Secret sharing allows three or more parties to share secret information which can only be decrypted through collaboration. It complements quantum key distribution as a valuable resource for securely distributing information. Here we take advantage of hybrid spin and orbital angular momentum states to access a high dimensional encoding space, demonstrating a protocol that is easily scalable in both dimension and participants. To illustrate the versatility of our approach, we first demonstrate the protocol in two dimensions, extending the number of participants to ten, and then demonstrate the protocol in three dimensions with three participants, the highest realisation of participants and dimensions thus far. We reconstruct secrets depicted as images with a fidelity of up to 0.979. Moreover, our scheme exploits the use of conventional linear optics to emulate the quantum gates needed for transitions between basis modes on a high dimensional Hilbert space with the potential of up to 1.225 bits of encoding capacity per transmitted photon. Our work offers a practical approach for sharing information across multiple parties, a crucial element of any quantum network.
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.
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 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…
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 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.
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…
Eavesdropping on the improved three-party quantum secret sharing protocol
Lin等[S. Lin，F. Gao，Q.- y. Wen，F.- C. Zhu，Opt. Commun. 281（2008）4553]指出多方量子秘密共享协议[Z.- j. Zhang，G. Gao、X.王湖，澳-地F.汉，S.- H. Shi，Opt. Commun. 269（2007）418]是不安全的，提出了一种改进的三方量子秘密共享协议。本文研究了改进的三方量子秘密共享协议的安全性，发现它仍然是不安全的。最后，提出了一个进一步改进的三方量子秘密共享协议。
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.
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-…
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.
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.
本文将Hillary，Bužek和Berthiaume[Phys. Rev. A59，1829（1999）]的量子秘密共享方案推广到任意多方。给出了共享秘密位的显式表达式。结果表明，在Hillery-Bužek-Berthiaume量子秘密共享方案中，秘密信息是以参与者的测量结果所形成的二进制串的奇偶性来共享的.此外，我们还推广了量子密钥分发中的两种技术，从而提高了量子秘密共享方案的效率。最优测量基量子秘密共享方案是在Lo-Chau-Ardehali技术的基础上发展起来的[H. K. Lo，H. F. Chau和M. Ardehali，quant-ph/0011056]，其中所有参与者非对称地选择测量基，测量基加密的量子秘密共享方案是在Hwang-Koh-Han技术[W. Y.黄岛G. Koh和Y. D. Han，Phys. Lett. A244，489（1998）]，其中所有参与者根据控制键选择他们的测量基础。这两个方案的效率都是渐近的100%，因此几乎所有的量子秘密共享过程中的GHZ态被用来产生共享的秘密信息。
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…
We propose a unitary procedure to reconstruct quantum secret for a quantum secret sharing scheme constructed from stabilizer quantum error-correcting codes. Erasure correcting procedures for stabilizer codes need to add missing shares for reconstruction of quantum secret while unitary reconstruction procedures for certain class of quantum secret sharing are known to work without adding missing shares. The proposed procedure also works without adding missing shares.
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…
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…
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…
Quantum secret sharing with continuous-variable cluster states
我们扩展了簇态量子秘密共享的形式主义，如Markham和Sanders [Phys.Rev.A78，042309（2008）]和Keet等人[Phy. Rev. A 82，062315（2010）]，到连续变量方案。我们表明，经典和量子信息可以通过分配连续变量集群状态通过公共或私人渠道共享。我们发现，如果集团态是无限压缩的，对手的结构是完全否认从秘密，但如果采用一个现实的双压缩状态将泄露一些秘密信息。我们建议的基准来评估的安全性，在挤压的情况下。对于经典秘密的共享，我们借用了连续变量量子密钥分发的技术来计算秘密共享率。对于量子态的共享，我们估计了从每个团簇态中提取的用于隐形传态的纠缠量。
