In this paper, we present a novel variation of the coded matrix multiplication problem which we refer to as fully private grouped matrix multiplication (FPGMM). In FPGMM, a master wants to compute a group of matrix products between two matrix libraries that can be accessed by all workers while ensuring that any number of prescribed colluding workers learn nothing about which matrix products the master desires, nor the number of matrix products. We present an achievable scheme using a variant of Cross-Subspace Alignment (CSA) codes that offers flexibility in communication and computation cost. Additionally, we demonstrate how our scheme can outperform naive applications of schemes used in a related privacy focused coded matrix multiplication problem.

翻译：在本文中，我们提出了一种编码矩阵乘法问题的新变体，称为完全私有化的分组矩阵乘法（FPGMM）。在FPGMM中，主节点希望计算两个矩阵库之间的矩阵乘积组，这些矩阵库可供所有工作节点访问，同时确保任意数量的指定合谋工作节点无法获知主节点期望计算的矩阵乘积以及乘积的数量。我们利用交叉子空间对齐（CSA）码的变体提出了一种可实现方案，该方案在通信和计算成本上具有灵活性。此外，我们证明了该方案在性能上优于朴素应用相关隐私保护编码矩阵乘法问题中的现有方案。