Group Theory in Lattice-Based Cryptography

Abstract

Group theory plays a fundamental role in lattice-based cryptography, providing a rich mathematical framework for the design and analysis of cryptographic protocols. This paper explores the application of group theory concepts within lattice-based cryptographic systems, focusing on the algebraic structures formed by lattices and their subgroups. The utilization of group theory in lattice-based cryptography enhances the security and efficiency of key exchange, encryption, and digital signatures. Through a mathematical lens, we investigate the foundational principles, theorems, and cryptographic constructions that leverage group theory, shedding light on the symbiotic relationship between group theory and lattice-based cryptography. The paper also proposes cryptographic scheme based on group theory in lattice-based.