Verifiable quantum secret sharing scheme based on orthogonal product states

In the domain of quantum cryptography,the implementation of quantum secret sharing stands as a pivotal element.In this paper,we propose a novel verifiable quantum secret sharing protocol using the d-dimensional product state and Lagrange interpolation techniques.This protocol is initiated by the dealer Alice,who initially prepares a quantum product state,selected from a predefined set of orthogonal product states within the C~d■C~d framework.Subsequently,the participants execute unitary operations on this product state to recover the underlying secret.Furthermore,we subject the protocol to a rigorous security analysis,considering both eavesdropping attacks and potential dishonesty from the participants.Finally,we conduct a comparative analysis of our protocol against existing schemes.Our scheme exhibits economies of scale by exclusively employing quantum product states,thereby realizing significant cost-efficiency advantages.In terms of access structure,we adopt a(t, n)-threshold architecture,a strategic choice that augments the protocol's practicality and suitability for diverse applications.Furthermore,our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.

Improvement and security analysis of multi-ring discrete modulation continuous variable quantum secret sharing scheme

In order to avoid the complexity of Gaussian modulation and the problem that the traditional point-to-point communication DM-CVQKD protocol cannot meet the demand for multi-user key sharing at the same time, we propose a multi-ring discrete modulation continuous variable quantum key sharing scheme(MR-DM-CVQSS). In this paper, we primarily compare single-ring and multi-ring M-symbol amplitude and phase-shift keying modulations. We analyze their asymptotic key rates against collective attacks and consider the security key rates under finite-size effects. Leveraging the characteristics of discrete modulation, we improve the quantum secret sharing scheme. Non-dealer participants only require simple phase shifters to complete quantum secret sharing. We also provide the general design of the MR-DM-CVQSS protocol.We conduct a comprehensive analysis of the improved protocol's performance, confirming that the enhancement through multi-ring M-PSK allows for longer-distance quantum key distribution. Additionally, it reduces the deployment complexity of the system, thereby increasing the practical value.

An efficient multiparty quantum secret sharing scheme using a single qudit

The aim of quantum secret sharing,as one of most promising components of quantum cryptograph,is one-tomultiparty secret communication based on the principles of quantum mechanics.In this paper,an efficient multiparty quantum secret sharing protocol in a high-dimensional quantum system using a single qudit is proposed.Each participant's shadow is encoded on a single qudit via a measuring basis encryption method,which avoids the waste of qudits caused by basis reconciliation.Security analysis indicates that the proposed protocol is immune to general attacks,such as the measure-resend attack,entangle-and-measure attack and Trojan horse attack.Compared to former protocols,the proposed protocol only needs to perform the single-qudit measurement operation,and can share the predetermined dits instead of random bits or dits.

Circular threshold quantum secret sharing

This paper proposes a circular threshold quantum secret sharing （TQSS） scheme with polarized single photons. A polarized single photon sequence runs circularly among any t or more of n parties and any t or more of n parties can reconstruct the secret key when they collaborate. It shows that entanglement is not necessary for quantum secret sharing. Moreover, the theoretic efficiency is improved to approach 100% as the single photons carrying the secret key are deterministically forwarded among any t or more of n parties, and each photon can carry one bit of information without quantum storage. This protocol is feasible with current technology.

High-dimension multiparty quantum secret sharing scheme with Einstein-Podolsky-Rosen pairs

In this paper a high-dimension multiparty quantum secret sharing scheme is proposed by using Einstein-Podolsky-Rosen pairs and local unitary operators. This scheme has the advantage of not only having higher capacity, but also saving storage space. The security analysis is also given.

Participant attack on quantum secret sharing based on entanglement swapping

The security of quantum secret sharing based on entanglement swapping is revisited and a participant attack is presented. In this attack two dishonest agents together can illegally recover the secret quantum state without the help of any other controller, and it will not be detected by any other users. Furthermore, by modifying the distribution process of particles and adding a detection step after each distribution process, we propose an improved protocol which can resist this kind of attack.

Measurement-device-independent quantum secret sharing with hyper-encoding

Quantum secret sharing(QSS) is a typical multi-party quantum communication mode, in which the key sender splits a key into several parts and the participants can obtain the key by cooperation. Measurement-device-independent quantum secret sharing(MDI-QSS) is immune to all possible attacks from measurement devices and can greatly enhance QSS's security in practical applications. However, previous MDI-QSS's key generation rate is relatively low. Here, we adopt the polarization-spatial-mode hyper-encoding technology in the MDI-QSS, which can increase single photon's channel capacity. Meanwhile, we use the cross-Kerr nonlinearity to realize the complete hyper-entangled Greenberger-Horne-Zeilinger state analysis. Both above factors can increase MDI-QSS's key generation rate by about 10^(3). The proposed hyper-encoded MDI-QSS protocol may be useful for future multiparity quantum communication applications.

Dynamic quantum secret sharing protocol based on two-particle transform of Bell states

To solve the problems of updating sub-secrets or secrets as well as adding or deleting agents in the quantum secret sharing protocol, we propose a two-particle transform of Bell states, and consequently present a novel dynamic quantum secret sharing protocol. The new protocol can not only resist some typical attacks, but also be more efficient than the existing protocols. Furthermore, we take advantage of the protocol to establish the dynamic secret sharing of a quantum state protocol for two-particle maximum entangled states.

