Lattice-based Cryptosystems in Standardisation Processes: A Survey

Abstract. This survey provides a comprehensive overview of lattice-based cryptosystems in the context of ongoing standardisation processes, particularly the NIST Post-Quantum Cryptography Standardization project. Lattice-based cryptography has emerged as one of the most promising families of post-quantum cryptographic primitives due to its strong security guarantees, good efficiency, and versatility. The paper reviews the main lattice-based cryptographic constructions, including key encapsulation mechanisms (such as Kyber, FrodoKEM, and Saber), digital signatures (such as Dilithium and Falcon), and fully homomorphic encryption schemes. It discusses the design principles, security foundations, performance characteristics, and implementation considerations of these schemes. The survey also examines the standardisation status and prospects of various lattice-based cryptosystems, providing insights into the future direction of post-quantum cryptographic infrastructure.