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 of group 2 in such a way that no subset of each group is efficient to read the secret message, but the entire set (not only group 1 but also group 2) is. We also show that it is unconditionally secure. This protocol is feasible with present-day techniques.
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.
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.
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 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…
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…
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 paper we investigate the use of quantum information to share classical secrets. While every quantum secret sharing scheme is a quantum error correcting code, the converse is not true. Motivated by this we sought to find quantum codes which can be converted to secret sharing schemes. If we are interested in sharing classical secrets using quantum information, then we show that a class of pure $[[n,1,d]]_q$ CSS codes can be converted to perfect secret sharing schemes. These secret sharing schemes are perfect in the sense the unauthorized parties do not learn anything about the secret. Go…
In this Letter, we present quantum secret sharing and secret splitting protocols with single photons running forth and back between the participating parties. The protocol has a high intrinsic efficiency, namely all photons except those chosen for eavesdropping check could be used for sharing secret. The participants need not to announce the measuring bases at most of the time and this reduces the classical information exchanged largely.
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…
I present a variety of results on the theory of quantum secret sharing. I show that any mixed state quantum secret sharing scheme can be derived by discarding a share from a pure state scheme, and that the size of each share in a quantum secret sharing scheme must be at least as large as the size of the secret. I show that the only constraints on the existence of quantum secret sharing schemes with general access structures are monotonicity (if a set is authorized, so are larger sets) and the no-cloning theorem. I also discuss some aspects of sharing classical secrets using quantum states. In …
Secret sharing is a procedure for sharing a secret among a number of participants such that only the qualified subsets of participants have the ability to reconstruct the secret. Even in the presence of eavesdropping, secret sharing can be achieved when all the members are quantum. So what happens if not all the members are quantum? In this paper we propose two semi-quantum secret sharing protocols using maximally entangled GHZ-type states in which quantum Alice shares a secret with two classical parties, Bob and Charlie, in a way that both parties are sufficient to obtain the secret, but one …
In a recent work, Markham and Sanders have proposed a framework to study quantum secret sharing (QSS) schemes using graph states. This framework unified three classes of QSS protocols, namely, sharing classical secrets over private and public channels, and sharing quantum secrets. However, most work on secret sharing based on graph states focused on threshold schemes. In this paper, we focus on general access structures. We show how to realize a large class of arbitrary access structures using the graph state formalism. We show an equivalence between $[[n,1]]$ binary quantum codes and graph st…
After analysing the main quantum secret sharing protocol based on the entanglement states, we propose an idea to directly encode the qubit of quantum key distributions, and then present a quantum secret sharing scheme where only product states are employed. As entanglement, especially the inaccessable multi-entangled state, is not necessary in the present quantum secret sharing protocol, it may be more applicable when the number of the parties of secret sharing is large. Its theoretic efficiency is also doubled to approach 100%.
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.
Quantum secret sharing is well known as a method for players to share a classical secret for secret sharing in quantum mechanical ways. Most of the results associated with quantum secret sharing are based on pure multipartite entangled states. In reality, however, it is difficult for players to share a pure entangled state, although they can share a state close to the state. Thus, it is necessary to study how to perform the quantum secret sharing based on a general multipartite state. We here present a quantum secret sharing protocol on an $N$-qubit state close to a pure $N$-qubit Greenberger-…
We present a general scheme for sharing quantum secrets, and an extension to sharing classical secrets, which contain all known quantum secret sharing schemes. In this framework we show the equivalence of existence of both schemes, that is, the existence of a scheme sharing a quantum secret implies the extended classical secret sharing scheme works, and vice versa. As a consequence of this we find new schemes sharing classical secrets for arbitrary access structures. We then clarify the relationship to quantum error correction and observe several restrictions thereby imposed, which for example…
This comment points out a problem in Song et al.'s (t, n) threshold quantum secret sharing [Scientific Reports, Vol. 7, No. 1 (2017), pp. 6366], indicating that the agent is unable to obtain the expected information.
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 analyze tolerable quantum bit error rates in secret sharing protocols, and show that using entangled encoding states is advantageous in the case when the eavesdropping attacks are local. We also provide a criterion for security in secret sharing -- a parallel of the Csiszar-Korner criterion in single-receiver cryptography.
