Wang Tao, Shi Zhiping, Yang Juan, Liu Sha
National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731, China.
School of Electronic Information and Automation, Guilin University of Aerospace Technology, Guilin 541004, China.
Entropy (Basel). 2024 Aug 30;26(9):743. doi: 10.3390/e26090743.
Secure distributed matrix multiplication (SDMM) schemes are crucial for distributed learning algorithms where extensive data computation is distributed across multiple servers. Inspired by the application of repairing Reed-Solomon (RS) codes in distributed storage and secret sharing, we propose SDMM schemes with reduced communication overhead through the use of trace polynomials. Specifically, these schemes are designed to address three critical concerns: (i) ensuring information-theoretic privacy against collusion among servers; (ii) providing security against Byzantine servers; and (iii) offering resiliency against stragglers to mitigate computing delays. To the best of our knowledge, security and resiliency are being considered for the first time within trace polynomial-based approaches. Furthermore, our schemes offer the advantage of reduced sub-packetization and a lower server-count requirement, which diminish the computational complexity and download cost for the user.
安全分布式矩阵乘法（SDMM）方案对于将大量数据计算分布在多个服务器上的分布式学习算法至关重要。受修复里德 - 所罗门（RS）码在分布式存储和秘密共享中的应用启发，我们通过使用迹多项式提出了具有降低通信开销的SDMM方案。具体而言，这些方案旨在解决三个关键问题：（i）确保对服务器之间勾结的信息理论隐私；（ii）提供针对拜占庭服务器的安全性；（iii）提供针对掉队者的弹性以减轻计算延迟。据我们所知，安全性和弹性首次在基于迹多项式的方法中得到考虑。此外，我们的方案具有减少子分组化和降低服务器数量要求的优点，这降低了用户的计算复杂度和下载成本。
