Security Bounds for Quantum Cryptography with Finite Resources

  • Valerio Scarani
  • Renato Renner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5106)


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.


Quantum Cryptography Security Proof Finite Resource Error Correction Scheme Collective Attack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Rev. Mod. Phys. 74, 145 (2002)Google Scholar
  2. 2.
    Dušek, M., Lütkenhaus, N., Hendrych, M.: Progress in Optics, Edt. E. Wolf, vol. 49, p. 381. Elsevier, Amsterdam (2007)Google Scholar
  3. 3.
    Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: arXiv:0802.4155v1Google Scholar
  4. 4.
    Shor, P.W., Preskill, J.: Phys. Rev. Lett. 85, 441 (2000)Google Scholar
  5. 5.
    Mayers, D.: Journal of the ACM  48, 351 (2001); and quant-ph/9802025Google Scholar
  6. 6.
    Lo, H.-K., Chau, H.F.: Science.  283, 2050 (1999)Google Scholar
  7. 7.
    Koashi, M.: quant-ph/0505108Google Scholar
  8. 8.
  9. 9.
    Devetak, I., Winter, A.: Proc. R. Soc. Lond. A  461, 207 (2005)Google Scholar
  10. 10.
    Inamori, H., Lütkenhaus, N., Mayers, D.: Eur. J. Phys. D 41, 599 (2007) and quant-ph/0107017Google Scholar
  11. 11.
    König, R., Renner, R., Bariska, A., Maurer, U.: Phys. Rev. Lett.  98, 140502 (2007)Google Scholar
  12. 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. 13.
    Meyer, T., Kampermann, H., Kleinmann, M., Bruß, D.: Phys. Rev. A 74, 042340 (2006)Google Scholar
  14. 14.
    Lo, H.-K., Chau, H.F., Ardehali, M.: J. Cryptology.  18, 133 (2005) and quant-ph/9803007Google Scholar
  15. 15.
    Ma, X., Qi, B., Zhao, Y., Lo, H.-K.: Phys. Rev. A.  72, 012326 (2005)Google Scholar
  16. 16.
    Wang, X.-B.: Phys. Rev. Lett. 94, 230503 (2005)Google Scholar
  17. 17.
    Hayashi, M.: Phys. Rev. A 76, 012329 (2007)Google Scholar
  18. 18.
    Hasegawa, J., Hayashi, M., Hiroshima, T., Tanaka, A., Tomita, A.: arXiv:0705.3081Google Scholar
  19. 19.
    Renner, R.: Security of Quantum Key Distribution, PhD thesis, Diss. ETH No 16242, quant-ph/0512258Google Scholar
  20. 20.
    Scarani, V., Renner, R.: arXiv:0708.0709v1Google Scholar
  21. 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. 22.
    Brassard, G., Salvail, L.: Advances in Cryptology - EUROCRYPT 1993. LNCS, vol. 765, pp. 410–423. Springer, Heidelberg (1994)Google Scholar
  23. 23.
    Renner, R.: Nature Physics  3, 645 (2007)Google Scholar
  24. 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. 25.
    Bennett, C.H., Brassard, G., Breidbart, S., Wiesner, S.: IBM Technical Disclosure Bulletin. 26, 4363 (1984)Google Scholar
  26. 26.
    Bruß, D.: Phys. Rev. Lett.  81, 3018 (1998)Google Scholar
  27. 27.
    Bechmann-Pasquinucci, H., Gisin, N.: Phys. Rev. A 59, 4238 (1999)Google Scholar
  28. 28.
    Gottesman, D., Lo, H.-K.: IEEE Trans. Inf. Theory 49, 457 (2003)Google Scholar
  29. 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. 30.
    Carter, J.L., Wegman, M.N.: Journal of Computer and System Sciences  18, 143 (1979)Google Scholar
  31. 31.
    Wegman, M.N., Carter, J.L.: Journal of Computer and System Sciences 22, 265 (1981)Google Scholar
  32. 32.
    Ekert, A.K.: Phys. Rev. Lett. 67, 661 (1991)Google Scholar
  33. 33.
    Acín, A., Massar, S., Pironio, S.: New J. Phys. 8, 126 (2006)Google Scholar
  34. 34.
    Acín, A., Brunner, N., Gisin, N., Massar, S., Pironio, S., Scarani, V.: Phys. Rev. Lett. 98, 230501 (2007)Google Scholar
  35. 35.
    Zhao, Y., Fung, C.-H.F., Qi, B., Chen, C., Lo, H.-K.: arXiv:0704.3253Google Scholar
  36. 36.
    Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Phys. Rev. Lett. 23, 880 (1969)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Valerio Scarani
    • 1
  • Renato Renner
    • 2
  1. 1.Centre for Quantum Technologies and Department of PhysicsNational University of SingaporeSingapore
  2. 2.Institute for Theoretical PhysicsETH ZurichSwitzerland

Personalised recommendations