Continuous variables quantum cryptography
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Transcript of Continuous variables quantum cryptography
![Page 1: Continuous variables quantum cryptography](https://reader033.fdocuments.us/reader033/viewer/2022052213/55648dc1d8b42a5f6c8b4b8c/html5/thumbnails/1.jpg)
Intro. Cont. Var. Information Theory CVQKD XP Next
Continuous VariableQuantum Cryptography
Towards High Speed Quantum Cryptography
Frédéric Grosshans
CNRS / ENS Cachan
Palacký University, Olomouc, 2011
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Intro. Cont. Var. Information Theory CVQKD XP Next
1 IntroductionPrefect Secrecy and Quantum CryptographyVarious Secure Systems
2 Continuous variablesField quadraturesHomodyne Detection : Theory
3 Information TheoryXXth century CVQKDWhere are the bits ?
4 Continuous Variable Quantum Key DistributionSpyingProtocols
5 Experimental systems1st and 2nd generation demonstratorsKey-RatesIntegration with classical cryptography
6 Open problems
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Intro. Cont. Var. Information Theory CVQKD XP Next
Conditions for Perfect Secrecy
Alice sends a secret message to Bob
through a channel observed by Eve.
She encrypts the message with a secret keyas long as the message.
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Intro. Cont. Var. Information Theory CVQKD XP Next
Conditions for Perfect Secrecy
Alice sends a secret message to Bobthrough a channel observed by Eve.
She encrypts the message with a secret keyas long as the message.
![Page 5: Continuous variables quantum cryptography](https://reader033.fdocuments.us/reader033/viewer/2022052213/55648dc1d8b42a5f6c8b4b8c/html5/thumbnails/5.jpg)
Intro. Cont. Var. Information Theory CVQKD XP Next
Conditions for Perfect Secrecy
Alice sends a secret message to Bobthrough a channel observed by Eve.
She encrypts the message with a secret key
as long as the message.
![Page 6: Continuous variables quantum cryptography](https://reader033.fdocuments.us/reader033/viewer/2022052213/55648dc1d8b42a5f6c8b4b8c/html5/thumbnails/6.jpg)
Intro. Cont. Var. Information Theory CVQKD XP Next
Conditions for Perfect Secrecy
Alice sends a secret message to Bobthrough a channel observed by Eve.
She encrypts the message with a secret keyas long as the message.
![Page 7: Continuous variables quantum cryptography](https://reader033.fdocuments.us/reader033/viewer/2022052213/55648dc1d8b42a5f6c8b4b8c/html5/thumbnails/7.jpg)
Intro. Cont. Var. Information Theory CVQKD XP Next
Quantum Key Distribution
Alice sends quantum objects to Bob
Eve’s Measurenents⇒measurable perturbations⇒ secret key generation
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Intro. Cont. Var. Information Theory CVQKD XP Next
Quantum Key Distribution
Alice sends quantum objects to Bob
Eve’s Measurenents
⇒measurable perturbations⇒ secret key generation
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Intro. Cont. Var. Information Theory CVQKD XP Next
Quantum Key Distribution
Alice sends quantum objects to Bob
Eve’s Measurenents⇒measurable perturbations⇒ secret key generation
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Intro. Cont. Var. Information Theory CVQKD XP Next
Unconditionnally Secure Systems . . .
Single Photon QKD
I Long Range (∼ 100 km)I Low rate (kbit/s)
maybe a few Mbit/s in the long run
Classical One-Time-PadI Very Long Range (Paris–Olomouc)I Not so small rate :
1 CD / year = 180 bits/s1 iPod (160 GB)/ year = 40 kbit/s
I But the data has to stay here
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Intro. Cont. Var. Information Theory CVQKD XP Next
Unconditionnally Secure Systems . . .
Single Photon QKD
I Long Range (∼ 100 km)I Low rate (kbit/s) maybe a few Mbit/s in the long run
Classical One-Time-PadI Very Long Range (Paris–Olomouc)I Not so small rate :
1 CD / year = 180 bits/s1 iPod (160 GB)/ year = 40 kbit/s
I But the data has to stay here
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Intro. Cont. Var. Information Theory CVQKD XP Next
Unconditionnally Secure Systems . . .
