Quantum Secret Sharing Research Articles

Dynamic (2, 3) Threshold Quantum Secret Sharing of Secure Direct Communication* *Supported in part by an International Macquarie University Research Excellence Scholarship (iMQRES), Australian Research Council Grant DP0987734. This work is also supported by the National Basic Research Program of China (973 Program) under Grant No. 2010CB923200, the National Natural Science Foundation of China under No. 61377067, Fund of State

In this paper, we show that a (2, 3) discrete variable threshold quantum secret sharing scheme of secure direct communication can be achieved based on recurrence using the same devices as in BB84. The scheme is devised by first placing the shares of smaller secret pieces into the shares of the largest secret piece, converting the shares of the largest secret piece into corresponding quantum state sequences, inserting nonorthogonal state particles into the quantum state sequences with the purpose of detecting eavesdropping, and finally sending the new quantum state sequences to the three participants respectively. Consequently, every particle can on average carry up to 1.5-bit messages due to the use of recurrence. The control codes are randomly prepared using the way to generate fountain codes with pre-shared source codes between Alice and Bob, making three participants can detect eavesdropping by themselves without sending classical messages to Alice. Due to the flexible encoding, our scheme is also dynamic, which means that it allows the participants to join and leave freely.

Two-party secret key distribution via a modified quantum secret sharing protocol.

We present and demonstrate a novel protocol for distributing secret keys between two and only two parties based on N-party single-qubit Quantum Secret Sharing (QSS). We demonstrate our new protocol with N = 3 parties using phase-encoded photons. We show that any two out of N parties can build a secret key based on partial information from each other and with collaboration from the remaining N - 2 parties. Our implementation allows for an accessible transition between N-party QSS and arbitrary two party QKD without modification of hardware. In addition, our approach significantly reduces the number of resources such as single photon detectors, lasers and dark fiber connections needed to implement QKD.

Quantum scheme for secret sharing based on local distinguishability

In this paper we analyze the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under {\em restricted local operation and classical communication}. Based on this local distinguishability analysis we propose a new scheme for quantum secret sharing (QSS). Our QSS scheme is quite general and cost efficient compared to other schemes. In our scheme no joint quantum operation is needed to reconstruct the secret. We also present an interesting $(2,n)$-threshold QSS scheme, where any two cooperating players, one from each of two disjoint groups of players, can always reconstruct the secret. This QSS scheme is quite uncommon, as most $(k,n)$-threshold schemes have the restriction $k\geq\lceil\frac{n}{2}\rceil$.

Enhancement of Quantum Secret Sharing Using Exclusive-OR and Shift Operation

We propose quantum secret sharing scheme that emphasizes on the cooperation (twice) of communicating parties to avoid untrustworthy members and improves the strength of the key. The proposed scheme is a new approach in quantum secret sharing in which cooperation of the parties is emphasized at the same time the key is strengthened by performing a shift operation on the received partial keys. In this method, we have managed to achieve the following: security of the key is significantly enhanced; cooperation between parties is also increased (to two) and improved. This method shows that it is difficult for an eavesdropper to obtain the key easily. It is also hard for the communicating parties to cheat since key verification is done twice and if any member cheats, it can easily be identified and communication can be aborted immediately.

A quantum secret-sharing protocol with fairness

A quantum secret-sharing (QSS) protocol consists of two main phases, called sharing and reconstruction. In the first phase, the dealer selects a secret, divides it into several shares, and sends each participant its share securely with a quantum channel. In the second phase, the participants run an interactive protocol in order to reconstruct the secret. If the participants can communicate via a broadcast channel, they can show their shares and learn the secrets simultaneously. So what happens if the channel is not simultaneous? In this paper, we propose a QSS protocol with cheaters by using partially and maximally entangled states. A secure and fair reconstruction mechanism is designed, in a way that each participant can learn or cannot learn the secret simultaneously.

Information Leakage in Quantum Secret Sharing of Multi-Bits by an Entangled Six-Qubit State

In a recent paper Long et al. (J. Phys. A: Math. Theor. 45: 195303, 2012), a quantum secret sharing protocol was presented, in which the genuinely maximally entangled six-qubit states were used. According to the protocol, Alice could share three bits among three agents, which showed that it was more efficient than previous protocols. Here, we analyze it and point out that the information about the transmitted secret will be partly leaked out unknowingly. Through the classical public channel, 2/3 of Alice’s secret messages is leaked out to Bob1 and Bob2, and 1/3 secret messages is leaked out to Bob3, respectively. This phenomenon should be strictly forbidden in a quantum secret sharing protocol.

