The Gram matrix of a matrix $A$ is defined as $AA^T$ (or $A^TA$). 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.

翻译：矩阵的Gram矩阵($A)被定义为$AQT$(或$AQTA$),计算Gram矩阵在许多应用中是一项重要操作,例如以最小方位法进行线性回归,其中明确的解决方案公式包括数据矩阵的Gram矩阵。安全分布式矩阵乘法(SDMM)可用于利用工人服务器的帮助计算两个矩阵的产物。如果使用SDMM计算Gram矩阵,则数据矩阵需要两次编码,从而在通信费用中造成不必要的间接费用。我们为此提出了一个新的方案,称为安全分布式矩阵乘法(SDGMM),它可以利用计算Gram矩阵而不是常规矩阵产品的优势。