Ring learning with errors key exchange: Difference between revisions

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Cryptography that is not susceptible to attack by a quantum computer is referred to as Quantum Resistant, Quantum Safe, or [[Post-quantum cryptography]]. One class of quantum resistant cryptographic algorithms is based on a concept called "[[Learning with errors]]" introduced by Oded Regev in 2005<ref>{{Cite journal|title = On Lattices, Learning with Errors, Random Linear Codes, and Cryptography|url = http://doi.acm.org/10.1145/1060590.1060603|publisher = ACM|journal = Proceedings of the Thirty-seventh Annual ACM Symposium on Theory of Computing|date = 2005|___location = New York, NY, USA|isbn = 1-58113-960-8|pages = 84–93|series = STOC '05|doi = 10.1145/1060590.1060603|first = Oded|last = Regev}}</ref>. A specialized form of Learning with errors operates within the Ring of Polynomials over a Finite Field. This specialized form is called Ring Learning with Errors or Ring-LWE.

There are a variety of cryptographic algorithms which work using the Ring-LWE paradigm. There are public key encryption algorithms, [[homomorphic encryption]] algorithms, and digital signatures in addition to the public key, key exchange algorithm presented in this article

=== Introduction ===