Machine Learning as a Service (MLaaS) is enabling a wide range of smart applications on end devices. However, privacy-preserved computation is still expensive. Our investigation has found that the most time-consuming component of the HE-based linear computation is a series of Permutation (Perm) operations that are imperative for dot product and convolution in privacy-preserved MLaaS. To this end, we propose GALA: Greedy computAtion for Linear Algebra in privacy-preserved neural networks, which views the HE-based linear computation as a series of Homomorphic Add, Mult and Perm operations and chooses the least expensive operation in each linear computation step to reduce the overall cost. GALA makes the following contributions: (1) It introduces a row-wise weight matrix encoding and combines the share generation that is needed for the GC-based nonlinear computation, to reduce the Perm operations for the dot product; (2) It designs a first-Add-second-Perm approach (named kernel grouping) to reduce Perm operations for convolution. As such, GALA efficiently reduces the cost for the HE-based linear computation, which is a critical building block in almost all of the recent frameworks for privacy-preserved neural networks, including GAZELLE (Usenix Security'18), DELPHI (Usenix Security'20), and CrypTFlow2 (CCS'20). With its deep optimization of the HE-based linear computation, GALA can be a plug-and-play module integrated into these systems to further boost their efficiency. Our experiments show that it achieves a significant speedup up to 700x for the dot product and 14x for the convolution computation under different data dimensions. Meanwhile, GALA demonstrates an encouraging runtime boost by 2.5x, 2.7x, 3.2x, 8.3x, 7.7x, and 7.5x over GAZELLE and 6.5x, 6x, 5.7x, 4.5x, 4.2x, and 4.1x over CrypTFlow2, on AlexNet, VGG, ResNet-18, ResNet-50, ResNet-101, and ResNet-152, respectively.

中文翻译：

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GALA：隐私保护神经网络中线性代数的贪婪计算

机器学习即服务（MLaaS）正在终端设备上启用各种智能应用程序。但是，保留隐私的计算仍然很昂贵。我们的研究发现，基于HE的线性计算中最耗时的部分是一系列置换（Perm）操作，这些操作对于保留隐私的MLaaS中的点积和卷积是必不可少的。为此，我们提出了GALA：隐私保护神经网络中线性代数的贪婪计算，该算法将基于HE的线性计算视为一系列同态加，多和彼尔姆运算，并在每个线性计算步骤中选择成本最低的运算降低整体成本。GALA做出以下贡献：（1）引入了行权矩阵编码，并结合了基于GC的非线性计算所需的份额生成，以减少点积的Perm运算；（2）设计了第一种Add-second-Perm方法（称为内核分组）以减少用于卷积的Perm操作。因此，GALA有效地降低了基于HE的线性计算的成本，这几乎是所有最近的所有隐私保护神经网络框架的重要组成部分，其中包括GAZELLE（Usenix Security'18），DELPHI（Usenix Security' 20）和CrypTFlow2（CCS'20）。通过对基于HE的线性计算进行深度优化，GALA可以作为即插即用模块集成到这些系统中，以进一步提高其效率。我们的实验表明，在不同数据尺寸下，点积和卷积计算的速度都可以明显提高到700倍和14倍。同时，GALA展示了令人鼓舞的运行时性能，与GAZELLE相比提高了2.5倍，2.7倍，3.2倍，8.3倍，7.7倍和7.5倍，与CrypTFlow2相比分别提高了6.5倍，6倍，5.7倍，4.5倍，4.2倍和4.1倍，分别在AlexNet，VGG，ResNet-18，ResNet-50，ResNet-101和ResNet-152上运行。