A Distributed and Parallel (k, n) QSS Scheme with Verification Capability

This paper presents a new quantum secret sharing scheme featuring a (k, n) threshold and built-in verification. This innovative protocol takes advantage of entanglement and unfolds in three distinct phases. In anticipation of the coming of the distributed quantum computing era, this protocol is designed to function entirely in parallel within a fully distributed environment, where the spymaster and her agents are located in different places. This is a significant shift from most similar protocols that assume that all information recipients are in one location. The spymaster can send all necessary information to her agents at once, streamlining the process. Each phase runs simultaneously, which helps to reduce the overall execution cost. Given its complexity, we offer a thorough analysis to ensure its information-theoretic security, protecting against both external eavesdroppers and internal rogue agents. The protocol does away with the need for quantum signatures or pre-shared keys, making it simpler and less complex. Lastly, its potential for implementation on current quantum computers looks promising since it relies only on CNOT and Hadamard gates, with all participants using similar or identical quantum circuits.