Verifiable Quantum Secret Sharing Based on a Single Qudit
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Verifiable Quantum Secret Sharing Based on a Single Qudit Dan-Li Zhi1 · Zhi-Hui Li1 · Zhao-Wei Han1 · Li-Juan Liu1 Received: 6 April 2020 / Accepted: 14 September 2020 / Published online: 19 November 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract To detect frauds from some internal participants or external attackers, some verifiable threshold quantum secret sharing schemes have been proposed. In this paper, we present a new verifiable threshold structure based on a single qudit using bivariate polynomial. First, Alice chooses an asymmetric bivariate polynomial and sends a pair of values from this polynomial to each participant. Then Alice and participants implement in sequence unitary transformation on the d-dimensional quantum state based on unbiased bases, where those unitary transformations are contacted by this polynomial. Finally, security analysis shows that the proposed scheme can detect the fraud from external and internal attacks compared with the exiting schemes and is comparable to the recent schemes. Keywords Verifiability · Mutually unbiased bases · Unitary transformation · Secret sharing scheme
1 Introduction Quantum secret sharing is an important issue in quantum cryptography, which combines classical secret sharing and quantum theory and plays an important role in applied cryptography. It means that classic or quantum secret information can be divided into shares by a dealer among participants, so that only authorized participants can recover the secret, and any one or more unauthorized participants cannot recover the secret. In a (t, n)-threshold quantum secret sharing scheme, the dealer splits secret into n shares sending them to each of n participants where any set of t or more shareholders can recover the shared secret cooperatively, however less than t shareholders can not recover it. Hillery et al. [1] firstly proposed quantum secret sharing (QSS) based on the quantum correlation of GreenbergerHorne-Zeilinger (GHZ) states in 1999. The main idea of this scheme is that an unknown quantum state is shared between two participants and only restored collaboratively. The fundamental theory of quantum determines that the QSS schemes are more secure than the
Zhi-Hui Li
[email protected] 1
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, China
International Journal of Theoretical Physics (2020) 59:3672–3684
3673
classic ones. There are many QSS schemes [2–9] that have been proposed. For example, a quantum secret sharing scheme was constructed using the product state rather than the entangled state in [4], such that the scheme is applicable when the number of participants is expanded. In addition, a (n, n)-threshold quantum secret sharing scheme that shares multiple classic information was proposed based on a single photon in [6]. Most of these schemes do not take into account two major security issues.During the secret distribution phase, an attacker may impersonate the dealer to send false information to the shareho
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