the first rlwe based signature was developed by lyubashevsky in his paper "fiat-shamir with aborts: applications to lattice and factoring-based signatures" and refined in "lattice signatures without trapdoors" in 2011. a number of refinements and variants have followed. this article highlights the fundamental mathematical structure of rlwe signatures and follows the original lyubashevsky work and the work of guneysu, lyubashevsky and popplemann (glp). this presentation is based on a 2017 update to the glp scheme called glyph.