Quantum Secret Sharing Scheme Research Articles

Verifiable Quantum Secret Sharing Scheme Based on LDPC Codes

Verifiable Quantum Secret Sharing Scheme Based on LDPC Codes

Dynamic and scalable secret sharing schemes based on matrix product compressed states

<sec>Currently, quantum secret sharing (QSS) schemes based on entangled states have not yet fully utilized the potential of the probability amplitude of entangled states. However, the probability amplitude is a key characteristic of quantum information science and possesses significant application prospects in the fields of quantum computing and quantum communication. It is worth noting that entangled states can be effectively represented by matrix product states (MPSs). The representation of entangled states using MPS can precisely reveal the entanglement characteristics closely related to the probability amplitude.</sec><sec>This study first focuses on the representation of the <i>W</i> state by using MPS, an approach that allows us to determine the key conditions for <i>W</i> state to achieve quantum advantage in QSS. Subsequently, this research demonstrates that by representing entangled states with MPS, a <i>W</i> state can be compressed into a single photon state and a simplified matrix form, presenting an innovative technical path.</sec><sec>Moreover, one of the most attractive features of our proposed QSS scheme is its ability to compress multiple different quantum states (represented by photons) into a unified state represented by a single photon. This characteristic endows our scheme with scalability and flexibility, meaning that the group of participants can be easily expanded or reduced according to their specific needs. The addition of new participants is managed by Alice, who is responsible for the distribution of quantum state shares. On the other hand, when a participant leaves the group, their old quantum state share can be simply ignored in the process of recovering the secret's quantum state, thereby simplifying the management process.</sec><sec>Through this strategy, we can not only make effective use of entangled resources but also meet the various requirements of the system, including but not limited to communication security, data transfer rates, and system scalability. This research provides new perspectives and possibilities for the field of quantum information science and may have a significant influence on the development of the field.</sec>

A verifiable (t,n) threshold quantum secret sharing scheme based on asymmetric binary polynomial

Threshold quantum secret sharing is a typical method for quantum secret sharing (QSS) schemes. In this paper, we propose a verifiable threshold QSS scheme based on the -dimensional Bell state and asymmetric binary polynomial. In this scheme, the dealer encodes the secret using the asymmetric binary polynomial and generates the corresponding secret share for each participant. Then, the dealer prepares the -dimensional Bell state, and the participants perform corresponding unitary operations on the particles in transmission to recover the secret. With the hash function and the session key pairs, not only the cheating behavior of the dishonest participants can be detected, but also the specific cheaters can be identified. Furthermore, we consider the case when no less than participants cooperate to recover the secret, which makes the proposed scheme more practical. Analyses show that the scheme can resist forgery attack, collusion attack and other common attacks.

Efficient multiparty quantum secret sharing based on a novel structure and single qubits

Quantum secret sharing (QSS) is a significant branch of quantum cryptography and can be widely used in various applications. Quantum secret sharing schemes can be developed by utilizing different features of quantum mechanics, and quantum secure direct communication (QSDC) is an effective way to achieve secret sharing using single qubits. The utilization of QSDC offers certain benefits, such as low cost, high security, and great potential for implementation with current technologies. However, the purpose of QSDC is different from that of QSS, which causes some vulnerabilities, such as dishonest participant attacks. We discover two critical factors that affect the security of traditional protocols. Firstly, they skip a few steps from the QSDC protocol to the QSS protocol. Secondly, the participants have different privileges. This can lead to participants with more privileges engaging in potential attack behavior. In light of these issues, this study proposes a new multiparty QSS scheme to address these vulnerabilities. The proposed protocol ensures the independence of each participant and grants them equal privileges. Analysis results demonstrate that it can defend against malicious attackers, retain the advantages of the QSDC protocol, and further reduce transmission costs. It achieves an excellent balance between security and performance.

A (t, n) Threshold Quantum Secret Sharing Scheme with Fairness

A (t, n) Threshold Quantum Secret Sharing Scheme with Fairness

A Kind of (t, n) Threshold Quantum Secret Sharing with Identity Authentication.

Quantum secret sharing (QSS) is an important branch of quantum cryptography. Identity authentication is a significant means to achieve information protection, which can effectively confirm the identity information of both communication parties. Due to the importance of information security, more and more communications require identity authentication. We propose a d-level (t,n) threshold QSS scheme in which both sides of the communication use mutually unbiased bases for mutual identity authentication. In the secret recovery phase, the sharing of secrets that only the participant holds will not be disclosed or transmitted. Therefore, external eavesdroppers will not get any information about secrets at this phase. This protocol is more secure, effective, and practical. Security analysis shows that this scheme can effectively resist intercept-resend attacks, entangle-measure attacks, collusion attacks, and forgery attacks.

