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Science China Information Sciences

Selection of unitary operations in quantum secret sharing without entanglement

Juan Xu, Hanwu Chen, Wenjie Liu, ZhiHao Liu

Published Apr 29, 2011• 10 citations
Publisher
DOI
10.1007/s11432-011-4240-9

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We propose a substitute-Bell-state attack strategy for quantum secret sharing schemes without en- tanglement, as well as a definition of the minimum failure probability of such attack strategy. A quantitative analysis of security degrees corresponding to different unitary operations is also provided, when the secret sharing schemes without entanglement are stricken by substitute-Bell-state attack. As a result, the relation between the selection of unitary operations and the effect of substitute-Bell-state attack is shown, which can serve as an important guidance for the selection of unitary operations in designing and implementing quantum secret sharing schemes.
Quantum secret sharing (QSS) protocols without entanglement have showed high security by virtue of the characteristics of quantum mechanics. However, it is still a challenge to compare the security of such protocols depending on quantitative security analysis. Based on our previous security analysis work on protocols using single qubits and two-level unitary operations, QSS protocols with single qutrits and three-level unitary operations are considered in this paper. Under the Bell-state attack we propose, the quantitative security analyses according to different three-level unitary operations are provided respectively in the one-step and two-step situations. Finally, important conclusions are drawn for designing and implementing such QSS protocols. The method and results may also contribute to analyze the security of other high-level quantum cryptography schemes based on unitary operations.
Based on the Einstein-Podolsky-Rosen (EPR) entangled state and the unitary operation, a quantum secret-sharing (QSS) scheme on access structure is proposed. The participants randomly choose their private keys themselves. Each participant keeps one private key even though he belongs to several qualified subsets. In the recovery, the participants in the qualified subset perform the unitary operations on the EPR pairs, and recover the secret through the Bell-state measurement. Compared to the existing QSS schemes on (n, n) or (t, n) structure, the proposed scheme on access structure is more flexible in practice.