IEEE Access (Jan 2023)

Precise Approximation of Convolutional Neural Networks for Homomorphically Encrypted Data

  • Junghyun Lee,
  • Eunsang Lee,
  • Joon-Woo Lee,
  • Yongjune Kim,
  • Young-Sik Kim,
  • Jong-Seon No

DOI
https://doi.org/10.1109/ACCESS.2023.3287564
Journal volume & issue
Vol. 11
pp. 62062 – 62076

Abstract

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Homomorphic encryption (HE) is one of the representative solutions to privacy-preserving machine learning (PPML) classification enabling the server to classify private data of clients while guaranteeing privacy. This work focuses on PPML using word-wise fully homomorphic encryption (FHE). In order to implement deep learning on word-wise HE, the ReLU and max-pooling functions should be approximated by polynomials for homomorphic operations. Most of the previous studies focus on HE-friendly networks, which approximate the ReLU and max-pooling functions using low-degree polynomials. However, this approximation cannot support deeper neural networks due to large approximation errors in general and can classify only relatively small datasets. Thus, we propose a precise polynomial approximation technique, a composition of minimax approximate polynomials of low degrees for the ReLU and max-pooling functions. If we replace the ReLU and max-pooling functions with the proposed approximate polynomials, standard deep learning models such as ResNet and VGGNet can still be used without further modification for PPML on FHE. Even pre-trained parameters can be used without retraining, which makes the proposed method more practical. We approximate the ReLU and max-pooling functions in the ResNet-152 using the composition of minimax approximate polynomials of degrees 15, 27, and 29. Then, we succeed in classifying the plaintext ImageNet dataset with 77.52% accuracy, which is very close to the original model accuracy of 78.31%. Also, we obtain an accuracy of 87.90% for classifying the encrypted CIFAR-10 dataset in the ResNet-20 without any additional training.

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