Project description: Homomorphic Encryption (HE) is one of the most promising security solutions to emerging Machine Learning as a Service (MLaaS). Several Leveled-HE (LHE)-enabled Convolutional Neural Networks (LHECNNs) are proposed to implement MLaaS to avoid the large bootstrapping overhead. However, prior LHECNNs have to pay significant computational overhead but achieve only low inference accuracy, due to their polynomial approximation activations and poolings. Stacking many polynomial approximation activation layers in a network greatly reduces the inference accuracy, since the polynomial approximation activation errors lead to a low distortion of the output distribution of the next batch normalization layer. So the polynomial approximation activations and poolings have become the obstacle to a fast and accurate LHECNN model. We present a Shift-accumulation-based LHE-enabled deep neural network (SHE) for fast and accurate inferences on encrypted data. We use the binary-operation-friendly leveled-TFHE (LTFHE) encryption scheme to implement ReLU activations and max poolings. We also adopt the logarithmic quantization to accelerate inferences by replacing expensive LTFHE multiplications with cheap LTFHE shifts. We propose a mixed bitwidth accumulator to expedite accumulations. Since the LTFHE ReLU activations, max poolings, shifts and accumulations have small multiplicative depth, SHE can implement much deeper network architectures with more convolutional and activation layers. Our experimental results show SHE achieves state-of-the-art inference accuracy and reduces the inference latency by 76.21% ~ 94.23% over prior LHECNNs on MNIST and CIFAR-10.