Homomorphic encryption (HE) is a promising technique for privacy-preserving computations, especially the word-wise HE schemes that allow batching. However, the high computational overhead hinders the deployment of HE in real-word applications. GPUs are often used to accelerate execution, but a comprehensive performance comparison of different schemes on the same platform is still missing. In this work, we fill this gap by implementing three word-wise HE schemes BGV, BFV, and CKKS on GPU, with both theoretical and engineering optimizations. We enhance the hybrid key-switching technique, significantly reducing the computational and memory overhead. We explore several kernel fusing strategies to reuse data, resulting in reduced memory access and IO latency, and enhancing the overall performance. By comparing with the state-of-the-art works, we demonstrate the effectiveness of our implementation. Meanwhile, we introduce a unified framework that finely integrates our implementation of the three schemes, covering almost all scheme functions and homomorphic operations. We optimize the management of pre-computation, RNS bases, and memory in the framework, to provide efficient and low-latency data access and transfer. Based on this framework, we provide a thorough benchmark of the three schemes, which can serve as a reference for scheme selection and implementation in constructing privacy-preserving applications.

Digital signatures are fundamental building blocks in various protocols to provide integrity and authenticity. The development of the quantum computing has raised concerns about the security guarantees afforded by classical signature schemes. CRYSTALS-Dilithium is an efficient post-quantum digital signature scheme based on lattice cryptography and has been selected as the primary algorithm for standardization by the National Institute of Standards and Technology. In this work, we present a high-throughput GPU implementation of Dilithium. For individual operations, we employ a range of computational and memory optimizations to overcome sequential constraints, reduce memory usage and IO latency, address bank conflicts, and mitigate pipeline stalls. This results in high and balanced compute throughput and memory throughput for each operation. In terms of concurrent task processing, we leverage task-level batching to fully utilize parallelism and implement a memory pool mechanism for rapid memory access. We propose a dynamic task scheduling mechanism to improve multiprocessor occupancy and significantly reduce execution time. Furthermore, we apply asynchronous computing and launch multiple streams to hide data transfer latencies and maximize the computing capabilities of both CPU and GPU. Across all three security levels, our GPU implementation achieves over 160× speedups for signing and over 80× speedups for verification on both commercial and server-grade GPUs. This achieves microsecond-level amortized execution times for each task, offering a high-throughput and quantum-resistant solution suitable for a wide array of applications in real systems.

The threat posed by quantum computing has precipitated an urgent need for post-quantum cryptography. Recently, the post-quantum digital signature draft FIPS 204 has been published, delineating the details of the ML-DSA, which is derived from the CRYSTALS-Dilithium. Despite these advancements, server environments, especially those equipped with GPU devices necessitating high- throughput signing, remain entrenched in classical schemes. A conspicuous void exists in the realm of GPU implementation or server-specific designs for ML-DSA. In this paper, we propose the first server-oriented GPU design tailored for the ML-DSA signing procedure in high- throughput servers. We introduce several innovative theoretical optimizations to bolster performance, including depth-prior sparse ternary polynomial multiplication, the branch elimination method, and the rejection-prioritized checking order. Furthermore, exploiting server-oriented features, we propose a comprehensive GPU hardware design, augmented by a suite of GPU implementation optimizations to further amplify performance. Additionally, we present variants for sampling sparse polynomials, thereby streamlining our design. The deployment of our implementation on both server-grade and commercial GPUs demonstrates significant speedups, ranging from 284.9× to 485.3× against the CPU baseline, and an improvement of up to 60.9% compared to related work, affirming the effectiveness and efficiency of the proposed GPU architecture for ML-DSA signing procedure

Homomorphic Encryption (HE) enhances data security by enabling computations on encrypted data, advancing privacy-focused computations. The BFV scheme, a promising HE scheme, raises considerable performance challenges. Graphics Processing Units (GPUs), with considerable parallel processing abilities, offer an effective solution. In this work, we present an in-depth study on accelerating and comparing BFV variants on GPUs, including Bajard-Eynard-Hasan-Zucca (BEHZ), Halevi-Polyakov-Shoup (HPS), and recent variants. We introduce a universal framework for all variants, propose optimized BEHZ implementation, and first support HPS variants with large parameter sets on GPUs. We also optimize low-level arithmetic and high-level operations, minimizing instructions for modular operations, enhancing hardware utilization for base conversion, and implementing efficient reuse strategies and fusion methods to reduce computational and memory consumption. Leveraging our framework, we offer comprehensive comparative analyses. Performance evaluation shows a 31.9X speedup over OpenFHE running on a multi-threaded CPU and 39.7% and 29.9% improvement for tensoring and relinearization over the state-of-the-art GPU BEHZ implementation. The leveled HPS variant records up to 4X speedup over other variants, positioning it as a highly promising alternative for specific applications.

Bit-wise Fully Homomorphic Encryption schemes like FHEW and TFHE offer efficient functional bootstrapping, enabling concurrent function evaluation and noise reduction. While advantageous for secure computations, these schemes suffer from high data expansion, posing significant performance challenges in practical ap- plications due to massive ciphertexts. To address these issues, we propose VeloFHE, a CUDA-accelerated design to enhance the efficiency of FHEW and TFHE schemes on GPUs. We develop a novel hybrid four-step Number Theoretic Transform (NTT) approach for fast polynomial multiplication. By decomposing large-scale NTTs into highly parallelizable submodules, incorporating cyclic and negacyclic convolutions, and introducing several memory-oriented optimizations, we significantly reduce both the computational complexity and memory requirements. For blind rotation, besides the gadget decomposition approach, we also apply a recent proposed modulus raising technique to both schemes to alleviate memory pressure. We further optimize it by refining computational flow to reduce noise from scaling and maintain accumulator compatibility. For key switching, we address input-output parallelism mismatches, and offloading suitable computations to the CPU, effectively hiding latency through asynchronous execution. Additionally, we explore batching in bootstrapping, de- veloping a general framework that accommodates both schemes with either gadget decomposition or modulus raising method.Our experimental results demonstrate significant performance improvements. The proposed NTT implementation shows over 35% improvement compared to recent GPU implementations. On an RTX 4090 GPU, we achieve speedups of 371.86x and 390.44x for FHEW and TFHE gate bootstrapping, respectively, compared to OpenFHE running on a 48-thread CPU at a 128-bit security level. The corresponding throughputs are 7,007 and 11,378 operations per second. Furthermore, relative to the state-of-the-art GPU implementation [XLK+25], our approach provides speedups of 2.56x, 2.24x, and 2.33x for TFHE gate bootstrapping, homomorphic evaluation of arbitrary functions, and homomorphic flooring operation, respectively. Our VeloFHE surpasses some current hardware designs, offering an effective solution for more practical and efficient privacy-preserving computations.