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.
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, a pivotal research domain within quantum cryptography, has significant applications across diverse fields such as information security and distributed quantum computing. This paper proposes a d-dimensional hierarchical quantum multi-secret sharing scheme with a general access structure. In the proposed scheme, the distributor constructs a special entangled state by leveraging the secret values at each level and a monotone span program. During the secret reconstruction phase, participants only need to measure the particles in their possession, and authorized participants at each level can recover multiple secrets shared at that level. Additionally, each participant can independently compute and obtain multiple lower-level secrets but cannot access any higher-level secret information. Compared to existing hierarchical quantum secret sharing schemes, the proposed scheme is better suited for specific application scenarios with unique requirements. Furthermore, security analysis demonstrates that the scheme can resist various attacks, such as measurement attacks, intercept-resend attacks, entanglement-measurement attacks, Trojan horse attacks, and collusion attacks.
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.
Quantum secret sharing (QSS) is a cryptography technique relying on the transmission and manipulation of quantum states to distribute secret information across multiple participants securely. However, quantum systems are susceptible to various types of noise that can compromise their security and reliability. Therefore, it is essential to analyze the influence of noise on QSS to ensure their effectiveness and practicality in real-world quantum communication. This paper studies the impact of various noisy environments on multi-dimensional QSS. Using quantum fidelity, we examine the influence of four noise models: d-phase-flip(dpf), dit-flip(df), amplitude damping(ad), and depolarizing(d). It has been discovered that the fidelity declines with an increase in the noise parameter. Furthermore, the results demonstrate that the efficiency of the QSS protocol differs significantly across distinct noise models.
Quantum secret sharing holds a significant place in quantum cryptography. In this paper, a (w, t, n)-weighted threshold dynamic quantum secret sharing scheme with cheating identification is constructed based on the CRT for a polynomial ring. In our scheme, on the premise of not altering the private shares of the old participants, the dynamic update of the participants can be realized without other participants’ help, and the shared secret will not be changed. During the secret reconstruction phase, via executing the quantum state digital signature, the proposed scheme not only can timely detect the existence of the cheating behavior, but also once exists, definitely can identify one cheater and eliminate him from the system, making the scheme more secure. Moreover, our scheme enables secret sharing among participants with different authorities, which enhances the practicability of the scheme. Finally, the security analysis shows our scheme not only is resistant to a range of typical external attacks but can detect forgery, collusion, denial and dishonest revoked participant attacks.
Abstract Based on the d-dimensional Greenberger–Horne–Zeilinger (GHZ) state, this paper proposes a novel multi-party quantum secret sharing scheme with the characteristics of identity authentication and dual-threshold. In the scheme, the dealer first constructs an asymmetric binary polynomial and decomposes it into two unary polynomials, then divides the participants into two groups, and generates secret shares and corresponding polynomial pairs for each participant. The dealer prepares a three-qudit GHZ state and uses two of them to perform dual-line transmission between the two groups of participants. The participants perform specific unitary transformations on the transmitted particles. Finally, the recovery agent collects and measures the information particles to recover the secret. The scheme uses a hash function and a session key to detect fraudulent behavior and identify specific participants to achieve identity authentication. Security analysis shows that the scheme can effectively resist intercept-resend attacks, entangle-measure attacks, dishonest participant attacks and Trojan horse attacks.
Abstract In the domain of quantum cryptography, the implementation of quantum secret sharing stands as a pivotal element. In this paper, we propose a novel verifiable quantum secret sharing protocol using the d-dimensional product state and Lagrange interpolation techniques. This protocol is initiated by the dealer Alice, who initially prepares a quantum product state, selected from a predefined set of orthogonal product states within the ℂ d ⊗ ℂ d framework. Subsequently, the participants execute unitary operations on this product state to recover the underlying secret. Furthermore, we subject the protocol to a rigorous security analysis, considering both eavesdropping attacks and potential dishonesty from the participants. Finally, we conduct a comparative analysis of our protocol against existing schemes. Our scheme exhibits economies of scale by exclusively employing quantum product states, thereby realizing significant cost-efficiency advantages. In terms of access structure, we adopt a (t,n)-threshold architecture, a strategic choice that augments the protocol’s practicality and suitability for diverse applications. Furthermore, our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.