# Analogy between Learning With Error Problem and Ill-Posed Inverse Problems

## TL;DR

This paper draws an analogy between the Learning With Error problem and ill-posed inverse problems, proposing new encryption schemes and analyzing their security based on this connection.

## Contribution

It introduces a novel perspective linking LWE to ill-posed inverse problems and develops new encryption schemes grounded in this analogy.

## Key findings

- LWE is shown to be a structured inverse problem
- A symmetric encryption scheme based on ill-posed problems is proposed
- A public key encryption scheme combining this symmetric scheme with CRYSTALS-Kyber is introduced

## Abstract

In this work, we unveil an analogy between well-known lattice based learning with error problem and ill-posed inverse problems. We show that LWE problem is a structured inverse problem. Further, we propose a symmetric encryption scheme based on ill-posed problems and thoroughly discuss its security. Finally, we propose a public key encryption scheme based on our symmetric encryption scheme and CRYSTALS-Kyber KEM (key encapsulation mechanism) and discuss its security.