Improvement and extension of quantum secret sharing using orthogonal product states

The improvement and extension of quantum secret sharing (QSS) using orthogonal product states (OPS) are studied in this paper. Based on such three typical schemes, a quantitative analysis on security is provided. The paper also discusses the simplification measures and their effect on security, and then the possibility to extend is proved. Finally, several conclusions about the methods to improve the security, simplify the schemes and extend to one-to-many situation are given.

Improvement of Efficient Multiparty Quantum Secret Sharing Based on Bell States and Continuous Variable Operations

Yuan et al. (Int. J. Theor. Phys. 51:3443, 2012) proposed a multiparty quantum secret sharing protocol using Bell states and continuous variable operations. Zhang and Qin (Int. J. Theor. Phys. 52:3953, 2013) showed that their protocol is not secure. In this paper, we will give an improvement of Yuan et al. protocol. Our improved protocol can stand against not only Zhang et al. attack strategies, but also the other ones efficiently.

Eavesdropping on Multiparty Quantum Secret Sharing Scheme Based on the Phase Shift Operations

In a recent paper (Du and Bao in Opt. Commun. 308:159, 2013), a scheme of multiparty quantum secret sharing based on the phase shift operations was presented. We study the security of this scheme and find that it is not secure for dishonest participants, who can illegally elicit all of the dealer’s secret message without any error.

High-efficient quantum secret sharing with arrangements of lines on two-dimensional planes

We investigate a simple (2; 2)-threshold scheme and its generalised (n; n)-threshold scheme for the quantum secret sharing (QSS) based on fundamental laws of analytic geometry. The dealer aptly selects the possible Greenberger-Horne-Zeilinger (GHZ) states related to the coefficients which determine the characteristics of straight lines on the same two-dimensional plane. By judging whether two lines intercept or not, we obtain a judging matrix whose rank can be used for determining the secret stored in entangled states. With the aid of the database technology, the authorised participant accesses to the database and achieves the useful information, where the secret never appears in the noisy channel. It is shown that the eavesdropper fails to obtain any secret by applying the individual attack strategy.

Solution to Information Leakage in a Quantum Network System of QSS-QDC Using χ-Type Entangled States

Recently, Hong et al. (Chin. Phys. Lett. 29:050303, 2012) put forward two quantum secret sharing (QSS) protocols of quantum direct communication (QDC) by using χ-type entangled states. Later, some studies (Gao et al. in Chin. Phys. Lett. 29:110305, 2012; Chin. Phys. Lett. 30:079904, 2013; Liu et al. in Chin. Phys. Lett. 30:039901, 2013; Hong and Yang in Chin. Phys. Lett. 30:069901, 2013; Liu and Chen in Chin. Phys. Lett. 30:079903, 2013) made up for the drawbacks of Hong et al.’s two protocols to some extent. However, the information leakage weakness is still not thoroughly solved. In this Letter, the author analyzes the inner reason of information leakage weakness in detail at first. And then he suggests an effective encoding rule to avoid this weakness.

A multiparty error-correcting method for quantum secret sharing

Quantum secret sharing (QSS) refers to the process in which the secret is divided into several sub-secrets and sent to different users utilizing quantum technology. Only the user belonging to a specific subset (authorized set) can reconstruct the initial secret correctly. In principle, the authorized set can regain the initial secret exactly via sub-secrets. However, when realizing QSS in practice, because of the interference of various noises, the secret obtained by the authorized set may not be consistent with the initial one. For a particular kind of QSS protocols, in which the bitwise XOR of sub-secrets is equal to the initial secret theoretically, we propose a feasible multiparty error-correcting method based on binary search technique and two-party Cascade error-correcting method. With this method, we can solve the problem that the authorized set cannot regain the initial secret correctly. Finally, we analyze the optimal block length, the amount of leaked information, and realize tripartite error-correcting method by experimental simulation.

Quantum secret sharing with continuous variable graph state

In this paper, we study several physically feasible quantum secret sharing (QSS) schemes using continuous variable graph state (CVGS). Their implementation protocols are given, and the estimation error formulae are derived. Then, we present a variety of results on the theory of QSS with CVGS. Any \((k,n)\) threshold protocol of the three specific schemes satisfying \(\frac{n}{2}<k\le n\), where \(n\) denotes the total number of players and \(k\) denotes the minimum number of players who can collaboratively access the secret, can be implemented by certain weighted CVGS. The quantum secret is absolutely confidential to any player group with number less than threshold. Besides, the effect of finite squeezing to these results is properly considered. In the end, the duality between two specific schemes is investigated.

