On the Security of Quantum Key Distribution Ping-Pong Protocol

Masakazu Yoshida, Takayuki Miyadera, Hideki Imai

Department of Nuclear Engineering, Kyoto University, Kyoto, Japan.
Graduate School of Science and Engineering, Chuo University, Tokyo, Japan.

DOI: 10.4236/jqis.2013.31004                

Abstract

Computational based cryptography might not guarantee long term security if computational algorithms, computers, and so on are made remarkable progress. Therefore, quantum cryptography with unconditionally security attracts attention. In this paper, we consider security of a two-way quantum key distribution protocol, so called Ping-Pong protocol. As a result, we introduce not only robustness but also a different information disturbance theorem, which denotes a trade-off relationship between information gain for an eavesdropper and error rate, from the related works for an attack model.

Keywords

Two-Way Quantum Key Distribution; Ping-Pong Protocol; Robustness; Information Disturbance Theorem

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. W. Shor, “Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer,” SIAM Journal on Computing, Vol. 26, No. 5, 1997, pp. 1484-1509. doi:10.1137/S0097539795293172
[2]	C. H. Bennett and G. Brassard, “Quantum Cryptography: Public Key Distribution and Coin Tossing,” Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, 10-19 December 1984, pp. 175-179.
[3]	A. Ekert, “Quantum Cryptography Based on Bell’s Theorem,” Physical Review Letters, Vol. 67, No. 6, 1991, pp. 661-663. doi:10.1103/PhysRevLett.67.661
[4]	K. Bostrom and T. Felbinger, “Deterministic Secure Direct Communication Using Entanglement,” Physical Review Letters, Vol. 89, No. 18, 2002, Article ID: 187902. doi:10.1103/PhysRevLett.89.187902
[5]	Q.-Y. Cai, “The ‘Ping-Pong’ Protocol Can Be Attacked without Eavesdropping,” Physical Review Letters, Vol. 91, No. 10, 2003, Article ID: 109801. doi:10.1103/PhysRevLett.91.109801
[6]	A. Wójcik, “Eavesdropping on the ‘Ping-Pong’ Quantum Communication Protocol,” Physical Review Letters, Vol. 90, No. 15, 2003, Article ID: 157901. doi:10.1103/PhysRevLett.90.157901
[7]	Z. Zhang, Z. Man and Y. Li, “Improving Wójcik’s Eavesdropping Attack on the Ping-Pong Protocol,” Physics Letters A, Vol. 333, No. 1-2, 2004, pp. 46-50. doi:10.1016/j.physleta.2004.10.025
[8]	Q.-Y. Cai and B.-W. Li, “Improving the Capacity of the Bostr?m-Felbinger Protocol,” Physics Letters A, Vol. 69, No. 5, 2004, Article ID: 054301. doi:10.1103/PhysRevA.69.054301
[9]	Q.-Y. Cai, “Eavesdropping on the Two-Way Quantum Communication Protocols with Invisible Photons,” Physics Letters A, Vol. 351, No. 1-2, 2006, pp. 23-25. doi:10.1016/j.physleta.2005.10.050
[10]	K. Bostr?m and T. Felbinger, “On the Security of the Ping-Pong Protocol,” Physics Letters A, Vol. 372, No. 22, 2008, pp. 3953-3956. doi:10.1016/j.physleta.2008.03.048
[11]	T. Miyadera, M. Yoshida and H. Imai, “On Ping-Pong Protocol and Its Variant,” Cornell University Library, Ithaca and New York, 2009.
[12]	J. A. Miszczak and P. Zawadzki, “General Method for the Security Analysis in a Quantum Direct Communication Protocol,” Cornell University Library, Ithaca and New York, 2013
[13]	M. Lucamarini and S. Mancini, “Secure Deterministic Communication without Entanglement,” Physical Review Letters, Vol. 94, No. 14, 2005, Article ID: 140501. doi:10.1103/PhysRevLett.94.140501
[14]	F.-G. Deng and G. L. Long, “Secure Direct Communication with a Quantum One-Time Pad,” Physical Review A, Vol. 69, No. 5, 2004, Article ID: 052319. doi:10.1103/PhysRevA.69.052319
[15]	H. Lu, C.-H. F. Fung, X. Ma and Q.-Y. Cai, “Unconditional Security Proof of a Deterministic Quantum Key Distribution with a Two-Way Quantum Channel,” Physical Review A, Vol. 84, No. 4, 2011, Article ID: 042344. doi:10.1103/PhysRevA.84.042344
[16]	N. J. Beaudry, M. Lucamarini, S. Mancini and R. Renner, “Security of Two-Way Quantum Key Distribution,” Cornell University Library, Ithaca and New York, 2013.
[17]	C.-H. F. Fung, X. Ma, H. F. Chau and Q.-Y. Cai, “Quantum Key Distribution with Delayed Privacy Amplification and Its Application to the Security Proof of a Two-Way Deterministic Protocol,” Physical Review A, Vol. 85, No. 3, 2012, Article ID: 032308. doi:10.1103/PhysRevA.85.032308