Fully homomorphic encryption (FHE) is a prospective tool for privacy-preserving machine learning (PPML). Several PPML models have been proposed based on various FHE schemes and approaches. Although FHE schemes are suitable as tools for implementing PPML models, previous PPML models based on FHE, such as CryptoNet, SEALion, and CryptoDL, are limited to simple and nonstandard types of machine learning models; they have not proven to be efficient and accurate with more practical and advanced datasets. Previous PPML schemes replaced non-arithmetic activation functions with simple arithmetic functions instead of adopting approximation methods and did not use bootstrapping, which enables continuous homomorphic evaluations. Thus, they could neither use standard activation functions nor employ large numbers of layers. In this work, we first implement the standard ResNet-20 model with the RNS-CKKS FHE with bootstrapping and verify the implemented model with the CIFAR-10 dataset and plaintext model parameters. Instead of replacing the non-arithmetic functions with simple arithmetic functions, we use state-of-the-art approximation methods to evaluate these non-arithmetic functions, such as ReLU and Softmax, with sufficient precision. Further, for the first time, we use the bootstrapping technique of the RNS-CKKS scheme in the proposed model, which enables us to evaluate an arbitrary deep learning model on encrypted data. We numerically verify that the proposed model with the CIFAR-10 dataset shows 98.43% identical results to the original ResNet-20 model with non-encrypted data. The classification accuracy of the proposed model is 92.43%±2.65%, which is quite close to that of the original ResNet-20 CNN model (91.89%). It takes approximately 3 h for inference on a dual Intel Xeon Platinum 8280 CPU (112 cores) with 172 GB of memory. We believe that this opens the possibility of applying FHE to an advanced deep PPML model.

Homomorphic Encryption (HE) makes it possible to compute on encrypted data without decryption. In lattice-based HE, a ciphertext contains noise, which accumulates along with homomorphic computations. Bootstrapping refreshes the noise and it is possible to perform arbitrary-depth computations on HE with bootstrapping, which we call Fully Homomorphic Encryption (FHE). In this article, we propose a new general bootstrapping technique for RLWE-based schemes and its practical instantiation for FHE. It can be applied to all three RLWE-based leveled FHE schemes: Brakerski-Gentry-Vaikuntanathan (BGV), Brakerski/Fan-Vercauteren (BFV), and Cheon-Kim-Kim-Song (CKKS) with minor deviations in the algorithms. Our new construction of bootstrapping extracts a noiseless ciphertext for a part of the input, scales it, and finally removes it. In contrast with previous bootstrapping algorithms, the proposed method consumes only 1–2 levels and uses smaller parameters. For BGV and BFV, our new bootstrapping does not have any restrictions on a plaintext modulus unlike typical cases of the previous methods. The error introduced by our approach for CKKS is comparable to a rescaling error, allowing us to preserve a large amount of precision after bootstrapping.

The residue number system (RNS) is an unconventional number system which can lead to parallel and fault-tolerant arithmetic operations. However, the complexity of residue-to-binary conversion for large number of moduli reduces the overall RNS performance, and makes it inefficient for nowadays high-performance computation systems. In this paper, we present an improved approximate Chinese remainder theorem (CRT) with the aim of performing efficient residue-to-binary conversion for general RNS moduli sets. To achieve this aim, the required number of fraction bits for accurate residue-to-binary conversion is derived. Besides, a method is proposed to substitute fractional calculations by similar computations based on integer numbers to have a hardware amenable algorithm. The proposed approach results in high-speed and low-area residue-to-binary converters for general RNS moduli sets. Therefore, with this conversion method, high dynamic range residue number systems suitable for cryptography and digital signal processing can be designed.