented By: Sarika.K II Sem

M.Tech,DEC

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Introduction• The great advances made in the classical computing devices are

still not suficient to solve certain categories of problems which are beyond the classical computational model.

• As the internet spreads through the entire globe, more and more people are getting connected and important data is getting tranferred over wires, the entire system is becoming more and more vulnerable to malicious people eager to eavesdrop on secret information. Can we have a way to detect presence of such malicious people ? ?

• Yes, the solution is “Quantum cryptography”.

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Quantum Cryptography History

• Early 1970’s Stephen Wiesner wrote “Conjugate Coding”• 1979 Charles H. Bennett and Gilles Brassard wrote

various papers on this subject

• Basis: quantum cryptography technique make use of underlying principles of quantum mechanics and Heisenberg Uncertainity principle for ensuring secure cryptography, which is not only resitant to eavesdropping (again due to probabilistic nature of it), but also has the potential to inform the communicating parties if a conversation has been compromised.

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Heisenberg Uncertainty Principle• Certain pairs of physical properties are related in such a

way that measuring one property prevents the observer from knowing the value of the other.

When measuring the polarization of a photon, the choice of what direction to measure affects all subsequent measurements.

• If a photon passes through a vertical filter it will have the vertical orientation regardless of its initial

direction of polarization.

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Quantum computer• A quantum computer (also known as a quantum

supercomputer) is a computation device that makes direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data.

• Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses qubits (quantum bits), which can be in superpositions of states.

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• A single qubit can represent a one, a zero, or any quantum superposition of these two qubit states; moreover, a pair of qubits can be in any quantum superposition of 4 states, and three qubits in any superposition of 8

• In general, a quantum computer with n qubits can be in an arbitrary superposition of up to 2n different states simultaneously.

• Consider first a classical computer that operates on a three-bit register. The state of the computer at any time is a probability distribution over the 23=8 different three-bit strings 000, 001, 010, 011, 100, 101, 110, 111

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Binary information• Each photon carries one qubit of information

• Polarization can be used to represent a 0 or 1.

• In quantum computation this is called qubit.

To determine photon’s polarization the recipient must measure the polarization by ,for example, passing it through a filter.

• A user can suggest a key by sending a stream of randomly polarized photons.This sequence can be converted to a binary key

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Current State of Affairs

• Current fiber-based distance record: 200 km (Takesue et al)

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Quantum Cryptography Setup• Most widely used is the BB84 Protocol developed by IBM

• The sending apparatus consists of a green light-emitting diode, a lens, a pinhole and mirrors that provide a collimated beam of horizontally polarized light. Next, electronic devices known as Pockels Cells are used to change the original horizontal polarization to any of four standard polarization states under the users control

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Quantum Cryptography Setup

• The receiving apparatus contains a similar Pockels cell, which

allows the user to choose the type of polarization he will

measure. After the beam passes through hte Pockels Cell, it is

split by a calcite prism into two perpendicularly polarized

beams, which are directed into two photomultiplier tubes for

the purpose of detecting individual photons

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Notation

• Representation of polarized photons:– horizontally: – vertically: – diagonally: and

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Polarized photons• Measurement of a state not only measures but actually

transforms that state to one of the basis vectors and • 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.

ψb

a

Photon Polarization

Vertical filter

Tilted filter at the angle

The first filter randomizes the measurements of the second filter.

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Polarization by a filter

• A pair of orthogonal filters such as vertical/horizontal is called a basis.

• A pair of bases is conjugate if the measurement in the first basis completely randomizes the measurements in the second basis.

• As in the previous slide example for =45deg.

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The Main contribution of Quantum Cryptography.

• It solved the key distribution problem.• Unconditionally secure key distribution method

proposed by:• Charles Bennett and Gilles Brassard in 1984.• The method is called BB84.• Once key is securely received it can be used to

encrypt messages transmitted by conventional channels.

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BB84• Set-up

– Alice• Has the ability to create qubits in two orthogonal bases

– Bob• Has the ability to measure qubits in those two bases.

BB84

• Alice– Encodes her information randomly in one

of the two bases…• For example,

Basis A Basis B

ￜ 0〉 = 0 ￜ +〉 = 0

ￜ 1〉 = 1 ￜ -〉 = 1

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BB84

Alice prepares 16 bits0101100010101100

in the following bases,BAABAABAAAABBBBA

Thus the following states are sent to Bob:+10-10+0101+--+0

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BB84

Then Alice and Bob compare their measurement bases, not the results, via a public channel.

Alice’s bits 0101100010101100Alice’s bases BAABAABAAAABBBBAStates sent +10-10+0101+--+0Bob’s bases ABAABAAABABBBBABBob’s results 1-00-0+0+0-+--1+

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BB84

• So Bob and Alice are left with 7 useable bits out of 16

_ _ 0 _ _ 0 _ 0 _ 0_ 0 1 1 _ _

These bits will be the shared key they use for encryption.

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Quantum Cryptography: The BB84 Portocol Ingredients: 1) One photon no copying,

2) Two non orthonormal bases sets 3) Insecure classical channel; Internet

What it does: Secure distribution of a key, can't be used to send messagesHow it works:

50% correlated Physikalische Blätter 55, 25 (1999)

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Alice Sends Polarizations

Bob randomly chooses measurement

Bob records the results

They Check the results

This then becomes the key

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BB84

• Now enter Eve… She wants to spy on Alice and Bob.

• So she intercepts the bit stream from Alice, measures it, and prepares a new bit stream to Bob based on her measurements…

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BB84

So how do we know when Eve is being nosy?

Well… Eve doesn’t know what bases to measure in, so she would have to measure randomly and 50% of the time she will be wrong…

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Eavesdropping• Eve has to randomly select basis for her measurement• Her basis will be wrong in 50% of the time.• Whatever basis Eve chose she will measure 1 or 0• When 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.

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Eves problem

• Eve 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 rate• 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.

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Detecting eavesdropping

• When Alice and Bob need to test for eavesdropping• By randomly selecting a number of bits from the key and

compute its error rate• Error rate < Emax assume no eavesdropping

• Error rate > Emax assume eavesdropping(or the channel is unexpectedly noisy)Alice and Bob should then discard the whole key and start over

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Pros

• Nearly Impossible to steal• Detect if someone is listening• “Secure”

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Cons

• Price limits length – Normally just for a local network about 10km – Record set by Los Almos is 31 miles– Longer length, signal is absorbed, noise increased

• Availability• Compete with traditional networks

– If was a straight pipe, distance could be limitless

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Conclusion

Quantum cryptography is very useful tool for exchange of keys

Actual transmission of data is done with classical algorithms

Alice & Bob can find out when Eve tries to eavesdrop.

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References• Wikipedia -The free encyclopedia

• Ppt of Introduction to Quantum Cryptography- Dr. Janusz Kowalik,IEEE talk,Seattle, February 9,2005

• Introduction to quantum computing and crypto:– qubit.org– “Quantum Computing and Communications”,- introductory

technical article on NIST

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Thank You