Oblivious Lookup-Tables

Accelerating the development of a practical Fully Homomorphic Encryption (FHE) scheme is the goal of the DARPA PROCEED program. For the past year, this program has had as its focus the acceleration of various aspects of the FHE concept toward practical implementation and use. FHE would be a game-changing technology to enable secure, general computation on encrypted data, e.g., on untrusted off-site hardware. However, FHE will still require several orders of magnitude improvement in computation before it will be practical for widespread use. Recent theoretical breakthroughs demonstrated the existence of FHE schemes [1, 2], and to date much progress has been made in both algorithmic and implementation improvements. Specifically our contribution to the Proceed program has been the development of FPGA based hardware primitives to accelerate the computation on encrypted data using FHE based on lattice techniques [3]. Our project, SIPHER, has been using a state of the art tool-chain developed by Mathworks to implement VHDL code for FPGA circuits directly from Simulink models. Our baseline Homomorphic Encryption prototypes are developed directly in Matlab using the fixed point toolbox to perform the required integer arithmetic. Constant improvements in algorithms require us to be able to quickly implement them in a high level language such as Matlab. We reported on our initial results at HPEC 2011 [4]. In the past year, increases in algorithm complexity have introduced several new design requirements for our FPGA implementation. This report presents new Simulink primitives that had to be developed to deal with these new requirements.

Fully Homomorphic Encryption (FHE) is pivotal for secure computation on encrypted data, crucial in privacy-preserving data analysis. However, efficiently processing high-dimensional data in FHE, especially for machine learning and statistical (ML/STAT) algorithms, poses a challenge. In this paper, we present an effective acceleration method using the kernel method for FHE schemes, enhancing time performance in ML/STAT algorithms within encrypted domains. This technique, independent of underlying FHE mechanisms and complementing existing optimizations, notably reduces costly FHE multiplications, offering near-constant time complexity relative to data dimension. Aimed at accessibility, this method is tailored for data scientists and developers with limited cryptography background, facilitating advanced data analysis in secure environments.

Fully Homomorphic Encryption (FHE) is the holy grail of encrypted communications. It opens the door to several advanced functionalities to overcome the security and trust issues of the IT world. After 2009, once Craig Gentry had shown that FHE could be achieved, a study in this field boomed, and significant improvement was made in identifying more efficient and realistic programs. FHE is primitive cryptography that enables arbitrary functions to be calculated via encrypted data. These systems are applicable in different ways since they permit users to encrypt their private information securely while still outsourcing the processing of protected data without fearing disclosing the real data. In 2012, LTV12 presented the first multi-key FHE system and demonstrated the possibility of using multi-key systems in somewhat homomorphic encryption (SHE). Like in the one key context, there have been many advances in the field, but no effort has been made to develop the multi-key methods. This paper presents a discussion of FHE and MKFHE with a specific focus on the current techniques and three implementations, comprising the first in the multi-key setups, to the extent of our understanding.

Statistical confidentiality focuses on protecting data to preserve its analytical value while preventing identity exposure, ensuring privacy and security in any system handling sensitive information. Homomorphic encryption allows computations on encrypted data without revealing it to anyone other than an owner or an authorized collector. When combined with other techniques, homomorphic encryption offers an ideal solution for ensuring statistical confidentiality. TFHE (Fast Fully Homomorphic Encryption over the Torus) is a fully homomorphic encryption scheme that supports efficient homomorphic operations on Booleans and integers. Building on TFHE, Zama’s Concrete project offers an open-source compiler that translates high-level Python code (version 3.9 or higher) into secure homomorphic computations. This study examines the feasibility of the Concrete compiler to perform core statistical analyses on encrypted data. We implement traditional algorithms for core statistical measures including the mean, variance, and five-point summary on encrypted datasets. Additionally, we develop a bitonic sort implementation to support the five-point summary. All implementations are executed within the Concrete framework, leveraging its built-in optimizations. Their performance is systematically evaluated by measuring circuit complexity, programmable bootstrapping count (PBS), compilation time, and execution time. We compare these results to findings from previous studies wherever possible. The results show that the complexity of sorting and statistical computations on encrypted data with the Concrete implementation of TFHE increases rapidly, and the size and range of data that can be accommodated is small for most applications. Nevertheless, this work reinforces the theoretical promise of Fully Homomorphic Encryption (FHE) for statistical analysis and highlights a clear path forward: the development of optimized, FHE-compatible algorithms.

