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Communications in Theoretical Physics

Multiparty Quantum Secret Sharing Using Quantum Fourier Transform

Dazu Huang, Zhigang Chen, Ying Guo

Published Feb 1, 2009• 12 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/51/2/06

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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.
(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 (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.
A novel (n, n) scheme of multiparty quantum group signature of classical or quantum message is proposed based on the discrete quantum Fourier transform. The generation and verification of the signature can be processed only if all the n participants work in concert. Moreover, a new verification manner, in which the message owner and the signing group separately verify the signature on both side by using the entangled state of EPR sequence, is involved in this paper. Security analysis shows that it is feasible to achieve a secure quantum group signature with the secure quantum computation.
Based on a quantum secure direct communication (QSDC) protocol [Phys. Rev. A 69 052319 (2004)], we propose a (n,n)(n,n)(n,n)-threshold scheme of multiparty quantum secret sharing of classical messages (QSSCM) using only single photons. We take advantage of this multiparty QSSCM scheme to establish a scheme of multiparty secret sharing of quantum information (SSQI), in which only all quantum information receivers collaborate can the original qubit be reconstructed. A general idea is also proposed for constructing multiparty SSQI schemes from any QSSCM scheme.
A quantum secret sharing scheme is proposed by making use of quantum registers. In the proposed scheme, secret message state is encoded into multipartite entangled states. Several identical multi-particle entanglement states are generated and each particle of the entanglement state is filled in different quantum registers which act as shares of the secret message. Two modes, i.e. the detecting mode and the message mode, are employed so that the eavesdropping can be detected easily and the secret message may be recovered. The security analysis shows that the proposed scheme is secure against eavesdropping of eavesdropper and cheating of participants.
Utilizing the advantage of Bell state,a multiparty quantum secret sharing protocol with authentication is put forward.In the protocol,the deal encodes two classical bits of secret message on the quantum carrier though performing local unitary operation.He splits the secret message into n shares and then distributes them to n agents via entanglement swapping.Each agent makes a Bell state measurement on the particles in his hand,and obtains his piece of secret according to the measurement result.In the process of reconstruction,these n agents declare respectively their pieces of secret,and recover the secret message if and only if they collaborate.At the same time,combining the technology of Hash function,the identities of the deal and the agents are authenticated.Hence,one main goal of designing the presented protocol,two-way authentication,is achieved.Moreover,we analyze the security and authentication of the presented protocol in detail.It is shown that this protocol can stand against the attacks of outside eavesdropper and inside participant,which means that it is secure in theory.In addition,since the Bell state was used at most,as compared with other quantum secret sharing protocols,the implementation of the presented protocol is more feasible in the current technical conditions.