Quantum secret sharing with (m, n) threshold: QFT and identity authentication

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 proposed, \((m, n)\) threshold quantum secret sharing (QSS) scheme introduces a unique approach to mutual identity authentication, utilizing mutually unbiased bases. Alice employs a symmetric bivariate polynomial to distribute the secret share among all participants in this algorithm. For secret reconstruction, a trusted participant, \({Bob}_{1}\), shares a GHZ state with a qualified group of \(m\) participants, including himself. Each participant applies QFT and a unitary transformation (related to their part of the shared secret) on their particle. 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, collision attacks, collective attacks, entangle-measure attacks, and forgery attacks according to a comprehensive security analysis.