Wth Slides Quantum Cryptography an Introduction Screen
Transcript of Wth Slides Quantum Cryptography an Introduction Screen
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Quantum CryptographyAn Introduction
Stephanie Wehner
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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
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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
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The Problem
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The Problem
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The Problem
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Secure Communication
Goal: Hide the message contents from eavesdroppers!
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Secure Communication
Goal: Hide the message contents from eavesdroppers!
Damn!!
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Secret Key Cryptography
Only Alice and Bob know the key.
?
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Secret Key Cryptography
Problem: Need to communicate the key!
?
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Secret Key Cryptography
Problem: Need to communicate the key!
!!!
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Secret Key Cryptography
Problem: Need to communicate the key!
!!!
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Examples:
Secret Key Cryptography
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
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One time pad
ki
mi
xor xor
ki
mi
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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
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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
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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
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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.
! ??
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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
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So.
Secret Key Cryptography
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
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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
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Two funny quantum effects
Interference
Entanglement
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Quantum Effects
Detector 2
Detector 1
Photon
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Quantum Effects
Detector 2
Detector 1
Photon
50%
50%
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Quantum Effects
Detector 2
Detector 1
Photon
Never
Always!!
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Quantum Effects
Detector 2
Detector 1
Photon
Never
Always!!
Classical: The photon takes
one of the two paths.
50%
50%
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Quantum Effects
Detector 2
Detector 1
Photon
Classical: The photon takes
one of the two paths.
Lets test this....
50%
50%
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Quantum Effects
Detector 2
Detector 1
Photon
50%
50%
Classical: The photon takes
one of the two paths.
Lets test this....
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Quantum Effects
Detector 2
Detector 1
Photon
50%
50%
Classical: The photon takes
one of the two paths.
Lets test this....
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Quantum Effects: Interference
Detector 2
Detector 1
Photon
Never
Always!!
Quantum: The photon takes
both paths at once.
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Quantum Effects: Interference
Detector 2
Detector 1
Photon
Quantum: The photon takes
both paths at once.
slow down one path....
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Quantum Effects: Interference
Detector 2
Detector 1
Photon
Never
Always!!
Quantum: The photon takes
both paths at once.
slow down one path....
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Quantum Bits
Classical Bits: 0 or 1
Quantum Bits: 0 or 1 at the same time!
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Quantum Bits
Classical Bits: 0 or 1
Quantum Bits: 0 or 1 at the same time! Cannot be copied.
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Measurements
50% 50%
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Measurements
50% 50%
State collapses
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Two funny quantum effects
Interference
Entanglement
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Entanglement
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Entanglement
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Entanglement
50%
50%
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Entanglement
50%
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Entanglement
50%
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Basis 1: Vertical and Horizontal
0 1
Basis 2: Diagonal
0 1
Different basis...
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Measurement in the same basis
0 0
1 1
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Measurement in the same basis
0 0
1 1
0 0
1 1
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Measurement in the same basis
0 0
1 1
0 0
1 1
Measurement in the same basisdoes not change the state.
Measurement in a different
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Measurement in a different
basis....
50% 50%
0
0 1
Measurement in a different
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Measurement in a different
basis....
50% 50%
1
0 1
Measurement in a different
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Measurement in a different
basis....
50% 50%
1
0 1
Measurement in a different
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Measurement in a different
basis....
50% 50%
0
0 1
Measurement in a different
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Measurement in a different
basis....
A0 or 1 encoded in basis 1, gives a completely
random outcome when measured in basis 2.
And vice versa.
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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
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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
Solve
using
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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
Solve
using
Advantages:
Proven secure No computational
assumptions
History of
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History of
Quantum Key Distribution
Wiesner, 70ties, published only in 1983
Bennett & Brassard, 1984
Entanglement based: Ekert, 1991
Bennett & Brassard, 1992
Main idea: Eavesdropping
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or ??
Main idea: Eavesdropping
causes detectable disturbance
b = 1
Basis 1:
Basis 2: 1
1
0
BB84 S 1
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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
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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
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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
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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
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A run of the protocol
0 1 0 0
A run of the protocol
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A run of the protocol
0 1 0 0
0/1 1 0/1 0
A run of the protocol
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A run of the protocol
0 1 0 0
0/1 1 0/1 0
A run of the protocol
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A run of the protocol
0 1 0 0
0/1 1 0/1 0
Got it
A run of the protocol
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A run of the protocol
0 1 0 0
0/1 1 0/1 0
Got it
A run of the protocol
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A run of the protocol
0 1 0 0
0/1 1 0/1 0
Got it
A run of the protocol
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A run of the protocol
0 1 0 0
0/1 1 0/1 0
A run of the protocol
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A run of the protocol
0 1 0 0
0/1 1 0/1 0
Send me the 4th outcome
A run of the protocol
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A run of the protocol
0 1 0 0
0/1 1 0/1 0
Send me the 4th outcome
0Are they equal?
0 = 0. OK!
Eves attack
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Eve s attack
0 1 0 0
0/1 1 0/10/1
Eves attack
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Eve s attack
0 1 0 0
0/1 1 0/1 1
Eves attack
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Eve s attack
0 1 0 0
0/1 1 0/1 1
Send me the 4th outcome
Eves
attack
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0 1 0 0
0/1 1 0/1 1
1Are they equal?
0 = 1?.REJECT!
Send me the 4th outcome
Eve s attack
Caveats...
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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
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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
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p
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
Commit Phase
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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
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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
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Number 7
Safe
7
Alice cannot change her mind
Bob cannot open the safe and learn the number
Reveal Phase
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Number 7
Safe
7
7
Bob opens the safe and checks that Alice
is telling the truth.
Can quantum help?
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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
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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?