Intro.   Cont. Var.       Information Theory    CVQKD   XP   Next                       Continuous Variable               ...
Intro.          Cont. Var.   Information Theory   CVQKD   XP   Next         1   Introduction                Prefect Secrec...
Intro.         Cont. Var.   Information Theory   CVQKD   XP   NextConditions for Perfect Secrecy         Alice sends a sec...
Intro.         Cont. Var.   Information Theory   CVQKD   XP        NextConditions for Perfect Secrecy         Alice sends ...
Intro.         Cont. Var.   Information Theory   CVQKD   XP        NextConditions for Perfect Secrecy         Alice sends ...
Intro.         Cont. Var.   Information Theory   CVQKD   XP        NextConditions for Perfect Secrecy         Alice sends ...
Intro.         Cont. Var.   Information Theory   CVQKD   XP   NextQuantum Key Distribution         Alice sends quantum obj...
Intro.         Cont. Var.     Information Theory   CVQKD   XP   NextQuantum Key Distribution         Alice sends quantum o...
Intro.         Cont. Var.   Information Theory   CVQKD   XP      NextQuantum Key Distribution         Alice sends quantum ...
Intro.         Cont. Var.    Information Theory   CVQKD   XP   NextUnconditionnally Secure Systems . . .         Single Ph...
Intro.         Cont. Var.    Information Theory   CVQKD   XP       NextUnconditionnally Secure Systems . . .         Singl...
Intro.         Cont. Var.    Information Theory   CVQKD   XP       NextUnconditionnally Secure Systems . . .         Singl...
Intro.         Cont. Var.     Information Theory   CVQKD   XP      NextUnconditionnally Secure Systems . . .         Singl...
Intro.         Cont. Var.     Information Theory     CVQKD   XP    NextUnconditionnally Secure Systems . . .         Singl...
Intro.         Cont. Var.     Information Theory     CVQKD   XP    NextUnconditionnally Secure Systems . . .         Singl...
Intro.     Cont. Var.   Information Theory   CVQKD   XP   Next. . . and Continuous Variable         Medium Range :∼ 25 km ...
Intro.     Cont. Var.   Information Theory   CVQKD   XP   Next. . . and Continuous Variable         Medium Range :∼ 25 km ...
Intro.     Cont. Var.   Information Theory   CVQKD      XP   Next. . . and Continuous Variable         Medium Range :∼ 25 ...
Intro.          Cont. Var.   Information Theory   CVQKD   XP   Next         1   Introduction                Prefect Secrec...
Intro.       Cont. Var.     Information Theory   CVQKD   XP   NextField quadratures    Classical field    Electromagnetic fi...
Intro.       Cont. Var.     Information Theory   CVQKD   XP   NextField quadratures    Classical field    Electromagnetic fi...
Intro.   Cont. Var.   Information Theory         CVQKD          XP            NextHomodyne Detection : Theory             ...
Intro.          Cont. Var.   Information Theory   CVQKD   XP   Next         1   Introduction                Prefect Secrec...
Intro.         Cont. Var.   Information Theory   CVQKD   XP       NextXXth century CVQKD         At the end of XXth centur...
Intro.         Cont. Var.   Information Theory   CVQKD   XP       NextXXth century CVQKD         At the end of XXth centur...
Intro.         Cont. Var.   Information Theory   CVQKD   XP       NextXXth century CVQKD         At the end of XXth centur...
Intro.         Cont. Var.   Information Theory   CVQKD     XP   NextWhere are the bits ?         Quite frequent discussion...
Intro.         Cont. Var.   Information Theory   CVQKD     XP       NextWhere are the bits ?         Quite frequent discus...
Intro.         Cont. Var.   Information Theory   CVQKD     XP       NextWhere are the bits ?         Quite frequent discus...
Intro.         Cont. Var.    Information Theory   CVQKD   XP   NextThey’re hidden         Availaible informationin a conti...
Intro.          Cont. Var.       Information Theory   CVQKD   XP   NextThey’re hidden         Availaible informationin a c...
Intro.          Cont. Var.       Information Theory         CVQKD       XP         NextThey’re hidden         Availaible i...
Intro.          Cont. Var.       Information Theory          CVQKD             XP          NextThey’re hidden         Avai...
Intro.          Cont. Var.   Information Theory   CVQKD   XP   Next         1   Introduction                Prefect Secrec...
Intro.          Cont. Var.      Information Theory   CVQKD   XP   NextThe spy’s power         Heisenberg :              ∆B...
