Exploring the Application and Characteristics of Homomorphic Encryption Based on Pixel Scrambling Algorithm in Image Processing

Homomorphic encryption is well known to researchers, yet its application in image processing is scarce. The diversity of image processing algorithms makes homomorphic encryption implementation challenging. Current research often uses the CKKS algorithm, but it has core bottlenecks in image encryption, such as the mismatch between image data and the homomorphic operation mechanism, high 2D-structure-induced costs, noise-related visual quality damage, and poor nonlinear operational support. This study, based on image pixel characteristics, analyzes homomorphic encryption via pixel scrambling algorithms. Using magic square, Arnold, Henon map, and Hilbert curve transformations as starting points, it reveals their homomorphic properties in image processing. This further explores general pixel scrambling algorithm homomorphic encryption properties, offering valuable insights for homomorphic encryption applications in image processing.