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Homomorphic encryption (HE) offers great capabilities that can solve a wide range of privacy-preserving computing problems. This tool allows anyone to process encrypted data producing encrypted results that only the decryption key’s owner can decrypt. Although HE has been realized in several public implementations, its performance is quite demanding. The reason for this is attributed to the huge amount of computation required by secure HE schemes. In this work, we present a CUDAbased implementation of the Fan and Vercauteren (FV) Somewhat HomomorphicEncryption (SHE) scheme. We demonstrate several algebraic tools such as the Chinese Remainder Theorem (CRT), Residual Number System (RNS) and Discrete Galois Transform (DGT) to accelerate and facilitate FV computation on GPUs. We also show how the entire FV computation can be done on GPU without multi-precision arithmetic. We compare our GPU implementation with two mature state-of-the-art implementations: 1) Microsoft SEAL v2.3.0-4 and 2) NFLlib-FV. Our implementation outperforms them and achieves on average 5.37x, 7.37x, 22.22x, 5.11x and 13.18x (resp. 2.03x, 2.94x, 27.86x, 8.53x and 18.69x) for key generation, encryption, decryption, homomorphic addition and homomorphic multiplication against SEAL-FVRNS (resp. NFLlib-FV).

Homomorphic encryption is an emerging form of encryption that provides the ability to compute on encrypted data without ever decrypting them. Potential applications include aggregating sensitive encrypted data on a cloud environment and computing on the data in the cloud without compromising data privacy. There have been several recent advances resulting in new homomorphic encryption schemes and optimized variants. We implement and evaluate the performance of two optimized variants, namely Bajard-Eynard-Hasan-Zucca (BEHZ) and Halevi-Polyakov-Shoup (HPS), of the most promising homomorphic encryption scheme in CPU and GPU. The most interesting (and also unexpected) result of our performance evaluation is that the HPS variant in practice scales significantly better (typically by 15%-30%) with increase in multiplicative depth of the computation circuit than BEHZ, implying that the HPS variant will always outperform BEHZ for most practical applications. For the multiplicative depth of 98, our fastest GPU implementation performs homomorphic multiplication in 51 ms for 128-bit security settings, which is faster by two orders of magnitude than prior results and already practical for cloud environments supporting GPU computations. Large multiplicative depths supported by our implementations are required for applications involving deep neural networks, logistic regression learning, and other important machine learning problems.

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The paper studies the spinorial wave equations, namely the Dirac and the Klein-Gordon equations, as well as the greybody radiations and quasinormal modes (QNMs) of the charged Taub NUT black hole (CTNBH). To obtain fermionic greybody factors (GFs) and QNMs, we study the charged fermions by employing the Dirac equation. To this end, we use a null tetrad in the Newman-Penrose formalism. Then, we separate the Dirac equation into radial and angular sets. Using the obtained radial equations, we convert them into the typical one dimensional Schrödinger-like wave equations with the aid of tortoise coordinate and derive the effective potentials. For bosonic GFs and QNMs, we study the Klein-Gordon equation in the CTNBH geometry and obtain the radial equation. We then derive the effective potential and investigate the effect of NUT parameter on it.We show that while the fermionic QNMs and GFs individually increase with the increasing NUT parameter, the increase of bosonic GFs with increasing NUT parameter is overwhelmingly greater than that of the bosonic QNMs.

Network Intrusion Detection Systems (NIDSs) are indispensable defensive tools against various cyberattacks. Lightweight, multipurpose, and anomaly-based detection NIDSs employ several methods to build profiles for normal and malicious behaviors. In this paper, we design, implement, and evaluate the performance of machine-learning-based NIDS in IoT networks. Specifically, we study six supervised learning methods that belong to three different classes: (1) ensemble methods, (2) neural network methods, and (3) kernel methods. To evaluate the developed NIDSs, we use the distilled-Kitsune-2018 and NSL-KDD datasets, both consisting of a contemporary real-world IoT network traffic subjected to different network attacks. Standard performance evaluation metrics from the machine-learning literature are used to evaluate the identification accuracy, error rates, and inference speed. Our empirical analysis indicates that ensemble methods provide better accuracy and lower error rates compared with neural network and kernel methods. On the other hand, neural network methods provide the highest inference speed which proves their suitability for high-bandwidth networks. We also provide a comparison with state-of-the-art solutions and show that our best results are better than any prior art by 1~20%.

We present a multi-GPU design, implementation and performance evaluation of the Halevi-Polyakov-Shoup (HPS) variant of the Fan-Vercauteren (FV) levelled Fully Homomorphic Encryption (FHE) scheme. Our design follows a data parallelism approach and uses partitioning methods to distribute the workload in FV primitives evenly across available GPUs. The design is put to address space and runtime requirements of FHE computations. It is also suitable for distributed-memory architectures, and includes efficient GPU-to-GPU data exchange protocols. Moreover, it is user-friendly as user intervention is not required for task decomposition, scheduling or load balancing. We implement and evaluate the performance of our design on 2 homogeneous and heterogeneous NVIDIA GPU clusters: K80, and a customized P100. We also provide a comparison with a recent shared-memory based multi-core CPU implementation using two homomorphic circuits as workloads: vector addition and multiplication. Moreover, we use our multi-GPU Levelled-FHE to implement the inference circuit of two Convolutional Neural Networks (CNNs) to perform homomorphically image classification on encrypted images from the MNIST and CIFAR-10 datasets. Our implementation provides 1 to 3 orders of magnitude speedup compared with the CPU implementation on vector operations. In terms of scalability, our design shows reasonable scalability curves when the GPUs are fully connected.