Quantum Secret Sharing Research Articles

A Quantum Secret Sharing Scheme Using Orbital Angular Momentum onto Multiple Spin States Based on Fibonacci Compression Encoding**Supported by the National Natural Science Foundation of China under No. 61702427 and the Doctoral Program of Higher Education under Grant No. SWU115091, the Fundamental Research Funds for the Central Universities (XDJK2018C048), and the financial support in part by the 1000-Plan of Chongqing

Since the use of a quantum channel is very expensive for transmitting large messages, it is vital to develop an effective quantum compression encoding scheme that is easy to implement. Given that, with the single-photon spin-orbit entanglement, we propose a quantum secret sharing scheme using orbital angular momentum onto multiple spin states based on Fibonacci compression encoding. In our proposed scheme, we can represent the frequency of any secret message which is typically collection of bits encodings of text or integers as a bitstring using the base Fibonacci sequence, which is encoded multiple spin states for secret shares transmitted to participants. We demonstrate that Fibonacci compression encoding carries excellent properties that enable us to achieve more robust quantum secret sharing schemes with fewer number of photons.

Improvement of a multi-layer quantum secret sharing based on GHZ state and Bell measurement

Recently, a novel Multi-layer Quantum Secret Sharing (MQSS) scheme based on GHZ state and generalized Bell measurement is presented in [X.-J. Wang, L.-X. An, X.-T. Yu and Z.-C. Zhang, Phys. Lett. A 381(38) (2017) 3282.]. The novelty of the MQSS scheme is that a quantum secret can be shared by up to [Formula: see text] parties at the [Formula: see text]th layer. In this paper, we show that the MQSS scheme can be significantly simplified and improved. The improved MQSS scheme is much easier to implement in practice and more efficient. In our improved scheme, the parties of the [Formula: see text]th layer need not put their particles together to carry out the generalized Bell measurement, which is needed to share the secret to the next layer in the original scheme. Instead, each party only has to carry out local operations.

Sequential Quantum Secret Sharing Using a Single Qudit**Sponsored by the National Natural Science Foundation of China under Grant Nos. 61373150 and 61602291, and Industrial Research and Development Project of Science and Technology of Shaanxi Province under Grant No. 2013k0611

In this paper we propose a novel and efficient quantum secret sharing protocol using d-level single particle, which it can realize a general access structure via the thought of concatenation. In addition, Our scheme includes all advantages of Tavakoli’s scheme [Phys. Rev. A 92 (2015) 030302(R)]. In contrast to Tavakoli’s scheme, the efficiency of our scheme is 1 for the same situation, and the access structure is more general and has advantages in practical significance. Furthermore, we also analyze the security of our scheme in the primary quantum attacks.

Analyzing the efficiency of partially entangled states in Vaidman’s-type games and its applications in Quantum Secret Sharing

We analyze the role of degree of entanglement for Vaidman’s game in a setting where the players share a set of partially entangled three-qubit states. Our results show that the entangled states combined with quantum strategies may not be always helpful in winning a game as opposed to the classical strategies. We further find the conditions under which quantum strategies are always helpful in achieving higher winning probability in the game in comparison to classical strategies. Moreover, we show that a special class of W states can always be used to win the game using quantum strategies irrespective of the degree of entanglement between the three qubits. Our analysis also helps us in comparing the Vaidman’s game with the secret sharing protocol. Furthermore, we propose a new Vaidman-type game where the rule maker itself is entangled with the other two players and acts as a facilitator to share a secret key with the two players. For practical purposes, the analysis is extended to study the proposed game under noisy conditions. In addition, the results obtained here are also generalized for multi-qubit games.

Detector-device-independent quantum secret sharing with source flaws

Measurement-device-independent entanglement witness (MDI-EW) plays an important role for detecting entanglement with untrusted measurement device. We present a double blinding-attack on a quantum secret sharing (QSS) protocol based on GHZ state. Using the MDI-EW method, we propose a QSS protocol against all detector side-channels. We allow source flaws in practical QSS system, so that Charlie can securely distribute a key between the two agents Alice and Bob over long distances. Our protocol provides condition on the extracted key rate for the secret against both external eavesdropper and arbitrary dishonest participants. A tight bound for collective attacks can provide good bounds on the practical QSS with source flaws. Then we show through numerical simulations that using single-photon source a secure QSS over 136 km can be achieved.

Dynamic Group Multi-party Quantum Key Agreement

This paper presents a novel dynamic group multi-party Quantum Key Agreement (DGMQKA) protocol, achieved by a multicast transmission method. The proposed method is able to achieve arbitrary number of groups and members under the same resources. In addition, it can be dynamically adjusted by joining a new member, combining two groups into one group, revoking an old member and dividing one group into two groups, for different and complex situations. Furthermore, the proposed protocol can be of help to research into Quantum Secret Sharing (QSS), which it complements. The security analysis shows that the proposed protocol can resist both external and internal attacks. In consumption comparison, the proposed protocol using the multicast transmission method is more effective than other current MQKA protocols.

