论文标题
安全分布式克矩阵乘法
Secure Distributed Gram Matrix Multiplication
论文作者
论文摘要
矩阵$ a $的克矩阵定义为$ aa^t $（或$ a^t \！a $）。计算革兰氏矩阵是许多应用程序中的重要操作，例如使用最小二乘方法的线性回归，其中显式解决方案公式包括数据矩阵的革兰氏矩阵。安全的分布式矩阵乘法（SDMM）可用于使用Worker服务器的帮助来计算两个矩阵的乘积。如果使用SDMM计算一个克矩阵，则需要对数据矩阵进行编码两次，这会导致通信成本中不必要的开销。我们为此提出了一个新方案，称为安全分布式矩阵乘法（SDGMM）。它可以利用计算革兰氏矩阵而不是常规矩阵产品的优势。
The Gram matrix of a matrix $A$ is defined as $AA^T$ (or $A^T\!A$). Computing the Gram matrix is an important operation in many applications, such as linear regression with the least squares method, where the explicit solution formula includes the Gram matrix of the data matrix. Secure distributed matrix multiplication (SDMM) can be used to compute the product of two matrices using the help of worker servers. If a Gram matrix were computed using SDMM, the data matrix would need to be encoded twice, which causes an unnecessary overhead in the communication cost. We propose a new scheme for this purpose called secure distributed Gram matrix multiplication (SDGMM). It can leverage the advantages of computing a Gram matrix instead of a regular matrix product.