Garbled computation in cloud

Fully homomorphic encryption (FHE) allows us to perform computations directly over encrypted data and can be widely used in some highly regulated industries. Gentry’s bootstrapping procedure is used to refresh noisy ciphertexts and is the only way to achieve the goal of FHE up to now. In this paper, we optimize the LWE-based GSW-type bootstrapping procedure. Our optimization decreases the lattice approximation factor for the underlying worst-case lattice assumption from \(\tilde{O}(N^{2.5})\) to \(\tilde{O}(N^{2})\), and is time-efficient by a \(O(\lambda )\) factor. Our scheme can also achieve the best factor in prior works on bootstrapping of standard lattice-based FHE by taking a larger lattice dimension, which makes our scheme as secure as the standard lattice-based PKE. Furthermore, in this work we present a technique to perform more operations per bootstrapping in the LWE-based FHE scheme. Although there have been studies to evaluate large FHE gates using schemes over ideal lattices, (i.e. using FHEW or TFHE), we are the first to study how to perform complex functions homomorphically over standard lattices.

Предметом дослідження є шифрування інформації в хмарних обчисленнях і сховищах даних. Хмарні технології дозволяють значно скоротити витрати на ІТ-інфраструктуру і гнучко реагувати на зміни обчислювальних потреб. В такому випадку має бути забезпечено можливість проведення обчислень над зашифрованими даними без їх дешифрування. Таку властивість має повністю гомоморфне шифрування. Метою даної статті є підвищення ефективності повністю гомоморфного шифрування (ПГШ) на основі матричних поліномів за допомогою методу пакетного шифрування в один шифротекст декількох відкритих текстів з наступною комплексною обробкою зашифрованих даних. Пакетне шифрування зводиться до того, що при одній операції над двома шифротекстами відбувається одночасне виконання операцій покоординатно над усіма даними, що містяться в цих шифротекстах у вигляді відкритих текстів (SIMD). Завданнями визначено побудову алгоритмів повністю гомоморфного шифрування даних за допомогою матричних поліномів. У статті використано методи шифрування: з використанням китайської теореми про залишки; шляхом запису в одній матриці декількох різних власних значень при різних власних векторах; за допомогою інтерполяції матричних поліномів. В результаті описано та проаналізовано можливі підходи до побудови пакетних ПГШ на підставі матричних поліномів, а також представлено набір алгоритмів, що реалізують криптосхему ПГШ з інтерполяцією матричних поліномів. Наведені алгоритми і криптосхеми дозволяють передавати інформацію в повідомленнях і дані в запитах як відкритий текст, бо над шифрованими даними можна здійснювати необмежену кількість складних алгебраїчних операцій. Це, у свою чергу, ускладнює можливість дешифрування і зчитування даних без знання всього алгоритму. Було показано, що побудовані криптосхеми перевершують аналоги по ефективності, які розроблені дослідниками з IBM. Можна зробити наступний висновок: пакетне повністю е шифрування на основі матричних поліномів здатне виключити необхідність хоча б часткового дешифрування даних для несанкціонованих обчислень над зашифрованими масивами даних у хмарних сховищах.

