Secret sharing is a multiparty cryptographic task in which some secret information is splitted into several pieces which are distributed among the participants such that only an authorized set of participants can reconstruct the original secret. Similar to quantum key distribution, in quantum secret sharing, the secrecy of the shared information relies not on computational assumptions, but on laws of quantum physics. Here, we present an experimental demonstration of four-party quantum secret sharing via the resource of four-photon entanglement.
Lin et al. [S. Lin, F. Gao, Q.-y. Wen, F.-c. Zhu, Opt. Commun. 281 (2008) 4553] pointed that the multiparty quantum secret sharing protocol [Z.-j. Zhang, G. Gao, X. Wang, L.-f. Han, S.-h. Shi, Opt. Commun. 269 (2007) 418] is insecure and proposed an improved three-party quantum secret sharing protocol. In this paper, we study the security of the improved three-party quantum secret sharing protocol and find that it is still insecure. Finally, a further improved three-party quantum secret sharing protocol is proposed.
In a conventional quantum (k,n) threshold scheme, a trusted party shares a secret quantum state with n participants such that any k of those participants can cooperate to recover the original secret, while fewer than k participants obtain no information about the secret. In this paper we show how to construct a quantum (k,n) threshold scheme without the assistance of a trusted party, who generates and distributes shares among the participants. Instead, each participant chooses his private state and contributes the same to the determination of the final secret quantum state.
We propose a quantum secret sharing protocol between multi-party ($m$ members in group 1) and multi-party ($n$ members in group 2) using a sequence of single photons. These single photons are used directly to encode classical information in a quantum secret sharing process. In this protocol, all members in group 1 directly encode their respective keys on the states of single photons via unitary operations, then the last one (the $m^{th}$ member of group 1) sends $1/n$ of the resulting qubits to each of group 2. Thus the secret message shared by all members of group 1 is shared by all members o…
We develop a three-party quantum secret sharing protocol based on arbitrary dimensional quantum states. In contrast to the previous quantum secret sharing protocols, the sender can always control the state, just using local operations, for adjusting the correlation of measurement directions of three parties and thus there is no waste of resource due to the discord between the directions. Moreover, our protocol contains the hidden value which enables the sender to leak no information of secret key to the dishonest receiver until the last steps of the procedure.
We propose a quantum secret sharing scheme between $m$-party and $n$-party using three conjugate bases, i.e. six states. A sequence of single photons, each of which is prepared in one of the six states, is used directly to encode classical information in the quantum secret sharing process. In this scheme, each of all $m$ members in group 1 choose randomly their own secret key individually and independently, and then directly encode their respective secret information on the states of single photons via unitary operations, then the last one (the $m$th member of group 1) sends $1/n$ of the resul…
In this paper, a novel multi-party quantum private comparison (MQPC) protocol with a semi-honest third party (TP) is proposed based on the entanglement swapping of d-level cat states and d-level Bell states. Here, TP is allowed to misbehave on his own but will not conspire with any party. In our protocol, n parties employ unitary operations to encode their private secrets and can compare the equality of their private secrets within one time execution of the protocol. Our protocol can withstand both the outside attacks and the participant attacks on the condition that none of the QKD methods is…
Security of the three-party quantum secret sharing (QSS) schemes based on entanglement and a collective eavesdropping check is analyzed in the case of considerable quantum channel losses. An opaque attack scheme is presented for the dishonest agent to eavesdrop the message obtained by the other agent freely, which reveals that these QSS schemes are insecure for transmission efficiencies lower than 50%, especially when they are used to share an unknown quantum state. Finally, we present a general way to improve the security of QSS schemes for sharing not only a private key but also an unknown q…
We propose a simultaneous quantum secure direct communication scheme between one party and other three parties via four-particle GHZ states and swapping quantum entanglement. In the scheme, three spatially separated senders, Alice, Bob and Charlie, transmit their secret messages to a remote receiver Diana by performing a series local operations on their respective particles according to the quadripartite stipulation. From Alice, Bob, Charlie and Diana's Bell measurement results, Diana can infer the secret messages. If a perfect quantum channel is used, the secret messages are faithfully transm…
Recently, Yang et al. (Quantum Inf Process:17:129, 2018) proposed a secure multi-party quantum summation protocol allowing the involved participants to sum their secrets privately. They claimed that the proposed protocol can prevent each participant's secret from being known by others. However, this study shows that the participant who prepares the initial quantum states can obtain other participants' secrets with an inverse quantum Fourier transform attack. A modification is then proposed here to solve this problem.
