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Achievable Bitrates for Quantum Key Distribution. Alexander Hentschel. April 24, 2009 University of Calgary. Classical Cryptography. Classical Cryptography Schemes:. Quantum Computer. Classical Algorithms. Are there efficient algorithms to crack cipher: unknown!. ?.

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Achievable Bitrates for Quantum Key Distribution

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Achievable bitrates for quantum key distribution

Achievable Bitrates for

Quantum Key Distribution

Alexander Hentschel

April 24, 2009

University of Calgary


Classical cryptography

Classical Cryptography

  • Classical Cryptography Schemes:

Quantum Computer

Classical Algorithms

Are there efficient algorithms to crack cipher: unknown!

?

  • Do we have a Quantum Computer?

Not yet!


Classical cryptography1

Classical Cryptography

One-Time-Pad Cryptography

  • Only classical cryptographic scheme: security mathematically proven

Sender: Alice

Receiver: Bob

private key

private key

insecure

medium

(Internet)

encrypted

encrypted

message

message

  • Message: string of N bits

+

=

  • One-Time-Pad: random sequence of N bits

  • How do we securely share the key ?


Quantum cryptography

Quantum Cryptography

Solution:Quantum Cryptography

  • eavesdropper can have unlimited computational power

  • security guaranteed by physical laws

BB84 Protocol: by Charles Bennett and Gilles Brassard in 1984

Eve

Alice

Bob

  • Generates a One-Time-Pad-Key for Alice & Bob

  • Guarantees detection of eavesdropping attempt during key sharing

  • If key shared safely:

    use key to encrypt message and send over public channel


Quantum cryptography1

Quantum Cryptography

Quantum Mechanics:

  • Superposition:

    Qubit (quantum bit) can be an arbitrary mixture of 0 and 1 at the same time

  • Probability to measure qubit in

state :

state :

  • Measurement: destructive

State after measurement

  • outcome :

  • outcome :


The bb84 protocol

The BB84 Protocol

Sharing the One-Time-Pad-Key:

  • Alice wants to share a One-Time-Pad-Key with Bob

Alice generates random bit sequences = 1 0 1 1 0 1 0 1 0 0 0 1 1 0

One-Time-Pad

b = 0 1 1 0 1 0 0 1 0 1 1 1 0 0

Encoding basis

  • Encodes bits of s in polarization of single photon

  • Rectangular basis R:

bi = 0:

  • Diagonal basis D:

bi = 1:


The bb84 protocol1

The BB84 Protocol

Receiving the One-Time-Pad-Key:

Bob receives sequence of photons:

  • does not know encoding basis

  • chooses randomly measurement basis

    (decoding basis)

For each photon: Bob saves

  • measurement basis

  • measurement result


The bb84 protocol2

The BB84 Protocol

Receiving the One-Time-Pad-Key:

Measurement in right basis:

  • measured polarization equals

    encoding polarization:

Measurement in wrong basis:

with 50% probability

  • result:

with 50% probability

  • with probability 50%


The bb84 protocol3

The BB84 Protocol

Receiving the One-Time-Pad-Key:

Key

  • Alice and Bob interchange Alice’s encoding basis

    Bob’s decoding basis

  • Keep bits where both choose same basis

Key

has length n/2

  • If Alice sends n bits:


The bb84 protocol4

The BB84 Protocol

Eavesdropping

  • At time of transmission: encoding basis unknown to Eve

X

Tactic for Eve

?

  • guess basis

  • Copy quantum bit

  • After disclosure of encoding Basis:

    measure

Quantum Information

cannot be copied

  • Measure in basis

Measurement

  • Send measurement result

    to Bob

eavesdropping

no eavesdropping

  • Alice and Bob use same basis:

    differentresult

    with probability 25%

  • Alice and Bob use same basis:

    same result

Detecting an eavesdropper

  • Alice & Bob compare ½ of bits with


Feasibility of quantum key distribution

Feasibility of Quantum Key Distribution

  • Area of active research

  • First commercial devices available

Id Quantique

Technical challenges

  • Generate single photons

  • no photon

  • more than one photon

  • Transfer single photons into glass fiber

  • Absorption of optical fibre

  • Reliably detect single photon

  • detector efficiency

  • dark counts


Feasibility of quantum key distribution1

Feasibility of Quantum Key Distribution

mean

Percent of matching key bits

variance

background noise

Risk of eavesdropping

frequency in kHz

  • simple setup

  • no error correction

Experiment at Humboldt-University Berlin 2005:

  • Rate of non-matching key-bits: QBER = Quantum Bit Error Rate


Feasibility of quantum key distribution2

Feasibility of Quantum Key Distribution

State of the art (Toshiba Research Europe Ltd):

  • unconditionally secure key distribution

  • secure key rate:1.02 Mbit/s for fiber distance 20km

  • use compact non-cryogenic detectors

  • eavesdropper could hide behind noise

    use privacy amplification to prevent information leak (raw secure key rate)

dark counts dominate

nominal capacity

usable capacity


Achievable bitrates for quantum key distribution

Thank you for your attention


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