Homomorphic Image Processing Over Geometric Product Spaces and Finite PAdic 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, cloudbased 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.

HEAX: An Architecture for Computing on Encrypted Data With the rapid increase in cloud computing, concerns surrounding data privacy, security, and confidentiality also have been increased significantly. Not only cloud providers are susceptible to internal and external hacks, but also in some scenarios, data owners cannot outsource the computation due to privacy laws such as GDPR, HIPAA, or CCPA. Fully Homomorphic Encryption (FHE) is a groundbreaking invention in cryptography that, unlike traditional cryptosystems, enables computation on encrypted data without ever decrypting it. However, the most critical obstacle in deploying FHE at largescale is the enormous computation overhead.  :89,this paper, we present HEAX, a novel hardware architecture for FHE that achieves unprecedented performance improvement. HEAX leverages multiple levels of parallelism, ranging from ciphertextlevel to finegrained modular arithmetic level. Our first contribution is a new highlyparallelizable architecture for numbertheoretic transform (NTT) which can be of independent interest as NTT is frequently used in many latticebased cryptography systems. Building on top of NTT engine, we design a novel architecture for computation on homomorphically encrypted data. We also introduce several techniques to enable an endtoend, fully pipelined design as well as reducing onchip memory consumption. Our implementation on reconfigurable hardware demonstrates 164268x performance improvement for a wide range of FHE parameters.