Revisiting Multivariate Ring Learning with Errors and Its Applications on Lattice-Based Cryptography

The “Multivariate Ring Learning with Errors” problem was presented as a generalization of Errors (RLWE), introducing efficiency improvements respect to the RLWE counterpart thanks its multivariate structure. Nevertheless, recent attack by Bootland, Castryck and Vercauteren has some important consequences on security “non-coprime” cyclotomics; this transforms instances m-RLWE power-of-two cyclotomic polynomials degree n=?ini into set samples dimension maxi{ni}. This is especially devastating for low-degree cyclotomics (e.g., ?4(x)=1+x2). In work, we revisit propose new alternative instantiations that avoid while still preserving advantages structure, when using polynomials. Additionally, show how parameterize these in secure practical way, therefore enabling constructions strategies based bring notable space time over current RLWE-based constructions.