even though we do not know when a quantum computer to break rsa and other digital signature algorithms will exist, there has been active research over the 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.