CRYSTALS-Dilithium is a lattice-based digital signature design whose arithmetic uses vectors of polynomials modulo a fixed polynomial and integer modulus. Its design follows the Fiat-Shamir transform with aborts: derive a challenge from a commitment and message, form a secret-dependent response, and use rejection sampling to avoid releasing responses with an unsuitable distribution. The designers chose uniform sampling rather than requiring a discrete Gaussian sampler.[ref]
Dilithium documentation by CRYSTALS project. Introduction and Scientific Background
The goal is efficient signing and verification while making forgery difficult even for proposed quantum attacks on its underlying assumptions. ML-DSA is the later standardized descendant. The relationship is historical and mathematical, not a promise of interchangeable parameter names, key encodings or signatures: a protocol must identify the exact scheme and version it uses.
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