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Fully homomorphic encryption (FHE) is one of the prospective tools for privacy-preserving machine learning (PPML), and several PPML models have been proposed based on various FHE schemes and approaches. Although the FHE schemes are known as suitable tools to implement PPML models, previous PPML models on FHE such as CryptoNet, SEALion, and CryptoDL are limited to only simple and non-standard types of machine learning models. These non-standard machine learning models are not proven efficient and accurate with more practical and advanced datasets. Previous PPML schemes replace non-arithmetic activation functions with simple arithmetic functions instead of adopting approximation methods and do not use bootstrapping, which enables continuous homomorphic evaluations. Thus, they could not use standard activation functions and could not employ a large number of layers. In this work, we firstly implement the standard ResNet-20 model with the RNS-CKKS FHE with bootstrapping and verify the implemented model with the CIFAR-10 dataset and the plaintext model parameters. Instead of replacing the non-arithmetic functions with the simple arithmetic function, we use state-of-the-art approximation methods to evaluate these non-arithmetic functions, such as the 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 the 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 about 3 hours for inference on a dual Intel Xeon Platinum 8280 CPU (112 cores) with 172 GB memory. We think that it opens the possibility of applying the FHE to the advanced deep PPML model.

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A collection of families of binary {O,l} pseudorandom sequences (referred to as the families of No sequences) is introduced in this paper. Each sequence within a family has period N = 2"-1, where n = 2.m is an even integer. There are 2"' sequences within a family and the maximum over all (nontrivial) auto and cross-correlation values equals 2"+ 1. Thus these sequences are optimum with respect to the Welch bound on the maximum correlation value.Each family contains a Gordon-Mills-Welch (GMW)sequence and the collection of families includes as a special case, the small set of Kasami sequences. The linear span of these sequences is large. The balance properties of such families are evaluated and a count of the number of distinct families of given period N that can be contructed also provided.