ML-DSA (FIPS 204) and SLH-DSA (FIPS 205)

ML-DSA (Module-Lattice-based Digital Signature Algorithm), standardized as FIPS 204, is derived from CRYSTALS-Dilithium. Dilithium was designed by Ducas, Kiltz, Lepoint, Lyubashevsky, Schwabe, Seiler, and Stehle and submitted to NIST in 2017. It uses the Fiat-Shamir with aborts framework applied to Module-LWE, producing a practical signature scheme with strong security proofs.

Classical Fiat-Shamir transforms interactive identification protocols into signatures. For lattice schemes, a direct application leaks information about the secret key through the response vector. The "with aborts" technique by Lyubashevsky adds rejection sampling: the signer checks if the response would reveal information and aborts and retries if so. This adds a small signing overhead but is essential for security.