Intro.          Cont. Var.      Information Theory   CVQKD   XP   NextThe spy’s power         Heisenberg :              ∆B...
Intro.         Cont. Var.    Information Theory   CVQKD      XP         NextQuantum Key Distribution Protocols         Cha...
Intro.         Cont. Var.    Information Theory   CVQKD       XP          NextQuantum Key Distribution Protocols         C...
Intro.         Cont. Var.    Information Theory   CVQKD         XP          NextQuantum Key Distribution Protocols        ...
Intro.         Cont. Var.   Information Theory   CVQKD   XP    NextTheoretical Progresses in the last 10 years         We ...
Intro.         Cont. Var.   Information Theory   CVQKD   XP     NextTheoretical Progresses in the last 10 years         We...
Intro.         Cont. Var.   Information Theory   CVQKD   XP     NextTheoretical Progresses in the last 10 years         We...
Intro.         Cont. Var.    Information Theory   CVQKD   XP    NextTheoretical Progresses in the last 10 years         We...
Intro.         Cont. Var.    Information Theory   CVQKD   XP    NextTheoretical Progresses in the last 10 years         We...
Intro.          Cont. Var.   Information Theory   CVQKD   XP   Next         1   Introduction                Prefect Secrec...
Intro.         Cont. Var.    Information Theory   CVQKD     XP   Next1st generation demonstratorF. Grosshans et. al., Natu...
Intro.   Cont. Var.   Information Theory   CVQKD   XP   NextIntegrated system
Intro.   Cont. Var.   Information Theory   CVQKD   XP   NextIntegrated system
Intro.   Cont. Var.   Information Theory   CVQKD   XP   NextIntegrated system
Intro.   Cont. Var.   Information Theory   CVQKD   XP   NextKey-Rates
Intro.              Cont. Var.          Information Theory                          CVQKD        XP        NextKey-Rates  ...
Intro.   Cont. Var.   Information Theory   CVQKD   XP   NextKey-Rates
Intro.                 Cont. Var.                        Information Theory                          CVQKD             XP ...
Intro.   Cont. Var.   Information Theory   CVQKD   XP   NextIntegration with classical cryptography
Intro.   Cont. Var.   Information Theory   CVQKD   XP   NextIntegration with classical cryptography
Intro.          Cont. Var.   Information Theory   CVQKD   XP   Next         1   Introduction                Prefect Secrec...
Intro.      Cont. Var.     Information Theory   CVQKD   XP     NextOpen Problems         Finite size effects         Link ...
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Continuous variables quantum cryptography

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Continuous variables quantum cryptography

  1. 1. Intro. Cont. Var. Information Theory CVQKD XP Next Continuous Variable Quantum Cryptography Towards High Speed Quantum Cryptography Frédéric Grosshans CNRS / ENS Cachan Palacký University, Olomouc, 2011
  2. 2. Intro. Cont. Var. Information Theory CVQKD XP Next 1 Introduction Prefect Secrecy and Quantum Cryptography Various Secure Systems 2 Continuous variables Field quadratures Homodyne Detection : Theory 3 Information Theory XXth century CVQKD Where are the bits ? 4 Continuous Variable Quantum Key Distribution Spying Protocols 5 Experimental systems 1st and 2nd generation demonstrators Key-Rates Integration with classical cryptography 6 Open problems
  3. 3. Intro. Cont. Var. Information Theory CVQKD XP NextConditions for Perfect Secrecy Alice sends a secret message to Bob
  4. 4. Intro. Cont. Var. Information Theory CVQKD XP NextConditions for Perfect Secrecy Alice sends a secret message to Bob through a channel observed by Eve.
  5. 5. Intro. Cont. Var. Information Theory CVQKD XP NextConditions for Perfect Secrecy Alice sends a secret message to Bob through a channel observed by Eve. She encrypts the message with a secret key
  6. 6. Intro. Cont. Var. Information Theory CVQKD XP NextConditions for Perfect Secrecy Alice sends a secret message to Bob through a channel observed by Eve. She encrypts the message with a secret key as long as the message.
