Tweaking ML-KEM (Kyber) and ML-DSA (Dilithium)

Abstract

Lattice-based cryptography is the use of conjectured hard problems on point lattices in Rn as the foundation for secure cryptographic systems. Attractive features of lattice cryptography include apparent resistance to quantum attacks (in contrast with most number-theoretic cryptography), high asymptotic efficiency and parallelism, security under worst-case intractability assumptions, and solutions to long-standing open problems in cryptography. This work surveys the structure, security, and optimization potential of two leading lattice-based cryptographic schemes: ML-KEM (Kyber) and ML-DSA (Dilithium). Special attention is given to their applicability in government-oriented post-quantum cryptographic systems, focusing on performance, implementation considerations, and resilience against known quantum threats. In particular, the study introduces tweaks to implementational-level components—such as encoding, compression, and sampling routines—to enhance efficiency and adaptability. Emphasis is placed on how the underlying Short Integer Solution (SIS) and Learning With Errors (LWE) problems—and their ring-based variants—form the mathematical backbone of these NIST-standardized algorithms.