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Ukrainian Scientific Journal of Information Security

Security amplification of the ping-pong protocol with many-qubit Greenberger-Horne-Zeilinger states

Yevhen Vasiliu, Sergiy O. Gnatyuk, Сергій Ніколаєнко, Тетяна Олександрівна Жмурко

Published Dec 18, 2012• 2 citations
Publisher

Abstract

In this paper the non-quantum method of security amplification for the ping-pong protocol with many-qubit entangled Greenberger-Horne-Zeilinger states (GHZ-states) is proposed. This method can be used in quantum cryptography and consists in invertible hashing of classical message blocks. The necessary sizes of matrices for hashing of message blocks are calculated at some values of the protocol parameters. The proposed method does not require the presence from legitimate users of any pre-established keys. Thus, the main advantage of the quantum secure direct communication protocols, namely the lack of necessity to distribute of secret key remains valid at usage of the proposed method.

DOI
10.18372/2225-5036.18.3470

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In this paper the non-quantum method of security amplification for the ping-pong protocol with many-qubit entangled Greenberger-Horne-Zeilinger states (GHZ-states) is proposed. This method can be used in quantum cryptography and consists in invertible hashing of classical message blocks. The necessary sizes of matrices for hashing of message blocks are calculated at some values of the protocol parameters. The proposed method does not require the presence from legitimate users of any pre-established keys. Thus, the main advantage of the quantum secure direct communication protocols, namely the lack of necessity to distribute of secret key remains valid at usage of the proposed method.
Particularly vulnerable spot for violation of information security is a data network, since it is impossible to guarantee the data protection when transferring them through a public environment (Internet, telephone lines, radio). Therefore, the information transmitted on different networks, particularly in need of security and the main way of providing it, is using the cryptographic methods. However, recent research has shown that classical cryptography gives a cause to look for new prospects and it could be quantum cryptography. Among all possible quantum cryptography technologies, quantum secure direct communication (e.g. Ping-Pong protocol) does not use any cryptographic transformations, so there is no key distribution problem and eavesdropping can be detected during transfer, thereby improving information transmitting reliability. In this paper security amplification method for Ping-Pong protocol was proposed. This method uses generated ternary pseudorandom sequence and transformations in Galois field. Accordingly, this could increase the protocol asymptotical security and accelerate its work at least 3 times.
Abstract We analyse the ping-pong (PP) protocol [K. Bostrom and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002)] using different sets of partially entangled three-qubit states. Interestingly, our results show that the partially entangled nonorthogonal three-qubit states are more useful as resources in comparison to three-qubit maximally entangled Greenberger–Horne–Zeilinger (GHZ) states. The properties of orthogonal set of partially entangled states as resources for PP protocol, however, are similar to that of maximally entangled GHZ states – both the states are not preferable due to the vulnerability towards eavesdropping. On the other hand, partially entangled nonorthogonal basis set holds importance for transferring two-bit information, one each from a sender, to a single receiver. The protocol is further analysed for various eavesdropping attacks, and the results are compared with the use of two shared Bell pairs for two-bit information transfer. Surprisingly, the use of partially entangled nonorthogonal set of states is found to offer better qubit efficiency and increased security, as against the use of two separate maximally entangled Bell states with orthogonal basis. In addition, we also propose a mixed-state sharing protocol to further enhance the security of the PP protocol.
In this paper, we develop, a quantum key distribution protocol based on the Greenberger-Horne-Zeilinger states (GHZs). The particles are exchanged among the users in blocks through two steps. In this protocol, for three-particle GHZs three keys can be simultaneously generated. The advantage of this is that the users can select the most suitable key for communication. The protocol can be generalized to N users to provide N keys. The protocol has two levels for checking the eavesdroppers. Moreover, we discuss the security of the protocol against different attacks.
A protocol for three-party quantum secure direct communication based on Greenberger–Horne–Zeilinger (GHZ) states was recently proposed by Jin et al. [Phys. Lett. A 354 (2006) 67] By analysing the protocol we find some security loopholes, e.g. one bit of secret messages of a party (Alice in the original paper) can always be leaked straight to the public without any eavesdropping. These problems suggested previously are discussed and possible solutions are presented to improve the security of the original protocol.
This work presents an analysis of a sequential passive eavesdropping attack by two eavesdroppers on the ping-pong protocol employing three-qubit Greenberger-Horne-Zeilinger (GHZ) entangled states. An analytical expression is derived for the probability of attack detection by legitimate users. It is shown that increasing the number of eavesdroppers in the quantum channel leads to a higher probability of attack detection. Expressions are also obtained for the maximum amount of information that two eavesdroppers can gain during their sequential passive attack. The analysis demonstrates that the ping-pong protocol with GHZ triplets is no more vulnerable to passive eavesdropping by two adversaries than it is to an attack by a single one. The results can be generalized to ping-pong protocols based on n-qubit GHZ states for arbitrary values of n\boldsymbol{n}n.