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

2025/08/29 by Gaurav Mittal, Mittal, Gaurav
Computer Science · Engineering · #65J22 #94A60 #Cryptography and Data Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Security in Wireless Sensor Networks #Wireless Communication Security Techniques

paper · pdf · doi:10.48550/arxiv.2508.21653

openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Classical Hardness of Learning with Errors
• The Learning with Errors Problem (Invited Survey)
• On lattices, learning with errors, random linear codes, and cryptography
• Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem
• LWE-based Identification Schemes