Verifiable Secret Sharing (VSS) has been widespread in Distributed Privacy-preserving Machine Learning (DPML), because invalid shares from malicious dealers or participants can be recognized by verifying the commitment of the received shares for honest participants. However, the consistency and the computation and communitation burden of the VSS-based DPML schemes are still two serious challenges. Although Byzantine Fault Tolerance (BFT) system has been brought to guarantee the consistency and improve the efficiency of the existing VSS-based DPML schemes recently, we explore an Adaptive Share Delay Provision (ASDP) strategy, and launch an ASDP-based Customized Model Poisoning Attack (ACuMPA) for certain participants in this paper. We theoretically analyzed why the ASDP strategy and the ACuMPA algorithm works to the existing schemes. Next, we propose an [E]fficient [By]zantine [F]ault [T]olerant-based [Ve]rifiable [S]ecret-sharing (EByFTVeS) scheme. Finally, the validity, liveness, consistency and privacy of the EByFTVeS scheme are theoretically analyzed, while the efficiency of the EByFTVeS scheme outperforms that of the-state-of-art VSS scheme according to comparative experiment results.

翻译：可验证秘密共享（VSS）在分布式隐私保护机器学习（DPML）中已广泛应用，因为诚实参与者可通过验证所收到份额的承诺来识别来自恶意分发者或参与者的无效份额。然而，基于VSS的DPML方案的一致性问题及其计算与通信负担仍是两大严峻挑战。尽管近期已有研究引入拜占庭容错（BFT）系统来保证一致性并提升现有基于VSS的DPML方案的效率，本文提出一种自适应份额延迟提供（ASDP）策略，并针对特定参与者发起基于ASDP的定制化模型投毒攻击（ACuMPA）。我们从理论上分析了ASDP策略与ACuMPA算法对现有方案生效的原因。随后，我们提出一种基于高效拜占庭容错的可验证秘密共享（EByFTVeS）方案。最后，我们从理论上分析了EByFTVeS方案的有效性、活性、一致性与隐私性，同时对比实验结果表明，该方案的效率优于当前最先进的VSS方案。