Multivariate lattices for encrypted image processing

Abstract

Images are inherently sensitive signals that require privacy-preserving solutions when processed in an untrusted environment, but their efficient encrypted processing is particularly challenging due to their structure and size. This work introduces a new cryptographic hard problem called m-RLWE (multivariate Ring Learning with Errors) extending RLWE. It gives support to lattice cryptosystems that allow for encrypted processing of multidimensional signals. We show an example cryptosystem and prove that it outperforms its RLWE counterpart in terms of security against basis-reduction attacks, efficiency and cipher expansion for encrypted image processing.