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<p>“Threshold quantum secret sharing" (TQSS) schemes of the form (<i>q</i>,&#xa0;<i>n</i>) provide enhanced practicality compared to traditional (<i>n</i>,&#xa0;<i>n</i>) models, offering improved scalability, fault tolerance, and operational flexibility. In this study, we propose a (<i>q</i>,&#xa0;<i>n</i>)-TQSS protocol utilizing “single photons" and “unitary phase shift" operations. The scheme leverages symmetric multivariate polynomials along with polynomial interpolation techniques to securely distribute both “classical information" and “quantum states". This method ensures the confidentiality and integrity of the transmitted data, while also incorporating mutual identity authentication between the dealer and participants to safeguard the reconstruction process. The original secret is accurately recovered through Lagrange interpolation, enabling precise reconstruction. Security analysis confirms that the proposed protocol is robust against a variety of adversarial strategies, including standard eavesdropping attempts and insider attacks such as “entanglement swapping". Furthermore, the scheme is characterized by its simplicity, ease of implementation within physical systems, and adaptability to a wide range of practical applications, making it a highly efficient and viable alternative to existing quantum secret sharing (QSS) protocols.</p>

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Multivariate polynomial-based (q, n) threshold quantum secret sharing using unitary phase operations

  • 期刊论文

  • 发表日期：

    2026年1月14日

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  • Darshana Yadav,
  • Vikash Siwach,
  • Poonam Redhu

摘要

“Threshold quantum secret sharing" (TQSS) schemes of the form (q, n) provide enhanced practicality compared to traditional (n, n) models, offering improved scalability, fault tolerance, and operational flexibility. In this study, we propose a (q, n)-TQSS protocol utilizing “single photons" and “unitary phase shift" operations. The scheme leverages symmetric multivariate polynomials along with polynomial interpolation techniques to securely distribute both “classical information" and “quantum states". This method ensures the confidentiality and integrity of the transmitted data, while also incorporating mutual identity authentication between the dealer and participants to safeguard the reconstruction process. The original secret is accurately recovered through Lagrange interpolation, enabling precise reconstruction. Security analysis confirms that the proposed protocol is robust against a variety of adversarial strategies, including standard eavesdropping attempts and insider attacks such as “entanglement swapping". Furthermore, the scheme is characterized by its simplicity, ease of implementation within physical systems, and adaptability to a wide range of practical applications, making it a highly efficient and viable alternative to existing quantum secret sharing (QSS) protocols.