Abstract
The “learning with errors” (LWE) problem is to distinguish random linear equations, which have been perturbed by a small amount of noise, from truly uniform ones. The problem has been shown to be as hard as worst-case lattice problems, and in recent years it has served as the foundation for a plethora of cryptographic applications.
Unfortunately, these applications are rather inefficient due to an inherent quadratic overhead in the use of LWE. After a short introduction to the area, we will discuss recent work on making LWE and its applications truly efficient by exploiting extra algebraic structure. Namely, we will define the ring-LWE problem, and prove that it too enjoys very strong hardness guarantees.
Based on joint work with Vadim Lyubashevsky and Chris Peikert.
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© 2010 Springer-Verlag Berlin Heidelberg
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Regev, O. (2010). Learning with Errors over Rings. In: Hanrot, G., Morain, F., Thomé, E. (eds) Algorithmic Number Theory. ANTS 2010. Lecture Notes in Computer Science, vol 6197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14518-6_3
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DOI: https://doi.org/10.1007/978-3-642-14518-6_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14517-9
Online ISBN: 978-3-642-14518-6
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