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Learning with Errors (LWE) was introduced by Oded Regev in 2005[R05], a survey of LWE can be found in [R10].

If you want to experiment with LWE, you can use the Frodo C library [Frodo], which is explained in [BCDMNNRS17].

Vinod Vaikutanathan shows Learning With Errors (LWE) in Lecture "L11. Learning With Errors" of an advanced course:

Another talk on LWE is Chris Peikert's "Learning With Errors" at the 2nd BIU Winter School on Cryptography, Lattice-based Cryptography and Applications, February 19-22, 2012 (all videos), organized by the Center for Research in Applied Cryptography and Cyber Security of the Bar-Ilan University. Slides1, Slides2.


  • [R05] Oded Regev: On Lattices, Learning with Errors, Random Linear Codes, and Cryptography. In: STOC'05, Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, May 22 - 24, 2005, pages 84-93 (acm.org paywalled, full pdf)
  • [R10] Oded Regev: The Learning with Errors Problem. (full pdf)
  • [Frodo] lwe-frodo (library)
  • [BCDMNNRS17] Joppe Bos, Craig Costello, Léo Ducas, Ilya Mironov, Michael Naehrig, Valeria Nikolaenko, Ananth Raghunathan, Douglas Stebila: Frodo, Take Off The Ring! Practical, Quantum-Secure Key Exchange from LWE. (iacr 2016/659, full pdf)

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