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Security Bounds for Quantum Cryptography with Finite Resources

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Theory of Quantum Computation, Communication, and Cryptography (TQC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5106))

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Abstract

A practical quantum key distribution (QKD) protocol necessarily runs in finite time and, hence, only a finite amount of communication is exchanged. This is in contrast to most of the standard results on the security of QKD, which only hold in the limit where the number of transmitted signals approaches infinity. Here, we analyze the security of QKD under the realistic assumption that the amount of communication is finite. At the level of the general formalism, we present new results that help simplifying the actual implementation of QKD protocols: in particular, we show that symmetrization steps, which are required by certain security proofs (e.g., proofs based on de Finetti’s representation theorem), can be omitted in practical implementations. Also, we demonstrate how two-way reconciliation protocols can be taken into account in the security analysis. At the level of numerical estimates, we present the bounds with finite resources for “device-independent security” against collective attacks.

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References

  1. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Rev. Mod. Phys. 74, 145 (2002)

    Google Scholar 

  2. Dušek, M., Lütkenhaus, N., Hendrych, M.: Progress in Optics, Edt. E. Wolf, vol. 49, p. 381. Elsevier, Amsterdam (2007)

    Google Scholar 

  3. Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: arXiv:0802.4155v1

    Google Scholar 

  4. Shor, P.W., Preskill, J.: Phys. Rev. Lett. 85, 441 (2000)

    Google Scholar 

  5. Mayers, D.: Journal of the ACM  48, 351 (2001); and quant-ph/9802025

    Google Scholar 

  6. Lo, H.-K., Chau, H.F.: Science.  283, 2050 (1999)

    Google Scholar 

  7. Koashi, M.: quant-ph/0505108

    Google Scholar 

  8. Ben-Or, M.: Security of BB84 QKD Protocol, http://www.msri.org/publications/ln/msri/2002/quantumintro/ben-or/2/

  9. Devetak, I., Winter, A.: Proc. R. Soc. Lond. A  461, 207 (2005)

    Google Scholar 

  10. Inamori, H., Lütkenhaus, N., Mayers, D.: Eur. J. Phys. D 41, 599 (2007) and quant-ph/0107017

    Google Scholar 

  11. König, R., Renner, R., Bariska, A., Maurer, U.: Phys. Rev. Lett.  98, 140502 (2007)

    Google Scholar 

  12. Renner, R., König, R.: Second Theory of Cryptography Conference TCC. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378. Springer, Heidelberg (2005)

    Google Scholar 

  13. Meyer, T., Kampermann, H., Kleinmann, M., Bruß, D.: Phys. Rev. A 74, 042340 (2006)

    Google Scholar 

  14. Lo, H.-K., Chau, H.F., Ardehali, M.: J. Cryptology.  18, 133 (2005) and quant-ph/9803007

    Google Scholar 

  15. Ma, X., Qi, B., Zhao, Y., Lo, H.-K.: Phys. Rev. A.  72, 012326 (2005)

    Google Scholar 

  16. Wang, X.-B.: Phys. Rev. Lett. 94, 230503 (2005)

    Google Scholar 

  17. Hayashi, M.: Phys. Rev. A 76, 012329 (2007)

    Google Scholar 

  18. Hasegawa, J., Hayashi, M., Hiroshima, T., Tanaka, A., Tomita, A.: arXiv:0705.3081

    Google Scholar 

  19. Renner, R.: Security of Quantum Key Distribution, PhD thesis, Diss. ETH No 16242, quant-ph/0512258

    Google Scholar 

  20. Scarani, V., Renner, R.: arXiv:0708.0709v1

    Google Scholar 

  21. Ben-Or, M., Horodecki, M., Leung, D.W., Mayers, D., Oppenheim, J.: Theory of Cryptography. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 386–406. Springer, Heidelberg (2005) (quant-ph/0409078)

    Google Scholar 

  22. Brassard, G., Salvail, L.: Advances in Cryptology - EUROCRYPT 1993. LNCS, vol. 765, pp. 410–423. Springer, Heidelberg (1994)

    Google Scholar 

  23. Renner, R.: Nature Physics  3, 645 (2007)

    Google Scholar 

  24. Bennett, C.H., Brassard, G.: Proceedings IEEE Int. Conf. on Computers, Systems and Signal Processing, Bangalore, India, pp. 175–179. IEEE, New York (1984)

    Google Scholar 

  25. Bennett, C.H., Brassard, G., Breidbart, S., Wiesner, S.: IBM Technical Disclosure Bulletin. 26, 4363 (1984)

    Google Scholar 

  26. Bruß, D.: Phys. Rev. Lett.  81, 3018 (1998)

    Google Scholar 

  27. Bechmann-Pasquinucci, H., Gisin, N.: Phys. Rev. A 59, 4238 (1999)

    Google Scholar 

  28. Gottesman, D., Lo, H.-K.: IEEE Trans. Inf. Theory 49, 457 (2003)

    Google Scholar 

  29. Kraus, B., Gisin, N., Renner, R.: Phys. Rev. Lett.  95, 080501 (2005); Renner, R., Gisin, N., Kraus, B.: Phys. Rev. A.  72, 012332 (2005)

    Google Scholar 

  30. Carter, J.L., Wegman, M.N.: Journal of Computer and System Sciences  18, 143 (1979)

    Google Scholar 

  31. Wegman, M.N., Carter, J.L.: Journal of Computer and System Sciences 22, 265 (1981)

    Google Scholar 

  32. Ekert, A.K.: Phys. Rev. Lett. 67, 661 (1991)

    Google Scholar 

  33. Acín, A., Massar, S., Pironio, S.: New J. Phys. 8, 126 (2006)

    Google Scholar 

  34. Acín, A., Brunner, N., Gisin, N., Massar, S., Pironio, S., Scarani, V.: Phys. Rev. Lett. 98, 230501 (2007)

    Google Scholar 

  35. Zhao, Y., Fung, C.-H.F., Qi, B., Chen, C., Lo, H.-K.: arXiv:0704.3253

    Google Scholar 

  36. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Phys. Rev. Lett. 23, 880 (1969)

    Google Scholar 

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Authors and Affiliations

  1. Centre for Quantum Technologies and Department of Physics, National University of Singapore, Singapore

    Valerio Scarani

  2. Institute for Theoretical Physics, ETH Zurich, Switzerland

    Renato Renner

Authors
  1. Valerio Scarani
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  2. Renato Renner
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Editors and Affiliations

  1. NTT Communication Science Laboratories, 3-1, Morinosato Wakamiya, Atsugi-shi, 243-0198, Kanagawa Pref., Japan

    Yasuhito Kawano

  2. Institute for Quantum Computing, University of Waterloo, N2L 3G1, Waterloo, ON, Canada

    Michele Mosca

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Scarani, V., Renner, R. (2008). Security Bounds for Quantum Cryptography with Finite Resources. In: Kawano, Y., Mosca, M. (eds) Theory of Quantum Computation, Communication, and Cryptography. TQC 2008. Lecture Notes in Computer Science, vol 5106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89304-2_8

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  • DOI: https://doi.org/10.1007/978-3-540-89304-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89303-5

  • Online ISBN: 978-3-540-89304-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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