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Physica Scripta

A ( t,n ) threshold quantum secret sharing with cheat identification and authenticity

Nancy Mittal, Sanjeev Kumar

Published Apr 27, 2026• 0 citations

Abstract

Abstract In this paper, we introduce an authenticable quantum secret sharing protocol by utilizing unitary diagonal operator and quantum SUM gate. Here, dealer distributes quantum and classical information simultaneously to participants. The cheat-detection mechanism is designed to identify and expose any malicious actions by participants. During this process, each subsequent participant can detect and recognize deceptive behaviour from dishonest members. To ensure that only legitimate participants are involved in the protocol, we introduce an identity authentication mechanism, where the dealer and each participant share a pair of secret PIN sequences. The implementation of the proposed scheme on the IBM quantum platform (restricted to d = 2) demonstrates its operational correctness and feasibility. Noise-aware simulations under realistic NISQ conditions show that, although performance degrades with increasing noise, the correct outcome remains dominant, indicating robust behaviour in the presence of decoherence, gate errors, and measurement imperfections. Additionally, a complementary analysis is performed under different noise environments, including dit-flip noise, d-phase-flip noise, and depolarizing noise. The obtained results indicate that the efficiency of the proposed protocol decreases with increasing channel noise parameter, with distinct performance variations observed across all the noise models. Furthermore, this work takes into account the situation in which at least t out of the n participants can use the Lagrange interpolation to recover the secret classical and quantum information. The security analysis demonstrates that the proposed protocol is resilient to intercept-resend, collusion, entangle-measure, forgery and denial attacks.

DOI: 10.1088/1402-4896/ae5ff7

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Abstract In this paper, we introduce an authenticable quantum secret sharing protocol by utilizing unitary diagonal operator and quantum SUM gate. Here, dealer distributes quantum and classical information simultaneously to participants. The cheat-detection mechanism is designed to identify and expose any malicious actions by participants. During this process, each subsequent participant can detect and recognize deceptive behaviour from dishonest members. To ensure that only legitimate participants are involved in the protocol, we introduce an identity authentication mechanism, where the dealer and each participant share a pair of secret PIN sequences. The implementation of the proposed scheme on the IBM quantum platform (restricted to d = 2) demonstrates its operational correctness and feasibility. Noise-aware simulations under realistic NISQ conditions show that, although performance degrades with increasing noise, the correct outcome remains dominant, indicating robust behaviour in the presence of decoherence, gate errors, and measurement imperfections. Additionally, a complementary analysis is performed under different noise environments, including dit-flip noise, d-phase-flip noise, and depolarizing noise. The obtained results indicate that the efficiency of the proposed protocol decreases with increasing channel noise parameter, with distinct performance variations observed across all the noise models. Furthermore, this work takes into account the situation in which at least t out of the n participants can use the Lagrange interpolation to recover the secret classical and quantum information. The security analysis demonstrates that the proposed protocol is resilient to intercept-resend, collusion, entangle-measure, forgery and denial attacks.

This work proposes a [Formula: see text]-dimensional quantum multi-secret sharing scheme with a cheat-detection mechanism. The dealer creates multiple secrets and distributes the shares of these secrets using multi-access structures and a monotone span program. The dealer detects the cheating of each participant using the black box’s cheat-detection mechanism. To detect the participants’ deceit, the dealer distributes secret shares’ shadows derived from a randomly invertible matrix [Formula: see text] to the participants, stored in the black box. The black box identifies the participant’s deceitful behavior during the secret recovery phase. Only honest participants authenticated by the black box acquire their secret shares to recover the multiple secrets. After the black box cheating verification, the participants reconstruct the secrets by utilizing the unitary operations and quantum Fourier transform. The proposed protocol is reliable in preventing attacks from eavesdroppers and participants. The scheme’s efficiency is demonstrated in different noise environments: dit-flip noise, [Formula: see text]-phase-flip noise and amplitude-damping noise, indicating its robustness in practical scenarios. The proposed protocol provides greater versatility, security and practicality.

