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：本文提出了一种线性安全分布式矩阵乘法（SDMM）的通用框架。该模型通过星积（star product）解释，能够简洁地处理掉队服务器与拜占庭服务器问题，并简化安全性证明。星积的已知性质可直接推导出恢复阈值（recovery threshold）的下界以及系统可容忍的合谋工作节点数量上界。解码可行性条件（decodability condition）给出了恢复阈值的另一个界，该条件推广了GASP码的界。该框架将多种已知SDMM方案作为特例纳入其中，从而统一了该领域的前期文献。此外，本文讨论了SDMM特有的错误行为，并提出交织码（interleaved codes）作为该模型中高效纠错方案的合适手段。基于交织码的成熟结论，本文在关于错误分布的合理假设下分析了纠错能力，同时讨论了错误检测及其他错误分布情形。