Hash-based signature
A signature scheme built only from hash functions, with no number-theoretic or lattice assumptions. Security reduces to the collision and preimage resistance of the hash, which is unusually well understood.
In practice
SLH-DSA is stateless; XMSS and LMS are stateful and must never reuse a one-time key.
Related terms
A stateless hash-based post-quantum signature scheme whose security depends only on the strength of its underlying hash function. Signatures are large and slow, but the security assumptions are the most conservative of the NIST signature standards.
A hash-based signature scheme that must track which one-time keys it has already used. Reusing a key catastrophically leaks the private key, which makes backups, replication and failover genuinely dangerous.
A quantum search algorithm that finds an item in an unstructured set of N in roughly √N steps. Against symmetric cryptography this halves effective key strength — a nuisance answered by doubling key sizes, not a break.