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International Journal of Quantum Information

ANALYZING AND REVISING A TWO-WAY PROTOCOL FOR QUANTUM CRYPTOGRAPHY WITH A NONMAXIMALLY ENTANGLED QUBIT PAIR

Zhihao Liu, Hanwu Chen, Wenjie Liu, Juan Xu, Zhiqiang Li

Published May 25, 2011• 16 citations
Publisher

Abstract

The security of the second (STF-B) protocol of quantum cryptography proposed by Shimizu, Tamaki and Fukasaka (STF) [Phys. Rev. A80 (2009) 022323] is analyzed in a general way, which shows that the STF-B protocol is vulnerable under a kind of generalized attack. Sufficient and necessary condition for which Eve can successfully attack the message M without introducing errors is deduced. It shows that the correlation-elicitation (CE) attack strategy found by Qin et al. [Phys. Rev. A82 (2010) 036301] is a special case of the sufficient and necessary condition. Next, we advance an effective and efficient strategy to prevent the general attack. Hence, the STF-B protocol is revised to a secure one by improving the control mode.

DOI
10.1142/s0219749911007885

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The security of the second (STF-B) protocol of quantum cryptography proposed by Shimizu, Tamaki and Fukasaka (STF) [Phys. Rev. A80 (2009) 022323] is analyzed in a general way, which shows that the STF-B protocol is vulnerable under a kind of generalized attack. Sufficient and necessary condition for which Eve can successfully attack the message M without introducing errors is deduced. It shows that the correlation-elicitation (CE) attack strategy found by Qin et al. [Phys. Rev. A82 (2010) 036301] is a special case of the sufficient and necessary condition. Next, we advance an effective and efficient strategy to prevent the general attack. Hence, the STF-B protocol is revised to a secure one by improving the control mode.
Three protocols of quantum cryptography with a nonmaximally entangled qubit pair [Phys. Rev. A 80, 022323 (2009)] were recently proposed by Shimizu, Tamaki, and Fukasaka. The security of these protocols is based on the quantum-mechanical constraint for a state transformation between nonmaximally entangled states. However, we find that the second protocol is vulnerable under the correlation-elicitation attack. An eavesdropper can obtain the encoded bit MMM although she has no knowledge about the random bit RRR.
Counterfactual quantum cryptography, recently proposed by Noh, is featured with no transmission of signal particles. This exhibits evident security advantages, such as its immunity to the well-known photon-number-splitting attack. In this paper, the theoretical security of counterfactual quantum cryptography protocol against the general intercept-resend attacks is proved by bounding the information of an eavesdropper Eve more tightly than in Yin's proposal [ Phys. Rev. A 82 042335 (2010) ]. It is also shown that practical counterfactual quantum cryptography implementations may be vulnerable when equipped with imperfect apparatuses, by proving that a negative key rate can be achieved when Eve launches a time-shift attack based on imperfect detector efficiency.
Counterfactual quantum cryptography, recently proposed by Noh, is featured with no transmission of signal particles. This exhibits evident security advantages, such as its immunity to the well-known photon-number-splitting attack. In this paper, the theoretical security of counterfactual quantum cryptography protocol against the general intercept-resend attacks is proved by bounding the information of an eavesdropper Eve more tightly than in Yin's proposal [Phys. Rev. A 82 042335 (2010)]. It is also shown that practical counterfactual quantum cryptography implementations may be vulnerable when equipped with imperfect apparatuses, by proving that a negative key rate can be achieved when Eve launches a time-shift attack based on imperfect detector efficiency.
Counterfactual quantum cryptography,recently proposed by Noh,is featured with no transmission of signal particles.This exhibits evident security advantages,such as its immunity to the well-known photon-number-splitting attack.In this paper,the theoretical security of counterfactual quantum cryptography protocol against the general interceptresend attacks is proved by bounding the information of an eavesdropper Eve more tightly than in Yin’s proposal [Phys.Rev.A 82 042335(2010)].It is also shown that practical counterfactual quantum cryptography implementations may be vulnerable when equipped with imperfect apparatuses,by proving that a negative key rate can be achieved when Eve launches a time-shift attack based on imperfect detector efficiency.
The participant attack is the most serious threat for quantum secret-sharing protocols. We present a method to analyze the security of quantum secret-sharing protocols against this kind of attack taking the scheme of Hillery, Bu\ifmmode \check{z}\else \v{z}\fi{}ek, and Berthiaume (HBB) [Phys. Rev. A 59, 1829 (1999)] as an example. By distinguishing between two mixed states, we derive the necessary and sufficient conditions under which a dishonest participant can attain all the information without introducing any error, which shows that the HBB protocol is insecure against dishonest participants. It is easy to verify that the attack scheme of Karlsson, Koashi, and Imoto [Phys. Rev. A 59, 162 (1999)] is a special example of our results. To demonstrate our results further, we construct an explicit attack scheme according to the necessary and sufficient conditions. Our work completes the security analysis of the HBB protocol, and the method presented may be useful for the analysis of other similar protocols.
Cryptanalysis is an important branch in the study of cryptography, including both the classical cryptography and the quantum one. In this paper we analyze the security of two three-party quantum key distribution protocols (QKDPs) proposed recently, and point out that they are susceptible to a simple and effective attack, i.e. the dense-coding attack. It is shown that the eavesdropper Eve can totally obtain the session key by sending entangled qubits as the fake signal to Alice and performing collective measurements after Alice's encoding. The attack process is just like a dense-coding communication between Eve and Alice, where a special measurement basis is employed. Furthermore, this attack does not introduce any errors to the transmitted information and consequently will not be discovered by Alice and Bob. The attack strategy is described in detail and a proof for its correctness is given. At last, the root of this insecurity and a possible way to improve these protocols are discussed.