Towards the AlexNet Moment for Homomorphic Encryption: HCNN, theFirst Homomorphic CNN on Encrypted Data with GPUs

Deep Learning as a Service (DLaaS) stands as a promising solution for cloud-based inference applications. In this setting, the cloud has a pre-learned model whereas the user has samples on which she wants to run the model. The biggest concern with DLaaS is user privacy if the input samples are sensitive data. We provide here an efficient privacy-preserving system by employing high-end technologies such as Fully Homomorphic Encryption (FHE), Convolutional Neural Networks (CNNs) and Graphics Processing Units (GPUs). FHE, with its widely-known feature of computing on encrypted data, empowers a wide range of privacy-concerned applications. This comes at high cost as it requires enormous computing power. In this paper, we show how to accelerate the performance of running CNNs on encrypted data with GPUs. We evaluated two CNNs to classify homomorphically the MNIST and CIFAR-10 datasets. Our solution achieved a sufficient security level (> 80 bit) and reasonable classification accuracy (99%) and (77.55%) for MNIST and CIFAR-10, respectively. In terms of latency, we could classify an image in 5.16 seconds and 304.43 seconds for MNIST and CIFAR-10, respectively. Our system can also classify a batch of images (> 8,000) without extra overhead

An Improved RNS Variant of the BFV Homomorphic Encryption Scheme

We present an optimized implementation of the Fan-Vercauteren variant of Brakerski\u27s scale-invariant homomorphic encryption scheme. Our algorithmic improvements focus on optimizing decryption and homomorphic multiplication in the Residue Number System (RNS), using the Chinese Remainder Theorem (CRT) to represent and manipulate the large coefficients in the ciphertext polynomials. In particular, we propose efficient procedures for scaling and CRT basis extension that do not require translating the numbers to standard (positional) representation. Compared to the previously proposed RNS design due to Bajard et al., our procedures are simpler and faster, and introduce a lower amount of noise. We implement our optimizations in the PALISADE library and evaluate the runtime performance for the range of multiplicative depths from 1 to 100. For example, homomorphic multiplication for a depth-20 setting can be executed in 62 ms on a modern server system, which is already practical for some outsourced-computing applications. Our algorithmic improvements can also be applied to other scale-invariant homomorphic encryption schemes, such as YASHE

Homomorphic Encryption for Machine Learning in Medicine and Bioinformatics

Machine learning techniques are an excellent tool for the medical community to analyzing large amounts of medical and genomic data. On the other hand, ethical concerns and privacy regulations prevent the free sharing of this data. Encryption methods such as fully homomorphic encryption (FHE) provide a method evaluate over encrypted data. Using FHE, machine learning models such as deep learning, decision trees, and naive Bayes have been implemented for private prediction using medical data. FHE has also been shown to enable secure genomic algorithms, such as paternity testing, and secure application of genome-wide association studies. This survey provides an overview of fully homomorphic encryption and its applications in medicine and bioinformatics. The high-level concepts behind FHE and its history are introduced. Details on current open-source implementations are provided, as is the state of FHE for privacy-preserving techniques in machine learning and bioinformatics and future growth opportunities for FHE

Revisiting Homomorphic Encryption Schemes for Finite Fields

The Brakerski-Gentry-Vaikuntanathan (BGV) and Brakerski/ Fan-Vercauteren (BFV) schemes are the two main homomorphic encryption (HE) schemes to perform exact computations over finite fields and integers. Although the schemes work with the same plaintext space, there are significant differences in their noise management, algorithms for the core homomorphic multiplication operation, message encoding, and practical usability. The main goal of our work is to revisit both schemes, focusing on closing the gap between the schemes by improving their noise growth, computational complexity of the core algorithms, and usability. The other goal of our work is to provide both theoretical and experimental performance comparison of BGV and BFV. More precisely, we propose an improved variant of BFV where the encryption operation is modified to significantly reduce the noise growth, which makes the BFV noise growth somewhat better than for BGV (in contrast to prior results showing that BGV has smaller noise growth for larger plaintext moduli). We also modify the homomorphic multiplication procedure, which is the main bottleneck in BFV, to reduce its algorithmic complexity. Our work introduces several other novel optimizations, including lazy scaling in BFV homomorphic multiplication and an improved BFV decryption procedure in the Residue Number System (RNS) representation. We also develop a usable variant of BGV as a more efficient alternative to BFV for common practical scenarios. We implement our improved variants of BFV and BGV in PALISADE and evaluate their experimental performance for several benchmark computations. The experimental results suggest that our BGV implementation is faster for intermediate and large plaintext moduli, which are often used in practical scenarios with ciphertext packing, while our BFV implementation is faster for small plaintext moduli

OpenFHE: Open-Source Fully Homomorphic Encryption Library

Fully Homomorphic Encryption (FHE) is a powerful cryptographic primitive that enables performing computations over encrypted data without having access to the secret key. We introduce OpenFHE, a new open-source FHE software library that incorporates selected design ideas from prior FHE projects, such as PALISADE, HElib, and HEAAN, and includes several new design concepts and ideas. The main new design features can be summarized as follows: (1) we assume from the very beginning that all implemented FHE schemes will support bootstrapping and scheme switching; (2) OpenFHE supports multiple hardware acceleration backends using a standard Hardware Abstraction Layer (HAL); (3) OpenFHE includes both user-friendly modes, where all maintenance operations, such as modulus switching, key switching, and bootstrapping, are automatically invoked by the library, and compiler-friendly modes, where an external compiler makes these decisions. This paper focuses on high-level description of OpenFHE design, and the reader is pointed to external OpenFHE references for a more detailed/technical description of the software library

Implementation and Performance Evaluation of RNS Variants of the BFV Homomorphic Encryption Scheme

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

Faster Homomorphic Encryption over GPGPUs via hierarchical DGT

Privacy guarantees are still insufficient for outsourced data processing in the cloud. While employing encryption is feasible for data at rest or in transit, it is not for computation without remarkable performance slowdown. Thus, handling data in plaintext during processing is still required, which creates vulnerabilities that can be exploited by malicious entities. Homomorphic encryption (HE) schemes are natural candidates for computation in the cloud since they enable processing of ciphertexts without any knowledge about the related plaintexts or the decryption key. This work focuses on the challenge of developing an efficient implementation of the BFV HE scheme on CUDA. This is done by combining and adapting different approaches from the literature, namely the double-CRT representation and the Discrete Galois Transform. Moreover, we propose and implement an improved formulation of the DGT inspired by classical algorithms, which computes the transform up to $2.6$ times faster than the state-of-the-art. By using these approaches, we obtain up to $3.6$ times faster homomorphic multiplication

On the Explanation and Implementation of Three Open-Source Fully Homomorphic Encryption Libraries

While fully homomorphic encryption (FHE) is a fairly new realm of cryptography, it has shown to be a promising mode of information protection as it allows arbitrary computations on encrypted data. The development of a practical FHE scheme would enable the development of secure cloud computation over sensitive data, which is a much-needed technology in today\u27s trend of outsourced computation and storage. The first FHE scheme was proposed by Craig Gentry in 2009, and although it was not a practical implementation, his scheme laid the groundwork for many schemes that exist today. One main focus in FHE research is the creation of a library that allows users without much knowledge of the complexities of FHE to use the technology securely. In this paper, we will present the concepts behind FHE, together with the introduction of three open-source FHE libraries, in order to bring better understanding to how the libraries function