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{{AFC submission|||ts=20150704210626|u=Cryptocat|ns=2}}
Ring Learning with Errors (RLWE) is a [[computational problem]] which serves as the foundation of new cryptographic algorithms designed to protect against cryptanalysis by [[quantum computers]] and also to provide the basis for [[homomorphic encryption]]. RLWE is more properly called Learning with Errors over Rings and is simply the larger [[Learning with errors|Learning with Errors]] problem specialized to polynomial rings over finite fields.<ref name=":0" /> Because of the presumed difficulty of solving the RLWE problem even on a quantum computer, RLWE based cryptography may form the fundamental base for [[Public-key cryptography|public key cryptography]] in the future just as the [[integer factorization]] and [[discrete logarithm]] problem have served as the base for public key cryptography since the early 1980's.<ref name=":2">{{Cite book|title = Lattice Cryptography for the Internet|url = http://link.springer.com/chapter/10.1007/978-3-319-11659-4_12|publisher = Springer International Publishing|isbn = 978-3-319-11658-7|pages = 197-219|series = Lecture Notes in Computer Science|language = en|first = Chris|last = Peikert|editor-first = Michele|editor-last = Mosca}}</ref> An important feature of basing cryptography on the Ring Learning with Errors problem is the fact that the solution to the RLWE problem may be reducible to the NP-Hard [[Shortest vector problem|Shortest Vector Problem]] (SVP) in a Lattice.<ref name=":0" />
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