past decade to create cryptographic algorithms which remain secure even when an attacker has the resources of a quantum computer at their disposal. This new area of cryptography is called Post Quantum or Quantum Safe cryptography. This article is about one class of these algorithms: digital signatures based on the Ring Learning with Errors problem. The use of the general Learning with Errors problem in cryptography was introduced by Oded Regev in 2005 and has been the source of several cryptographic designs. The creators of the Ring-based Learning with Errors (RLWE) basis for cryptography believe that an important feature of these algorithms based on Ring-Learning with Errors is their provable reduction to known hard problems. The signature described below has a provable reduction to the Shortest Vector Problem in an ideal lattice. This means that if an attack can be found on the Ring-LWE cryptosystem then a whole class of presumed hard computational problems will have a solution. 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. A RLWE-SIG works in the quotient ring of polynomials modulo a degree n polynomial Φ(x) with coefficients in the finite field Zq for an odd prime q ( i.e. the ring Zq[x]/Φ(x) ). Multiplication and addition of polynomials will work in the usual fashion with results of a multiplication reduced mod Φ(x). For this presentation a typical polynomial is expressed as: The field Zq has its representative elements in the set { -(q-1)/2, ...-1, 0, 1, ... (q-1)/2 }. When n is a power of 2, the polynomial Φ(x) will be the cyclotomic polynomial xn + 1. Other choices of n are possible but the corresponding cyclotomic polynomials are more complicated or their security not as well studied. Generating "small" polynomials. A RLWE signature uses polynomials which are considered "small" with respect to a measure called the "infinity norm". The infinity norm for a polynomial is simply the largest absolute value of the coefficients of the polynomial when those coefficients are viewed as integers in