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Security of ping-pong protocol based on pairs of completely entangled qudits

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Abstract

Quantum secure direct communication protocols offer confidential transmission of classic information over quantum channel without prior key agreement. The ping-pong based protocols provide asymptotic security and detailed analysis of security level provided by each variant of the protocol is required. The paper presents a general method of calculation of the eavesdropped information as a function of the attack detection probability. The method is applied to the ping-pong protocol based on completely entangled pairs of qudits. The upper and lower bounds on the amount of the leaked information and eavesdropping detection probability are provided.

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References

  1. Bechmann-Pasquinucci H., Peres A.: Quantum cryptography with 3-state systems. Phys. Rev. Lett. 85(15), 3313–3316 (2000). doi:10.1103/PhysRevLett.85.3313

    Article  MathSciNet  MATH  ADS  Google Scholar 

  2. Beige A., Englert B.G., Kurtsiefer Ch., Weinfurter H.: Secure communication with a publicly known key. Act. Phys. Pol. 101(3), 357–368 (2002)

    Article  MATH  Google Scholar 

  3. Bengtsson, I.: Three ways to look at mutually unbiased bases. quant-ph/0610216v1 (2006)

  4. Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of International Conference on Computers, Systems and Signal Processing, pp. 175–179. New York (1984)

  5. Boström K., Felbinger T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89(18), 187–902 (2002). doi:10.1103/PhysRevLett.89.187902

    Article  Google Scholar 

  6. Boström K., Felbinger T.: On the security of the ping-pong protocol. Phys. Lett. A 372(22), 3953–3956 (2008)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  7. Cai Q.Y., Li B.W.: Improving the capacity of the Boström-Felbinger protocol. Phys. Rev. A 69(5), 054–301 (2004). doi:10.1103/PhysRevA.69.054301

    Article  Google Scholar 

  8. Chamoli A., Bhandari C.: Secure direct communication based on ping-pong protocol. Quantum Inf. Process. 8, 347–356 (2009). doi:10.1007/s11128-009-0112-2

    Article  MathSciNet  MATH  Google Scholar 

  9. Deng F.G., Long G.L.: Quantum privacy amplification for a sequence of single qubits. Commun. Theor. Phys. 46(3), 443 (2006)

    Article  ADS  Google Scholar 

  10. Deng, F.G., Long, G.L., Wang, Y., Xiao, L.: Increasing the efficiencies of random-choice-based quantum communication protocols with delayed measurement. Chin. Phys. Lett. 21(11), 2097–2100 (2004). URL:http://cpl.iphy.ac.cn/qikan/manage/wenzhang/0212097.pdf

  11. Durt T., Kaszlikowski D., Chen J.L., Kwek L.C.: Security of quantum key distributions with entangled qudits. Phys. Rev. A 69(3), 032–313 (2004). doi:10.1103/PhysRevA.69.032313

    Article  Google Scholar 

  12. Ekert A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67(6), 661–663 (1991). doi:10.1103/PhysRevLett.67.661

    Article  MathSciNet  MATH  ADS  Google Scholar 

  13. Gao T., Yan F.L., Wang Z.X.: Deterministic secure direct communication using GHZ states and swapping quantum entanglement. J. Phys. A Math. Gen. 38(25), 5761 (2005). doi:10.1088/0305-4470/38/25/011

    Article  MathSciNet  MATH  ADS  Google Scholar 

  14. Keyl M.: Fundamentals of quantum information theory. Phys. Rep. 369(5), 431–548 (2002). doi:10.1016/S0370-1573(02)00266-1

    Article  MathSciNet  MATH  ADS  Google Scholar 

  15. Korchenko, O., Vasiliu, Y., Gnatyuk, S.: Modern quantum technologies of information security against cyberterrorist attacks. Aviation 14(2), 58–69 (2010). doi:10.3846/aviation.2010.10 URL:http://arxiv.org/abs/1005.5553

  16. Liu X.S., Long G.L., Tong D.M., Li F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65(2), 022–304 (2002). doi:10.1103/PhysRevA.65.022304

    Google Scholar 

  17. Long G.l., Deng F.g., Wang C., Li X.h., Wen K., Wang W.y.: Quantum secure direct communication and deterministic secure quantum communication. Front. Phys. China 2(3), 251–272 (2007). doi:10.1007/s11467-007-0050-3

    Article  ADS  Google Scholar 

  18. Long G.L., Liu X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65(3), 032302 (2002). doi:10.1103/PhysRevA.65.032302

    Article  ADS  Google Scholar 

  19. Ostermeyer, M., Walenta, N.: On the implementation of a deterministic secure coding protocol using polarization entangled photons. Opt. Commun. 281(17), 4540–4544 (2008). doi:10.1016/j.optcom.2008.04.068. URL: http://quant-ph/0703242v2.

  20. Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978). doi:10.1145/359340.359342. URL:http://theory.lcs.mit.edu/rivest/rsapaper.pdf

  21. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Sci. Stat. Comput. 26, 1484–1509 (1997). URL:http://www.citebase.org/abstract?id=oai:arXiv.org:quant-ph/9508027

  22. Vasiliu, E.V.: Asymptotic security of the ping-pong quantum direct communication protocol with three-qubit Greenberger-Horne-Zeilinger states. Georgian Elec. Sci. J. Comput. Sci. Telecomm. 3(20), 3–15 (2009). URL:http://gesj.internet-academy.org.ge/gesj_articles/1427.pdf

  23. Vasiliu E.V.: Non-coherent attack on the ping-pong protocol with completely entangled pairs of qutrits. Quantum Inf. Process. 10, 189–202 (2011). doi:10.1007/s11128-010-0188-8

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang C., Deng F.G., Li Y.S., Liu X.S., Long G.L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71(4), 044305 (2005). doi:10.1103/PhysRevA.71.044305

    Article  ADS  Google Scholar 

  25. Wójcik A.: Eavesdropping on the ping-pong quantum communication protocol. Phys. Rev. Lett. 90(15), 157–901 (2003)

    Article  Google Scholar 

  26. Yang Y.G., Teng Y.W., Chai H.P., Wen Q.Y.: Revisiting the security of secure direct communication based on ping-pong protocol. Quantum Inf. Process. (2010). doi:10.1007/s11128-010-0199-5

  27. Zawadzki P.: A fine estimate of quantum factorization success probability. Int. J. Quantum Inf. 8(8), 1233–1238 (2010). doi:10.1142/S0219749910006940

    Article  MATH  Google Scholar 

  28. Zawadzki P.: Numerical estimation of the quantum factorization effectiveness. Theor. Appl. Inf. 22(1), 63–72 (2010)

    Google Scholar 

  29. Zhang Z., Man Z., Li Y.: Improving Wójciks eavesdropping attack on the ping-pong protocol. Phys. Lett. A 333, 46–50 (2004). doi:10.1016/j.physleta.2004.10.025

    Article  MathSciNet  MATH  ADS  Google Scholar 

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Zawadzki, P. Security of ping-pong protocol based on pairs of completely entangled qudits. Quantum Inf Process 11, 1419–1430 (2012). https://doi.org/10.1007/s11128-011-0307-1

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