Revisiting Multivariate Lattices for Encrypted Signal Processing

Multimedia contents are inherently sensitive signals that must be protected when processed in untrusted environments. The field of Secure Signal Processing addresses this challenge by developing methods which enable operating with sensitive signals in a privacy-conscious way. Recently, we introduced a hard lattice problem called m-RLWE (multivariate Ring Learning with Errors) which gives support to efficient encrypted processing of multidimensional signals. Afterwards, Bootland et al. presented an attack to m-RLWE that reduces the security of the underlying scheme from a lattice with dimension \prod_in_i to \max\n_i\ _i . Our work introduces a new pre-/post-coding block that addresses this attack and achieves the efficient results of our initial approach while basing its security directly on RLWE with dimension \prod_in_i, hence preserving the security and efficiency originally claimed. Additionally, this work provides a detailed comparison between a conventional use of RLWE, m-RLWE and our new pre-/post-coding procedure, which we denote "packed''-RLWE. Finally, we discuss a set of encrypted signal processing applications which clearly benefit from the proposed framework, either alone or in a combination of baseline RLWE, m-RLWE and "packed''-RLWE.