Analogy between Learning With Error Problem and Ill-Posed Inverse Problems
Numerical Analysis
2025-09-01 v1 Cryptography and Security
Numerical Analysis
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.
Cite
@article{arxiv.2508.21653,
title = {Analogy between Learning With Error Problem and Ill-Posed Inverse Problems},
author = {Gaurav Mittal},
journal= {arXiv preprint arXiv:2508.21653},
year = {2025}
}