We propose here a quantum secret sharing scheme that works for both quantum and classical secrets. The proposed scheme is based on both entanglement swapping and teleportation together. It allows sender to encrypt his/her secret and simultaneously distribute decryption information of the encrypted secret among distant parties where decryption shares are nonlocally correlated with each other. Two-fold quantum non-local correlations, generated through entanglement swapping and then teleporting quantum states over swapped maximally entangled pairs, guarantee both authentication and secrecy of the…
Quantum secret sharing is a scheme for encoding a quantum state (the secret) into multiple shares and distributing them among several participants. If a sufficient number of shares are put together, then the secret can be fully reconstructed. If an insufficient number of shares are put together however, no information about the secret can be revealed. In quantum ramp secret sharing, partial information about the secret is allowed to leak to a set of participants, called an unqualified set, that cannot fully reconstruct the secret. By allowing this, the size of a share can be drastically reduce…
We proposed a scheme on secret sharing of quantum information based on entanglement swapping in cavity QED. In our scheme, the effects of cavity decay and thermal field are all eliminated.
We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties over both classical and quantum channels.
Quantum secret sharing schemes encrypting a quantum state into a multipartite entangled state are treated. The lower bound on the dimension of each share given by Gottesman [Phys. Rev. A \textbf{61}, 042311 (2000)] is revisited based on a relation between the reversibility of quantum operations and the Holevo information. We also propose a threshold ramp quantum secret sharing scheme and evaluate its coding efficiency.
An important metric of the performance of a quantum secret sharing scheme is its information rate. Beyond the fact that the information rate is upper bounded by one, very little is known in terms of bounds on the information rate of quantum secret sharing schemes. Further, not every scheme can be realized with rate one. In this paper we derive new upper bounds for the information rates of quantum secret sharing schemes. We show that there exist quantum access structures on $n$ players for which the information rate cannot be better than $O((\log_2 n)/n)$. These results are the quantum analogue…
In this paper we introduce a quantum information theoretical model for quantum secret sharing schemes. We show that quantum information theory provides a unifying framework for the study of these schemes. We prove that the information theoretical requirements for a class of quantum secret sharing schemes reduce to only one requirement (the recoverability condition) as a consequence of the no-cloning principle. We give also a shorter proof of the fact that the size of the shares in a quantum secret sharing scheme must be at least as large as the secret itself.
We study a simple graph-based classical secret sharing scheme: every player's share consists of a random key together with the encryption of the secret with the keys of his neighbours. A characterisation of the authorised and forbidden sets of players is given. Moreover, we show that this protocol is equivalent to the graph state quantum secret sharing (GS-QSS) schemes when the secret is classical. When the secret is an arbitrary quantum state, a set of players is authorised for a GS-QSS scheme if and only if, for the corresponding simple classical graph-based protocol, the set is authorised a…
In the paper [Quantum Inf. Process. 14, 4237-4244 (2015)], Qin and Dai proposed a proactive quantum secret sharing scheme. We study the security of the proposed scheme and find that it is not secure. In the distribution phase of the proposed scheme, two dishonest participants may collaborate to eavesdrop the secret of the dealer without introducing any error. Incidentally, a possible improvement of the distribution phase is given.
With the advantages of both classical and quantum secret sharing, many practical hybrid quantum secret sharing have been proposed. In this paper, we propose a hybrid quantum secret sharing scheme based on mutually unbiased bases and monotone span program. First, the dealer sends the shares in the linear secret sharing to the participants in the authorization set via a secure channel. Then, the dealer and participants perform unitary transformation on a d-dimensional quantum state sequentially, and the dealer publishes the measurement result confidentially to the participants in the authorizati…
In secret sharing protocols, a secret is to be distributed among several partners so that leaving out any number of them, the rest do not have the complete information. Strong multiqubit correlations in the state by which secret sharing is carried out, had been proposed as a criterion for security of such protocols against individual attacks by an eavesdropper. However we show that states with weak multiqubit correlations can also be used for secure secret sharing. That our state has weak multiqubit correlations, is shown from the perspective of violation of local realism, and also by showing …
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…
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.
Based on a quantum secure direct communication (QSDC) protocol [Phys. Rev. A69(04)052319], we propose a $(n,n)$-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.
We present two optimal methods of teleporting an unknown qubit using any pure entangled state. We also discuss how such methods can also have succesful application in quantum secret sharing with pure multipartite entangled states.
In this work we address the issue of sharing a quantum secret over untrusted channels between the dealer and players. Existing methods require entanglement over a number of systems which scales with the security parameter, quickly becoming impractical. We present protocols (interactive and a non-interactive) where single copy encodings are sufficient. Our protocols work for all quantum secret sharing schemes and access structures, and are implementable with current experimental set ups. For a single authorised player, our protocols act as quantum authentication protocols.
