A survey on Lattice-Based Key Establishment Schemes: Types, Evolution and Advances

A key establishment (KE) scheme enables the secure sharing of secret keys or keying material among parties. The National Institute of Standards and Technology (NIST) chose CRYSTALS-KYBER, further developed as the Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM), now an approved standard for KE, considered secure even against adversaries with large-scale, fault-tolerant quantum computers. This paper reviews, categorizes, and examines the development of public-key encryption (PKE) and KE algorithms based on lattice among the candidates in NIST’s Post-Quantum Cryptography (PQC) standardization process, with emphasis on schemes relying on lattice hardness assumptions. By covering the theoretical background, classification, evolution, and a simplified summary of the ML-KEM, along with known attacks, countermeasures, and property analysis of good schemes, this paper aims to simplify the complexity, assisting students, researchers, academicians, and industry professionals in advancing further.