In this paper, a general framework for linear secure distributed matrix multiplication (SDMM) is introduced. The model allows for a neat treatment of straggling and Byzantine servers via a star product interpretation as well as simplified security proofs. Known properties of star products also immediately yield a lower bound for the recovery threshold as well as an upper bound for the number of colluding workers the system can tolerate. Another bound on the recovery threshold is given by the decodability condition, which generalizes a bound for GASP codes. The framework produces many of the known SDMM schemes as special cases, thereby providing unification for the previous literature on the topic. Furthermore, error behavior specific to SDMM is discussed and interleaved codes are proposed as a suitable means for efficient error correction in the proposed model. Analysis of the error correction capability under natural assumptions about the error distribution is also provided, largely based on well-known results on interleaved codes. Error detection and other error distributions are also discussed.

翻译：本文提出了一种针对线性安全分布式矩阵乘法（SDMM）的通用框架。该模型通过星积解释优雅地处理了掉队服务器和拜占庭服务器问题，并简化了安全性证明。星积的已知性质可直接推导出恢复阈值的下界以及系统可容忍的合谋工作节点数量的上界。另一个恢复阈值上界由可解码性条件给出，该条件推广了GASP码的界。该框架将许多已知SDMM方案作为特例，从而统一了该课题的先前文献。此外，本文讨论了SDMM特有的错误行为，并提出交错码作为所提模型中高效纠错的合适手段。在关于错误分布的自然假设下，本文还基于交错码的已知结论分析了纠错能力，并进一步讨论了错误检测及其他错误分布情形。