Fully Homomorphic Encryption (FHE) is a promising solution to enable privacy-preserving inference and training of machine learning models over encrypted data. Among the machine learning methods used in practice, Extreme Gradient Boosting (XGBoost) is one technique that shines in many applications. While previous works have tackled the problem of training tree-based models over FHE, these works either rely on interaction with the client, which adds the extra burden of communication, or consume a typically unreasonable amount of time to train a large model. In this work, we present an efficient system for a non-interactive XGBoost training over FHE that achieves up to 360 imes speedup compared to the state of the art. The argmax operation is a basic building block invoked repeatedly during the XGBoost training as well as other machine learning algorithms, but computing it over FHE is time consuming. When utilizing the Single Instruction Multiple Data (SIMD) parallelism capability offered by most FHE schemes and using a configuration with s slots, the state of the art methods compute argmax on n <= s values using either O(log_2 n) SIMD-comparisons in tournament-style comparison or ceil{n^2 /s} SIMD-comparisons using all pairs comparison. As a second contribution of this work, we propose an efficient argmax algorithm that is based on a novel technique to maximize SIMD-utilization, and computes the argmax of n <= s values using only O(log_2(log_2(n)) SIMD-comparisons. The method extends to n > s with complexity O(n/s) + log_2(log_2(s)), compared to O(n/s) + log_2(s) for state of the art methods. We conduct empirical experiments to compare our method with other existing argmax methods, and show that when using the HEaaN FHE scheme with a configuration of s=2^15 to compute the argmax of n=s values, our implementation is about 1.6 times faster than the state of the art.

The electrical grid has significantly evolved over the years, thus creating a smart paradigm, which is well known as the smart electrical grid. However, this evolution creates critical cybersecurity risks due to the vulnerable nature of the industrial systems and the involvement of new technologies. Therefore, in this paper, the ELECTRON architecture is presented as an integrated platform to detect, mitigate and prevent potential cyberthreats timely. ELECTRON combines both cybersecurity and energy defence mechanisms in a collaborative way. The key aspects of ELECTRON are (a) dynamic risk assessment, (b) asset certification, (c) federated intrusion detection and correlation, (d) Software Defined Networking (SDN) mitigation, (e) proactive islanding and (f) cybersecurity training and certification.

Privacy-preserving solutions enable companies to offload confidential data to third-party services while fulfilling their government regulations. To accomplish this, they leverage various cryptographic techniques such as Homomorphic Encryption (HE), which allows performing computation on encrypted data. Most HE schemes work in a SIMD fashion, and the data packing method can dramatically affect the running time and memory costs. Finding a packing method that leads to an optimal performant implementation is a hard task. We present a simple and intuitive framework that abstracts the packing decision for the user. We explain its underlying data structures and optimizer, and propose a novel algorithm for performing 2D convolution operations. We used this framework to implement an inference operation over an encrypted HE-friendly AlexNet neural network with large inputs, which runs in around five minutes, several orders of magnitude faster than other state-of-the-art non-interactive HE solutions.