Quantum secret sharing for general access structures based on multiparticle entanglements

In this paper, we study the implementation of quantum secret sharing (QSS) schemes for general access structures rather than the threshold structure. Using multiparticle entanglements in high-dimensional system, three novel multipartite QSS formalisms for general access structures are proposed. The method of how to build general access structures in these formalisms is discussed. A major feature of these formalisms is that a variety of secret sharing schemes with different access structures can be constructed depending on the dealer's wish. Besides, hierarchic and threshold authorized structures can also be built. All of which make our formalisms highly flexible.

Experimental single qubit quantum secret sharing in a fiber network configuration

We present a robust single-photon quantum secret sharing (QSS) scheme with phase encoding in three-party implementations and a design way of more parties over a 50 km single-mode fiber network using a single QSS protocol. This scheme automatically provides perfect compensation for birefringence. A high visibility of 99.4% is obtained over three hours in visibility and stability measurements without any system adjustments, showing good potential for practical systems. Furthermore, polarization-insensitive phase modulators are realized using this system.

Accessing quantum secrets via local operations and classical communication

Quantum secret-sharing and quantum error-correction schemes rely on multipartite decoding protocols, yet the non-local operations involved are challenging and sometimes infeasible. Here we construct a quantum secret-sharing protocol with a reduced number of quantum communication channels between the players. Our scheme is based on embedding a classical linear code into a quantum error-correcting code. Our work paves the way towards the more general problem of simplifying the decoding of quantum error-correcting codes.

Quantum simultaneous secret distribution with dense coding by using cluster states

A new communication mode, quantum simultaneous secret distribution (QSSD) is put forward, where one sender distributes different classical secret message to multiparty receivers simultaneously. Based on the properties of the one-dimensional four-qubit cluster states, a three-party QSSD protocol is proposed, and then it is extended to the case that there are many receivers. Owing to the idea of quantum dense coding, each receiver can receive two bits of classical message by the sender only using a cluster state. In order to check security of quantum channels, a strategy which can prevent common attacks efficiently is put forward. QSSD is distinct from quantum secret sharing (QSS) and quantum broadcast communication (QBC), but it can be easily converted into QSS and QBC. QSSD is also different from the multiple-QKD communication mode where the sender shares a private key with each receiver at first, while in QSSD the sender doesn't; in addition, only one round of one-to-many communication is performed in QSSD, while in multiple-QKD communication mode many rounds of one-to-one communication are performed.

Experimental circular quantum secret sharing over telecom fiber network

We present a robust single photon circular quantum secret sharing (QSS) scheme with phase encoding over 50 km single mode fiber network using a circular QSS protocol. Our scheme can automatically provide a perfect compensation of birefringence and remain stable for a long time. A high visibility of 99.3% is obtained. Furthermore, our scheme realizes a polarization insensitive phase modulators. The visibility of this system can be maintained perpetually without any adjustment to the system every time we test the system.

Comment on “Cryptanalysis and Improvement of a Quantum Network System of QSS-QDC Using χ-Type Entangled States" [Chin. Phys. Lett. 29 (2012) 110305

We point out that the quantum secret sharing (QSS) protocol proposed by Gao et al. [Chin. Phys. Lett. 29 (2012) 110305] has some defects. Thus, some strategies are given to mend them.

Improved Three-Party Quantum Secret Sharing Based on Bell States

Hwang et al. (Phys. Scr. 83:045004, 2011) proposed a high efficient multiparty quantum secret sharing by using Greenberger-Horne-Zeilinger (GHZ) states. But Liu et al. (Phys. Scr. 84:045015, 2011) analyzed the security of Hwang et al.’s protocol and found that it was insecure for Charlie who might obtain half of information about the dealer’s secret directly. They put forward an improved protocol by adding operation on photons in sequence S3. However, we point out Liu et al.’s protocol is not secure too if a dishonest participant Charlie carries out intercept-resend attack. And a further improved quantum secret sharing protocol is proposed based on Bell states in this paper. Our newly proposed protocol can stand against participant attack, provide a higher efficiency in transmission and reduce the complexity of implementation.