Quantum Secret Sharing Based on Continuous-Variable GHZ States
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Quantum Secret Sharing Based on Continuous-Variable GHZ States Ye Kang1 · Ying Guo2 · Yanyan Feng1 Received: 7 December 2019 / Accepted: 30 May 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Based on the continuous-variable GHZ states, an efficient (n, n) quantum secret sharing protocol is designed, where the Dealer can distribute the various shares to different participants at one time. Likewise, every participant can transfer the same message (share) to other participants simultaneously in the secret recovery process. In this way, the cost of time and quantum photons sharply decreases. What’s more, the proposed QSS is proved to be feasible in the terrible quantum channel with low transmission efficiency and be secure without any secret information leakage under the participant attack. Keywords Quantum secret sharing · Continuous-Variable GHZ states · Beam splitter attack
1 Introduction Traditionally, the secret sharing (SS) aims to manage the key (secret) by a set of participants securely. Different from the real secure communication, the information transferred is not the original secret, but its shadows which can be used to reconstruct the secret. Thus, the SS contains two processes, i.e., distribution of shadows and recovery of the secret. As for classical SS schemes, their main purpose is to design a perfect threshold architecture, such as the first (k, n) threshold scheme proposed by Shamir [1]. However, the security of distribution
Yanyan Feng
[email protected] Ye Kang [email protected] Ying Guo [email protected] 1
School of Computer Science and Engineering, Central South University, Changsha, 410083, China
2
School of Automation, Central South University, Changsha, 410083, China
International Journal of Theoretical Physics
is neglected. Fortunately, in 1999, Hillery et al. [2] brought the SS into the quantum domain and proposed the first quantum secret sharing (QSS) scheme. Owing to the quantum physical properties such as quantum non-cloning theorem and Heisenberg uncertainty principle, the message (secret) can be distributed in unconditional security. So, more and more achievements about QSS [3–5] have been created since 1999. Converse to classical SS, the QSS schemes pay more attention on the security and efficiency of distribution shadows. However, the threshold structures are mainly adopted from classical SS schemes, like Chinese Remainder Theorem [6], Lagrange interpolation formula [7], error-correcting code [8] and so on. But the most popular method is the binary addition, in this way, the secret key can be simply recovered by calculating the modulo 2 sums of all participants’ shadows [9–11]. So, most QSS schemes mainly design various quantum channels to distribute messages (shadows) to participants in secure. Yan et al. proposed a QSS protocol between multiparty (m members in group 1) and multiparty (n members in group 2) using a sequence of single photons which is used directly to encode classical messages (shadows) for distribution [12]. Deng
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