A novel verifiable weighted threshold quantum secret sharing scheme

Threshold quantum secret sharing is a cryptography technique for dividing and reconstructing secret information. The dealer shares a secret based on quantum mechanics principles, and a subset of participants cooperate to recover that secret. For example, in quantum threshold scheme and quantum threshold scheme, the former can only reconstruct the secret when at least k shares are collected. The latter requires all n shares to be collected to reconstruct the secret. However, in real scenarios, the priority of participant identities may vary. In order to meet the actual needs of participants with different rights, this paper proposes a quantum secret sharing (QSS) scheme. When the sum of participants’ weights w is greater than or equal to a threshold ω, they can cooperate to reconstruct the secret. In order to achieve this, this paper uses the entangled state of single particles and constructs a verifiable QSS scheme based on the Chinese remainder theorem. Significantly, in case of a dishonest participant, the dealer can delete the participant before recovering the secret to ensure the security of the communication. This scheme is more flexible than other threshold protocols. At the same time, it reduces the communication cost of the participants. In addition, security analysis shows that the scheme resists typical external and internal attacks.

Continuous variable quantum secret sharing using directly modulated lasers

Quantum secret sharing (QSS) allows multiple players to achieve unconditional secure communication through an unsecure quantum channel; however, the actual implementation requires a modulator with a high extinction ratio, which means high system expense and miniaturization and commercialization difficulties. In this paper, we propose a continuous variable QSS scheme that can replace the traditional lasers and modulators with directly modulated lasers (DML). Each player prepares quantum states through a DML and sends the signal light to the dealer through a beam splitter into a quantum channel. The method provides a new way for realizing secret key sharing. Moreover, we introduce the chirp estimation algorithm to realize the phase modulation, which can achieve a two-dimensional modulation scheme under a single laser.

Efficient Verifiable Quantum Secret Sharing Schemes via Eight-Quantum-Entangled States

Quantum secret sharing (QSS) protocols are designed to allow a secret message to be divided into several shadows, and the secret can be reconstructed cooperatively. Motivated by the eight quantum entangled (EQE) state, a tripartite verifiable QSS scheme is proposed. It involves three agents, in four phases, i.e., shadow distribution phase, eavesdropping detection phase, measurement and secret sharing phase, verification and secret recover phase. The protocol can not only share and recover the secret correctly, but also verify whether there are dishonest participants in communication. In addition, the protocol is extended to a multiparty quantum secret sharing scheme by utilizing the unitary operations. Security analysis shows that the proposed schemes achieve the fundamental security requirements against the external and internal attackers with the aid of the quantum decoy states. It is shown that the efficiency in classical and quantum transmission is higher than the other protocols.

Multiparty weighted threshold quantum secret sharing based on the Chinese remainder theorem to share quantum information

Secret sharing is a widely-used security protocol and cryptographic primitive in which all people cooperate to restore encrypted information. The characteristics of a quantum field guarantee the security of information; therefore, many researchers are interested in quantum cryptography and quantum secret sharing (QSS) is an important research topic. However, most traditional QSS methods are complex and difficult to implement. In addition, most traditional QSS schemes share classical information, not quantum information which makes them inefficient to transfer and share information. In a weighted threshold QSS method, each participant has each own weight, but assigning weights usually costs multiple quantum states. Quantum state consumption will therefore increase with the weight. It is inefficient and difficult, and therefore not able to successfully build a suitable agreement. The proposed method is the first attempt to build multiparty weighted threshold QSS method using single quantum particles combine with the Chinese remainder theorem (CRT) and phase shift operation. The proposed scheme allows each participant has its own weight and the dealer can encode a quantum state with the phase shift operation. The dividing and recovery characteristics of CRT offer a simple approach to distribute partial keys. The reversibility of phase shift operation can encode and decode the secret. The proposed weighted threshold QSS scheme presents the security analysis of external attacks and internal attacks. Furthermore, the efficiency analysis shows that our method is more efficient, flexible, and simpler to implement than traditional methods.

Improvement of a Level Quantum Secret Sharing Scheme

Recently, a threshold 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.

(t,n) Threshold d-level QSS based on QFT

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 Scheme with Credible Authentication based on Quantum Walk

Quantum Secret Sharing Scheme with Credible Authentication based on Quantum Walk

Improving Continuous Variable Quantum Secret Sharing with Weak Coherent States

Quantum secret sharing (QSS) can usually realize unconditional security with entanglement of quantum systems. While the usual security proof has been established in theoretics, how to defend against the tolerable channel loss in practices is still a challenge. The traditional ( t , n ) threshold schemes are equipped in situation where all participants have equal ability to handle the secret. Here we propose an improved ( t , n ) threshold continuous variable (CV) QSS scheme using weak coherent states transmitting in a chaining channel. In this scheme, one participant prepares for a Gaussian-modulated coherent state (GMCS) transmitted to other participants subsequently. The remaining participants insert independent GMCS prepared locally into the circulating optical modes. The dealer measures the phase and the amplitude quadratures by using double homodyne detectors, and distributes the secret to all participants respectively. Special t out of n participants could recover the original secret using the Lagrange interpolation and their encoded random numbers. Security analysis shows that it could satisfy the secret sharing constraint which requires the legal participants to recover message in a large group. This scheme is more robust against background noise due to the employment of double homodyne detection, which relies on standard apparatuses, such as amplitude and phase modulators, in favor of its potential practical implementations.

