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.
Chapter PDF
Similar content being viewed by others
References
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)
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)
Canetti, R., Fischlin, M.: Universally Composable Commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)
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
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)
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)
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)
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)
Goldreich, O.: Foundations of Cryptography. Basic Tools, vol. I. Cambridge University Press, Cambridge (2001)
Goldreich, O.: Zero-knowledge twenty years after its invention (2002), http://www.wisdom.weizmann.ac.il/~oded/papers.html
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)
van de Graaf, J.: Towards a formal definition of security for quantum protocols. PhD thesis, Université de Montréal (1997)
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)
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)
Naor, M.: Bit commitment using pseudorandomness. Journal of Cryptology 4(2), 151–158 (1991)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
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)
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)
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)
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)
Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299, 802–803 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Damgård, I., Lunemann, C. (2009). Quantum-Secure Coin-Flipping and Applications. In: Matsui, M. (eds) Advances in Cryptology – ASIACRYPT 2009. ASIACRYPT 2009. Lecture Notes in Computer Science, vol 5912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10366-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-10366-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10365-0
Online ISBN: 978-3-642-10366-7
eBook Packages: Computer ScienceComputer Science (R0)