Precise Approximation of Convolutional Neural Networks for Homomorphically Encrypted Data

by   Eunsang Lee, et al.

Homomorphic encryption 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 homomorphic encryption (HE), the ReLU and max-pooling functions should be approximated by some polynomials for homomorphic operations. Most of the previous studies focus on HE-friendly networks, where the ReLU and max-pooling functions are approximated using low-degree polynomials. However, for the classification of the CIFAR-10 dataset, using a low-degree polynomial requires designing a new deep learning model and training. In addition, this approximation by low-degree polynomials cannot support deeper neural networks due to large approximation errors. Thus, we propose a precise polynomial approximation technique for the ReLU and max-pooling functions. Precise approximation using a single polynomial requires an exponentially high-degree polynomial, which results in a significant number of non-scalar multiplications. Thus, we propose a method to approximate the ReLU and max-pooling functions accurately using a composition of minimax approximate polynomials of small degrees. If we replace the ReLU and max-pooling functions with the proposed approximate polynomials, well-studied 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. 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 78.31


page 1

page 2

page 3

page 4


CryptoDL: Deep Neural Networks over Encrypted Data

Machine learning algorithms based on deep neural networks have achieved ...

The Theoretical Expressiveness of Maxpooling

Over the decade since deep neural networks became state of the art image...

Tropical Polynomial Division and Neural Networks

In this work, we examine the process of Tropical Polynomial Division, a ...

Privacy-Preserving Machine Learning with Fully Homomorphic Encryption for Deep Neural Network

Fully homomorphic encryption (FHE) is one of the prospective tools for p...

Representational Power of ReLU Networks and Polynomial Kernels: Beyond Worst-Case Analysis

There has been a large amount of interest, both in the past and particul...

Self-interpretable Convolutional Neural Networks for Text Classification

Deep learning models for natural language processing (NLP) are inherentl...

Please sign up or login with your details

Forgot password? Click here to reset