Single Photon QKD
I Long Range (∼ 100 km)I Low rate (kbit/s) maybe a few Mbit/s in the long run
Classical One-Time-PadI Very Long Range (Paris–Olomouc)I Not so small rate :
1 CD / year = 180 bits/s1 iPod (160 GB)/ year = 40 kbit/s
I But the data has to stay here
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Intro. Cont. Var. Information Theory CVQKD XP Next
Unconditionnally Secure Systems . . .
Single Photon QKD
I Long Range (∼ 100 km)I Low rate (kbit/s) maybe a few Mbit/s in the long run
Classical One-Time-PadI Very Long Range (Paris–Olomouc)I Not so small rate :
1 CD / year = 180 bits/s
1 iPod (160 GB)/ year = 40 kbit/s
I But the data has to stay here
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Intro. Cont. Var. Information Theory CVQKD XP Next
Unconditionnally Secure Systems . . .
Single Photon QKD
I Long Range (∼ 100 km)I Low rate (kbit/s) maybe a few Mbit/s in the long run
Classical One-Time-PadI Very Long Range (Paris–Olomouc)I Not so small rate :
1 CD / year = 180 bits/s1 iPod (160 GB)/ year = 40 kbit/s
I But the data has to stay here
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Intro. Cont. Var. Information Theory CVQKD XP Next
Unconditionnally Secure Systems . . .
Single Photon QKD
I Long Range (∼ 100 km)I Low rate (kbit/s) maybe a few Mbit/s in the long run
Classical One-Time-PadI Very Long Range (Paris–Olomouc)I Not so small rate :
1 CD / year = 180 bits/s1 iPod (160 GB)/ year = 40 kbit/s
I But the data has to stay here
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Intro. Cont. Var. Information Theory CVQKD XP Next
. . . and Continuous Variable
I Medium Range :∼ 25 km
; 80 km soon ?
I Medium Rate :∼ a few kbit/s
; Mbits/s soon ?I Much less mature
⇒ Much room for improvements
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Intro. Cont. Var. Information Theory CVQKD XP Next
. . . and Continuous Variable
I Medium Range :∼ 25 km
; 80 km soon ?
I Medium Rate :∼ a few kbit/s
; Mbits/s soon ?
I Much less mature
⇒ Much room for improvements
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Intro. Cont. Var. Information Theory CVQKD XP Next
. . . and Continuous Variable
I Medium Range :∼ 25 km ; 80 km soon ?I Medium Rate :∼ a few kbit/s ; Mbits/s soon ?I Much less mature⇒ Much room for improvements
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Intro. Cont. Var. Information Theory CVQKD XP Next
1 IntroductionPrefect Secrecy and Quantum CryptographyVarious Secure Systems
2 Continuous variablesField quadraturesHomodyne Detection : Theory
3 Information TheoryXXth century CVQKDWhere are the bits ?
4 Continuous Variable Quantum Key DistributionSpyingProtocols
5 Experimental systems1st and 2nd generation demonstratorsKey-RatesIntegration with classical cryptography
6 Open problems
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Intro. Cont. Var. Information Theory CVQKD XP Next
Field quadratures
Classical fieldElectromagnetic fielddescribed by QA and PAE(t) = QA cosωt + PA sinωt
Quantum descriptionQ and P do not commute:
[Q,P] ∝ i~.Add a
“quantum noise”:Q = QA + BQ et P = PA + BP
Heisenberg =⇒ ∆BQ∆BP ≥ 1
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Intro. Cont. Var. Information Theory CVQKD XP Next
Field quadratures
Classical fieldElectromagnetic fielddescribed by QA and PAE(t) = QA cosωt + PA sinωt
Quantum descriptionQ and P do not commute:
[Q,P] ∝ i~.Add a
“quantum noise”:Q = QA + BQ et P = PA + BP
Heisenberg =⇒ ∆BQ∆BP ≥ 1
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Intro. Cont. Var. Information Theory CVQKD XP Next
Homodyne Detection : Theory
Photocurrents:
i± ∝ (Eosc.(t) ± Esignal(t))2
∝ Eosc.(t)2± 2Eosc.(t)Esignal(t)
after substraction:
δi ∝ Eosc.(t)Esignal(t)
∝ Eosc.(Qsignal cosϕ + Psignal sinϕ)
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Intro. Cont. Var. Information Theory CVQKD XP Next
