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Journal of Applied Security Research

Improvement of a (t,n) Threshold d−Level Quantum Secret Sharing Scheme

Samaneh Mashhadi

Published Nov 11, 2020• 21 citations
Publisher

Abstract

Recently, a threshold d−level quantum secret sharing scheme was presented by Song et al. However, Kao et al. showed that in contrary to Song claim, the reconstructor cannot recover the secret without receiving any information from the other participants. To remedy this weakness, we will propose a new version of Song scheme.
DOI
10.1080/19361610.2020.1840894

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One crucial and basic method for disclosing a secret to every participant in quantum cryptography is quantum secret sharing. Numerous intricate protocols, including secure multiparty summation, multiplication, sorting, voting, and more, can be designed with it. A quantum secret sharing protocol with a (t,n)(t,n)(t,n) threshold approach and modulo d, where t and n represent the threshold number of participants and the total number of participants, respectively was recently discussed by Song et al. Kao et al. notes that without the information of other participants, the secret in Song {\em et al.'s}protocol cannot be reconstructed. We address a protocol that solves this issue in this paper.
Abstract Most of Quantum Secret Sharing(QSS) are (n, n) threshold 2-level schemes, in which the 2-level secret cannot be reconstructed until all n shares are collected. In this paper, we propose a (t, n) threshold d-level QSS scheme, in which the d-level secret can be reconstructed only if at least t shares are collected. Compared with (n, n) threshold 2-level QSS, the proposed QSS provides better universality, flexibility, and practicability. Moreover, in this scheme, any one of the participants does not know the other participants’ shares, even the trusted reconstructor Bob1 is no exception. The transformation of the particles includes some simple operations such as d-level CNOT, Quantum Fourier Transform(QFT), Inverse Quantum Fourier Transform(IQFT), and generalized Pauli operator. The transformed particles need not to be transmitted from one participant to another in the quantum channel. Security analysis shows that the proposed scheme can resist intercept-resend attack, entangle-measure attack, collusion attack, and forgery attack. Performance comparison shows that it has lower computation and communication costs than other similar schemes when 2 < t < n − 1.
Quantum secret sharing (QSS) is an important branch of secure multiparty quantum computation. Several schemes for (n, n) threshold QSS based on quantum Fourier transformation (QFT) have been proposed. Inspired by the flexibility of (t, n) threshold schemes, Song {\it et al.} (Scientific Reports, 2017) have proposed a (t, n) threshold QSS utilizing QFT. Later, Kao and Hwang (arXiv:1803.00216) have identified a {loophole} in the scheme but have not suggested any remedy. In this present study, we have proposed a (t, n)threshold QSS scheme to share a d dimensional classical secret. This scheme can be implemented using local operations (such as QFT, generalized Pauli operators and local measurement) and classical communication. Security of the proposed scheme is described against outsider and participants' eavesdropping.