Stateful signature
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.
In practice
XMSS and LMS are stateful and are described in NIST SP 800-208. The Quantum Resistant Ledger uses XMSS.
Related terms
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.
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.