Learning with Errors over Rings
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.