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Homomorphic encryption is a powerful privacy-preserving technology that is notoriously difficult to configure and use, even for experts. The key difficulties include restrictive programming models of homomorphic schemes and choosing suitable parameters for an application. In this tutorial, we outline methodologies to solve these issues and allow for conversion of any application to the encrypted domain using both leveled and fully homomorphic encryption. The first approach, called Walrus, is suitable for arithmetic-intensive applications with limited depth and applications with high throughput requirements. Walrus provides an intuitive programming interface and handles parameterization automatically by analyzing the application and gathering statistics such as homomorphic noise growth to derive a parameter set tuned specifically for the application. We provide an in-depth example of this approach in the form of a neural network inference as well as guidelines for using Walrus effectively. Conversely, the second approach (HELM) takes existing HDL designs and converts them to the encrypted domain for secure outsourcing on powerful cloud servers. Unlike Walrus, HELM supports FHE backends and is well-suited for complex applications. At a high level, HELM consumes netlists and is capable of performing logic gate operations homomorphically on encryptions of individual bits. HELM incorporates both CPU and GPU acceleration by taking advantage of the inherent parallelism provided by Boolean circuits. As a case study, we walk through the process of taking an off-the-shelf HDL design in the form of AES-128 decryption and running it in the encrypted domain with HELM. 

As cloud computing continues to gain widespread adoption, safeguarding the confidentiality of data entrusted to third-party cloud service providers becomes a critical concern. While traditional encryption methods offer protection for data at rest and in transit, they fall short when it comes to where it matters the most, i.e., during data processing. To address this limitation, we present HELM, a framework for privacy-preserving data processing using homomorphic encryption. HELM automatically transforms arbitrary programs expressed in a Hardware Description Language (HDL), such as Verilog, into equivalent homomorphic circuits, which can then be efficiently evaluated using encrypted inputs. HELM features three modes of encrypted evaluation: a) a gate mode that consists of Boolean gates, b) a small-precision lookup table mode which significantly reduces the size of the circuit by combining multiple gates into lookup tables, and c) a high-precision lookup table mode tuned for multi-bit arithmetic evaluations. Finally, HELM introduces a scheduler that leverages the parallelism inherent in arithmetic and Boolean circuits to efficiently evaluate encrypted programs. We evaluate HELM with the ISCAS'85 and ISCAS'89 benchmark suites, as well as real-world applications such as image filtering and neural network inference. In our experimental results, we report that HELM can outperform prior works by up to 65x. 

Homomorphic encryption can address key privacy challenges in cloud-based outsourcing by enabling potentially untrusted servers to perform meaningful computation directly on encrypted data. While most homomorphic encryption schemes offer addition and multiplication over ciphertexts natively, any non-linear functions must be implemented as costly polynomial approximations due to this restricted computational model. Nevertheless, the CGGI cryptosystem is capable of performing arbitrary univariate functions over ciphertexts in the form of lookup tables through the use of programmable bootstrapping. While promising, this procedure can quickly become costly when high degrees of precision are required. To address this challenge, we propose Ripple: a framework that introduces different approximation methodologies based on discrete wavelet transforms (DWT) to decrease the number of entries in homomorphic lookup tables while maintaining high accuracy. Our empirical evaluations demonstrate significant error reduction compared to plain quantization methods across multiple non-linear functions. Notably, Ripple improves runtime performance for realistic applications, such as logistic regression and Euclidean distance. 

Cloud computing has been a prominent technology that allows users to store their data and outsource intensive computations. However, users of cloud services are also concerned about protecting the confidentiality of their data against attacks that can leak sensitive information. Although traditional cryptography can be used to protect static data or data being transmitted over a network, it does not support processing of encrypted data. Homomorphic encryption can be used to allow processing directly on encrypted data, but a dishonest cloud provider can alter the computations performed, thus violating the integrity of the results. To overcome these issues, we propose PEEV (Parse, Encrypt, Execute, Verify), a framework that allows a developer with no background in cryptography to write programs operating on encrypted data, outsource computations to a remote server, and verify the correctness of the computations. The proposed framework relies on homomorphic encryption techniques as well as zero-knowledge proofs to achieve verifiable privacy-preserving computation. It supports practical deployments with low performance overheads and allows developers to express their encrypted programs in a high-level language, abstracting away the complexities of encryption and verification. 

Fully homomorphic encryption (FHE) has become progressively more viable in the years since its original inception in 2009. At the same time, leveraging state-of-the-art schemes in an efficient way for general computation remains prohibitively difficult for the average programmer. In this work, we introduce a new design for a fully homomorphic processor, dubbed Juliet, to enable faster operations on encrypted data using the state-of-the-art TFHE and cuFHE libraries for both CPU and GPU evaluation. To improve usability, we define an expressive assembly language and instruction set architecture (ISA) judiciously designed for end-to-end encrypted computation. We demonstrate Juliet’s capabilities with a broad range of realistic benchmarks including cryptographic algorithms, such as the lightweight ciphers SIMON and SPECK, as well as logistic regression (LR) inference and matrix multiplication.