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Quantum Information and Computation

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

QinaSu-Juan, GaoFei, WenQiao-Yan, ZhuFu-Chen

Published Sep 1, 2009• 0 citations
Publisher

Abstract

Security is the most important criterion to evaluate cryptography protocols. We inves-tigate the security of one important quantum secret sharing protocol [Phys. Rev. A59, 162 (1999)] (KKI protocol...
DOI
10.5555/2011804.2011807

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In a recent paper [V. Karimipour and M. Asoudeh, Phys. Rev. A 92, 030301(R) (2015)], a multiparty quantum secret-sharing protocol based on ddd-level single particles was proposed. We discussed the security of this protocol and found that it is not secure for any one dishonest participant who can recover the secret without the aid of other participants.
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.
The participant attack is the most serious threat for quantum secret-sharing protocols. However, it is only during the transmission of quantum information carriers that attention is paid to this kind of attack in the existing quantum secret-sharing protocols. The security considerations of the secret reconstruction phase of quantum secret-sharing protocols against this kind of attack are neglected. We demonstrate our viewpoint by taking the scheme of Hillery, Buzěk, and Berthiaume (HBB) [Phys. Rev. A59 (1999) 18–29] as an example. By telling a lie in the reconstruction phase, a dishonest participant can easily attain the entire secret key instead of eavesdropping during the transmission awkwardly, whereas the honest one cannot judge whether the dishonest one tells the truth and the obtained secret random key is identical to what the secret distributor owns because of lack of verification mechanism in the HBB protocol. It is not difficult to find that almost all the quantum secret-sharing protocols have such disadvantages. Our viewpoint presented may be useful for the design of other similar protocols.
Abstract Semi-quantum secret sharing (SQSS) is an important branch of semi-quantum cryptography, and differs from quantum secret sharing (QSS) in that not all parties are required to possess quantum capabilities. All previous SQSS protocols have three common features: (i) they adopt product states or entangled states as initial quantum resource; (ii) the particles prepared by quantum party are transmitted in a tree-type way; and (iii) they require the classical parties to possess the measurement capability. In this paper, two circular SQSS protocols with single particles are suggested, where the first one requires the classical parties to possess the measurement capability while the second one does not have this requirement. Compared with the previous SQSS protocols, the proposed SQSS protocols have some distinct features: (i) they adopt single particles rather than product states or entangled states as initial quantum resource; (ii) the particles prepared by quantum party are transmitted in a circular way; and (iii) the second protocol releases the classical parties from the measurement capability. The proposed SQSS protocols are robust against some famous attacks from an eavesdropper, such as the measure-resend attack, the intercept-resend attack and the entangle-measure attack, and are feasible with present quantum technologies in reality .