Growing concerns over data privacy underscore the need for deep learning methods capable of processing sensitive information without compromising confidentiality. Among privacy-enhancing technologies, Homomorphic Encryption (HE) stands out by providing post-quantum cryptographic security and end-to-end data protection, safeguarding data even during computation. While Deep Neural Networks (DNNs) have gained attention in HE settings, their use has largely been restricted to encrypted inference. Prior research on encrypted training has primarily focused on logistic regression or has relied on multi-party computation to enable model fine-tuning. This stems from the substantial computational overhead and algorithmic complexity involved in DNNs training under HE. In this paper, we present ReBoot, the first framework to enable fully encrypted and non-interactive training of DNNs. Built upon the CKKS scheme, ReBoot introduces a novel HE-compliant neural network architecture based on local error signals, specifically designed to minimize multiplicative depth and reduce noise accumulation. ReBoot employs a tailored packing strategy that leverages real-number arithmetic via SIMD operations, significantly lowering both computational and memory overhead. Furthermore, by integrating approximate bootstrapping, ReBoot learning algorithm supports effective training of arbitrarily deep multi-layer perceptrons, making it well-suited for machine learning as-a-service. ReBoot is evaluated on both image recognition and tabular benchmarks, achieving accuracy comparable to 32-bit floating-point plaintext training while enabling fully encrypted training. It improves test accuracy by up to +3.27% over encrypted logistic regression, and up to +6.83% over existing encrypted DNN frameworks, while reducing training latency by up to 8.83x. ReBoot is made available to the scientific community as a public repository.
Pirillo et al. (Tue,) studied this question.