In this work, we generalize the quantum secret sharing scheme of Hillary, Bužek and Berthiaume[Phys. Rev. A59, 1829(1999)] into arbitrary multi-parties. Explicit expressions for the shared secret bit is given. It is shown that in the Hillery-Bužek-Berthiaume quantum secret sharing scheme the secret information is shared in the parity of binary strings formed by the measured outcomes of the participants. In addition, we have increased the efficiency of the quantum secret sharing scheme by generalizing two techniques from quantum key distribution. The favored-measuring-basis Quantum secret shari…
The work presents an amalgam of quantum search algorithm (QSA) and quantum secret sharing (QSS). The proposed QSS scheme utilizes Grover's three-particle quantum state. In this scheme, the dealer prepares an encoded state by encoding the classical information as a marked state and shares the states' qubits between three participants. The participants combine their qubits and find the marked state as a measurement result of the three-qubit state. The security analysis shows the scheme is stringent against malicious participants or eavesdroppers. In comparison to the existing schemes, our protoc…
In this paper, a novel multi-party quantum private comparison (MQPC) protocol for equality comparison with n-level single-particle states is constructed, where the encoded particles are transmitted in a circular way. Here, n parties employ the qudit shifting operation to encode their private secrets and can compare the equality of their private secrets within one time execution of protocol. The proposed MQPC protocol can overcome both the outside attack and the participant attack. Specially, each party's secret can be kept unknown to other parties and the third party (TP).
We analyze the capacity of a simultaneous quantum secure direct communication scheme between the central party and other $M$ parties via $M+1$-particle GHZ states and swapping quantum entanglement. It is shown that the encoding scheme should be secret if other $M$ parties wants to transmit $M+1$ bit classical messages to the center party secretly. However when the encoding scheme is announced publicly, we prove that the capacity of the scheme in transmitting the secret messages is 2 bits, no matter how big $M$ is.
Broadcast encryption allows the sender to securely distribute his/her secret to a dynamically changing group of users over a broadcast channel. In this paper, we just consider a simple broadcast communication task in quantum scenario, which the central party broadcasts his secret to multi-receiver via quantum channel. We present three quantum broadcast communication schemes. The first scheme utilizes entanglement swapping and Greenberger-Horne-Zeilinger state to realize a task that the central party broadcasts his secret to a group of receivers who share a group key with him. In the second sch…
The quantum key distribution network with Vernam's One Time Pad encryption and secret sharing are powerful security tools to realize an information theoretically secure distributed storage system. In our previous work, a single-password-authenticated secret sharing scheme based on the QKD network and Shamir's secret sharing was experimentally demonstrated; it confirmed ITS data transmission, storage, authentication, and integrity. To achieve data integrity, an ITS message authentication code tag is employed and a data owner of the secret sharing performs both the MAC tag generation and verific…
Quantum secret sharing allows each player to have classical information for secret sharing in quantum mechanical ways. In this work, we construct a class of quantum states on which players can quantumly perform secret sharing secure against dishonest players as well as eavesdropper. We here call them the genuine secret-sharing states. In addition, we show that if $N$ players share an $N$-party genuine secret-sharing state, then arbitrary $M$ players out of the total players can share an $M$-party genuine secret-sharing state by means of local operations and classical communication on the state…
In this paper, by using d-level single-particle states, two novel multi-party quantum private comparison protocols for size relation comparison with two semi-honest third parties and one semi-honest third party are constructed, respectively. Here, each protocol can compare the size relation of secret integers from n parties rather than just the equality within one time execution. In each protocol, every third party is assumed to be semi-honest in the sense that she may misbehave on her own but is not allowed to collude with anyone else; and each party employs the qudit shifting operation to en…
Recently, Sun et al. [Quant Inf Proc DOI: 10.1007/s11128-013-0569-x] presented an efficient multi-party quantum key agreement (QKA) protocol by employing single particles and unitary operations. The aim of this protocol is to fairly and securely negotiate a secret session key among $N$ parties with a high qubit efficiency. In addition, the authors claimed that no participant can learn anything more than his/her prescribed output in this protocol, i.e., the sub-secret keys of the participants can be kept secret during the protocol. However, here we points out that the sub-secret of a participan…
Quantum secret sharing is one of the most important and interesting quantum information processing task. In quantum secret sharing, information is split among several parties such that only one of them is able to recover the qubit exactly provided all the other parties agree to cooperate. To achieve this task, all the parties need to share entangled state. As far as my knowledge, all the previous quantum secret sharing protocol used either pure tripartite or pure bipartite entangled state. In this work we use for the first time bipartite two qubit mixed state (formed due to noisy environment) …
We investigate definitions of and protocols for multi-party quantum computing in the scenario where the secret data are quantum systems. We work in the quantum information-theoretic model, where no assumptions are made on the computational power of the adversary. For the slightly weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to establish that any multi-party quantum computation can be securely performed as long as the number of dishonest players is less than n/6.
