Computational cryptography › Hashes and symmetric ciphers
SIGNATUREPrimitive

SLH-DSA (SPHINCS+), XMSS, LMS

In plain words

Signatures built only from hash functions: big, but resting on the safest assumption around.

The idea: The simplest hash-based signature (Lamport, 1979): pick pairs of random secrets and publish their hashes as your public key. To sign, go through the bits of the message's hash and reveal one secret from each pair: the first for a 0, the second for a 1. Anyone can hash what you revealed and compare. Each key can sign only once, since revealing more secrets would let others mix and match. SPHINCS+ (SLH-DSA) builds a huge tree of such one-time keys, so you can sign many messages without keeping track of which keys you've used.

Why it matters: A conservative quantum-safe choice for signing software and firmware.

Signing by revealing secrets
message hash10110010secret for 0•s••ss•ssecret for 1s•ss••s•public keythe hashes of all 16 secretssignature = the 8 orange secrets: anyone hashes themand compares with the public key
A toy Lamport signature with an 8-bit hash (real ones use 256). For each bit of the message's hash you reveal one of two secrets. Checking only needs hashing. Signing a second, different message would reveal secrets from the other row too, letting a forger mix and match, so each key is used once. SPHINCS+ (SLH-DSA) organizes a huge tree of one-time keys so that a signer never needs to remember which keys it has used.

The details

On the map: FIPS 205: needs nothing but a hash

Signatures whose security rests only on properties of a hash function, the most conservative post-quantum option.

Used for firmware and software signing, where size matters less than confidence.

Rests on

If any of these breaks, this breaks too.

If it falls

If this breaks, these break with it.

Nothing on the map depends on it: it is an end point, something people use directly.

References

  1. NIST. Stateless hash-based digital signature standard. NIST FIPS 205, 2024. doi:10.6028/NIST.FIPS.205
  2. Daniel J. Bernstein, Andreas Hülsing, Stefan Kölbl et al. The SPHINCS + Signature Framework. Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security. doi:10.1145/3319535.3363229
  3. A. Huelsing, D. Butin, S. Gazdag et al. XMSS: eXtended Merkle Signature Scheme. RFC 8391, 2018. rfc-editor.org/rfc/rfc8391
  4. D. McGrew, M. Curcio and S. Fluhrer. Leighton-Micali Hash-Based Signatures. RFC 8554, 2019. rfc-editor.org/rfc/rfc8554
  5. David A. Cooper, Daniel C. Apon, Quynh H. Dang et al. Recommendation for Stateful Hash-Based Signature Schemes. National Institute of Standards and Technology, 2020. doi:10.6028/NIST.SP.800-208