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arXiv:2204.13397 · Symmetry

A Symmetric Extensible Protocol for Quantum Secret Sharing

Michael Ampatzis, Theodore Andronikos

Published Aug 15, 2022• 12 citations
arXivHTMLPDF

Abstract

This paper introduces the Symmetric Extensible Quantum Secret Sharing protocol, a novel quantum protocol for secret sharing. At its heart, it is an entanglement-based protocol that relies on the use of maximally entangled GHZ tuples, evenly distributed among the players, endowing the spymaster with the ability to securely share a secret message with the agents. Its security stems from the fact that it is highly improbable for a malicious eavesdropper or a rogue double agent to disrupt its successful execution. It is characterized by symmetry, since all agents are treated indiscriminately, utilizing identical quantum circuits. Furthermore, it can be seamlessly extended to an arbitrary number of agents. Finally, after the completion of the quantum part of the protocol, the spymaster will have to publicly transmit some information, in order to allow the agents to unlock the secret message. This part of the protocol can be considered as an additional advantage, due to the fact that it gives the spymaster the privilege of deciding if, or when, it is the right time for the agents to unlock the secret message, after the completion of the quantum part of the protocol.

DOI
10.3390/sym14081692

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This paper introduces the Symmetric Extensible Quantum Secret Sharing protocol, a novel quantum protocol for secret sharing. At its heart, it is an entanglement-based protocol that relies on the use of maximally entangled GHZ tuples, evenly distributed among the players, endowing the spymaster with the ability to securely share a secret message with the agents. Its security stems from the fact that it is highly improbable for a malicious eavesdropper or a rogue double agent to disrupt its successful execution. It is characterized by symmetry, since all agents are treated indiscriminately, utilizing identical quantum circuits. Furthermore, it can be seamlessly extended to an arbitrary number of agents. Finally, after the completion of the quantum part of the protocol, the spymaster will have to publicly transmit some information, in order to allow the agents to unlock the secret message. This part of the protocol can be considered as an additional advantage, due to the fact that it gives the spymaster the privilege of deciding if, or when, it is the right time for the agents to unlock the secret message, after the completion of the quantum part of the protocol.
Suppose that the renowned spymaster Alice controls a network of spies who all happen to be deployed in different geographical locations. Let us further assume that all spies have managed to get their hands on a small, albeit incomplete by itself, secret, which actually is just a part of a bigger secret. In this work, we consider the following problem: given the above situation, is it possible for the spies to securely transmit all these partial secrets to the spymaster so that they can be combined together in order to reveal the big secret to Alice? We call this problem, which, to the best of our knowledge, is a novel one for the relevant literature, the quantum secret aggregation problem. We propose a protocol, in the form of a quantum game, that addresses this problem in complete generality. Our protocol relies on the use of maximally entangled GHZ tuples, shared among Alice and all her spies. It is the power of entanglement that makes possible the secure transmission of the small partial secrets from the agents to the spymaster. As an additional bonus, entanglement guarantees the security of the protocol, by making it statistically improbable for the notorious eavesdropper Eve to steal the big secret.
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it. While several variants of this protocol have been investigated, including realizations using quantum systems, the security of quantum secret sharing schemes against eavesdroppers and dishonest participants remained unproven. Here we establish an unconditional security proof for continuous variable entanglement-based quantum secret sharing schemes, in the limit of asymptotic keys and for an arbitrary number of players, by utilizing ideas from the recently developed one-sided device-independent approach to quantum key distribution. We demonstrate the practical feasibility of our scheme, which can be implemented by Gaussian states and homodyne measurements, with no need for ideal single-photon sources or quantum memories. Our results establish quantum secret sharing as a viable and practically relevant primitive for quantum communication technologies.
Utilizing the advantage of Bell state,a multiparty quantum secret sharing protocol with authentication is put forward.In the protocol,the deal encodes two classical bits of secret message on the quantum carrier though performing local unitary operation.He splits the secret message into n shares and then distributes them to n agents via entanglement swapping.Each agent makes a Bell state measurement on the particles in his hand,and obtains his piece of secret according to the measurement result.In the process of reconstruction,these n agents declare respectively their pieces of secret,and recover the secret message if and only if they collaborate.At the same time,combining the technology of Hash function,the identities of the deal and the agents are authenticated.Hence,one main goal of designing the presented protocol,two-way authentication,is achieved.Moreover,we analyze the security and authentication of the presented protocol in detail.It is shown that this protocol can stand against the attacks of outside eavesdropper and inside participant,which means that it is secure in theory.In addition,since the Bell state was used at most,as compared with other quantum secret sharing protocols,the implementation of the presented protocol is more feasible in the current technical conditions.
Using entanglement swapping, a quantum secret sharing protocol is proposed. After sharing three-EPR among users, for encoding the message, the sender prepares an auxiliary EPR pair and by operating defined Pauli operations, she transmits six-bit message to her two agents. Since using entanglement swapping, no qubits carrying message are transmitted. So, if the perfect quantum channel is used, the protocol is unconditional secure. In addition, this protocol enhances the efficiency of Zhang-Man and Chou et al. protocols and with the comparison of previous works has better performance.
Quantum secret sharing (QSS) is a crucial quantum cryptographic method that provides unconditional secu-rity through the principles of quantum mechanics and enables practical applications in information security and distributed computing. Many QSS protocols have been proposed based on various quantum properties and operations. In this study, we propose a new and efficient multiparty quantum secret sharing protocol that utilizes entanglement swapping with the Greenberger-Horne-Zeilinger (GHZ) state and introduces a novel structure to efficiently and securely distribute and recover secrets. Due to entanglement swapping, participants can entangle systems without directly interacting with each other, enhancing practical usage. Through GHZ entanglement swapping, initial particle states cannot be directly inferred. The proposed QSS protocol leverages this property to encode information among participants. To decode the secret, participants only require measuring particles on a GHZ basis to get the corresponding information without performing operations. Through security analysis, it is shown that any eavesdropper or dishonest participant will be detected. Efficiency analysis indicates that the proposed protocol substantially reduces costs and significantly enhances efficiency. As the number of participants increases, the resource consumption of the proposed protocol becomes much lower than that of other QSS protocols. In summary, the proposed protocol efficiently achieves unconditional security in QSS, ensuring the secure transmission and sharing of quantum information.
Security of a quantum secret sharing of quantum state protocol proposed by Guo et al. [Chin. Phys. Lett. 25 (2008) 16] is reexamined. It is shown that an eavesdropper can obtain some of the transmitted secret information by monitoring the classical channel or the entire secret by intercepting the quantum states, and moreover, the eavesdropper can even maliciously replace the secret message with an arbitrary message without being detected. Finally, the deep reasons why an eavesdropper can attack this protocol are discussed and the modified protocol is presented to amend the security loopholes.