Five-Partite Continuous-Variable Quantum State Sharing

Quantum secret sharing (QSS) is a project to distribute a secret message to multi-parties, who cannot restore it individually only need to cooperate in order to decode it. Here we design a five-partite QSS scheme to perform continuous-variable threshold quantum secret sharing. To finish the secret reconstruction for five players, we use two different methods including feedfoward loop and Mach-Zehnder interferometers. It shows that this scheme can yield perfect secret reconstruction.

Improved quantum secret sharing scheme based on GHZ states

With the rapid progress of quantum cryptography, secret sharing has been developed in the quantum setting for achieving a high level of security, which is known as quantum secret sharing (QSS). The first QSS scheme was proposed by Hillery et al. in 1999 [Phys. Rev. A, Vol. 59, p.1829 (1999)] based on entangled Greenberger-Horne-Zeilinger (GHZ) states. However, only 50% of the entangled quantum states are effective for eavesdropping detection and secret splitting in the original scheme. In this paper, we introduce a possible method, called measurement-delay strategy, to improve the qubit efficiency of the GHZ-based QSS scheme. By using this method, the qubit efficiency of the improved QSS scheme can reach 100% for both security detection and secret distribution. The improved QSS scheme can be implemented experimentally based on current technologies.

Continuous Variable Quantum Secret Sharing with Fairness

The dishonest participants have many advantages to gain others’ shares by cheating in quantum secret sharing (QSS) protocols. However, the traditional methods such as identity authentication and message authentication can not resolve this problem due to the reason that the share has already been released to dishonest participants before realizing the deception. In this paper, a continuous variable QSS (CVQSS) scheme is proposed with fairness which ensures all participants can acquire or can not acquire the secret simultaneously. The quantum channel based on two-mode squeezing states provides secure communications through which it can send shares successfully, as long as setting the squeezing and modulation parameters according to the quantum channel transmission efficiency and the Shannon information of shares. In addition, the Chinese Remainder Theorem (CRT) can provides tunable threshold structures according to demands of the complex quantum network and the strategy for fairness can be incorporated with other sharing schemes, resulting in perfect compatibility for practical implementations.

A verifiable framework of entanglement-free quantum secret sharing with information-theoretical security

Quantum secret sharing (QSS) schemes without entanglement have huge advantages in scalability and are easier to realize as they only require sequential communications of a single quantum system. However, these schemes often come with drawbacks such as exact ($n, n$) structure, security flaws and absences of effective cheating detections. To address these problems, we propose a verifiable framework by utilizing entanglement-free states to construct ($t, n$)-QSS schemes. Our work is the heuristic step towards information-theoretical security in entanglement-free QSS, and it sheds light on how to establish effective verification mechanism against cheating. As a result, the proposed framework has a significant importance in constructing QSS schemes for versatile applications in quantum networks due to its intrinsic scalability, flexibility and information theoretical security.

Measurement-device-independent quantum secret sharing and quantum conference based on Gaussian cluster state

Cluster state is the basic resource for one-way quantum computation and a valuable resource for establishing quantum network, because it has a flexible and varied composition form. We present measurement-device-independent quantum secret sharing (QSS) and quantum conference (QC) schemes based on continuous variable (CV) four-mode cluster state with different structures. The users of the protocol prepare their own Einstein-Podolsky-Rosen (EPR) states, respectively. One mode of these EPR states is sent to an untrusted relay where a generalized Bell measurement creates different types of CV cluster states among four users, while the other mode is kept at their own station. We show that a shared secret key for QSS and QC schemes is distilled based on the shared quantum correlation among four users. QC and four users QSS are implemented based on the star shape CV cluster state. QSS with three users are implemented based on the linear or square shape CV cluster states. The results show that the secure transmission distance for an asymmetric network, where the transmission distances between the users and relay are different, is longer than that of a symmetric network, where the transmission distances between the users and relay are the same. The presented schemes provide concrete references for establishing quantum network with the CV cluster state.

A New Quantum Secret Sharing Scheme Based on Mutually Unbiased Bases

In this paper, we put forward a new secret sharing scheme. First, we give the mutually unbiased bases on the p2-dimensional quantum system where p is an odd prime number, and then we construct the corresponding unitary transformation based on the properties of these mutually unbiased bases. Second, we construct a (N, N) threshold secret sharing scheme by using unitary transformation between these mutually unbiased bases. At last, we analyze the scheme’s security by several ways, for example, intercept-and-resend attack, entangle-and-measure attack, trojan horse attack, and so on. Using our method, we construct a single-particle quantum protocol involving only one qudit, and the method shows much more scalability than other schemes.