1 IntroductionPrefect Secrecy and Quantum CryptographyVarious Secure Systems
2 Continuous variablesField quadraturesHomodyne Detection : Theory
3 Information TheoryXXth century CVQKDWhere are the bits ?
4 Continuous Variable Quantum Key DistributionSpyingProtocols
5 Experimental systems1st and 2nd generation demonstratorsKey-RatesIntegration with classical cryptography
6 Open problems
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Intro. Cont. Var. Information Theory CVQKD XP Next
XXth century CVQKD
At the end of XXth century it was obvious that ageneralization of QKD to continuous variables could beinteresting.Problem : discrete bits , continuous variable
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Intro. Cont. Var. Information Theory CVQKD XP Next
XXth century CVQKD
At the end of XXth century it was obvious that ageneralization of QKD to continuous variables could beinteresting.Problem : discrete bits , continuous variable
Adapting BB84?Mark Hillery, “Quantum Cryptography withSqueezed States”,arXiv:quant-ph/9909006/PRA 61 022309
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Intro. Cont. Var. Information Theory CVQKD XP Next
XXth century CVQKD
At the end of XXth century it was obvious that ageneralization of QKD to continuous variables could beinteresting.Problem : discrete bits , continuous variable
Natural modulation + information theory!Nicolas J. Cerf, Marc Lévy, Gilles VanAssche : “Quantum distribution of Gaussiankeys using squeezed states”,arXiv:quant-ph/0008058/PRL 63 052311
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Intro. Cont. Var. Information Theory CVQKD XP Next
Where are the bits ?
Quite frequent discussion with discrete quantumcryptographers :
DQC : How do you encode a 0 or a 1 in CVQKD?Me : I don’t care, C. E. Shannon tells me
“∀ε > 0,∃ code of rate I − ε.”
Computation of the ideal code performance is easy !
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Intro. Cont. Var. Information Theory CVQKD XP Next
Where are the bits ?
Quite frequent discussion with discrete quantumcryptographers :
DQC : How do you encode a 0 or a 1 in CVQKD?Me : Gilles/Jérôme/Anthony/Sébastien developed
a really efficient code, using slicedreconciliation/LDPC matrices/R8 rotations andoctonions. Only he knows how it works.
Computation of the ideal code performance is easy !
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Intro. Cont. Var. Information Theory CVQKD XP Next
Where are the bits ?
Quite frequent discussion with discrete quantumcryptographers :
DQC : How do you encode a 0 or a 1 in CVQKD?Me : Gilles/Jérôme/Anthony/Sébastien developed
a really efficient code, using slicedreconciliation/LDPC matrices/R8 rotations andoctonions. Only he knows how it works.
Computation of the ideal code performance is easy !
![Page 30: Continuous variables quantum cryptography](https://reader033.fdocuments.us/reader033/viewer/2022052213/55648dc1d8b42a5f6c8b4b8c/html5/thumbnails/30.jpg)
Intro. Cont. Var. Information Theory CVQKD XP Next
They’re hidden
Availaible informationin a continuous signal
with noise ?
Differential entropy
H(X) = −∑P(x) dx logP(x) dx
'
∫dxP(x) logP(x)︸ ︷︷ ︸
H(X)
− log dx︸︷︷︸constante
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Intro. Cont. Var. Information Theory CVQKD XP Next
They’re hidden
Availaible informationin a continuous signal
with noise ?
Differential entropy
H(X) = −∑P(x) dx logP(x) dx
'
∫dxP(x) logP(x)︸ ︷︷ ︸
H(X)
− log dx︸︷︷︸constante
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Intro. Cont. Var. Information Theory CVQKD XP Next
They’re hidden
Availaible informationin a continuous signalwith noise ?
