With growing emphasis on privacy protection, homomorphic encryption (HE) has emerged as a core method for privacy-preserving image processing, as it enables operations directly on encrypted data. However, existing research predominantly focuses on low-resolution image processing, and techniques for privacy-preserving high-resolution image processing remain underexplored. As the image size increases, the HE parameters must be adjusted accordingly, and directly applying existing methods can lead to significant computational overhead. In this work, we propose a multi-ciphertext privacy-preserving framework for large images, enabling efficient image encryption and computation under the semi-honest model. Specifically, we divide the large image into multiple sub-images, which allows us to maintain smaller HE parameters and reduce key size. By parallel processing the sub-image ciphertexts and introducing a new bootstrapping placement strategy, we significantly reduce encryption overhead and enhance user experience. On the server side, we optimize the large image convolution operation through a repeated packing technique and implement the Sobel operator computation based on HE. To improve gradient direction calculation for the Sobel operator, we introduce a new polynomial approximation method for the reciprocal function based on the sign function, which can be applied to other HE-based protocols.

翻译：随着隐私保护意识的日益增强，同态加密已成为隐私保护图像处理的核心方法，因其可直接在加密数据上执行操作。然而，现有研究主要聚焦于低分辨率图像处理，针对高分辨率图像的隐私保护技术仍鲜有探索。随着图像尺寸增大，同态加密参数需相应调整，直接应用现有方法将导致显著的计算开销。本文提出一种面向大图像的多密文隐私保护框架，能够在半诚实模型下实现高效的图像加密与计算。具体而言，我们将大图像划分为多个子图像，从而保持较小的同态加密参数并降低密钥规模。通过并行处理子图像密文并引入新型自举放置策略，我们显著降低了加密开销并提升用户体验。在服务器端，我们通过重复打包技术优化大图像卷积运算，并基于同态加密实现了Sobel算子计算。为改进Sobel算子的梯度方向计算，我们基于符号函数提出一种新的倒数函数多项式逼近方法，该方法可推广至其他基于同态加密的协议。