Transcript Kvantekryptografi med fotoner i optiske fibre

Norsk kryptoseminar, 17-18. oktober 2002. NTNU, Trondheim
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Quantum Cryptography
Vadim Makarov and Dag R. Hjelme
Institutt for fysikalsk elektronikk NTNU
www.vad1.com/qcr/
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FoU
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Classical vs. quantum information
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
Classical information
Perfect copy
Unchanged original

Quantum information
Imperfect copy
Broken original
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Qubit: polarization state
of a single photon
Measure?
Measure?
50%
50%
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What is the problem with classical
cryptography?
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
Secret key cryptography
 Requires secure channel for key distribution
 In principle every classical channel can be monitored passively
 Security is mostly based on complicated non-proven algorithms

Public key cryptography
 Security is based on non-proven mathematical assumptions
(e.g. difficulty of factoring large numbers)
 We DO know how to factorize in polynomial time! Shor’s
algorithm for quantum computers. Just wait until one is built.
 Breakthrough renders messages insecure retroactively
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The holy grail: One-time pad
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

The only cipher mathematically proven
Requires massive amounts of key material
m
m
c
k
k
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Key distribution
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Message
Alice
Bob
Open (insecure) channel
Encoder
Encoded message
Message
Decoder
Key
Secure channel


Secret key cryptography requires secure channel for key
distribution.
Quantum cryptography distributes the key by transmitting
quantum states in open channel.
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Quantum key distribution
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Bob
Alice
Diagonal
polarization filters
Horizontal-vertical
polarization filters
Diagonal
detector basis
Horizontalvertical
detector basis
Light source
Alice’s bit sequence 1 0 1 1 0 0 1 1 0 0 1 1 1 0
Bob’s detection basis
Bob’s measurement 1 0 0 1 0 0 1 1 0 0 0 1 0 0
Retained bit sequence 1 – – 1 0 0 – 1 0 0 – 1 – 0
Image reprinted from article: W. Tittel, G. Ribordy, and N. Gisin, "Quantum cryptography," Physics World, March 1998
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Eavesdropping with wrong reference
system
Tyvlytter
50%
Sender
Mottaker
Referanse
50%
Rett
Galt
Rett
50%
"1"
Galt
Rett
50%
"0"
Galt
Rett
Sender
"0"
Rett
"0"
Rett
"1"
Galt
Rett
Galt
Rett
Galt
"1"
Rett
Rett
"0"
"1"
Galt
Rett
Rett
Galt
Rett
Galt
"0"
Rett
Rett
"1"
"0"
Galt
Rett
Rett
Galt
Rett
Galt
"1"
Rett
Rett
"1"
Rett
"0"
Galt
Rett
50%
"0"
50%
Resultat av mеling
Eavesdropper
Receiver
"1"
Galt
Rett
Galt
Rett
Galt
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Interferometric QKD channel
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Sender (Alice)
Receiver (Bob)
L1
Source
f1
f =
1
f2
S1
0 or 90 - "1"
f = 180 or 270 - "0"
1
Transmission
line
L2
D0
S2
D1
Reference
systems:
f = 0
2
f = 90
2
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Implementation: interferometer structure
Alice
Variable Ratio
PM Coupler
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Variable
Delay Line
Polarizer
Laser
Phase
Modulator 1
PM fiber
1300 nm (or 1550 nm)
Polarization
Combiner
Attenuator
Alice's
PC
Pulse Rate = 10 MHz
Public
Communication
Channel
Eve's Territory
Bob
Line
Standard
SM fiber
Bob's
PC
APD
PM Coupler
50/50
Phase
Modulator 2
Polarization
Controller
'0'
Polarization
Combiner
'1'
PM fiber
Polarizing
Splitter
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Photo 1. Alice (uncovered, no thermoisolation installed)
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Photo 2. Bob (uncovered, no thermoisolation installed)
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Single-photon detector:
APD in Geiger mode
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Gate Pulse
Generator
Bias
-VAPD
tgate
VE
Transmission
Lines, Z=50
C = CAPD
APD Inside Cryostat
VB
T=1/(gate pulse rate)
Vbias
Differential
Amplifier
t
tgate down to 1ns
gate pulse rate = 20 MHz
Epitaxx APD
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Recovery from errors
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Eve’s information
Bob’s information
QBER limit:


Individual attacks: 15%
All theoretically possible attacks: 11%
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Distance limitation
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,
Maximum link
distance, km
nm
850
1300
1550
70
Fiber
attenuation,
Detectors
dB/km
2
Si, room temperature
0.35
Ge, -196C
0.2
InGaAs,  60C
1550 nm
30
20
1300 nm
5
0
850 nm
0
5E-5
Few %
Detector noise level
(dark count probability)
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Components of security
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1
1
2 3
Alice
Bob
1. Conventional security
2. Security against quantum attacks
3. Security against Trojan horse attacks
- ones that don’t deal with quantum states, but use loopholes
in optical scheme
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Practical security: large pulse attack
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Alice
Phase
Modulator
Attenuator
Alice's
PC
Line
Eve’s Equipment
- interrogating Alice’s phase modulator with powerful external pulses
(can give Eve bit values directly)
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Eavesdropping experiment
Alice
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4% reflection
Phase
Modulator
Laser
Vmod
Eve
L1
Out
OTDR
Received
OTDR
pulse
Variable
attenuator
In
L2
Fine length
adjustment
to get L1 = L2
0
4.1
8.2
Vmod, V
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Photo 3. Artem Vakhitov tunes up Eve’s setup
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Re-keying satellites/
Global key distribution network
1.9 km
10 km
23.4 km
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Quantum key distribution in network
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
Multi-user key distribution
Bob 1
Passive splitter
Bob 2
Alice
Bob 3

Multiplexing with telecom traffic
1300 nm
Alice
Data
transmitter
28 km
WDM
1550 nm
1.2 Gbit/s
WDM
Bob
Data
receiver
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Entangled photon pairs
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1560nm
Entangled
Photon Pairs
Nonlinear
Crystal
Pump
Pulses
780nm
To Bob
Passive
Measurement
Alice
Random state
prepared
passively
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Advanced multi-party protocols:
Secret sharing and splitting
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A
B
A
C
B
A
C
B
C
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Commercial status
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
id Quantique (Geneva)
first commercially available quantum key distribution
system:

MagiQ Technologies (Boston)

EQUIS project (Heriot-Watt University and Corning; UK)
compact integration into standard PCs

+ several research groups, telecom/ electronics companies
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