Computing on quantum shared secrets

A (k,n)-threshold secret-sharing scheme allows for a string to be split into n shares in such a way that any subset of at least k shares suffices to recover the secret string, but such that any subset of at most k-1 shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation on quantum shared secrets. We introduce a (n,n)-quantum secret sharing scheme together with a set of protocols that allow quantum circuits to be evaluated on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the protocol.

Improving Continuous-Variable Measurement-Device-Independent Multipartite Quantum Communication with Optical Amplifiers**Supported by National Natural Science Foundation of China under Grant Nos. 61379153, 61579725

The developing tendency of continuous-variable (CV) measurement-device-independent (MDI) quantum cryptography is to cope with the practical issue of implementing scalable quantum networks. Up to now, most theoretical and experimental researches on CV-MDI QKD are focused on two-party protocols. However, we suggest a CV-MDI multipartite quantum secret sharing (QSS) protocol use the EPR states coupled with optical amplifiers. More remarkable, QSS is the real application in multipartite CV-MDI QKD, in other words, is the concrete implementation method of multipartite CV-MDI QKD. It can implement a practical quantum network scheme, under which the legal participants create the secret correlations by using EPR states connecting to an untrusted relay via insecure links and applying the multi-entangled Greenberger–Horne–Zeilinger (GHZ) state analysis at relay station. Even if there is a possibility that the relay may be completely tampered, the legal participants are still able to extract a secret key from network communication. The numerical simulation indicates that the quantum network communication can be achieved in an asymmetric scenario, fulfilling the demands of a practical quantum network. Additionally, we illustrate that the use of optical amplifiers can compensate the partial inherent imperfections of detectors and increase the transmission distance of the CV-MDI quantum system.

(t, n) Threshold d-Level Quantum Secret Sharing

Most of Quantum Secret Sharing(QSS) are (n, n) threshold 2-level schemes, in which the 2-level secret cannot be reconstructed until all n shares are collected. In this paper, we propose a (t, n) threshold d-level QSS scheme, in which the d-level secret can be reconstructed only if at least t shares are collected. Compared with (n, n) threshold 2-level QSS, the proposed QSS provides better universality, flexibility, and practicability. Moreover, in this scheme, any one of the participants does not know the other participants’ shares, even the trusted reconstructor Bob1 is no exception. The transformation of the particles includes some simple operations such as d-level CNOT, Quantum Fourier Transform(QFT), Inverse Quantum Fourier Transform(IQFT), and generalized Pauli operator. The transformed particles need not to be transmitted from one participant to another in the quantum channel. Security analysis shows that the proposed scheme can resist intercept-resend attack, entangle-measure attack, collusion attack, and forgery attack. Performance comparison shows that it has lower computation and communication costs than other similar schemes when 2 < t < n − 1.

Quantum Secret Broadcast for Wireless Quantum Networks

In wireless quantum networks, nodes communicate by means of pre-distribution for entangled pairs and relay path establishment for quantum teleportation. However, simple point-to-point communication seriously restricts the efficiency of quantum communication. Inspired by sharing idea of quantum secret sharing (QSS), which is based on three collaborative nodes with pre-shared GHZ (Greenberger-Horne-Zeilinger) states, we propose a quantum secret broadcast scheme to improve network performance. In a cluster net-work cored on three parties of QSS, three cluster heads with pre-shared GHZ states are senders, while cluster members are receivers. One cluster head encodes secret messages on auxiliary particles by performing certain operations on them with GHZ particles, then three cluster heads measure their own par-ticles and broadcast measurement results honestly. Based on the specific correlation of measurement results and secret messages, all receivers can re-cover the secret messages. Furthermore, to prevent eavesdropping, cluster heads can update an encoding key periodically. Analysis shows the proposed scheme is more efficient than previous schemes in wireless quantum net-works, especially when the number of receivers is larger. Besides, in the proposed scheme, attacks on quantum channel based on GHZ state can be detected, and eavesdroppers cannot recover messages correctly for lack of suitable decoding key.

(4,4)的量子秘密共享协议及其模型化检测

(4,4)的量子秘密共享协议及其模型化检测

A Generalized Information Theoretical Model for Quantum Secret Sharing

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 analyse two kinds of important quantum access structures to illustrate the existence and rationality of the generalized quantum secret sharing schemes and consider the security of the scheme by simple examples.

