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arXiv:2511.04399

Tight Analysis of a One-Shot Quantum Secret Sharing Scheme

Santanu Majhi, Debajyoti Bera

quant-phcs.CRSubmitted Nov 6, 2025• Announced Nov 7, 2025• 0 citations• Revised Dec 18, 2025 (v2)
v1 · Nov 6, 2025v2 · Dec 18, 2025
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Abstract

Quantum communication protocols can be designed to detect eavesdropping attacks, something that classical technologies are unable to do since classical information can be replicated in a non-destructive manner. Eavesdropping detection is, therefore, a standard feature in all the proposed quantum secret sharing (QSS) protocols. However, detection is often done by a statistical analysis of the outcome of multiple decoy rounds, and this causes a significant communication overhead. In our quest for a QSS protocol that works even in one round, we came across a one-shot secret-sharing framework proposed by Hsu (Phys. Rev. A 2003). The scheme was designed to work over public channels without requiring multiple rounds to detect eavesdropping but it lacked a thorough security analysis. In this work we present a complete characterisation of the correctness and security properties of this framework. Our characterisation allowed us to improve the original protocol to be more resistant towards eavesdropping. However, we prove a couple of impossibility results, including one that dictates that complete security against an eavesdropper is not possible in this framework. Thus, it is not possible to design a perfect QSS using this framework.

Comments
Add impossibility results; Updated protocol. Largely rewritten

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Quantum communication protocols can be designed to detect eavesdropping attacks, something that classical technologies are unable to do since classical information can be replicated in a non-destructive manner. Eavesdropping detection is, therefore, a standard feature in all the proposed quantum secret sharing (QSS) protocols. However, detection is often done by a statistical analysis of the outcome of multiple decoy rounds, and this causes a significant communication overhead.
In our quest for a QSS protocol that works even in one round, we came across a one-shot secret-sharing framework proposed by Hsu (Phys. Rev. A 2003). The scheme was designed to work over public channels without requiring multiple rounds to detect eavesdropping but it lacked a thorough security analysis. In this work we present a complete characterisation of the correctness and security properties of this framework. Our characterisation allowed us to improve the original protocol to be more resistant towards eavesdropping. However, we prove a couple of impossibility results, including one that dictates that complete security against an eavesdropper is not possible in this framework. Thus, it is not possible to design a perfect QSS using this framework.
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.
Abstract Quantum secret sharing (QSS) is a fundamental primitive in quantum cryptography, enabling secure distribution of sensitive information among multiple parties. However, existing protocols often suffer from vulnerabilities such as collusion attacks, uneven share distribution, and protocol failure due to random basis selection. This paper proposes a novel QSS protocol that integrates hash-based measurement basis derivation with decoy photon-enhanced eavesdropping detection. The scheme ensures fair and deterministic secret reconstruction while eliminating the need for entangled states or complex quantum operations, thereby significantly reducing the quantum operational complexity and hardware requirements. The protocol’s correctness, security against both internal and external adversaries, and efficiency in terms of qubit usage, transmission delay, and computational overhead are rigorously analyzed. Notably, the protocol supports dynamic participant management, allowing agents to join or leave securely without re-executing the entire protocol. Comparative analysis demonstrates that the proposed approach outperforms existing QSS protocols across multiple performance metrics. By minimizing quantum resource requirements-such as the elimination of entanglement generation and complex quantum operations-our protocol enhances compatibility with near-term quantum networks, thus facilitating the transition from theoretical QSS models to experimentally feasible implementations.
The quantum secret sharing protocol with collective detection has garnered significant attention due to its high communication efficiency and low demands on agent capabilities. However, practical implementations face challenges such as intolerance to channel loss and insufficient practical security analysis. To address these issues, this paper proposes a decoy quantum secret sharing protocol with collective detection. First, we analyze the potential security threats posed by multi-photon signals and propose two attack methods, rigorously demonstrating their severe impact on protocol security. Subsequently, to mitigate the adverse effects of multi-photon signals, we introduce a decoy state strategy to enhance the protocol’s reliability under non-ideal conditions. Finally, detailed security analysis against the proposed attacks confirms that the improved protocol effectively resists both attacks even in non-ideal scenarios, thereby ensuring secure and reliable quantum secret sharing.
Abstract Quantum secret sharing (QSS) is a fundamental primitive in quantum cryptography, enabling secure distribution of sensitive information among multiple parties. However, existing protocols often suffer from vulnerabilities such as collusion attacks, uneven share distribution, and protocol failure due to random basis selection. In this paper, we propose a novel QSS protocol that integrates hash-based measurement basis derivation with decoy photon-enhanced eavesdropping detection. Our scheme ensures fair and deterministic secret reconstruction while eliminating the need for entangled states or complex quantum operations. We rigorously analyze the protocol's correctness, security against both internal and external adversaries, and efficiency in terms of qubit usage, transmission delay, and computational overhead. Notably, our protocol supports dynamic participant management, allowing agents to join or leave securely without re-executing the entire protocol. Comparative analysis demonstrates that our approach outperforms existing QSS protocols across multiple performance metrics. This work bridges the gap between theoretical robustness and practical deployment, offering a scalable and resilient solution for post-quantum secure communication.
Security of the one-way quantum secret sharing (QSS) schemes based on entanglement and a collective eavesdropping check is analyzed in the case of considerable quantum channel losses. An opaque cheat attack scheme is presented for the dishonest agent, which reveals that these QSS schemes are completely insecure for transmission efficiencies lower than 50%. That is, the dishonest agent can eavesdrop fully and freely in almost all the one-way QSS schemes based on entanglement if the quantum channel induces 50% losses, including the two pioneer works, the Hillery-Bu\v{z}ek-Berthiaume scheme and the Karlsson-Koashi-Imoto scheme. Finally, we present two ways for possible improvement of these schemes.
Classical secret sharing proposed by Shamir used classical computational power in classical cryptography to achieve secret key sharing, but with the advent of quantum systems, computational power can be overruled. To ensure a secure secret sharing scheme independent of computational power, a scheme independent of computational complexity is needed to achieve security. This paper will provide a protocol dependent on inherent secure nature of quantum cryptography (quantum no cloning theorem and quantum measurement rule). A secure multiparty quantum secret sharing scheme has been proposed to ensure that no one can eavesdrop or extract any share of the secret message via inherent security provided by quantum entanglement swapping and quantum teleportation. Entanglement swapping is a process that allows two non-interacting quantum systems to be entangled. Whereas, Quantum teleportation allows a party to send a qubit to another entangled party without sending the qubit over the channel. Moreover, in order to ensure security against possible active attacks, sender himself will generate and distribute EPR pairs to be used in the scheme. Result will be a secure multiparty QSS scheme which will be secure against internal and external eavesdropping, masquerading and brute-force attacks.