Multiparty Quantum Secret Sharing Using Two-Photon Three-Dimensional Bell States

We present a two-photon three-dimensional multiparty quantum secret sharing scheme.The secret messagesare encoded by performing local operations.This is different from those quantum secret sharing protocols that all sharersmust make a state measurement.The merit of our protocol is the high capacity.

Quantum Secret Sharing Based on Chinese Remainder Theorem

A novel quantum secret sharing （QSS） scheme is proposed on the basis of Chinese Remainder Theorem （CRT）. In the scheme, the classical messages are mapped to secret sequences according to CRT equations, and distributed to different receivers by different dimensional superdense-coding respectively. CRT＇s secret sharing function, together with high-dimensional superdense-eoding, provide convenience, security, and large capability quantum channel for secret distribution and recovering. Analysis shows the security of the scheme.

Multiparty Quantum Secret Sharing Using Quantum Fourier Transform

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. Fhrthermore, 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.

High-capacity three-party quantum secret sharing with superdense coding

This paper presents a scheme for high-capacity three-party quantum secret sharing with quantum superdense coding, following some ideas in the work by Liuet al （2002 Phys. Rev. A 65 022304） and the quantum secret sharing scheme by Deng et al （2008 Phys. Lett. A 372 1957）. Instead of using two sets of nonorthogonal states, the boss Alice needs only to prepare a sequence of Einstei^Podolsky-l^osen pairs in d-dimension. The two agents Bob and Charlie encode their information with dense coding unitary operations, and security is checked by inserting decoy photons. The scheme has a high capacity and intrinsic efficiency as each pair can carry 21bd bits of information, and almost all the pairs can be used for carrying useful information.

Quantum Secret Sharing Using GHZ-Like State

This paper presents a simple and novel quantum secret sharing scheme using GHZ-like state. The characteristics of the GHZ-like state are used to develop the quantum secret sharing scheme. In contrast with the other GHZ-based QSS protocols with the same assumptions, the proposed protocol provides the best quantum bit efficiency.

Universal Three-Party Quantum Secret Sharing Against Collective Noise

we present a robust and universal quantum secret sharing protocol with four-qubit decoherence-free （DF） states against collective noise. The transmission＇s safety is ensured by the nonorthogonality of the noiseless states traveling on the quantum channel. Although this scheme uses entangled states for encoding, only single-particle product measurements are required.

Enhancement of GAO's Multiparty Quantum Secret Sharing

A multiparty quantum secret sharing (MQSS) protocol with two-photon three-dimensional Bell states was proposed by Gao [Commun. Theor. Phys. 52 (2009) 421] recently. This study points out that the performance of Gao's protocol can be much improved by using the technique of decoy single photons and carefully modifying the protocol to remove some unnecessary unitary operations, devices, and transmissions.

Multiparty Quantum Secret Sharing of Secure Direct Communication Using Teleportation

We present an （n, n） threshold quantum secret sharing scheme of secure direct communication using Greenberger-Horne-Zeilinger state and teleportation. After ensuring the security of the quantum channel, the sender encodes the secret message directly on a sequence of particle states and transmits it to the receivers by teleportation. The receivers can recover the secret message by combining their measurement results with the sender＇s result. Ira perfect quantum channel is used, our scheme is completely secure because the transmitting particle sequence does not carry the secret message. We also show our scheme is secure for noise quantum channel.

Multiparty Quantum Secret Sharing via Introducing Auxiliary Particles Using a Pure Entangled State

We propose a new multiparty quantum secret sharing protocol via introducing auxiliary particles using a non-maximally entangled （pure） two-particle state without a Bell measurement. The communication parties utilize decoy particles tO check eavesdropping. After ensuring the security of the quantum channel, the sender encodes the secret message and transmits it to the receiver by using controlled-NOT operation and von Neumann measurement. If and only if all the agents agree to collaborate, they can read out the secret message.

Three-party quantum secret sharing of secure direct communication based on χ-type entangled states

Based on x-type entangled states and the two-step protocol [Deng F G, Long G L and Liu X S 2003 Phys. Rev. A 68 042317], a quantum secret sharing protocol of secure direct communication based on x-type entangled states ｜X00〉3214 is proposed. Using some interesting entanglement properties of this state, the agent entirety can directly obtain the secret message from the message sender only if they collaborate together. The security of the scheme is also discussed.

Cryptanalysis and improvement of a quantum secret sharing scheme based on χ-type entangled states

In the paper [2010 Chin. Phys. B 19 050306], Yang et al. put forward a novel three-party quantum secret sharing protocol of secure direct communication based on x-type entangled states, they claimed that the scheme is secure. However, in this paper, we study the security of the protocol and find that it is insecure. Applying intercept and resend attack, the agent Bob can obtain Alice＇s secret without the help from the other agent Charlie. In the end, we give our effective modification for its improvement.

Enhancing the security of quantum secret sharing against multiphoton attack

It is generally believed that nonorthogonal operations which can realize the state transformation between two nonorthogonal bases may ensure the security of many quantum communication protocols. However, in this paper, we present a powerful attack against quantum secret sharing protocols of these kinds. Applying entangled photons as fake signals, Eve can successfully steal the exact information without being revealed. We also give our effective modification to improve it. Under the suggested checking strategy, even to Eve＇s most general attack, it is robust and secure.