Fully homomorphic encryption (FHE) has recently attracted significant attention as both a cryptographic primitive and a systems challenge. Given the latest advances in accelerated computing, FHE presents a promising opportunity for progress, with applications ranging from machine learning to information security. We target the most computationally intensive operation in deep neural networks from a hardware perspective, matrix multiplication (matmul), and adapt it for execution on AMD GPUs. We propose a new optimized method that improves the runtime and complexity of ciphertext matmul by using FIDESlib, a recent open-source FHE library designed specifically for GPUs. By exploiting sparsity in both operands, our sparse matmul implementation outperforms its CPU counterpart by up to $3.0\times$ and reduces the time complexity from cubic to semi-linear, demonstrating an improvement over existing FHE matmul implementations.

翻译：全同态加密（FHE）近年来作为密码学基元和系统挑战备受关注。随着加速计算领域的最新进展，FHE在从机器学习到信息安全的众多应用中展现了极具前景的发展机遇。我们从硬件角度出发，聚焦深度神经网络中计算密集度最高的矩阵乘法运算，并针对AMD GPU进行适配优化。本文提出一种新型优化方法，通过利用最新开源的GPU专用FHE库FIDESlib，有效改善密文矩阵乘法的运行时间和计算复杂度。通过开发两个操作数的稀疏性，我们的稀疏矩阵乘法实现相比CPU版本性能提升高达3.0倍，并将时间复杂度从三次方降至半线性，展现出超越现有FHE矩阵乘法实现的显著改进。