Wth Slides Quantum Cryptography an Introduction Screen

8/8/2019 Wth Slides Quantum Cryptography an Introduction Screen

1/82

Quantum CryptographyAn Introduction

Stephanie Wehner


2/82

What to expect

Goal: Secure communication

The problem

Classical solutions and their shortcomings

Quantum Computing

Quantum Bits and what makes them different

Implications for classical cryptography

Quantum Key Distribution

How does it work?

Current state of the art Practical issues.

Other Cryptographic Problems


3/82

What to expect


The problem


Quantum Computing




How does it work?




4/82

The Problem


5/82

The Problem


6/82

The Problem


7/82

Secure Communication

Goal: Hide the message contents from eavesdroppers!


8/82

Secure Communication

Goal: Hide the message contents from eavesdroppers!

Damn!!


9/82

Secret Key Cryptography

Only Alice and Bob know the key.

?


10/82


Problem: Need to communicate the key!

?


11/82



!!!


12/82



!!!


13/82

Examples:


Algorithms: DES, IDEA, AES (Rijndael),

Advantage: Short keys

One-time pad (Vernam cipher) Disadvantage: Key as a long as the message itself

This is the only system which is secure without

imposing any restrictions on the eavesdropper


14/82

One time pad

ki

mi

xor xor

ki

mi


15/82

One time pad

Message: 0 1 0 0 1 1 0 0

Key: 0 0 1 0 1 0 0 1

ki

mi

xor xor

ki

mi


16/82

One time pad

Message: 0 1 0 0 1 1 0 0

Key: 0 0 1 0 1 0 0 1

Encryption: 0 1 1 0 0 1 0 1

ki

mi

xor xor

ki

mi

xor


17/82

One time pad

Message: 0 1 0 0 1 1 0 0

Key: 0 0 1 0 1 0 0 1

Encryption: 0 1 1 0 0 1 0 1

ki

mi

xor xor

ki

mi

xor xor


18/82

Public Key Cryptography

Advantage: No need to communicate the decryption key

Disadvantage: Based on non-proven assumptions (e.g.

factoring is hard) Can be broken with a quantum computer.

! ??


19/82

Public Key Cryptography

Advantage: No need to communicate the decryption key

Disadvantage: Based on non-proven assumptions (e.g.

factoring is hard) Can be broken with a quantum computer.

! !!Quantum Computer


20/82

So.


Needs a secure channel to distribute the key

If the key is shorter then the message, security is based on

non-proven algorithms (DES, ) Public Key Cryptography

Security based on non-proven assumptions (e.g. factoringis hard)

Can be broken with a quantum computer (also

retroactively!)Want: Perfect security from a one time pad, without the

need for a secure channel


21/82

What to expect


The problem


Quantum Computing




How does it work?




22/82

Two funny quantum effects

Interference

Entanglement


23/82

Quantum Effects

Detector 2

Detector 1

Photon


24/82

Quantum Effects

Detector 2

Detector 1

Photon

50%

50%


25/82

Quantum Effects

Detector 2

Detector 1

Photon

Never

Always!!


26/82

Quantum Effects

Detector 2

Detector 1

Photon

Never

Always!!

Classical: The photon takes

one of the two paths.

50%

50%


27/82

Quantum Effects

Detector 2

Detector 1

Photon



Lets test this....

50%

50%


28/82

Quantum Effects

Detector 2

Detector 1

Photon

50%

50%



Lets test this....


29/82

Quantum Effects

Detector 2

Detector 1

Photon

50%

50%



Lets test this....


30/82

Quantum Effects: Interference

Detector 2

Detector 1

Photon

Never

Always!!

Quantum: The photon takes

both paths at once.


31/82


Detector 2

Detector 1

Photon


both paths at once.

slow down one path....


32/82


Detector 2

Detector 1

Photon

Never

Always!!


both paths at once.

slow down one path....


33/82

Quantum Bits

Classical Bits: 0 or 1

Quantum Bits: 0 or 1 at the same time!


34/82

Quantum Bits

Classical Bits: 0 or 1

Quantum Bits: 0 or 1 at the same time! Cannot be copied.


35/82

Measurements

50% 50%


36/82

Measurements

50% 50%

State collapses


37/82

Two funny quantum effects

Interference

Entanglement


38/82

Entanglement


39/82

Entanglement


40/82

Entanglement

50%

50%


41/82

Entanglement

50%


42/82

Entanglement

50%


43/82

Basis 1: Vertical and Horizontal

0 1

Basis 2: Diagonal

0 1

Different basis...


44/82

Measurement in the same basis

0 0

1 1


45/82


0 0

1 1

0 0

1 1


46/82


0 0

1 1

0 0

1 1

Measurement in the same basisdoes not change the state.

Measurement in a different


47/82


basis....

50% 50%

0

0 1



48/82


basis....

50% 50%

1

0 1



49/82


basis....

50% 50%

1

0 1



50/82


basis....

50% 50%

0

0 1



51/82


basis....

A0 or 1 encoded in basis 1, gives a completely

random outcome when measured in basis 2.

