论文标题
私有分布式矩阵矩阵乘法的无重量代码
Rateless Codes for Private Distributed Matrix-Matrix Multiplication
论文作者
论文摘要
我们考虑设计无等级编码的私有分布式矩阵矩阵乘法的问题。主服务器拥有两个私有矩阵$ \ MATHBF {a} $和$ \ MATHBF {B} $，并希望雇用工人节点来帮助计算乘法。从信息理论意义上讲，矩阵应保持私密性。在文献中已经考虑了这个问题，并构建了具有预先设计阈值的代码。更确切地说，主人将任务分配给工人，并等待预定数量的工人来完成分配的任务。分配给工人的任务的大小取决于设计的阈值。我们对任务大小必须较小且独立于设计阈值的设置感兴趣。我们设计了一个无重量的私有矩阵矩阵乘法方案，称为rpm3。我们的方案修复了任务的大小，并允许主人向工人发送多个任务。主继续接收结果，直到可以解码乘法为止。两个主要应用程序需要此属性：i）利用系统中可能的异质性，并将更多任务分配给更快的工人； ii）自适应分配任务以说明可能是时变的系统。
We consider the problem of designing rateless coded private distributed matrix-matrix multiplication. A master server owns two private matrices $\mathbf{A}$ and $\mathbf{B}$ and wants to hire worker nodes to help compute the multiplication. The matrices should remain private from the workers, in an information-theoretic sense. This problem has been considered in the literature and codes with a predesigned threshold are constructed. More precisely, the master assigns tasks to the workers and waits for a predetermined number of workers to finish their assigned tasks. The size of the tasks assigned to the workers depends on the designed threshold. We are interested in settings where the size of the task must be small and independent of the designed threshold. We design a rateless private matrix-matrix multiplications scheme, called RPM3. Our scheme fixes the size of the tasks and allows the master to send multiple tasks to the workers. The master keeps receiving results until it can decode the multiplication. Two main applications require this property: i) leverage the possible heterogeneity in the system and assign more tasks to workers that are faster; and ii) assign tasks adaptively to account for a possibly time-varying system.
