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Quantum Information and Computation

Security of quantum secret sharing with two-particle entanglement against individual attacks

S.-J. Qin, Fei Gao, Qiaoyan Wen, F.-C. Zhu

Published Sep 1, 2009• 10 citations
Publisher

Abstract

Security is the most important criterion to evaluate cryptography protocols. We investigate the security of one important quantum secret sharing protocol (KKI protocol). By discriminating two mixed states, we derive the optimal relationship between the induced error rate (QBER) and the maximal amount of information gained by a dishonest participant. For a specific amount of eavesdropper's knowledge on the shared secret that we consider, the disturbance on the quantum state in terms of QBER is actually larger for the hybrid protocol than the KKI protocol. Therefore, the hybrid protocol appears to be better able to detect eavesdroppers than the KKI protocol. For this reason, we do not see any reason to employ the KKI protocol against individual attacks.

DOI
10.26421/qic9.9-10-3

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Security is the most important criterion to evaluate cryptography protocols. We investigate the security of one important quantum secret sharing protocol (KKI protocol). By discriminating two mixed states, we derive the optimal relationship between the induced error rate (QBER) and the maximal amount of information gained by a dishonest participant. For a specific amount of eavesdropper's knowledge on the shared secret that we consider, the disturbance on the quantum state in terms of QBER is actually larger for the hybrid protocol than the KKI protocol. Therefore, the hybrid protocol appears to be better able to detect eavesdroppers than the KKI protocol. For this reason, we do not see any reason to employ the KKI protocol against individual attacks.
An attempt to eavesdrop a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, both in the two-state B92 and the four-state BB84 quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently form other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are included. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi information, and with respect only to bits received error-free by Bob. This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.
In this paper, the perfect secret sharing in quantum cryptography is investigated. On one hand, the security of a recent protocol [Adhikari et al. Quantum Inform. \& Comput. 12 (2012) 0253-0261] is re-examined. We find that it violates the requirement of information theoretic security in the secret sharing and suffers from the information leakage. The cryptanalysis including several specific attack strategies are given, which shows that a dishonest participant can steal half or all of the secrets without being detected. On the other hand, we design a new quantum secret sharing protocol. The security of protocol is rigorously proved. It meets the fundamental requirement of information theoretic security. Furthermore, the security analysis including both the outside attacks and participant attacks is given in details. It is shown that our proposed protocol can achieve perfect secret sharing.
Security of a quantum secret sharing of quantum state protocol proposed by Guo et al. [Chin. Phys. Lett. 25 (2008) 16] is reexamined. It is shown that an eavesdropper can obtain some of the transmitted secret information by monitoring the classical channel or the entire secret by intercepting the quantum states, and moreover, the eavesdropper can even maliciously replace the secret message with an arbitrary message without being detected. Finally, the deep reasons why an eavesdropper can attack this protocol are discussed and the modified protocol is presented to amend the security loopholes.
An attempt to eavesdrop on a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, in both the two-state B92 [B92 refers to the work of C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992)] and the four-state BB84 [BB84 refers to the work of C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175--179] quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently from other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are covered. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi (rather than Shannon) information, and with respect only to bits received error-free by Bob (rather than all bits). This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.