And vice versa.


52/82

What to expect


The problem


Quantum Computing

Quantum Bits and what makes them different Implications for classical cryptography


How does it work?

Current state of the art

Practical issues.



53/82

What to expect


The problem


Quantum Computing



How does it work?


Practical issues.


Solve

using


54/82

What to expect


The problem


Quantum Computing



How does it work?


Practical issues.


Solve

using

Advantages:

Proven secure No computational

assumptions

History of


55/82

History of


Wiesner, 70ties, published only in 1983

Bennett & Brassard, 1984

Entanglement based: Ekert, 1991

Bennett & Brassard, 1992

Main idea: Eavesdropping


56/82

or ??

Main idea: Eavesdropping

causes detectable disturbance

b = 1

Basis 1:

Basis 2: 1

1

0

BB84 S 1


57/82

1. Picks a bit b (0 or 1)

2. Pick basis 1 or 2

3. Send b encoded in the

chosen basis to Bob

1. Picks basis 1 or 2

2. Measures in the chosen

basis and records

outcome

BB84: Step 1

Repeat many (n)

times.

At the end, Bob has n bits. However, he may not have chosen the

right basis.....

BB84 St 2


58/82

1. Bob tells Alice that he is done receiving.

2. Tells Alice which basis he used in each round.

1. Tells Bob which basis she used in each round.

BB84: Step 2

So, Alice must tell Bob which basis she used...

Both discard all rounds where Bob had

chosen a different basis.

BB84 St 2


59/82

BB84: Step 2

But if the same basis is used, nothing is changed and Bob receivedthe bit correctly!

On average, in about half the rounds Alice and Bob will have chosen

the same basis.

So, after Step 2, Alice and Bob share about n/2 bits.

But what about Eve???

Must check if Eve tried to listen in.....

BB84 St 3


60/82

BB84: Step 3

Use some of the shared bits to check whether Eve tried to listen in..

Chooses half of the remaining rounds at

random. Tells Alice his choice and the outcome in

each such round.

Alice checks that for each check-round Bobs

measurement outcome equals her input bit of this

round. If this is not the case, abort.

Recall: If the same basis was used, the Bob measurement outcome

must equal Alice input bit. Otherwise, Eve was listening...

A f th t l


61/82

A run of the protocol

0 1 0 0



62/82


0 1 0 0

0/1 1 0/1 0



63/82


0 1 0 0

0/1 1 0/1 0



64/82


0 1 0 0

0/1 1 0/1 0

Got it



65/82


0 1 0 0

0/1 1 0/1 0

Got it



66/82


0 1 0 0

0/1 1 0/1 0

Got it



67/82


0 1 0 0

0/1 1 0/1 0



68/82


0 1 0 0

0/1 1 0/1 0

Send me the 4th outcome



69/82


0 1 0 0

0/1 1 0/1 0


0Are they equal?

0 = 0. OK!

Eves attack


70/82

Eve s attack

0 1 0 0

0/1 1 0/10/1

Eves attack


71/82

Eve s attack

0 1 0 0

0/1 1 0/1 1

Eves attack


72/82

Eve s attack

0 1 0 0

0/1 1 0/1 1


Eves

attack


73/82

0 1 0 0

0/1 1 0/1 1

1Are they equal?

0 = 1?.REJECT!


Eve s attack

Caveats...


74/82

Caveats...

Some more complicated postprocessing

Authentication: Alice and Bob initially need to sharea small amount of key to authenticate theircommunication.

Practical aspects:

Single photons are difficult to come by.....

In the real world, errors happen...

Practical attacks can sometimes be mounted if the

implementation does not correspond to the idealsystem.

Off the shelf systems


75/82

y

ID Quantique (http://www.idquantique.com) (up to100km, > 1500bits/s)

Also Quantum random number generator (4 mbits/s) MagicQ (http://www.magicqtech.com)

What to expect


76/82

p

Goal: Secure communication The problem


Quantum Computing



How does it work?


Practical issues.


Commit Phase


77/82

Ill choose number 7 Has Alice made her choice?

Alice cannot change her mind about the chosen number

Yet, Bob cannot learn the number before Alice tells

him

Commit Phase


78/82

Number 7

Safe

7

Alice cannot change her mind about the chosen number Yet, Bob cannot learn the number before Alice tells

him

Commit Phase


79/82

Number 7

Safe

7

Alice cannot change her mind

Bob cannot open the safe and learn the number

Reveal Phase


80/82

Number 7

Safe

7

7

Bob opens the safe and checks that Alice

is telling the truth.

Can quantum help?


81/82

Negative: Not for single bits.

Positive: For strings (larger numbers) arelaxed version is possible.

Many other quantum applications, even toprove properties ofclassical protocols usingquantum techniques.

See http://www.cwi.nl/~wehner/for details.

Summary


82/82

Quantum Computing differs dramatically

from computing

Quantum effects can also be useful for

cryptography (e.g. Key exchange)

How can quantum effects help in the

construction of other protocols?

Wth Slides Quantum Cryptography an Introduction Screen

Documents