Differential entropy
H(X) = −∑P(x) dx logP(x) dx
'
∫dxP(x) logP(x)︸ ︷︷ ︸
H(X)
− log dx︸︷︷︸constante
H(X) = log ∆X + constante
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Intro. Cont. Var. Information Theory CVQKD XP Next
They’re hidden
Availaible informationin a continuous signalwith noise ?
Differential entropy
H(X) = −∑P(x) dx logP(x) dx
'
∫dxP(x) logP(x)︸ ︷︷ ︸
H(X)
− log dx︸︷︷︸constante
Mutual information
I(X : Y) = H(Y) −H(Y|X)= H(Y) −H(Y|X)
= 12 log
∆Y2
∆Y2|X
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Intro. Cont. Var. Information Theory CVQKD XP Next
1 IntroductionPrefect Secrecy and Quantum CryptographyVarious Secure Systems
2 Continuous variablesField quadraturesHomodyne Detection : Theory
3 Information TheoryXXth century CVQKDWhere are the bits ?
4 Continuous Variable Quantum Key DistributionSpyingProtocols
5 Experimental systems1st and 2nd generation demonstratorsKey-RatesIntegration with classical cryptography
6 Open problems
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Intro. Cont. Var. Information Theory CVQKD XP Next
The spy’s power
Heisenberg :∆BEve∆BBob ≥ 1
⇒ ∆BBob gives I IEve
I IBob
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Intro. Cont. Var. Information Theory CVQKD XP Next
The spy’s power
Heisenberg :∆BEve∆BBob ≥ 1
⇒ ∆BBob gives I IEve
I IBob
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Intro. Cont. Var. Information Theory CVQKD XP Next
Quantum Key Distribution Protocols
Channel Evauation (noise measure)
Alice&Bob evaluate IEve
Reconciliation (error correction)
Alice&Bob share IBob identical bits.Ève knows IEve.
Privacy AmplificationAlice&Bob share IBob − IEve identical bits.
Ève knows ∼ 0.
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Intro. Cont. Var. Information Theory CVQKD XP Next
Quantum Key Distribution Protocols
Channel Evauation (noise measure)
Alice&Bob evaluate IEve
Reconciliation (error correction)
Alice&Bob share IBob identical bits.Ève knows IEve.
Privacy AmplificationAlice&Bob share IBob − IEve identical bits.
Ève knows ∼ 0.
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Intro. Cont. Var. Information Theory CVQKD XP Next
Quantum Key Distribution Protocols
Channel Evauation (noise measure)
Alice&Bob evaluate IEve
Reconciliation (error correction)
Alice&Bob share IBob identical bits.Ève knows IEve.
Privacy AmplificationAlice&Bob share IBob − IEve identical bits.
Ève knows ∼ 0.
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Intro. Cont. Var. Information Theory CVQKD XP Next
Theoretical Progresses in the last 10 years
We went from a protocolI using squeezed states,I insecure beyond 50% losses (15 km),I proved secure against Gaussian individual attack
to a protocol
I using coherent statesI with no fundamental range limitI proved secure against collective attacksI likely secure against coherent attacksI and experimentally working
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Intro. Cont. Var. Information Theory CVQKD XP Next
Theoretical Progresses in the last 10 years
We went from a protocolI using squeezed states,I insecure beyond 50% losses (15 km),I proved secure against Gaussian individual attack
to a protocolI using coherent states
I with no fundamental range limitI proved secure against collective attacksI likely secure against coherent attacksI and experimentally working
![Page 42: Continuous variables quantum cryptography](https://reader033.fdocuments.us/reader033/viewer/2022052213/55648dc1d8b42a5f6c8b4b8c/html5/thumbnails/42.jpg)
Intro. Cont. Var. Information Theory CVQKD XP Next
Theoretical Progresses in the last 10 years
We went from a protocolI using squeezed states,I insecure beyond 50% losses (15 km),I proved secure against Gaussian individual attack
to a protocolI using coherent statesI with no fundamental range limitI proved secure against collective attacks
I likely secure against coherent attacksI and experimentally working
![Page 43: Continuous variables quantum cryptography](https://reader033.fdocuments.us/reader033/viewer/2022052213/55648dc1d8b42a5f6c8b4b8c/html5/thumbnails/43.jpg)
Intro. Cont. Var. Information Theory CVQKD XP Next