  7. 7. Intro. Cont. Var. Information Theory CVQKD XP NextQuantum Key Distribution Alice sends quantum objects to Bob
  8. 8. Intro. Cont. Var. Information Theory CVQKD XP NextQuantum Key Distribution Alice sends quantum objects to Bob Eve’s Measurenents
  9. 9. Intro. Cont. Var. Information Theory CVQKD XP NextQuantum Key Distribution Alice sends quantum objects to Bob Eve’s Measurenents ⇒ measurable perturbations ⇒ secret key generation
  10. 10. Intro. Cont. Var. Information Theory CVQKD XP NextUnconditionnally Secure Systems . . . Single Photon QKD Long Range (∼ 100 km) Low rate (kbit/s)
  11. 11. Intro. Cont. Var. Information Theory CVQKD XP NextUnconditionnally Secure Systems . . . Single Photon QKD Long Range (∼ 100 km) Low rate (kbit/s) maybe a few Mbit/s in the long run
  12. 12. Intro. Cont. Var. Information Theory CVQKD XP NextUnconditionnally Secure Systems . . . Single Photon QKD Long Range (∼ 100 km) Low rate (kbit/s) maybe a few Mbit/s in the long run Classical One-Time-Pad Very Long Range (Paris–Olomouc) Not so small rate :
  13. 13. Intro. Cont. Var. Information Theory CVQKD XP NextUnconditionnally Secure Systems . . . Single Photon QKD Long Range (∼ 100 km) Low rate (kbit/s) maybe a few Mbit/s in the long run Classical One-Time-Pad Very Long Range (Paris–Olomouc) Not so small rate : 1 CD / year = 180 bits/s
  14. 14. Intro. Cont. Var. Information Theory CVQKD XP NextUnconditionnally Secure Systems . . . Single Photon QKD Long Range (∼ 100 km) Low rate (kbit/s) maybe a few Mbit/s in the long run Classical One-Time-Pad Very Long Range (Paris–Olomouc) Not so small rate : 1 CD / year = 180 bits/s 1 iPod (160 GB)/ year = 40 kbit/s
  15. 15. Intro. Cont. Var. Information Theory CVQKD XP NextUnconditionnally Secure Systems . . . Single Photon QKD Long Range (∼ 100 km) Low rate (kbit/s) maybe a few Mbit/s in the long run Classical One-Time-Pad Very Long Range (Paris–Olomouc) Not so small rate : 1 CD / year = 180 bits/s 1 iPod (160 GB)/ year = 40 kbit/s But the data has to stay here
  16. 16. Intro. Cont. Var. Information Theory CVQKD XP Next. . . and Continuous Variable Medium Range :∼ 25 km Medium Rate :∼ a few kbit/s
  17. 17. Intro. Cont. Var. Information Theory CVQKD XP Next. . . and Continuous Variable Medium Range :∼ 25 km Medium Rate :∼ a few kbit/s Much less mature
  18. 18. Intro. Cont. Var. Information Theory CVQKD XP Next. . . and Continuous Variable Medium Range :∼ 25 km ; 80 km soon ? Medium Rate :∼ a few kbit/s ; Mbits/s soon ? Much less mature ⇒ Much room for improvements
  19. 19. Intro. Cont. Var. Information Theory CVQKD XP Next 1 Introduction Prefect Secrecy and Quantum Cryptography Various Secure Systems 2 Continuous variables Field quadratures Homodyne Detection : Theory 3 Information Theory XXth century CVQKD Where are the bits ? 4 Continuous Variable Quantum Key Distribution Spying Protocols 5 Experimental systems 1st and 2nd generation demonstrators Key-Rates Integration with classical cryptography 6 Open problems
  20. 20. Intro. Cont. Var. Information Theory CVQKD XP NextField quadratures Classical field Electromagnetic field described by QA and PA E(t) = QA cos ωt + PA sin ωt
  21. 21. Intro. Cont. Var. Information Theory CVQKD XP NextField quadratures Classical field Electromagnetic field described by QA and PA E(t) = QA cos ωt + PA sin ωt Quantum description Q and P do not commute: [Q, P] ∝ i . Add a “quantum noise”: Q = QA + BQ et P = PA + BP Heisenberg =⇒ ∆BQ ∆BP ≥ 1
  22. 22. Intro. Cont. Var. Information Theory CVQKD XP NextHomodyne 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 cos ϕ + Psignal sin ϕ)
  23. 23. Intro. Cont. Var. Information Theory CVQKD XP Next 1 Introduction Prefect Secrecy and Quantum Cryptography Various Secure Systems 2 Continuous variables Field quadratures Homodyne Detection : Theory 3 Information Theory XXth century CVQKD Where are the bits ? 4 Continuous Variable Quantum Key Distribution Spying Protocols 5 Experimental systems 1st and 2nd generation demonstrators Key-Rates Integration with classical cryptography 6 Open problems
  24. 24. Intro. Cont. Var. Information Theory CVQKD XP NextXXth century CVQKD At the end of XXth century it was obvious that a generalization of QKD to continuous variables could be interesting. Problem : discrete bits continuous variable
  25. 25. Intro. Cont. Var. Information Theory CVQKD XP NextXXth century CVQKD At the end of XXth century it was obvious that a generalization of QKD to continuous variables could be interesting. Problem : discrete bits continuous variable Adapting BB84? Mark Hillery, “Quantum Cryptography with Squeezed States”, arXiv:quant-ph/9909006/PRA 61 022309
  26. 26. Intro. Cont. Var. Information Theory CVQKD XP NextXXth century CVQKD At the end of XXth century it was obvious that a generalization of QKD to continuous variables could be interesting. Problem : discrete bits continuous variable Natural modulation + information theory! Nicolas J. Cerf, Marc Lévy, Gilles Van Assche : “Quantum distribution of Gaussian keys using squeezed states”, arXiv:quant-ph/0008058/PRL 63 052311
  27. 27. Intro. Cont. Var. Information Theory CVQKD XP NextWhere are the bits ? Quite frequent discussion with discrete quantum cryptographers : 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.”
