Threshold Quantum Secret Sharing

TL;DR

The paper tackles threshold quantum secret sharing by addressing reconstruction without a trusted reconstructor in a $(t,n)$, $d$-level setting. It combines Shamir's secret sharing with a hash-sharing mechanism and leverages $QFT$/$IQFT$-based entanglement to securely reconstruct the secret when at least $t$ participants cooperate, while verifying integrity via a hash comparison. Key contributions include resistance to collision, coherent, and collective attacks, and a design that detects eavesdropping through hash verification, all with a more cost-efficient implementation than prior protocols. The results have practical implications for secure multiparty quantum tasks, enabling verifiable secret sharing in settings like voting, summation, and distributed computation. Overall, the protocol advances secure, scalable quantum secret sharing by removing the need for a trusted reconstructor and enhancing attack resilience and verifiability.

Abstract

One crucial and basic method for disclosing a secret to every participant in quantum cryptography is quantum secret sharing. Numerous intricate protocols, including secure multiparty summation, multiplication, sorting, voting, and more, can be designed with it. A quantum secret sharing protocol with a $(t,n)$ threshold approach and modulo d, where t and n represent the threshold number of participants and the total number of participants, respectively was recently discussed by Song et al. Kao et al. notes that without the information of other participants, the secret in Song {\em et al.'s}protocol cannot be reconstructed. We address a protocol that solves this issue in this paper.