Analyses of the consistent eavesdropping attack of several eavesdroppers on the ping-pong protocol with entangled pairs of qubits
DOI:
https://doi.org/10.18372/2410-7840.15.4217Keywords:
quantum cryptography, a ping-pong protocol, eavesdropping attack of several eavesdroppers, the probability of eavesdroppers' detection, eavesdroppers' amount of informationAbstract
In this paper the analyses of the eavesdropping attack of two or more eavesdroppers on the original ping-pong protocol with entangled pairs of qubits is carried out. General recursive expression for probability d of attack detection for any number n of eavesdroppers that allows to calculate this probability through the corresponding probability when n – 1 eavesdroppers attack is obtained. It is shown that an increase in the number of attackers in the quantum channel leads to an increase in the probability of detecting these attacks by legitimate users. The expressions for the maximum eavesdroppers' amount of information during a consistent attack of two and three eavesdroppers are obtained. It is indicated that the maximum eavesdroppers' amount of information determined by the same expression as in the case of one eavesdropper's attack, only the value of d is varying. It is shown that the ping-pong protocol with pairs of entangled qubits is vulnerable to eavesdropping attack of several eavesdroppers not more than to one eavesdropper's attack.
References
Boström K. Deterministic secure direct communication using entanglement / K. Boström, T. Felbinger // Physical Review Letters. – 2002. – Vol. 89, issue 18. – 187902.
Cai Q.-Y. Improving the capacity of the Boström – Felbinger protocol / Q.-Y. Cai, B.-W. Li // Physical Review A. – 2004. – V. 69, issue 5. – 054301.
Василиу Е.В. Анализ безопасности пинг-понг протокола с квантовым плотным кодированием / Е.В. Василиу // Наукові праці ОНАЗ ім. О.С. Попова. – 2007. – № 1. – С. 32–38.
Vasiliu E.V. Non-coherent attack on the ping-pong protocol with completely entangled pairs of qutrits / Eugene V. Vasiliu // Quantum Information Pro-cessing. – 2011. – V. 10, num. 2. – P. 189–202.
Li X.-H. Multiparty Quantum Remote Secret Con-ference / X.-H. Li, C.-Y. Li, F.-G. Deng et al // Chinese Physics Letters. – 2007. – V. 24, № 1. – P. 23–26.
Jin X.-R. Three-party quantum secure direct com-munication based on GHZ states / X.-R. Jin, X. Ji, Y.-Q. Zhang et al // Physics Letters A. – 2006. – V. 354, № 1-2. – P. 67–70.
Василиу Е.В. Пинг – понг протокол с трех– и четырехкубитными состояниями Гринбергера – Хорна – Цайлингера / Е.В. Василиу, Л.Н. Василиу // Труды Одесского политехнического университета. – 2008. – Вып. 1(29). – С. 171–176.
Ostermeyer, M. On the implementation of a deter-ministic secure coding protocol using polarization entangled photons / M. Ostermeyer, N. Walenta // Optics Communications. – 2008. – V. 281, issue 17. – P. 4540–4544.
Jung E. Attack of many eavesdroppers via optimal strategy in quantum cryptography / E. Jung, M.-R. Hwang, D.K. Park [et al.] // Physical Review A. – 2009. – V. 79, issue 3. – 032339.
Василиу Е.В. Синтез основанной на пинг-понг протоколе квантовой связи безопасной системы прямой передачи сообщений / Е.В. Василиу, С.В. Николаенко // Наукові праці ОНАЗ ім. О.С. Попова. – 2009, № 1. – С. 83–91.
Boström K. Deterministic secure direct communication using entanglement / K. Boström, T. Felbinger // Physical Review Letters, 2002, Vol. 89, issue 18. – 187902.
Cai Q.-Y. Improving the capacity of the Boström – Felbinger protocol / Q.-Y. Cai, B.-W. Li // Physical Review A., 2004, V. 69, issue 5. – 054301.
Vasiliu Ye.V. Security analysis of ping-pong protocol with quantum thick coding / Ye.V.Vasiliu // Science works of ONAZ n.a. O.S.Popov, 2007, № 1, P. 32–38.
Vasiliu E.V. Non-coherent attack on the ping-pong protocol with completely entangled pairs of qutrits / Eugene V. Vasiliu // Quantum Information Pro-cessing, 2011, V. 10, num. 2, P. 189–202.
Li X.-H. Multiparty Quantum Remote Secret Con-ference / X.-H. Li, C.-Y. Li, F.-G. Deng et al // Chinese Physics Letters, 2007, V. 24, № 1, P. 23–26.
Jin X.-R. Three-party quantum secure direct com-munication based on GHZ states / X.-R. Jin, X. Ji, Y.-Q. Zhang et al // Physics Letters A, 2006, V. 354, № 1-2, P. 67–70.
Vasiliu Ye.V. Ping-pong protocol with 3- and 4-qubits Greenberger-Horne-Zeilinger states / Ye.V.Vasiliu, L.N.Vasiliu // Works of Odessa polytechnic university, 2008, Vol. 1(29), P. 171–176.
Ostermeyer, M. On the implementation of a deter-ministic secure coding protocol using polarization entangled photons / M. Ostermeyer, N. Walenta // Optics Communications., 2008, V. 281, issue 17. – P. 4540–4544.
Jung E. Attack of many eavesdroppers via optimal strategy in quantum cryptography / E. Jung, M.-R. Hwang, D.K. Park [et al.] // Physical Review A. – 2009. – V. 79, issue 3. – 032339.
Vasiliu Ye.V. Synthesis of safety system direct mes-sage transferring based on ping-pong protocol of quantum communications / Ye.V.Vasiliu, S.V.Niko-laenko // Science works of ONAZ n.a. O.S.Popov, 2009, № 1, P. 83–91.
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