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1
candidate: Vadim Makarov
and
Defence for the degree doktor ingeniør
at the Norwegian University of Science and Technology, April 30, 2007
SPbSPUSt. Petersburg StatePolytechnic University
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ca. 1970
2004 First commercial offers
Concept (“money physically impossible
to counterfeit”)
...... Market?
1984 Key distribution protocol (BB84)
1989 Proof-of-the-principle experiment
1993 Key transmission over fiber optic link
Quantum cryptography timeline
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Encoder Decoder
Open (insecure)channel
BobAlice
Key
Secure channel
MessageMessage
Encoded message
• Secret key cryptography requires secure channel
for key distribution.
• Quantum cryptography distributes the key
by transmitting quantum states in open channel.
Key distribution
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Retained bit sequence 1 – – 1 0 0 – 1 0 0 – 1 – 0
Bob’s measurement 1 0 0 1 0 0 1 1 0 0 0 1 0 0
Bob’s detection basis
Alice’s bit sequence 1 0 1 1 0 0 1 1 0 0 1 1 1 0
Light source
Alice
Bob
Diagonaldetector basis
Horizontal-verticaldetector basis
Diagonalpolarization filters
Horizontal-verticalpolarization filters
Image reprinted from article: W. Tittel, G. Ribordy, and N. Gisin, "Quantum cryptography," Physics World, March 1998
Quantum key distribution
0
0
1
1
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ϕA = – 45° or + 45° : 0
Detector bases:
ϕB = – 45° : X
ϕB = + 45° : Zϕ
A = +135° or – 135° : 1
ϕA
Lightsource
D0ϕB
Alice Bob
LA
SA
Transmission
lineSB
LB
D1
Interferometric QKD channel
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Quantum cryptography at NTNU
Fiber optic QKD setup
1. Optimal tracking of phase drift
2. Single photon detector
with afterpulse blocking
Security against practical attacks
3. Large pulse attack: experiment
4. Faked states attack
5. Detector efficiency mismatch ”0"
”1"
t
BOB
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QKD setup
Bob
Laser
APD
1310 nm
Pulse rate = 10 MHz
Line
Polarizationсontroller
Attenuator
Alice’sPC
Publiccommunication(TCP/IP)
Bob’sPC
Polarizationcombiner
Polarizationсombiner
Phasemodulator 2
Polarizingsplitter
Phasemodulator 1
PM coupler50/50
Variabledelay linePolarizer
Variable ratioPM coupler
“1”
“0”
Alice
PM fiberstandard SM fiber
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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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Tracking phase drift
To get phase accuracy ∆φ within ±10° (QBERopt ∆ϕ < 1%),
no more than Na = ~ 200 detector counts per adjustment
are required.
Optimally counted at ±90° points from the extreme of the
interference curves. Exact required number of counts
where k is the number of standard deviations of not exceeding ∆φ.
( ) ,
2
2
2
QBER21
12
−ϕ∆= k
Na
J. Appl. Opt. 43, 4385 (2004)
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Tracking phase drift
+π
–π
0
0 60 minTime
J. Appl. Opt. 43, 4385 (2004)
To get phase accuracy ∆φ within ±10° (QBERopt ∆ϕ < 1%),
no more than Na = ~ 200 detector counts per adjustment
are required.
Experiment: adjustment every 3 s, Na = 230:
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Test of QKD in laboratory conditions
Test run No. 2
QBER =
.5.7% average
QB
ER
, %
50
11
00 5 min
Time
Test run No. 1
best QBER
~ 4%
QB
ER
, %
50
11
00 5 min
Time
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tgate down to 1ns
Gate pulse rate = 20 MHz
VE
Vbias
VB
t
T=1/(Gate pulse rate)
tgate–VAPD
Single photon detector:avalanche photodiode in Geiger mode
APD: Ge FD312L
T=77K, QE=16%, DC=5·10
–5
APD inside cryostatC = CAPD
Differential
amplifier
50 Ω coaxial cables
Gate pulse
generator Bias
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Afterpulse blocking
• In QKD systems, probability of detecting a photon per pulse is always
much lower than 1 (e.g., ~ 1/1000). This makes afterpulse blocking
efficient, allowing without much loss in detection probability:
• In our QKD system: 20 MHz gate pulse rate
• In principle: a few orders of magnitude faster gate pulse rate
–VAPD
Detector
output
Hold-off time: N pulses are blocked
after detecting avalanche
t
VB
t
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Hardware implementation ofafterpulse blocking
APD
Differential
amplifier
Gate pulse
generator BiasRF switch
= =
Set
Reset
Trigger
ComparatorIntegrator
Digital
output
0 0
N set
by switch
CLK
Load
Counter
Overflow
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Test of afterpulse blocking
APD: Ge FD312L
Gate pulse rate = 12 MHz
QE = 7%
T = 77K
Number of gate pulses blocked
0.00
0.05
0.10
0.15
0.20
Co
un
t p
rob
ab
ilit
y,
%
Dark counts
Counts at 0.005 photon per pulse
0 2 5 12 18 34
N
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1. Conventional security; trusted equipment manufacturer
2. Security against quantum attacks – security proofs for idealized model of equipment
3. Loopholes in optical scheme – imperfections not yet accounted in the proof
Quantum key distribution:components of security
2 311
Alice Bob
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Large pulse attackAlice
Line
Attenuator
Alice’sPC
Eve’s equipment
Phasemodulator
