An efficient quantum secret sharing scheme for general access structure based on a novel partitioning technique

Abstract

Secret sharing is a fundamental cryptographic technique that distributes confidential information into multiple shares, ensuring that only authorized subsets of participants can reconstruct the original secret. In this paper, we propose a novel qubit-based approach to the Quantum General Secret Sharing Scheme, enhancing security for general access structures. Our framework efficiently supports all monotone access structures by representing the collection of minimal qualified sets, offering a flexible and scalable quantum solution. We introduce an innovative partitioning method for the minimal qualified sets, ensuring quantum-compatible share generation. The scheme employs a structured quantum encoding mechanism to generate quantum shares, or shadow qubits, providing robust security against unauthorized access. Using linear algebra and quantum information-theoretic techniques, we rigorously prove that unauthorized participants gain no information about the secret. Additionally, we design an efficient quantum reconstruction algorithm that enables authorized participants to recover the secret from their distributed shadow qubits. Unlike previous works, our approach avoids the use of quantum Fourier transform (QFT), which, while powerful, leads to deeper circuits and high gate complexity that are impractical for NISQ devices. By relying solely on CNOT and Hadamard gates, our construction enables low-depth, hardware-friendly circuits suitable for implementation. The circuit complexity is linear in the number of participants, offering better scalability than previous quantum constructions for general access structures. By using qubits instead of qudits, we reduce noise and improve performance. Furthermore, by incorporating entanglement for enhanced security, our scheme eliminates the need for secure communication channels, requiring only a classically authenticated quantum channel. We have also implemented this in Python using Criq, which verifies our protocol.