A gentle introduction to lattice-based cryptography

Alfred Menezes

Paper 2026/1098

A gentle introduction to lattice-based cryptography

Alfred Menezes, University of Waterloo

Abstract

We present three quantum-safe schemes: the Kyber key encapsulation mechanism (ML-KEM), the Dilithium signature scheme (ML-DSA), and the Falcon signature scheme (FN-DSA). We also develop the mathematical background on lattices needed to understand why Kyber, Dilithium and Falcon are regarded as lattice-based cryptosystems, and we provide insight into the computational hardness of the underlying lattice problems. The exposition is intended to be accessible to senior undergraduate students and beginning graduate students.

Note: Comments and suggestions are welcome at any time!

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Kyber (ML-KEM)Dilithium (ML-DSA)Falcon (FN-DSA)lattice-based cryptography LWE LLL lattice basis reduction
Contact author(s): ajmeneze @ uwaterloo ca
History: 2026-08-02: last of 4 revisions; 2026-05-29: received; See all versions
Short URL: https://ia.cr/2026/1098
License: CC BY

BibTeX

@misc{cryptoeprint:2026/1098,
      author = {Alfred Menezes},
      title = {A gentle introduction to lattice-based cryptography},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1098},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1098}
}