Multi-party Weighted Threshold d-Dimensional Semi-Quantum Secret Sharing Based on the Chinese Remainder Theorem

Quantum secret sharing (QSS) is an integral part of quantum cryptography, widely used in many fields. Many QSS schemes rely on a secret distributor to distribute keys, with all participants working together to recover the shared secret information. Currently, compared to existing similar protocols: Most of the particle states used in existing semi-quantum secret sharing (SQSS) are entangled states. The preparation of entangled states, compared to the preparation of single-particle states, is relatively more difficult. Moreover, multi-QSS requires the cooperation of all participants to recover the shared secret. The traditional Lagrange interpolation method, which is now used to design sharing schemes, mainly shares classical bits, not quantum bits. Finally, the efficiency of the protocol is also not high. In this protocol, a multi-party weighted threshold d-dimensional SQSS scheme based on the Chinese remainder theorem (CRT) is proposed. The protocol encodes the bit information intended for transmission and utilizes d-dimensional single-particle states as the conveyance medium, facilitating a secure and efficient approach to multi-party SQSS. The scheme has been thoroughly vetted for security, and it is demonstrated to effectively safeguard against a spectrum of potential threats, including intercept-resend attacks, measure-resend attacks, entanglement measuring attacks, dishonest participant attacks, and Trojan horse attacks. An analysis of efficiency reveals that this protocol surpasses existing methods in computational proficiency and security, underscoring its superior practical application merits.