Theoretical Progresses in the last 10 years
We went from a protocolI using squeezed states,I insecure beyond 50% losses (15 km),I proved secure against Gaussian individual attack
to a protocolI using coherent statesI with no fundamental range limitI proved secure against collective attacksI likely secure against coherent attacks
I and experimentally working
![Page 44: Continuous variables quantum cryptography](https://reader033.fdocuments.us/reader033/viewer/2022052213/55648dc1d8b42a5f6c8b4b8c/html5/thumbnails/44.jpg)
Intro. Cont. Var. Information Theory CVQKD XP Next
Theoretical Progresses in the last 10 years
We went from a protocolI using squeezed states,I insecure beyond 50% losses (15 km),I proved secure against Gaussian individual attack
to a protocolI using coherent statesI with no fundamental range limitI proved secure against collective attacksI likely secure against coherent attacksI and experimentally working
![Page 45: Continuous variables quantum cryptography](https://reader033.fdocuments.us/reader033/viewer/2022052213/55648dc1d8b42a5f6c8b4b8c/html5/thumbnails/45.jpg)
Intro. Cont. Var. Information Theory CVQKD XP Next
1 IntroductionPrefect Secrecy and Quantum CryptographyVarious Secure Systems
2 Continuous variablesField quadraturesHomodyne Detection : Theory
3 Information TheoryXXth century CVQKDWhere are the bits ?
4 Continuous Variable Quantum Key DistributionSpyingProtocols
5 Experimental systems1st and 2nd generation demonstratorsKey-RatesIntegration with classical cryptography
6 Open problems
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Intro. Cont. Var. Information Theory CVQKD XP Next
1st generation demonstratorF. Grosshans et. al., Nature (2003) & Brevet US
m
Key rate I 75 kbit/s 3.1 dB (51%) lossesI 1.7 Mbit/s without losses
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Intro. Cont. Var. Information Theory CVQKD XP Next
Integrated system
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Intro. Cont. Var. Information Theory CVQKD XP Next
Integrated system
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Intro. Cont. Var. Information Theory CVQKD XP Next
Integrated system
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Intro. Cont. Var. Information Theory CVQKD XP Next
Key-Rates
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Intro. Cont. Var. Information Theory CVQKD XP Next
Key-Rates
Losses onlyExcess noise95% efficient code
90% efficient codeSlow code
100 kb/s
10 kb/s
1 kb/s 0 km
10 km
20 km
30 km
40 km
50 km
SECOQC Performance(2008)
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Intro. Cont. Var. Information Theory CVQKD XP Next
Key-Rates
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Intro. Cont. Var. Information Theory CVQKD XP Next
Key-Rates
Losses onlyExcess noise95% efficient code
90% efficient codeSlow code
100 kb/s
10 kb/s
1 kb/s 0 km
10 km
20 km
30 km
40 km
50 km
SECOQC Performance(2008)
use GPUsIncr
ease
s m
odul
atio
n ra
te :
×10
easy
, ×10
0 do
able
use modern codes :ocotonion based protocol+multi-edge LDPC codes
+ repetition codes
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Intro. Cont. Var. Information Theory CVQKD XP Next
Integration with classical cryptography
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Intro. Cont. Var. Information Theory CVQKD XP Next
Integration with classical cryptography
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Intro. Cont. Var. Information Theory CVQKD XP Next
1 IntroductionPrefect Secrecy and Quantum CryptographyVarious Secure Systems
2 Continuous variablesField quadraturesHomodyne Detection : Theory
3 Information TheoryXXth century CVQKDWhere are the bits ?
4 Continuous Variable Quantum Key DistributionSpyingProtocols
5 Experimental systems1st and 2nd generation demonstratorsKey-RatesIntegration with classical cryptography
6 Open problems
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Intro. Cont. Var. Information Theory CVQKD XP Next
Open Problems
I Finite size effectsI Link with post-selection based protocols (.de, .au)I Side-channels and quantum hackingI Other cryptographic applications