A ($t$, $n$) threshold quantum secret sharing (QSS) is proposed based on a single $d$-level quantum system. It enables the ($t$, $n$) threshold structure based on Shamir's secret sharing and simply requires sequential communication in $d$-level quantum system to recover secret. Besides, the scheme provides a verification mechanism which employs an additional qudit to detect cheats and eavesdropping during secret reconstruction, and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. Moreover, the scheme is salable in partici…
An information theoretical model for quantum secret sharing was introduced by A. C. A. Nascimento et al.[Quantum Inf. Comput. Vol.5,1,205,68-79(2003)], which was analyzed by quantum information theory. In this paper, we analyze this information theoretical model using the properties of the quantum access structure. By the analysis we propose a generalized model definition for the quantum secret sharing schemes. In our model, there are more quantum access structures which can be realized by our generalized quantum secret sharing schemes than those of the previous one. In addition, we also analy…
Some of the secret sharing schemes having unique quantum features like parallelism and entanglement are supposed to be relatively secure. Different schemes proposed by various researchers over the years have features which could be specific to the nature and need of a situation. Following Hsu's proposed scheme we propose a secret sharing scheme using Grover's search algorithm for a four qubit system with several marked states. Further, the scheme has been generalised to an n-qubit syatem.
A circular quantum secret sharing protocol is proposed, which is useful and efficient when one of the parties of secret sharing is remote to the others who are in adjacent, especially the parties are more than three. We describe the process of this protocol and discuss its security when the quantum information carrying is polarized single photons running circularly. It will be shown that entanglement is not necessary for quantum secret sharing. Moreover, the theoretic efficiency is improved to approach 100% as almost all the instances can be used for generating the private key, and each photon…
Our aim is to formulate continuous-variable quantum secret sharing as a continuous-variable ramp quantum secret sharing protocol, provide a certification procedure for it and explain the criteria for the certification. Here we introduce a technique for certifying continuous-variable ramp quantum secret-sharing schemes in the framework of quantum interactive-proof systems. We devise pseudocodes in order to represent the sequence of steps taken to solve the certification problem. Furthermore, we derive the expression for quantum mutual information between the quantum secret extracted by any mult…
We extend the formalism of cluster state quantum secret sharing, as presented in Markham and Sanders [Phys. Rev. A 78, 042309 (2008)] and Keet et al. [Phy. Rev. A 82, 062315 (2010)], to the continuous-variable regime. We show that both classical and quantum information can be shared by distributing continuous-variable cluster states through either public or private channels. We find that the adversary structure is completely denied from the secret if the cluster state is infinitely squeezed, but some secret information would be leaked if a realistic finitely squeezed state is employed. We sugg…
In this work, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, and hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.
We propose an efficient scheme for sharing a continuous variable quantum secret using passive optical interferometry and squeezers: this efficiency is achieved by showing that a maximum of two squeezers is required to replicate the secret state, and we obtain the cheapest configuration in terms of total squeezing cost. Squeezing is a cost for the dealer of the secret as well as for the receivers, and we quantify limitations to the fidelity of the replicated secret state in terms of the squeezing employed by the dealer.
In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing…
We show a potential eavesdropper can eavesdrop whole secret information when the legitimate users use secure carrier to encode and decode classical information repeatedly in the protocol [proposed in Bagherinezhad S and Karimipour V 2003 Phys. Rev. A \textbf{67} 044302]. Then we present a revised quantum secret sharing protocol by using Greenberger-Horne-Zeilinger state as secure carrier. Our protocol can resist Eve's attack.
Analyzing carefully an experimentally feasible non-entangled single qubit quantum secret sharing protocol and its modified version [Phys. Rev. Lett. 95, 230505 (2005); ibid. 98, 028902 (2007)], it is found that both versions are insecure against coherent attacks though the original idea is so remarkable. To overcome this fatal flaw, here we propose a protocol with a distinct security checking strategy, which still involves single qubit operations only, making it possible to achieve better security of quantum secret sharing with current technology.
A corresponding comment, raised by Kao and Hwang, claims that the reconstructor Bob1 is unable to obtain the expected secret information in (t, n) Threshold d-level Quantum Secret Sharing (TDQSS)[Scientific Reports, Vol. 7, No. 1 (2017), pp.6366] . In this reply, we show the TDQSS scheme can obtain the dealer's secret information in the condition of adding a step on disentanglement.
