Quantum Cryptography Name – Sourav Acharya Stream – ECE Roll no - 04

What is Cryptography ?:

What is Cryptography ? Cryptography is the art of encoding and decoding messages and has existed as long as people have distrusted each other and sought forms of secure communications. The purpose of cryptography is to transmit information such that only the intended recipient receives it. Cryptography is of increasing importance in our technological age using broadcast, network communications, Internet ,e-mail, cell phones which may transmit sensitive information related to finances, politics, business and private confidential matters Encrypted messages can sometimes be broken by cryptanalysis, also called code-breaking , although modern cryptography techniques are virtually unbreakable.

PowerPoint Presentation:

The process Plaintext Cryptotext Decryption Plaintext Recipient Message encryption Key Key ready for use Secure key distribution Encryption Secure transmission Hard Problem for conventional encryption

What is Quantum Cryptography ?:

What is Quantum Cryptography ? Although the field of cryptography is ancient, but it is not static. Quantum cryptography is a relatively new concept in cryptography. Quantum cryptography is based on two important principles – polarization of light. Heisenberg’s uncertainty principle.

Polarization of light:

Polarization of light the plane of the electric field in an electromagnetic wave such as light is called its plane of polarization. The polarization may be rectilinear (horizontal or vertical) or diagonal (45° or 135°). Symbols:- Horizontal polarizations - → Vertical polarization - ↑ 45° polarization - ↗ 135° polarization - ↖

Elements of the Quantum Theory:

Light waves are propagated as discrete quanta called photons. Photons are massless but they have energy, momentum and anguler momentum which is called spin. Spin carries the polarization. If on its way we put a polarization filter a photon may pass through it or may not. We can use a detector to check of a photon that has passed through a filter Elements of the Quantum Theory

Photon polarization:

Photon polarization

Heisenberg’s uncertainty principle:

Heisenberg’s 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.

Key distribution:

Key distribution Alice Alice and Bob first agree on two representations for ones and zeroes . This agreement can be done in public. 1=↑ , 0=→ (in rectilinear basis) 1=↖, 0= ↗ (in diagonal basis)

Quantum Key Distribution:

Quantum Key Distribution BB84 protocol – Bennett and Brassard, 1984 Alice Bob measures in random basis Result + X + X X +

BB84 Quantum Key Distribution:

BB84 Quantum Key Distribution Alice tells basis used Bob compares w/ his basis + X + X X Throw away Throw away 0 1 0 + 0

Steps : :

Steps : Alice prepares photons randomly with either rectilinear or diagonal polarization. Alice records the polarization of each photon and then sends it to Bob. Bob receives each photon and randomly measures polarization according to rectilinear or diagonal. He also records the measurement types and resulting polarizations. Bob publicly tells Alice what the measurement types were but not the results. Alice publicly tells Bob which measurements are of correct type. Alice and Bob each throw out the data which are not of the correct type.

Quantum Key Distribution – detecting eavesdropping:

Quantum Key Distribution – detecting eavesdropping Alice Eve's basis Result + X X Throw away Throw away ERROR! Eve detected! 1 0 + 0 + Bob measures in basis X + X + X X +

Eavesdropping:

Eavesdropping Alice’s basis Alice’s bit Alice’s photon Eve’s basis Correct Eve’s photon Eve’s bit Correct { ,} 1 { ,} Yes 1 Yes { , } No 1 Yes 0 No 0 { ,} Yes 0 Yes { , } No 1 No 0 Yes { , } 1 { ,} No 1 Yes 0 No { , } Yes 1 Yes 0 { ,} No 1 No 0 Yes { , } yes 0 Yes

Eves problem:

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.

Detecting eavesdropping:

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 < E max assume no eavesdropping Error rate > E max assume eavesdropping (or the channel is unexpectedly noisy) Alice and Bob should then discard the whole key and start over

Noise:

Noise The presence of noise can impact detecting attacks. Eavesdropper and noise on the quantum channel are indistinguishable. (1) Malicious eavesdropper can prevent communication. (2) Detecting eavesdropper in the presence of noise is hard.

solutions:

solutions send the photons according to a time schedule. Then Bob knows when to expect a photon and discard those which do not fit into the fixed time schedule.

State of the Quantum Cryptography technology.:

State of the Quantum Cryptography technology. Experimental implementations have existed since 1990. Current (2004) QC is performed over distances of 30-40 kilometers using optical fiber. In general we need two capabilities. Single photon gun . (2) Being able to measure single photons.

State of the QC technology.:

State of the QC technology. Efforts are being made to use Pulsed Laser Beam with low intensity for firing single photons. Detecting and measuring photons is hard. The most common method is exploiting Avalanche Photodiodes in the Geiger mode where single photon triggers a detectable electron avalanche.

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