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 for full-support maximum distance separable (MDS) encoding, as well as an upper bound for the colluding workers the system can tolerate. It produces many of the known SDMM schemes as special cases, hence 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 is also provided, largely based on well-known results on interleaved codes.

翻译：本文采用了线性安全分布式矩阵乘法总框架(SDMM),该模型通过恒星产品解释和简化安全证明,对悬浮和拜占庭服务器进行整齐处理。已知的恒星产品特性也立即为完全支持最大距离分离编码(MDS)的回收阈值设定下限,并为系统能够容忍的串通工人设定上限。它作为特例产生了许多已知的SDMM计划,从而统一了以前关于该专题的文献。此外,还讨论了SDMM的错误行为,并提议将内部编码作为拟议模型中有效纠正错误的适当手段。还主要根据众所周知的关于不同编码的结果,对错误纠正能力进行了分析。