In this note, we study some properties of the GHZ state. First, we present a quantum secret sharing scheme in which the participants require only classical channels in order to reconstruct the secret; our protocol is significantly more efficient than the trivial usage of teleportation. Second, we show that the classical simulation of an n-party GHZ state requires at least n log n - 2n bits of communication. Finally, we present a problem simpler than the complete simulation of the multi-party GHZ state, that could lead to a no-go theorem for GHZ state simulation.
In this paper, we propose a novel secure multi-party quantum summation protocol based on quantum Fourier transform, where the traveling particles are transmitted in a tree-type mode. The party who prepares the initial quantum states is assumed to be semi-honest, which means that she may misbehave on her own but will not conspire with anyone. The proposed protocol can resist both the outside attacks and the participant attacks. Especially, one party cannot obtain other parties' private integer strings; and it is secure for the colluding attack performed by at most n-2 parties, where n is the nu…
In this work, we present a quantum secret sharing scheme based on Bell state entanglement and sequential projection measurements. The protocol verifies the $n$ out of $n$ scheme and supports the aborting of the protocol in case all the parties do not divulge in their valid measurement outcomes. The operator-qubit pair forms an integral part of the scheme determining the classical secret to be shared. The protocol is robust enough to neutralize any eavesdropping on a particular qubit of the dealer. The experimental demonstration of the scheme is done on IBM-QE cloud platform with backends \text…
This study presents the first semi-quantum private comparison protocol under an almost-dishonest third party. The proposed protocol allows two classical participants to compare their secret information without compromising it's privacy. The security analyses indicate that the protocol is free from several well-known attacks.
A general proof of the security against eavesdropping of a previously introduced protocol for two-party quantum key distribution based on entanglement swapping [Phys. Rev. A {\bf 61}, 052312 (2000)] is provided. In addition, the protocol is extended to permit multiparty quantum key distribution and secret sharing of classical information.
In this paper, a multi-party quantum private comparison (MQPC) scheme is suggested based on entanglement swapping of Bell entangled states within d-level quantum system, which can accomplish the equality comparison of secret binary sequences from n users via one execution of scheme. Detailed security analysis shows that both the outside attack and the participant attack are ineffective. The suggested scheme needn't establish a private key among n users beforehand through the quantum key distribution (QKD) method to encrypt the secret binary sequences. Compared with previous MQPC scheme based o…
In this paper, we consider the secret-string-learning problem in the teacher-student setting: the teacher has a secret string $s\in {\{0,1\}^{n}}$, and the student wants to learn the secret $s$ by question-answer interactions with the teacher, where at each time, the student can ask the teacher with a pair $(x, q) \in {\{0,1\}^{n}}\times\{0,1,\cdots, n-1\}$ and the teacher returns a bit given by the oracle $f_{s}(x,q)$ that indicates whether the length of the longest common prefix of $s$ and $x$ is greater than $q$ or not. Our contributions are as follows. (i) We prove that any classical deter…
Device-Independent Quantum Secret Sharing Protocol Enhanced by Advantage Distillation
Henan Key Laboratory of Quantum Information and Cryptography（河南省量子信息与密码学重点实验室）；Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学量子信息与量子物理协同创新中心）
We present a scheme for three-party simultaneous quantum secure direct communication by using EPR pairs. In the scheme, three legitimate parties can simultaneously exchange their secret messages. It is also proved to be secure against the intercept-and-resend attack, the disturbance attack and the entangled-and-measure attack.
A rational secret sharing scheme is a game in which each party responsible for reconstructing a secret tries to maximize his utility by obtaining the secret alone. Quantum secret sharing schemes, either derived from quantum teleportation or from quantum error correcting code, do not succeed when we assume rational participants. This is because all existing quantum secret sharing schemes consider that the secret is reconstructed by a party chosen by the dealer. In this paper, for the first time, we propose a quantum secret sharing scheme which is resistant to rational parties. The proposed sche…
Quantum secure direct communication (QSDC) and deterministic secure quantum communication (DSQC) are two important branches of quantum cryptography, where one can transmit a secret message securely without encrypting it by a prior key. In the practical scenario, an adversary can apply detector-side-channel attacks to get some non-negligible amount of information about the secret message. Measurement-device-independent (MDI) quantum protocols can remove this kind of detector-side-channel attack, by introducing an untrusted third party (UTP), who performs all the measurements during the protocol…
Recently, Liu W et al. proposed a two-party quantum private comparison (QPC) protocol using entanglement swapping of Bell entangled state (Commun. Theor. Phys. 57(2012)583-588). Subsequently, Liu W J et al. pointed out that in Liu W et al.'s protocol, the TP can extract the two users' secret inputs without being detected by launching the Bell-basis measurement attack, and suggested the corresponding improvement to mend this loophole (Commun. Theor. Phys. 62(2014)210-214). In this paper, we first point out the information leakage problem toward TP existing in both of the above two protocols, an…
In this paper, we present a quantum secure multi-party summation protocol, which allows multiple mutually distrustful parties to securely compute the summation of their secret data. In the presented protocol, a semitrusted third party is introduced to help multiple parties to achieve this secure task. Besides, the entanglement swapping of $d$-level cat states and Bell states is employed to securely transmit message between each party and the semitrusted third party. At last, its security against some common attacks is analyzed, which shows that the presented protocol is secure in theory.
