Fully homomorphic encryption (FHE) is a promising cryptographic primitive for realizing private neural network inference (PI) services by allowing a client to fully offload the inference task to a cloud server while keeping the client data oblivious to the server. This work proposes NeuJeans, an FHE-based solution for the PI of deep convolutional neural networks (CNNs). NeuJeans tackles the critical problem of the enormous computational cost for the FHE evaluation of convolutional layers (conv2d), mainly due to the high cost of data reordering and bootstrapping. We first propose an encoding method introducing nested structures inside encoded vectors for FHE, which enables us to develop efficient conv2d algorithms with reduced data reordering costs. However, the new encoding method also introduces additional computations for conversion between encoding methods, which could negate its advantages. We discover that fusing conv2d with bootstrapping eliminates such computations while reducing the cost of bootstrapping. Then, we devise optimized execution flows for various types of conv2d and apply them to end-to-end implementation of CNNs. NeuJeans accelerates the performance of conv2d by up to 5.68 times compared to state-of-the-art FHE-based PI work and performs the PI of a CNN at the scale of ImageNet (ResNet18) within a mere few seconds

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