论文标题
与拜占庭服务器的线性安全分布式矩阵乘法的一般框架
General Framework for Linear Secure Distributed Matrix Multiplication with Byzantine Servers
论文作者
论文摘要
在本文中，引入了线性安全分布式矩阵乘法（SDMM）的一般框架。该模型允许通过恒星产品解释以及简化的安全性证明对散落和拜占庭式服务器进行整洁的处理。恒星产品的已知特性还立即产生恢复阈值的下限，以及系统可以忍受的勾结工人数量的上限。在恢复阈值上的另一个结合是由可解释性条件给出的，该条件概括了gasp代码的界限。该框架生产许多已知的SDMM方案作为特殊情况，从而为先前的有关该主题的文献提供了统一。此外，讨论了特定于SDMM的错误行为，并提出了交错的代码作为在建议模型中有效纠正误差的合适手段。还提供了关于误差分布的自然假设下的误差校正能力的分析，这主要基于关于交织代码的众所周知的结果。还讨论了错误检测和其他错误分布。
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.