Quantum privacy comparison(QPC) plays an important role in secret ballot elections, private auctions and so on. To date, many multi-party QPC(MQPC) protocols have been proposed to compare the equality of $k(k\geq 3)$ participants. However, there are few examples of MQPC used to compare the sizes or values of their privacies. In this paper, we propose a MQPC protocol by which any $k(k\geq 3)$ participants can compare the sizes of their privacies with executing the protocol just once. The proposed MQPC protocol takes the $d-level$ GHZ states as quantum resources, and a semi-honest $TP$ is introd…
A multiparty quantum secret sharing (QSS) protocol is proposed by using swapping quantum entanglement of Bell states. The secret messages are imposed on Bell states by local unitary operations. The secret messages are split into several parts and each part is distributed to a party so that no action of a subset of all the parties but their entire cooperation is able to read out the secret messages. In addition, the dense coding is used in this protocol to achieve a high efficiency. The security of the present multiparty QSS against eavesdropping has been analyzed and confirmed even in a noisy …
Recently, it was discovered that the `quantum partial information' needed to merge one party's state with another party's state is given by the conditional entropy, which can be negative [Horodecki, Oppenheim, and Winter, Nature 436, 673 (2005)]. Here we find a classical analogue of this, based on a long known relationship between entanglement and shared private correlations: namely, we consider a private distribution held between two parties, and correlated to a reference system, and ask how much secret communication is needed for one party to send her distribution to the other. We give optim…
We present a quantum secure direct communication protocol and a multiparty quantum secret sharing protocol based on Einstein-Podolsky-Rosen pairs and entanglement swapping. The present quantum secure direct communication protocol makes use of the ideal of block transmission. We also point out that the sender can encode his or her secret message without ensuring the security of the quantum channel firstly. In the multiparty quantum secret sharing protocol, the communication parties adopt checking mode or encoding mode with a certain probability. It is not necessary for the protocol to perform l…
Quantum protocols for secret sharing usually rely on multi-party entanglement which with present technology is very difficult to achieve. Recently it has been shown that sequential manipulation and communication of a single $d-$ level state can do the same task of secret sharing between $N$ parties, hence alleviating the need for entanglement. However the suggested protocol which is based on using mutually unbiased bases, works only when $d$ is a prime number. We propose a new sequential protocol which is valid for any $d$.
We propose a new quantum secret sharing scheme using a single non-entangled qubit. In the scheme, by transmitting a qubit to the next party sequentially, a sender can securely transmit a secret message to $N$ receivers who could only decode the message cooperatively after randomly shuffling the polarization of the qubit. We explain this quantum secret sharing scheme into the one between a sender and two receivers, and generalize the scheme between a sender and $N$ receivers. Since our scheme is capable of using a faint coherent pulse as a qubit, it is experimentally feasible within current tec…
Semi-quantum secret sharing (SQSS) is an important branch of semi-quantum cryptography, and differs from quantum secret sharing (QSS) in that not all parties are required to possess quantum capabilities. All previous SQSS protocols have three common features: (1) they adopt product states or entangled states as initial quantum resource; (2) the particles prepared by quantum party are transmitted in a tree-type way; and (3) they require the classical parties to possess the measurement capability. In this paper, two circular SQSS protocols with single particles are suggested, where the first one…
An authentic digital signature scheme based on the correlation of Greenberger-Horne-Zeilinger (GHZ) states was presented. In this scheme, by performing a local unitary operation on the third particles of each GHZ triplet, Alice can encode message M and get its signature S. Bob performs CNOT operation on the combined GHZ triplets can recovery the message M and directly authenticates Alice's signature S. Our scheme was designed to use quantum secret key to guaranteed unconditional security, as well as use quantum fingerprinting to avoid trick attacks and reduce communication complexity.