With the wide adoption of cloud computing paradigm, it is important to develop appropriate techniques to protect client data privacy in the cloud. Encryption is one of the major techniques that could be used to achieve this goal. However, data encryption at the rest alone is insufficient for secure cloud computation environments. There is also the need for efficient techniques to carry out computation over encrypted data. Fully homomorphic encryption (FHE) and garbled circuits are naturally used to process encrypted data without leaking any information about the data. However, existing FHE schemes are inefficient for processing large amount of data in cloud and garbled circuits are one time programs and cannot be reused. Based on quaternion/octonion algebra and Jordan algebra over finite rings \(\mathbb {Z}_q\), this paper designs efficient fully homomorphic symmetric key encryption (FHE) schemes without bootstrapping (that is, noise-free FHE schemes) that are secure in the weak ciphertext-only security model assuming the hardness of solving multivariate quadratic equation systems and solving univariate high degree polynomial equation systems in \(\mathbb {Z}_q\). The FHE scheme designed in this paper is sufficient for privacy preserving computation in cloud.

As a major breakthrough, in 2009 Gentry introduced the first plausible construction of a fully homomorphic encryption (FHE) scheme. FHE allows the evaluation of arbitrary functions directly on encrypted data on untwisted servers. In 2010, Gentry and Halevi presented the first FHE implementation on an IBM x3500 server. However, this implementation remains impractical due to the high latency of encryption and recryption. The Gentry-Halevi (GH) FHE primitives utilize multi-million-bit modular multiplications and additions which are time-consuming tasks for a general purpose computer. In the GH-FHE implementation, the most computationally intensive arithmetic operation is modular multiplication. In this paper, the million-bit modular multiplication is computed in two steps. For large number multiplication, Strassen's FFT based algorithm is employed and accelerated on a graphics processing unit (GPU) through its massive parallelism. Subsequently, Barrett modular reduction algorithm is applied to implement modular reduction. As an experimental study, we implement the GH-FHE primitives for the small setting with a dimension of 2048 on NVIDIA C2050 GPU. The experimental results show the speedup factors of 7.68, 7.4 and 6.59 for encryption, decryption and recrypt respectively, when compared with the existing CPU implementation.

The first plausible scheme of fully homomorphic encryption (FHE), introduced by Gentry in 2009, was considered a major breakthrough in the field of information security. FHE allows the evaluation of arbitrary functions directly on encrypted data on untrusted servers. However, previous implementations of FHE on general-purpose processors had very long latency, which makes it impractical for cloud computing. The most computationally intensive components in the Gentry-Halevi FHE primitives are the large-number modular multiplications and additions. In this paper, we attempt to use customized circuits to speedup the large number multiplication. Strassen's algorithm is employed in the design of an efficient, high-speed large-number multiplier. In particular, we propose an architecture design of an 768K-bit multiplier. As a key compoment, an 64K-point finite-field fast Fourier transform (FFT) processor is designed and prototyped on the Stratix-V FPGA. At 100 MHz, the FPGA implementation is about twice as fast as the same FFT algorithm executed on the NVIDA C2050 GPU which has 448 cores running at 1.15 GHz but at much lower power consumption.

Fully Homomorphic Encryption (FHE) is an advanced cryptographic technique that enables computation on encrypted data without requiring decryption. This capability eliminates the need to expose sensitive data during processing, making FHE particularly suitable for cloud computing, healthcare analytics, financial systems, and privacypreserving artificial intelligence. Despite its strong theoretical foundation, FHE faces practical challenges including high computational complexity, large ciphertext expansion, and bootstrapping overhead. This paper presents a comprehensive study of FHE, including its theoretical background, working mechanism, security properties, real-world applications, limitations, and emerging research trends.

A KPU is a replacement for a standard RISC processor that natively runs encrypted machine code on encrypted data in registers and memory — a 'general-purpose crypto-processor', in other words. It works because the processor's arithmetic is customised to make the chosen encryption into a mathematical homomorphism, resulting in what is called a 'fully-homomorphic encryption' design. This paper discusses the problems and solutions associated with implementing a KPU in hardware.