  28. 28. Intro. Cont. Var. Information Theory CVQKD XP NextWhere are the bits ? Quite frequent discussion with discrete quantum cryptographers : DQC : How do you encode a 0 or a 1 in CVQKD? Me : Gilles/Jérôme/Anthony/Sébastien developed a really efficient code, using sliced reconciliation/LDPC matrices/R8 rotations and octonions. Only he knows how it works.
  29. 29. Intro. Cont. Var. Information Theory CVQKD XP NextWhere are the bits ? Quite frequent discussion with discrete quantum cryptographers : DQC : How do you encode a 0 or a 1 in CVQKD? Me : Gilles/Jérôme/Anthony/Sébastien developed a really efficient code, using sliced reconciliation/LDPC matrices/R8 rotations and octonions. Only he knows how it works. Computation of the ideal code performance is easy !
  30. 30. Intro. Cont. Var. Information Theory CVQKD XP NextThey’re hidden Availaible informationin a continuous signal
  31. 31. Intro. Cont. Var. Information Theory CVQKD XP NextThey’re hidden Availaible informationin a continuous signal Differential entropy H(X) = − P(x) dx log P(x) dx dx P(x) log P(x) − log dx H(X) constante
  32. 32. Intro. Cont. Var. Information Theory CVQKD XP NextThey’re hidden Availaible informationin a continuous signal with noise ? Differential entropy H(X) = − P(x) dx log P(x) dx H(X) = log ∆X + constante dx P(x) log P(x) − log dx H(X) constante
  33. 33. Intro. Cont. Var. Information Theory CVQKD XP NextThey’re hidden Availaible informationin a continuous signal with noise ? Differential entropy Mutual information I(X : Y) = H(Y) − H(Y|X) H(X) = − P(x) dx log P(x) dx = H(Y) − H(Y|X) dx P(x) log P(x) − log dx ∆Y2 = 1 log H(X) constante 2 ∆Y2 |X
  34. 34. Intro. Cont. Var. Information Theory CVQKD XP Next 1 Introduction Prefect Secrecy and Quantum Cryptography Various Secure Systems 2 Continuous variables Field quadratures Homodyne Detection : Theory 3 Information Theory XXth century CVQKD Where are the bits ? 4 Continuous Variable Quantum Key Distribution Spying Protocols 5 Experimental systems 1st and 2nd generation demonstrators Key-Rates Integration with classical cryptography 6 Open problems
  35. 35. Intro. Cont. Var. Information Theory CVQKD XP NextThe spy’s power Heisenberg : ∆BEve ∆BBob ≥ 1
  36. 36. Intro. Cont. Var. Information Theory CVQKD XP NextThe spy’s power Heisenberg : ∆BEve ∆BBob ≥ 1 ⇒ ∆BBob gives IEve IBob
  37. 37. Intro. Cont. Var. Information Theory CVQKD XP NextQuantum Key Distribution Protocols Channel Evauation (noise measure) Alice&Bob evaluate IEve
  38. 38. Intro. Cont. Var. Information Theory CVQKD XP NextQuantum Key Distribution Protocols Channel Evauation (noise measure) Alice&Bob evaluate IEve Reconciliation (error correction) Alice&Bob share IBob identical bits. Ève knows IEve .
  39. 39. Intro. Cont. Var. Information Theory CVQKD XP NextQuantum Key Distribution Protocols Channel Evauation (noise measure) Alice&Bob evaluate IEve Reconciliation (error correction) Alice&Bob share IBob identical bits. Ève knows IEve . Privacy Amplification Alice&Bob share IBob − IEve identical bits. Ève knows ∼ 0.
