Implementing Homomorphic Encryption for Image Manipulation on GPU

This paper presents a homomorphic encryption cipher, which allows the manipulation of encrypted data without decrypting it. The algorithm is based on the GSW-leveled encryption scheme, optimized for GPUs using the CUDA language. The GSW algorithm handles longer key lengths, rigorous security proofs based mainly on standard lattice problems, adaptability in parameters, with a built-in mechanism for managing error growth. The main objective is to encrypt the images, perform operations between encrypted images using XOR and NAND, decrypt them, and validate the homomorphism of the operation. As a proof of concept, we show that the operations on GPU perform better than CPU by twice as much. It demonstrates that might be interesting for cloud applications, given the large amount of data processed and the security measures needed for compliance. Our proposal is a GPU-based solution that shows how to manipulate images, storing encrypted data on the file itself, and making it indistinguishable to the user. Our results show that it is possible to process and recover the original image without loss of information.