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.
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) Threshold d-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) 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.
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.
A (n, n)-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform. In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert. Furthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant. Security analysis shows that our scheme is secure. Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.
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.
(t, n) Threshold Quantum Secret Sharing based on a Single d-level Quantum System
A (t, n) threshold quantum secret sharing (QSS) is proposed based on a single d-level quantum system. It enables the (t, n) threshold structure based on Shamir's secret sharing and simply requires sequential communication in the d-level quantum system to recover secret. Besides, the scheme employs an additional qudit to detect cheats and eavesdropping during secret reconstruction, and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. The scheme is scalable in the number of participants and easier to realize compared to related schemes. More generally, our scheme also presents a generic method to construct new (t, n) threshold QSS schemes based on d-level quantum system with other classical threshold secret sharing.
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.