Abstract
We present an approach to automate Shor-Preskill style unconditional security proof of QKDs. In Shor-Preskill’s proof, the target QKD, BB84, is transformed into another QKD based on an entanglement distillation protocol (EDP), which is more feasible for direct analysis. We formalized heir method as program transformation in a quantum programming language, QPL. The transform is defined as rewriting rules which are sound with respect to the security in the semantics of QPL. We proved that rewriting always terminates for any program and that the normal form is unique under appropriate conditions. By applying the rewriting rules to the program representing BB84, we can obtain the corresponding EDP-based protocol automatically. We finally proved the security of the obtained EDP-based protocol formally in the quantum Hoare logic, which is a system for formal verification of quantum programs. We show also that this method can be applied to B92 by a simple modification.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bennett, C.H., Brassard, G.: Quantum cryptography: Public-key distribution and coin tossing. In: IEEE International Conference on Computers, Systems and Signal Processing, pp. 175–179 (1984)
Ekert, A.K.: Quantum cryptography based on bell’s theorem. Phys. Rev. Lett. 67(6), 661–663 (1991)
Bennet, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68(21), 3121–3124 (1992)
Inoue, K., Waks, E., Yamamoto, Y.: Differential phase shift quantum key distribution. Phys. Rev. Lett. 89(3), 037902 (2002)
Stucki, D., Brunner, N., Gisin, N., Scarani, V., Zbinden, H.: Fast and simple one-way quantum key distribution. Appl. Phys. Lett. 87(19), 194108–194108–3 (2005)
Nagy, M., Akl, S.G.: Entanglement verification with an application to quantum key distribution protocols. Parallel Processing Letters, 227–237 (2010)
Mayers, D.: Unconditional security in quantum cryptography. J. ACM 48, 351–406 (2001)
Lo, H.-K., Chau, H.F.: Unconditional security of quantum key distribution over arbitrarily long distances. Phys. Rev. Lett. 283(5410), 2050–2056 (1999)
Shor, P.W., Preskill, J.: Simple proof of security of the bb84 quantum key distribution protocol. Phys. Rev. Lett. 85(2), 441–444 (2000)
Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54(2), 1098–1105 (1996)
Tamaki, K., Koashi, M., Imoto, N.: Unconditionally secure key distribution based on two nonorthogonal states. Phys. Rev. Lett. 90(16), 167904 (2003)
Hwang, W.-Y., Wang, X.-B., Matsumoto, K., Kim, J., Lee, H.-W.: Shor-preskill-type security proof for quantum key distribution without public announcement of bases. Phys. Rev. A 67(1), 012302 (2003)
Blanchet, B., Jaggard, A.D., Scedrov, A., Tsay, J.-K.: Computationally sound mechanized proofs for basic and public-key kerberos. In: Proceedings of the 2008 ACM Symposium on Information, Computer and Communications Security, ASIACCS 2008, pp. 87–99. ACM, New York (2008)
Neuman, C., Yu, T., Hatman, S., Raeburn, K.: The kerberos network authentication service (v5) (July 2005), http://www.ietf.org/rfc/rfc4120
Selinger, P.: Towards a quantum programming language. Mathematical Structures in Computer Science 14, 527–586 (2004)
Kakutani, Y.: A logic for formal verification of quantum programs. In: Datta, A. (ed.) ASIAN 2009. LNCS, vol. 5913, pp. 79–93. Springer, Heidelberg (2009)
Kubota, T.: Formalization and Automation of Unconditional Security Proof of QKD. Master thesis, the University of Tokyo (February 2011)
Nagarajan, R., Papanikolaou, N., Bowen, G., Gay, S.: An Automated Analysis of the Security of Quantum Key Distribution. ArXiv Computer Science e-prints (February 2005)
Lo, H.-K.: Proof of unconditional security of six-state quantum key distribution scheme, http://arxiv.org/cits/quant-ph/0102138
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kubota, T., Kakutani, Y., Kato, G., Kawano, Y. (2011). A Formal Approach to Unconditional Security Proofs for Quantum Key Distribution. In: Calude, C.S., Kari, J., Petre, I., Rozenberg, G. (eds) Unconventional Computation. UC 2011. Lecture Notes in Computer Science, vol 6714. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21341-0_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-21341-0_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21340-3
Online ISBN: 978-3-642-21341-0
eBook Packages: Computer ScienceComputer Science (R0)