Graph State-Based Quantum Secret Sharing with the Chinese Remainder Theorem

Quantum secret sharing (QSS) is a significant quantum cryptography technology in the literature. Dividing an initial secret into several sub-secrets which are then transferred to other legal participants so that it can be securely recovered in a collaboration fashion. In this paper, we develop a quantum route selection based on the encoded quantum graph state, thus enabling the practical QSS scheme in the small-scale complex quantum network. Legal participants are conveniently designated with the quantum route selection using the entanglement of the encoded graph states. Each participant holds a vertex of the graph state so that legal participants are selected through performing operations on specific vertices. The Chinese remainder theorem (CRT) strengthens the security of the recovering process of the initial secret among the legal participants. The security is ensured by the entanglement of the encoded graph states that are cooperatively prepared and shared by legal users beforehand with the sub-secrets embedded in the CRT over finite fields.

Cryptanalysis of quantum secret sharing withd-level single particles

In a recent paper [V. Karimipour and M. Asoudeh, Phys. Rev. A 92, 030301(R) (2015)], a multiparty quantum secret-sharing protocol based on $d$-level single particles was proposed. We discussed the security of this protocol and found that it is not secure for any one dishonest participant who can recover the secret without the aid of other participants.

Exploiting a Fock Cavity Field to Enhance Quantum Secret Sharing Through a Phase-Damping Noisy Channel

The eavesdropping attacks applied in the quantum secret sharing (QSS) protocols through a phase-damping noisy environment are very easy to be realized. In fact, the QSS fidelity has an ordinary behaviour with just one peak according to the noise rate value for many values of the quantum message amplitude. The present work employs a Fock cavity field in such protocols to complicate any eavesdropping attacks through a phase-damping noisy environment. Indeed, only the legitimate users who can adjust the cavity parameters to reach periodically the fidelity peaks.

An efficient (t,n) threshold quantum secret sharing without entanglement

An efficient [Formula: see text] threshold quantum secret sharing (QSS) scheme is proposed. In our scheme, the Hash function is used to check the eavesdropping, and no particles need to be published. So the utilization efficiency of the particles is real 100%. No entanglement is used in our scheme. The dealer uses the single particles to encode the secret information, and the participants get the secret through measuring the single particles. Compared to the existing schemes, our scheme is simpler and more efficient.

Quantum secret sharing protocol based on four-dimensional three-particle entangled states

In this paper, we proposed a three-party quantum secret sharing (QSS) scheme using four-dimensional three-particle entangled states. In this QSS scheme, each agent can obtain a shadow of the secret key by performing single-particle measurements. Compared with the existing QSS protocol, this scheme has high efficiency and can resist the eavesdropping attack and entangle-measuring attack, which using three-particle entangled states are based on four-dimensional Hilbert space.

Mermin Non-Locality in Abstract Process Theories

The study of non-locality is fundamental to the understanding of quantum mechanics. The past 50 years have seen a number of non-locality proofs, but its fundamental building blocks, and the exact role it plays in quantum protocols, has remained elusive. In this paper, we focus on a particular flavour of non-locality, generalising Mermin's argument on the GHZ state. Using strongly complementary observables, we provide necessary and sufficient conditions for Mermin non-locality in abstract process theories. We show that the existence of more phases than classical points (aka eigenstates) is not sufficient, and that the key to Mermin non-locality lies in the presence of certain algebraically non-trivial phases. This allows us to show that fRel, a favourite toy model for categorical quantum mechanics, is Mermin local. We show Mermin non-locality to be the key resource ensuring the device-independent security of the HBB CQ (N,N) family of Quantum Secret Sharing protocols. Finally, we challenge the unspoken assumption that the measurements involved in Mermin-type scenarios should be complementary (like the pair X,Y), opening the doors to a much wider class of potential experimental setups than currently employed. In short, we give conditions for Mermin non-locality tests on any number of systems, where each party has an arbitrary number of measurement choices, where each measurement has an arbitrary number of outcomes and further, that works in any abstract process theory.

A quantum secret sharing scheme on access structure

Based on the Einstein-Podolsky-Rosen (EPR) entangled state and the unitary operation, a quantum secret-sharing (QSS) scheme on access structure is proposed. The participants randomly choose their private keys themselves. Each participant keeps one private key even though he belongs to several qualified subsets. In the recovery, the participants in the qualified subset perform the unitary operations on the EPR pairs, and recover the secret through the Bell-state measurement. Compared to the existing QSS schemes on (n, n) or (t, n) structure, the proposed scheme on access structure is more flexible in practice.

Fundamental Two-Party Quantum Secret Sharing Protocol without Quantum Entanglement

Quantum key distribution (QKD) protocol techniques are used in the distribution of keys using the laws of physics. Quantum secret sharing (QSS), quantum secure direct communication, and quantum teleportation, which are all included under QKD, are used to share or distribute a secure key in a quantum environment. In QSS, we share a key based on the quantum properties of light. We emphasize cooperation between communicating parties to eliminate untrustworthy members and to improve the strength of the key. The results obtained showed that using the proposed method, it is difficult for eavesdroppers to obtain the key.