Quantum-Secure Coin-Flipping and Applications

  • Ivan Damgård
  • Carolin Lunemann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5912)

Abstract

In this paper, we prove classical coin-flipping secure in the presence of quantum adversaries. The proof uses a recent result of Watrous [20] that allows quantum rewinding for protocols of a certain form. We then discuss two applications. First, the combination of coin-flipping with any non-interactive zero-knowledge protocol leads to an easy transformation from non-interactive zero-knowledge to interactive quantum zero-knowledge. Second, we discuss how our protocol can be applied to a recently proposed method for improving the security of quantum protocols [4], resulting in an implementation without set-up assumptions. Finally, we sketch how to achieve efficient simulation for an extended construction in the common-reference-string model.

Keywords

quantum cryptography coin-flipping common reference string quantum zero-knowledge 

References

  1. 1.
    Bennett, C.H., Brassard, G., Crépeau, C., Skubiszewska, M.-H.: Practical quantum oblivious transfer. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 351–366. Springer, Heidelberg (1992)Google Scholar
  2. 2.
    Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications (extended abstract). In: 20th Annual ACM Symposium on Theory of Computing (STOC), pp. 103–112 (1988)Google Scholar
  3. 3.
    Canetti, R., Fischlin, M.: Universally Composable Commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Damgård, I.B., Fehr, S., Lunemann, C., Salvail, L., Schaffner, C.: Improving the security of quantum protocols via commit-and-open. In: Halevi, S. (ed.) Advances in Cryptology—CRYPTO 2009. LNCS, vol. 5677, pp. 408–427. Springer, Heidelberg (2009), http://arxiv.org/abs/0902.3918 CrossRefGoogle Scholar
  5. 5.
    Damgård, I.B., Fehr, S., Salvail, L.: Zero-knowledge proofs and string commitments withstanding quantum attacks. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 254–272. Springer, Heidelberg (2004)Google Scholar
  6. 6.
    Damgård, I.B., Fehr, S., Salvail, L., Schaffner, C.: Secure identification and QKD in the bounded-quantum-storage model. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 342–359. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Damgård, I.B., Goldreich, O., Wigderson, A.: Hashing functions can simplify zero-knowledge protocol design (too). Technical Report RS-94-39, BRICS, Department of Computer Science, Aarhus University, Denmark (1994)Google Scholar
  8. 8.
    Fehr, S., Schaffner, C.: Composing quantum protocols in a classical environment. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 350–367. Springer, Heidelberg (2009)Google Scholar
  9. 9.
    Goldreich, O.: Foundations of Cryptography. Basic Tools, vol. I. Cambridge University Press, Cambridge (2001)MATHGoogle Scholar
  10. 10.
    Goldreich, O.: Zero-knowledge twenty years after its invention (2002), http://www.wisdom.weizmann.ac.il/~oded/papers.html
  11. 11.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems (extended abstract). In: 17th Annual ACM Symposium on Theory of Computing (STOC), pp. 291–304 (1985)Google Scholar
  12. 12.
    van de Graaf, J.: Towards a formal definition of security for quantum protocols. PhD thesis, Université de Montréal (1997)Google Scholar
  13. 13.
    Hallgren, S., Kolla, A., Sen, P., Zhang, S.: Making classical honest verifier zero knowledge protocols secure against quantum attacks. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 592–603. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Kobayashi, H.: Non-interactive quantum perfect and statistical zero-knowledge. In: Ibaraki, T., Katoh, N., Ono, H. (eds.) ISAAC 2003. LNCS, vol. 2906, pp. 178–188. Springer, Heidelberg (2003)Google Scholar
  15. 15.
    Naor, M.: Bit commitment using pseudorandomness. Journal of Cryptology 4(2), 151–158 (1991)MATHCrossRefGoogle Scholar
  16. 16.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  17. 17.
    Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008)Google Scholar
  18. 18.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 84–93 (2005)Google Scholar
  19. 19.
    Watrous, J.: Limits on the power of quantum statistical zero-knowledge. In: 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 459–468 (2002)Google Scholar
  20. 20.
    Watrous, J.: Zero-knowledge against quantum attacks. SIAM Journal on Computing 39.1, 25–58 (2009); Preliminary version in 38th Annual ACM Symposium on Theory of Computing (STOC), pp. 296–305 (2006)Google Scholar
  21. 21.
    Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299, 802–803 (1982)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ivan Damgård
    • 1
  • Carolin Lunemann
    • 1
  1. 1.DAIMIAarhus UniversityDenmark

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