Abstract
In this work, we study formalization and construction of non-interactive statistically binding quantum bit commitment scheme (QBC), as well as its application in quantum zero-knowledge (QZK) proof. We explore the fully quantum model, where both computation and communication could be quantum. While most of the proofs here are straightforward based on previous works, we have two technical contributions. First, we show how to use reversibility of quantum computation to construct non-interactive QBC. Second, we identify new issue caused by quantum binding in security analysis and give our idea to circumvent it, which may be found useful elsewhere.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Hiding an binding properties cannot be simultaneously information-theoretic secure either [13].
References
Adcock, M., Cleve, R.: A quantum goldreich-levin theorem with cryptographic applications. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 323–334. Springer, Heidelberg (2002)
Ambainis, A., Rosmanis, A., Unruh, D.: Quantum attacks on classical proof systems: the hardness of quantum rewinding. In: FOCS, pp. 474–483 (2014)
Blum, M.: How to prove a theorem so no one else can claim it. In: Proceedings of the International Congress of Mathematicians, vol. 1, p. 2 (1986)
Chailloux, A., Kerenidis, I., Rosgen, B.: Quantum commitments from complexity assumptions. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 73–85. Springer, Heidelberg (2011)
Crépeau, C., Dumais, P., Mayers, D., Salvail, L.: Computational collapse of quantum state with application to oblivious transfer. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 374–393. Springer, Heidelberg (2004)
Dumais, P., Mayers, D., Salvail, L.: Perfectly concealing quantum bit commitment from any quantum one-way permutation. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 300–315. Springer, Heidelberg (2000)
Goldreich, O.: Foundations of Cryptography, Basic Tools, vol. I. Cambridge University Press, Cambridge (2001)
Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity for all languages in NP have zero-knowledge proof systems. J. ACM 38(3), 691–729 (1991)
Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)
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)
Kobayashi, H.: General properties of quantum zero-knowledge proofs. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 107–124. Springer, Heidelberg (2008)
Lin, D., Quan, Y., Weng, J., Yan, J.: Quantum bit commitment with application in quantum zero-knowledge proof. Cryptology ePrint Archive, Report 2014/791, this is a preliminary version; the final full version is in preparation
Mayers, D.: Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett. 78(17), 3414–3417 (1997)
Naor, M.: Bit commitment using pseudorandomness. J. Cryptology 4(2), 151–158 (1991)
Nielsen, M.A., Chuang, I.L.: Quantum computation and Quantum Informatioin. Cambridge University Press, Cambridge (2000)
Ong, S.J., Vadhan, S.P.: An equivalence between zero knowledge and commitments. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 482–500. Springer, Heidelberg (2008)
Unruh, D.: Quantum proofs of knowledge. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 135–152. Springer, Heidelberg (2012)
Vadhan, S.P.: An unconditional study of computational zero knowledge. SIAM J. Comput. 36(4), 1160–1214 (2006)
Watrous, J.: Limits on the power of quantum statistical zero-knowledge. In: FOCS, pp. 459–468 (2002)
Watrous, J.: Zero-knowledge against quantum attacks. SIAM J. Comput. 39(1), 25–58 (2009). preliminary version appears in STOC 2006
Yan, J.: Complete problem for perfect zero-knowledge quantum proof. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 419–430. Springer, Heidelberg (2012)
Acknowledgement
We thank Yi Deng for helpful discussion during the progress of this work. Thanks also go to Dominique Unruh and anonymous referees of several conferences for their invaluable insights and comments.
Jun Yan is supported in part by the Fundamental Research Funds for the Central Universities (21615317), by the Open Project Program of the State Key Laboratory of Information Security (2015-MS-08), by the PhD Start-up Fund of Natural Science Foundation of Guangdong Province, China (2014A030310333), and by the National Natural Science Foundation of China (61501207). Jian Weng is supported in part by National Science Foundation of China (61272413, 61133014, 61272415 and 61472165), by Fok Ying Tong Education Foundation (131066), by Program for New Century Excellent Talents in University (NCET-12-0680), by Research Fund for the Doctoral Program of Higher Education of China (20134401110011), by Foundation for Distinguished Young Talents in Higher Education of Guangdong (2012LYM 0027), and by China Scholarship Council. Dongdai Lin is supported in part by National Science Foundation of China (61379139) and by the Strategic Priority Research Program of the Chinese Academy of Science (XDA06010701). Yujuan Quan is supported in part by Special Project on the Integration of Industry, Education and Research of Guangdong Province (2013B090500030) and by Key Technology R&D Program of Guangzhou,China (2014Y2-00133).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yan, J., Weng, J., Lin, D., Quan, Y. (2015). Quantum Bit Commitment with Application in Quantum Zero-Knowledge Proof (Extended Abstract). In: Elbassioni, K., Makino, K. (eds) Algorithms and Computation. ISAAC 2015. Lecture Notes in Computer Science(), vol 9472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48971-0_47
Download citation
DOI: https://doi.org/10.1007/978-3-662-48971-0_47
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-48970-3
Online ISBN: 978-3-662-48971-0
eBook Packages: Computer ScienceComputer Science (R0)