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Frontiers in Physics

Quantitative security analysis of three-level unitary operations in quantum secret sharing without entanglement

Juan Xu, Xi Li, Yun-Guang Han, Yuqian Zhou, Zhihao Liu, Zhengye Zhang, Yinxiu Song

Published Jun 19, 2023• 5 citations
Publisher

Abstract

Quantum secret sharing (QSS) protocols without entanglement have showed high security by virtue of the characteristics of quantum mechanics. However, it is still a challenge to compare the security of such protocols depending on quantitative security analysis. Based on our previous security analysis work on protocols using single qubits and two-level unitary operations, QSS protocols with single qutrits and three-level unitary operations are considered in this paper. Under the Bell-state attack we propose, the quantitative security analyses according to different three-level unitary operations are provided respectively in the one-step and two-step situations. Finally, important conclusions are drawn for designing and implementing such QSS protocols. The method and results may also contribute to analyze the security of other high-level quantum cryptography schemes based on unitary operations.

DOI
10.3389/fphy.2023.1213153

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Quantum secret sharing (QSS) protocols without entanglement have showed high security by virtue of the characteristics of quantum mechanics. However, it is still a challenge to compare the security of such protocols depending on quantitative security analysis. Based on our previous security analysis work on protocols using single qubits and two-level unitary operations, QSS protocols with single qutrits and three-level unitary operations are considered in this paper. Under the Bell-state attack we propose, the quantitative security analyses according to different three-level unitary operations are provided respectively in the one-step and two-step situations. Finally, important conclusions are drawn for designing and implementing such QSS protocols. The method and results may also contribute to analyze the security of other high-level quantum cryptography schemes based on unitary operations.
We propose a substitute-Bell-state attack strategy for quantum secret sharing schemes without en- tanglement, as well as a definition of the minimum failure probability of such attack strategy. A quantitative analysis of security degrees corresponding to different unitary operations is also provided, when the secret sharing schemes without entanglement are stricken by substitute-Bell-state attack. As a result, the relation between the selection of unitary operations and the effect of substitute-Bell-state attack is shown, which can serve as an important guidance for the selection of unitary operations in designing and implementing quantum secret sharing schemes.
Two schemes for quantum secret sharing of single-qubit state were proposed.A symmetric threequbit entangled state and an asymmetric three-qubit entangled state were used as quantum channel,respectively. The sender performs Bell-basis measurements on her particles,and the cooperator operates single-particle measurements on his particles,then the state receiver can reconstruct the original state by applying the appropriate unitary operation.The schemes can also be generalized to the case of arbitrary two-qubit and multi-particle entangled state.The security against certain eavesdropping attacks is also considered.These protocols are considered to be secure.
The insecurity of the protocols for quantum secret sharing(QSS) based on entanglement swapping was analyzed,and a new method of QSS based on entanglement swapping was proposed.The entanglement states were all generated by the sender,and the order of two photons sent to the same agent was randomly changed.After the photons arrived at the receiver,for the detection mode,the order of the two photons was announced,so that the two parties detected the security of the quantum channel;for the information mode,the two receivers respectively did Bell measurement on the two photons they owned,and then communicated through classical channel to share the secret key with the sender.Analysis results show that this protocol not only ensures the validity and security of the shared information,but also only uses the entanglement states of two photons without unitary operation.
Abstract Quantum secret sharing (QSS) is a significant branch of quantum cryptography and can be widely used in various applications. Quantum secret sharing schemes can be developed by utilizing different features of quantum mechanics, and quantum secure direct communication (QSDC) is an effective way to achieve secret sharing using single qubits. The utilization of QSDC offers certain benefits, such as low cost, high security, and great potential for implementation with current technologies. However, the purpose of QSDC is different from that of QSS, which causes some vulnerabilities, such as dishonest participant attacks. We discover two critical factors that affect the security of traditional protocols. Firstly, they skip a few steps from the QSDC protocol to the QSS protocol. Secondly, the participants have different privileges. This can lead to participants with more privileges engaging in potential attack behavior. In light of these issues, this study proposes a new multiparty QSS scheme to address these vulnerabilities. The proposed protocol ensures the independence of each participant and grants them equal privileges. Analysis results demonstrate that it can defend against malicious attackers, retain the advantages of the QSDC protocol, and further reduce transmission costs. It achieves an excellent balance between security and performance.
Abstract Semi-quantum secret sharing (SQSS) is an important branch of semi-quantum cryptography, and differs from quantum secret sharing (QSS) in that not all parties are required to possess quantum capabilities. All previous SQSS protocols have three common features: (i) they adopt product states or entangled states as initial quantum resource; (ii) the particles prepared by quantum party are transmitted in a tree-type way; and (iii) they require the classical parties to possess the measurement capability. In this paper, two circular SQSS protocols with single particles are suggested, where the first one requires the classical parties to possess the measurement capability while the second one does not have this requirement. Compared with the previous SQSS protocols, the proposed SQSS protocols have some distinct features: (i) they adopt single particles rather than product states or entangled states as initial quantum resource; (ii) the particles prepared by quantum party are transmitted in a circular way; and (iii) the second protocol releases the classical parties from the measurement capability. The proposed SQSS protocols are robust against some famous attacks from an eavesdropper, such as the measure-resend attack, the intercept-resend attack and the entangle-measure attack, and are feasible with present quantum technologies in reality .
With the rise of quantum computing, traditional cryptography is facing serious threats. Secret sharing, as an important primitive of cryptography, is also affected. Because secret sharing is widely used in many fields, researchers have started to explore quantum secret sharing (QSS). QSS uses basic principles of quantum mechanics to provide strong security and can protect against both eavesdropping and malicious attacks. However, most existing QSS studies focus on specific situations and lack the flexibility needed for complex multiparty environments. In this work, we propose a general QSS framework that can be applied to different scenarios. We first design a basic [Formula: see text] QSS protocol, and then extend it to support multiparty communication and dynamic changes in participants. Our security analysis shows that the proposed method keeps strong security, uses fewer resources, and works independently without the need for a trusted third party (TP). This protocol offers a unified solution that can meet different application needs and provides a new approach to handling diverse QSS tasks more efficiently.