Distributed quantum communication and quantum computing offer many new opportunities for quantum information processing. Here networks based on highly nonlocal quantum resources with complex entanglement structures have been proposed for distributing, sharing and processing quantum information. Graph states in particular have emerged as powerful resources for such tasks using measurement-based techniques. We report an experimental demonstration of graph-state quantum secret sharing, an important primitive for a quantum network. We use an all-optical setup to encode quantum information into pho…
Secure multi-party computing, also called "secure function evaluation", has been extensively studied in classical cryptography. We consider the extension of this task to computation with quantum inputs and circuits. Our protocols are information-theoretically secure, i.e. no assumptions are made on the computational power of the adversary. For the weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to show how to perform any multi-party quantum computation as long as the …
Distributing secret keys with information-theoretic security is arguably one of the most important achievements of the field of quantum information processing and communications. The rapid progress in this field has enabled quantum key distribution (QKD) in real-world conditions and commercial devices are now readily available. QKD systems based on continuous variables present the major advantage that they only require standard telecommunication technology, and in particular, that they do not use photon counters. However, these systems were considered up till now unsuitable for long-distance c…
In this article, we propose an interactive protocol for one party (the verifier) holding a quantum computer to verify the quantum computation power of another party's (the prover) device via a one-way quantum channel. This protocol is referred to as the dihedral coset problem (DCP) challenge. The verifier needs to prepare quantum states encoding secrets (DCP samples) and send them to the prover. The prover is then tasked with recovering those secrets with a certain accuracy. Numerical simulation demonstrates that this accuracy is sensitive to errors in quantum hardware. Additionally, the DCP c…
The efficacies of maximally and that of non-maximally entangled mixed states as teleportation channels have been studied. A new class of non-maximally entangled mixed states have been proposed also. Their advantages as quantum teleportation channels over existing non-maximally entangled mixed states have been verified. The mixed states can also be generated using quantum cloning machines. We have also studied how one can utilize the mixed entangled states obtained as output from a state independent quantum cloning machine in teleportation and dense coding. Mixed states can also be used in secr…
Quantum key distribution (QKD) is a provably secure way for two distant parties to establish a common secret key, which then can be used in a classical cryptographic scheme. Using quantum entanglement, one can reduce the necessary assumptions that the parties have to make about their devices, giving rise to device-independent QKD (DIQKD). However, in all existing protocols to date the parties need to have an initial (at least partially) random seed as a resource. In this work, we show that this requirement can be dropped. Using recent advances in the fields of randomness amplification and rand…
Quantum key distribution (QKD) is a promising technology aiming at solving the security problem arising from the advent of quantum computers. While the main theoretical aspects are well developed today, limited performances, in terms of achievable link distance and secret key rate, are preventing the deployment of this technology on a large scale. More recent QKD protocols, which use multiple degrees of freedom for the encoding of the quantum states, allow an enhancement of the system performances. Here, we present the experimental demonstration of the differential phase-time shifting protocol…
Recently, Shi et al. (Phys. Rev. A, 2015) proposed Quantum Oblivious Set Member Decision Protocol (QOSMDP) where two legitimate parties, namely Alice and Bob, play a game. Alice has a secret $k$ and Bob has a set $\{k_1,k_2,\cdots k_n\}$. The game is designed towards testing if the secret $k$ is a member of the set possessed by Bob without revealing the identity of $k$. The output of the game will be either "Yes" (bit $1$) or "No" (bit $0$) and is generated at Bob's place. Bob does not know the identity of $k$ and Alice does not know any element of the set. In a subsequent work (Quant. Inf. Pr…
Multiparty quantum communication provides delightful applications including quantum cryptographic communication and quantum secret sharing. Measurement-Device-Independent (MDI) quantum communication based on the Greenberg-Horne-Zeilinger (GHZ) state measurement provides a practical way to implement multiparty quantum communication. With the standard spatially localized GHZ state measurement, however, information can be imbalanced among the communication parties that can cause significant problems in multiparty cryptographic communication. Here, we propose an equitable multiparty quantum commun…
The twin-field (TF) quantum key distribution (QKD) protocol and its variants are highly attractive because they can beat the well-known rate-loss limit (i.e., the PLOB bound) for QKD protocols without quantum repeaters. In this paper, we perform a proof-of-principle experimental demonstration of TF-QKD based on the protocol proposed by Curty et al. which removes from the original TF-QKD scheme the need for post-selection on the matching of a global phase, and can deliver nearly an order of magnitude higher secret key rate. Furthermore, we overcome the major difficulty in the practical implemen…
