The CRYSTALS project developed the lattice-based designs CRYSTALS-Kyber and CRYSTALS-Dilithium. They solve different tasks: Kyber is a key encapsulation mechanism, while Dilithium provides digital signatures. Their compact representations use structured polynomial arithmetic and explicit computational hardness assumptions. Kyber's construction uses module learning with errors; Dilithium combines a Fiat-Shamir transform with response rejection. ML-KEM and ML-DSA are the corresponding standardized descendants, so a project submission and a final standard should be distinguished when choosing precise encodings or parameters.[ref]
Kyber documentation by CRYSTALS project. Introduction and Scientific Background
[ref]Dilithium documentation by CRYSTALS project. Introduction and Scientific Background
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