Learning-With-Errors (LWE) and Ring-LWE (RLWE)
Modern lattice based cryptography relies on hard mathematical problems that remain secure even against quantum computers. Two foundational assumptions in this area are Learning-With-Errors (LWE) and its more efficient variant, that is, Ring-LWE (RLWE). These problems form the backbone of many encryption, signature, and homomorphic encryption schemes. Learning-With-Error (LWE) The LWE problem was introduced by Regev in 2005 [1]. Imagine a scenario where we have a secret key (s). We construct many linear equations related to this secret. However, unlike a standard algebra problem, we introduce a small, random error (or noise) into the result of every single equation. The objective is to find the original secret key (s) using only the set of these noisy equations. If there were no error, t...