CRYSTALS-Dilithium: A Lattice-Based Digital Signature Scheme

TLDR

The paper introduces Dilithium, a lattice‑based signature scheme part of the CRYSTALS suite submitted to NIST for post‑quantum standards. Dilithium is designed without discrete Gaussian sampling, enabling constant‑time implementation, and incorporates a faster number‑theoretic transform to accelerate lattice‑based operations. Dilithium achieves a 2.5× smaller public key than prior non‑Gaussian lattice schemes with comparable signature size, and its AVX2 implementation delivers about a two‑fold speed‑up, a technique that benefits other lattice constructions.

Abstract

In this paper, we present the lattice-based signature scheme Dilithium, which is a component of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) suite that was submitted to NIST’s call for post-quantum cryptographic standards. The design of the scheme avoids all uses of discrete Gaussian sampling and is easily implementable in constant-time. For the same security levels, our scheme has a public key that is 2.5X smaller than the previously most efficient lattice-based schemes that did not use Gaussians, while having essentially the same signature size. In addition to the new design, we significantly improve the running time of the main component of many lattice-based constructions – the number theoretic transform. Our AVX2-based implementation results in a speed-up of roughly a factor of 2 over the previously best algorithms that appear in the literature. The techniques for obtaining this speed-up also have applications to other lattice-based schemes.