  40. 40. Intro. Cont. Var. Information Theory CVQKD XP NextTheoretical Progresses in the last 10 years We went from a protocol using squeezed states, insecure beyond 50% losses (15 km), proved secure against Gaussian individual attack
  41. 41. Intro. Cont. Var. Information Theory CVQKD XP NextTheoretical Progresses in the last 10 years We went from a protocol using squeezed states, insecure beyond 50% losses (15 km), proved secure against Gaussian individual attack to a protocol using coherent states
  42. 42. Intro. Cont. Var. Information Theory CVQKD XP NextTheoretical Progresses in the last 10 years We went from a protocol using squeezed states, insecure beyond 50% losses (15 km), proved secure against Gaussian individual attack to a protocol using coherent states with no fundamental range limit proved secure against collective attacks
  43. 43. Intro. Cont. Var. Information Theory CVQKD XP NextTheoretical Progresses in the last 10 years We went from a protocol using squeezed states, insecure beyond 50% losses (15 km), proved secure against Gaussian individual attack to a protocol using coherent states with no fundamental range limit proved secure against collective attacks likely secure against coherent attacks
  44. 44. Intro. Cont. Var. Information Theory CVQKD XP NextTheoretical Progresses in the last 10 years We went from a protocol using squeezed states, insecure beyond 50% losses (15 km), proved secure against Gaussian individual attack to a protocol using coherent states with no fundamental range limit proved secure against collective attacks likely secure against coherent attacks and experimentally working
  45. 45. Intro. Cont. Var. Information Theory CVQKD XP Next 1 Introduction Prefect Secrecy and Quantum Cryptography Various Secure Systems 2 Continuous variables Field quadratures Homodyne Detection : Theory 3 Information Theory XXth century CVQKD Where are the bits ? 4 Continuous Variable Quantum Key Distribution Spying Protocols 5 Experimental systems 1st and 2nd generation demonstrators Key-Rates Integration with classical cryptography 6 Open problems
  46. 46. Intro. Cont. Var. Information Theory CVQKD XP Next1st generation demonstratorF. Grosshans et. al., Nature (2003) & Brevet US m Key rate 75 kbit/s 3.1 dB (51%) losses 1.7 Mbit/s without losses
  47. 47. Intro. Cont. Var. Information Theory CVQKD XP NextIntegrated system
  48. 48. Intro. Cont. Var. Information Theory CVQKD XP NextIntegrated system
  49. 49. Intro. Cont. Var. Information Theory CVQKD XP NextIntegrated system
  50. 50. Intro. Cont. Var. Information Theory CVQKD XP NextKey-Rates
  51. 51. Intro. Cont. Var. Information Theory CVQKD XP NextKey-Rates SECOQC Performance 100 kb/s (2008) L Exce osses o ss n n 95% oise ly effi 90 cie % nt c eff ode ici 10 kb/s Slo en t w co co de de 1 kb/s 0k 10 20 30 40 50 km km km km km m
  52. 52. Intro. Cont. Var. Information Theory CVQKD XP NextKey-Rates
  53. 53. Intro. Cont. Var. Information Theory CVQKD XP NextKey-Rates SECOQC Performance 100 kb/s (2008) L Exce osses o ss n n 95% oise ly Increases modulation rate : effi 90 cie ×10 easy, ×100 doable % nt c eff ode ici 10 kb/s Slo en t w co co de de use modern codes : ocotonion based protocol us +multi-edge LDPC codes eG + repetition codes PU s 1 kb/s 0k 10 20 30 40 50 km km km km km m
  54. 54. Intro. Cont. Var. Information Theory CVQKD XP NextIntegration with classical cryptography
  55. 55. Intro. Cont. Var. Information Theory CVQKD XP NextIntegration with classical cryptography
  56. 56. Intro. Cont. Var. Information Theory CVQKD XP Next 1 Introduction Prefect Secrecy and Quantum Cryptography Various Secure Systems 2 Continuous variables Field quadratures Homodyne Detection : Theory 3 Information Theory XXth century CVQKD Where are the bits ? 4 Continuous Variable Quantum Key Distribution Spying Protocols 5 Experimental systems 1st and 2nd generation demonstrators Key-Rates Integration with classical cryptography 6 Open problems
  57. 57. Intro. Cont. Var. Information Theory CVQKD XP NextOpen Problems Finite size effects Link with post-selection based protocols (.de, .au) Side-channels and quantum hacking Other cryptographic applications

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