Concept

# Learning with errors

Summary
In cryptography, Learning with errors (LWE) is a mathematical problem that is widely used in cryptography to create secure encryption algorithms. It is based on the idea of representing secret information as a set of equations with errors. In other words, LWE is a way to hide the value of a secret by introducing noise to it. In more technical terms, it refers to the computational problem of inferring a linear n-ary function f over a finite ring from given samples y_i = f(\mathbf{x}_i) some of which may be erroneous. The LWE problem is conjectured to be hard to solve, and thus to be useful in cryptography. More precisely, the LWE problem is defined as follows. Let \mathbb{Z}_q denote the ring of integers modulo q and let \mathbb{Z}_q^n denote the set of n-vectors over \mathbb{Z}_q . There exists a certain unknown linear function f:\mathbb{Z}_q^n \rightarrow
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