Fully homomorphic encryption (FHE) enables direct computation on encrypted data without decryption, ensuring data privacy in cloud computing scenarios and preventing the leakage of sensitive information. However, the computational overhead of HE typically exceeds that of plaintext computation by 4 to 5 orders of magnitude, while energy consumption is 5 to 6 orders of magnitude higher. These substantial performance and energy overheads significantly hinder the widespread adoption of FHE. This paper proposed LP-HENN, a novel low-power and energy-efficient FHE accelerator architecture that leverages a RISC-V vector coprocessor and ReRAM crossbar arrays. LP-HENN targets power-constrained application scenarios such as edge devices, aiming to provide highly energy-efficient acceleration support for FHE applications. LP-HENN leverages the collaborative work of the vector processor and ReRAM crossbars, employing optimization strategies to achieve full pipelining and minimize memory access. Furthermore, this paper proposed a parameter selection model for early-stage architecture design, which achieves an optimal balance between performance and energy consumption through the collaborative optimization of multiple parameters. Experimental results show that, for an FHE-based convolutional neural network (HE-CNN) inference application, LP-HENN achieves a 31.82Ã- and 11920.56Ã- improvement in performance and energy efficiency, respectively, compared to CPU. Compared to FxHENN, the state-of-the-art FPGA-based FHE accelerator with high energy efficiency for edge devices, LP-HENN achieves a 2.36Ã- and 10.04Ã- improvement in performance and energy efficiency, respectively. The energy efficiency of LP-HENN is comparable to that of F1, the state-of-the-art ASIC FHE accelerator, while featuring a low power design suitable for edge computing.

Privacy-preserving machine learning (PPML) demands secure inference on sensitive data in untrusted environments. Fully homomorphic encryption (FHE) enables computation directly on encrypted data, but it incurs prohibitive communication and computational overhead on edge devices. Hybrid homomorphic encryption (HHE) mitigates this by combining symmetric encryption with FHE, reducing client-side costs; however, existing implementations remain impractical for resource-constrained deployments. This paper proposes the first end-to-end hardware-accelerated HHE framework, which integrates a lightweight symmetric cipher optimized for FHE compatibility with a dedicated hardware accelerator. Beyond this integration, we introduce a microarchitectural optimization for throughput and energy efficiency. The proposed architecture is validated within a complete PPML pipeline, demonstrating significantly lower latency and power consumption than software implementations. Experimental results on a PYNQ-Z2 platform with MNIST validate our approach, achieving a 50× reduction in client-side encryption latency and a 2× throughput gain over existing FPGA-based HHE accelerators. These improvements enable practical and secure inference on edge devices. Our contributions establish a hardware-software co-design methodology for deploying scalable, secure machine learning in resource-constrained environments, validating the feasibility of low-power HHE for edge deployment.

Fully Homomorphic Encryption (FHE) allows computations on encrypted data without decryption, providing strong security for sensitive information. However, computational and memory demands for FHE are significant challenges, particularly in the Number Theoretic Transform (NTT) phase. This paper presents three efficient Twiddle Factor Generators (TFGs) to address these challenges: the Half-Memory TFG, the On-the-fly Serial TFG, and the On-the-fly Parallel TFG. The Half-Memory TFG reduces memory usage by storing only half of the twiddle factors and calculating the rest as needed. The On-the-fly Serial TFG eliminates memory requirements by computing twiddle factors, while the On-the-fly Parallel TFG enhances computational speed through parallel processing. Implemented on the FPGA KCU105 board, these TFGs demonstrated significant improvements in hardware resource utilization and computational efficiency. The Half-Memory TFG effectively reduces memory footprint, the On-the-fly Serial TFG eliminates memory usage with acceptable computational overhead, and the On-the-fly Parallel TFG offers superior performance for high-throughput applications. These innovations make FHE more practical for real-world applications, contributing to the broader goal of enabling secure, privacy-preserving computations on encrypted data.