– interrogating Alice’s phase modulator with powerful
external pulses (can give Eve bit values directly)
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Large pulse attack: experiment
Laser
4% reflection
Vmod
OTDR
Out
In
Fine lengthadjustment
to get L1 = L2
L2
L1
ReceivedOTDRpulse
Vmod, V4.1 8.20
Variableattenuator
Alice
Phasemodulator
Eve
J. Mod. Opt. 48, 2023 (2001)
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Photo 3. Artem Vakhitov tunes up Eve’s setup
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Conventional intercept -resend:
Faked states attack:
(no alarm)
Faked states attack
J. Mod. Opt. 52, 691 (2005)
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”0"
”1"
t
BOB
Exploiting common imperfection:detector gate misalignment
Phys. Rev. A 74, 022313 (2006)
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”0"
”1"
t
BOB
Laser pulse from Alice
Detector gate misalignment
Phys. Rev. A 74, 022313 (2006)
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”0"
”1"
t
BOB
Detector gate misalignment
Phys. Rev. A 74, 022313 (2006)
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”0"
”1"
t
BOB
Detector gate misalignment
Phys. Rev. A 74, 022313 (2006)
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”0"
”1"
t
Example: Eve measured with basis Z (90°), obtained bit 1
0°
BOB
=0°
Detector gate misalignment
(Eve resends the opposite bit 0 in the opposite basis X, shifted in time)
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(Eve resends the opposite bit 0 in the opposite basis X, shifted in time)
”0"
”1"
t
Example: Eve measured with basis Z (90°), obtained bit 1
90°
BOB
=0°
Detector gate misalignment
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De
tec
tor
eff
icie
nc
y
t
0
t0
t1
η0(t0)
η1(t0) η
0(t1)
η1(t1)
Partial efficiency mismatch
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Partial efficiency mismatch
In the symmetric case (when η1(t0)/η
0(t0) = η
0(t1)/η
1(t1) ),
Eve causes less than 11% QBER if mismatch is larger than 1:15
A. Practical faked states attack:
B. General security bound (incomplete):
where
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-3 -2 -1 1 2 30
t, ns
0
No
rma
lize
d d
ete
cto
r s
en
sit
ivit
y,
arb
. u
.
Detector model 1.Sensitivity curves
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0 1 2 3 4 5 6 7 8 9 10 11 12
t, ns
0
10
20
De
tec
tor
qu
an
tum
eff
icie
nc
y,
% t = 5.15 ns
1/9
t = 7.40 ns
1/30
0 1
≈ ≈ηη
ηη
1
0
0
1
Detector model 2.Sensitivity curves at low photon number µ=0.5
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Detector efficiency mismatch
• Detector efficiency mismatch is a problem for many
protocols and encodings: BB84 (considered above),
SARG04, phase-time, DPSK and Ekert protocols.
• Control parameter t that changes detector efficiencies
shall not be necessarily timing; it can be, e.g., wavelength
or polarization.
• The worst-case mismatch, no matter how small,
must be characterized and accounted for during
privacy amplification.
[quant-ph/0702262]
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Conclusion
• A phase tracking technique and detector with afterpulse
blocking were successfully developed.
(QKD was demonstrated with a very limited success.)
• Our group has built unique expertise in quantum
cryptanalysis of attacks via optical loopholes.
Several attacks have been proposed, studied in detail,
and protection measures suggested.
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Possible future research
• Continuing security studies beyond those presented in the
thesis; we have experimented with passively-quenched
Si APD; we are trying to incorporate detector efficiency
mismatch into general proof... With sufficient financing,
a study of high-power damage can be attempted.
• Improving the QKD experiment, demonstrating it over
at least ~ 20 km distance. Performance of detector
and phase tracking can be more accurately characterized.
• The QKD field is abound with novel ideas that can be tried...
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Optional slides
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0.00 0.11
QBER
0
1
R
0
Handling errors in raw key
R = 1 – 2 h(QBER)
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• MagiQ Tecnologies
USA
• id Quantique
Switzerland
Standard VPN router + QKD equipment for frequent key changes
Several other companies also have the QKD technology, but are not selling yet
Commercial offers (as of late 2006)
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Photo 4. Bob (left) and Alice (right), thermoisolation partially installed
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Typical values of reflection coefficients for different fiber-optic components
(courtesy Opto-Electronics, Inc.)
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( Eve’s basis = Bob’s basis )is sufficient for eavesdropping
Alice
Eve’s basis det. result
Bob
Incompatible basis –discarded by Alice and Bob during sifting
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0 1η0.00
0.11
QBER
Not proven(assumed insecure)
Insecure
0.0660
Securewith reduced key rate
Security state of QKD system
( reduced rate at QBER=0 line, too )
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Trondheim
St. Petersburg