Homomorphic Image Processing Over Geometric Product Spaces and Finite P-Adic Arithmetic

The ability of securely perform computations over encrypted data creates the opportunity of outsourcing data processing without compromising its privacy. With the always increasing data availability, cloud-based applications are becoming the new norm, which makes securely storing homomorphically encrypted data on the cloud a much current need since it allows one to conciliate availability with confidentiality. We introduce a homomorphic image encryption framework with which images can be processed while encrypted. We demonstrate the practicability of our construction by implementing a set of pixel transformations that are only performed over encrypted images. We present the results of our experiments in terms of image transformations, security and efficiency.