A Systematic Review of Algebraic Curve Constructions for Lightweight Key Establishment: Methods, Architectures, and Future Research Directions

Abstract

Lightweight key establishment has emerged as a fundamental requirement in resource-constrained environments such as Internet of Things ecosystems, embedded systems, and edge computing infrastructures. Algebraic curve constructions, particularly those derived from elliptic and hyperelliptic curves, have gained prominence due to their efficiency, compact key sizes, and strong security guarantees rooted in hard mathematical problems. This paper presents a systematic review of algebraic curve-based approaches for lightweight key establishment, focusing on methods, architectures, and emerging research directions. The study analyzes recent advancements between 2018 and 2025, emphasizing curve optimization techniques, implementation strategies, and integration with modern software engineering paradigms. It also explores the intersection of algebraic cryptography with generative artificial intelligence for automated parameter tuning and security validation. The findings reveal a shift toward hybrid constructions, AI-assisted cryptographic design, and post-quantum considerations. The paper contributes a structured synthesis of existing research, identifies key limitations such as side-channel vulnerabilities and scalability constraints, and outlines future research opportunities in adaptive cryptographic systems and secure DevSecOps pipelines.