We explore a generalization of quantum secret sharing (QSS) in which classical shares play a complementary role to quantum shares, exploring further consequences of an idea first studied by Nascimento, Mueller-Quade and Imai (Phys. Rev. {\bf A64} 042311 (2001)). We examine three ways, termed inflation, compression and twin-thresholding, by which the proportion of classical shares can be augmented. This has the important application that it reduces quantum (information processing) players by replacing them with their classical counterparts, thereby making quantum secret sharing considerably easier and less expensive to implement in a practical setting. In compression, a QSS scheme is turned into an equivalent scheme with fewer quantum players, compensated for by suitable classical shares. In inflation, a QSS scheme is enlarged by adding only classical shares and players. In a twin-threshold scheme, we invoke two separate thresholds for classical and quantum shares based on the idea of information dilution.
A secret sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum secret sharing schemes. In addition to providing a new perspe…
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…
A resilient secret sharing scheme is supposed to generate the secret correctly even after some shares are damaged. In this paper, we show how quantum error correcting codes can be exploited to design a resilient quantum secret sharing scheme, where a quantum state is shared among more than one parties.
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…
In TCSS (Threshold Changeable Secret Sharing) scheme, the threshold can be changed to deal with share leakage in the long term. But in classical TCSS, there is no guarantee that old shares are deleted even if the participated parties are honest. So, the changed threshold may not prevent an adversary from reconstructing the secret by the old shares and old threshold number of parties. We show how to tackle this problem quantum mechanically. I.e., quantum mechanically we can make the changed threshold mandatory. So, there is quantum advantage of quantum TCSS over classical TCSS.
Recently, Li et al. [Phys. Rev. A, 82(2), 022303] presented two semi-quantum secret sharing (SQSS) protocols using GHZ-like states. The proposed schemes are rather practical because only the secret dealer requires to equip with advanced quantum devices such as quantum memory, whereas the other agents can merely perform classical operations to complete the secret sharing. However, this study points out that a security pitfall exists in the eavesdropping check phase of both schemes that could mount to an Intercept-resend attack and a Trojan horse attack on the two schemes, respectively, to discl…
We present a new quantum secret sharing protocol based on recent advances in Mermin-type contextuality scenarios, which has some security guarantees against postquantum nonsignaling attackers. It is a fundamental assumption of secret sharing protocols that not all players are trusted parties, and that some may collude amongst themselves and with eavesdroppers to break confidentiality. To this extent, quantum secret sharing introduces a new layer of security, enabling eavesdropping detection via entangled states and noncommuting observables. A more thorough security analysis, however, becomes c…
Secret sharing schemes for classical secrets can be classified into classical secret sharing schemes and quantum secret sharing schemes. Classical secret sharing has been known to be able to distribute some shares before a given secret. On the other hand, quantum mechanics extends the capabilities of secret sharing beyond those of classical secret sharing. We propose quantum secret sharing with the capabilities in designing of access structures more flexibly and realizing higher efficiency beyond those of classical secret sharing, that can distribute some shares before a given secret.
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…
We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert-Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple symbols in its classical secret are revealed to an intermediate set, and justify the necessity of incorporating strong security criterion of conventional secret sharing. Finally, we propose an explic…
We consider secret sharing schemes with a classical secret and quantum shares. One example of such schemes was recently reported whose access structure cannot be realized by any secret sharing schemes with classical shares. In this paper, we report further quantum secret sharing schemes whose access structures cannot be realized by any classical secret sharing schemes.
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.
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 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.
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…
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.
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%.
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.
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…
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.
The multiple assignment scheme is to assign one or more shares to single participant so that any kind of access structure can be realized by classical secret sharing schemes. We propose its quantum version including ramp secret sharing schemes. Then we propose an integer optimization approach to minimize the average share size.
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 …
We show a simple example of a secret sharing scheme encoding classical secret to quantum shares that can realize an access structure impossible by classical information processing with limitation on the size of each share. The example is based on quantum stabilizer codes.
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…
The work presents a novel quantum secret sharing strategy based on GHZ product state sharing between three parties. The dealer, based on the classical information to be shared, toggles his qubit and shares the product state. The other parties make their Bell measurements and collude to reconstruct the secret. Unlike the other protocols, this protocol does not involve the entire initial state reconstruction, rather uses selective qubits to discard the redundant qubits at the time of reconstruction to decrypt the secret. The protocol also allows for security against malicious attacks by an adver…
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.
