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arXiv:2501.09559

Threshold Quantum Secret Sharing

Kartick Sutradhar

Published Jan 16, 2025• 0 citations
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Abstract

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 $(t,n)$ 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.

DOI
10.48550/arxiv.2501.09559

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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.
The quantum secret sharing is an essential and fundamental technique for sharing a secret with the all participants in quantum cryptography. It can be used to design many complex protocols such as secure multiparty summation, multiplication, sorting, voting, etc. Recently, Song et al. have discussed a quantum protocol for secret sharing, which has (t, n) threshold approach and modulo d, where t and n denote the threshold number of participants and total number of participants, respectively. Kao et al. point out that the secret in the Song et al.'s protocol cannot be reconstructed without other participants' information. In this paper, we discuss a protocol that overcomes this problem.
In quantum cryptography, quantum secret sharing (QSS)(QSS)(QSS) is a fundamental primitive. QSSQSSQSS can be used to create complex and secure multiparty quantum protocols. Existing QSSQSSQSS protocols are either at the (n,n)(n, n)(n,n) threshold 222 level or at the (t,n)(t, n)(t,n) threshold ddd level with a trusted player, where nnn denotes the number of players and ttt denotes the threshold number of players. Here, we propose a secure ddd-level QSSQSSQSS protocol for sharing a secret with efficient simulation. This protocol is more secure, flexible, and practical as compared to the existing QSSQSSQSS protocols: (n,n)(n, n)(n,n) threshold 222-level and (t,n)(t,n)(t,n) threshold ddd-level with a trusted player. Further, it does not disclose any information about the secret to players. Its security analysis shows that the intercept-resend, intercept, entangle-measure, forgery, collision and collusion attacks are not possible in this protocol.
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.
(t,n)(t, n)(t,n) Threshold ddd-level quantum secret sharing based on quantum Fourier transformation
Quantum secret sharing (QSS) is an important branch of secure multiparty quantum computation. Several schemes for (n,n)(n, n)(n,n) threshold QSS based on quantum Fourier transformation (QFT) have been proposed. Inspired by the flexibility of (t,n)(t, n)(t,n) threshold schemes, Song {\it et al.} (Scientific Reports, 2017) have proposed a (t,n)(t, n)(t,n) threshold QSS utilizing QFTQFTQFT. 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)(t, n)(t,n) threshold QSS scheme to share a ddd dimensional classical secret. This scheme can be implemented using local operations (such as QFTQFTQFT, generalized Pauli operators and local measurement) and classical communication. Security of the proposed scheme is described against outsider and participants' eavesdropping.
Quantum secret sharing is an important branch of quantum cryptography, and secure multi-party quantum key distribution protocols can be constructed using quantum secret sharing. In this paper, we construct a quantum secret sharing scheme built on a constrained (t, n ) threshold access structure, where n is the number of participants and t is the threshold number of participants and the distributor. Participants from two different sets perform the corresponding phase shift operations on two particles in the GHZ state passed to them, and then t−1 participants with the distributor can recover the key, where the participant recovering the key measures the particles received by himself and finally obtains the key through the collaboration of the distributors. Security analysis shows that this protocol can be resistant to direct measurement attacks, interception retransmission attacks, and entanglement measurement attacks. This protocol is more secure, flexible, and efficient compared with similar existing protocols, which can save more quantum resources.