Abstract Quantum secret sharing plays a key role as a foundational method for disseminating a secret to all participants in quantum cryptography. Group authentication plays a significant role in safeguarding information, as it confirms the identity of communication parties. This paper presents a

d-

level

(t, m)

threshold quantum secret-sharing scheme combined with group authentication. Group members can simultaneously authenticate their identities through group authentication. Leveraging the Lagrange interpolation polynomial, the group authentication method disperses multiple secret shares to group members and later allows joint verification of some or all members. According to our analysis, the complexities of our group authentication scheme are much lower than those found in widely recognized existing group authentication methods. This algorithm allows each participant to keep their secret shares secure and undisclosed. By avoiding transmission of these shares, external eavesdroppers are unable to obtain any secret information. This protocol offers security, efficiency, and practicality. Security analysis reveals its ability to resist intercept-resend attacks, entangle-measure attacks, collusion attacks, and forgery attacks. The proposed scheme ensures both confidentiality and integrity.

Abstract Quantum secret sharing (QSS) has significant potential to improve secure communications. However, conventional QSS protocols, typically based on (n, n) or (t, n) threshold structures, require participants to possess symmetric authority, which is often impractical. To address scenarios with participants holding asymmetric privileges, we propose an innovative QSS scheme that realizes a hypergraph structure. This enables secret recovery only for authorized sets with the appropriate privileges. In detail, a specialized hypergraph structure is investigated to construct d-dimensional multipartite entangled states. Using these states, we develop an authenticated QSS protocol that enables secret recovery by authorized sets. Security analysis confirms the protocol’s resilience against common attacks, including intercept-resend, entangle-measure, dishonest participant and Trojan horse attacks. We further characterize the distinct impacts of dit-flip, phase-flip, dit-phase-flip, and depolarizing noise channels on quantum state transmission within the protocol. This characterization demonstrates that dynamically adapting error probability threshold according to prevailing noise conditions is essential to maintain security. Compared with existing protocols, our scheme improves quantum efficiency and reduces the number of unitary operations, which enhances its experimental feasibility.

Abstract In the field of quantum cryptography, Quantum Secret Sharing (QSS) holds substantial importance, with identity authentication emerging as a key strategy for safeguarding information. It efficiently certifies the identification of both persons involved in the conversation, which contributes to increased security measures. Our proposal, a (m, n) threshold Quantum Secret Sharing (QSS) scheme introduces a unique approach to mutual identity authentication, utilizing mutually unbiased bases. During the secret recovery phase, the scheme ensures that secrets exclusively held by participants remain undisclosed and are not transmitted, reinforcing the security of the communication process. As a result, external eavesdroppers are left empty-handed in their attempt to access information about secrets during this phase. Our protocol surpasses in terms of security, effectiveness, and practicality, proving its resilience against intercept–resend attacks, collusion attacks, collective attacks, and forgery attacks according to a comprehensive security analysis.

The security of a secret sharing protocol is compromised if one or more dishonest participants can reconstruct the secret by deviating from the prescribed protocol, particularly when such malicious behavior remains undetected. Semi-Quantum Secret Sharing (SQSS) is a variant of secret sharing in which the participants possess only classical capabilities, such as preparing and measuring qubits in the computational (

Z

) basis, while a quantum-capable third party assists the dealer in generating and distributing quantum shares of a classical secret. The limited quantum capabilities of the participants in SQSS protocols may introduce vulnerabilities to collusion attacks, enabling an assisting quantum third party, in collaboration with a dishonest classical participant, to jointly recover the secret even without detection. In this work, we propose a novel SQSS protocol that eliminates this vulnerability and achieves information-theoretic security against collusion attacks. We further prove that the proposed protocol is secure against a broad class of external and internal attacks. Finally, a comparative analysis demonstrates that our construction advances existing SQSS protocols by simultaneously optimizing qubit efficiency, involves a classical dealer, and resilience against DCNA attacks using basic Bell states.

Abstract Threshold quantum secret sharing is a typical method for quantum secret sharing (QSS) schemes. In this paper, we propose a verifiable t , n threshold QSS scheme based on the d -dimensional Bell state and asymmetric binary polynomial. In this scheme, the dealer encodes the secret using the asymmetric binary polynomial and generates the corresponding secret share for each participant. Then, the dealer prepares the d -dimensional Bell state, and the participants perform corresponding unitary operations on the particles in transmission to recover the secret. With the hash function and the session key pairs, not only the cheating behavior of the dishonest participants can be detected, but also the specific cheaters can be identified. Furthermore, we consider the case when no less than t participants cooperate to recover the secret, which makes the proposed scheme more practical. Analyses show that the scheme can resist forgery attack, collusion attack and other common attacks.