Here at wolfSSL, we don’t just love coding! We love telling the world about what we code. To that end, we want you to understand the differences between LMS, XMSS, and SLH-DSA. Here are their official standard specifications:
- LMS (Leighton-Micali Hash-Based Signatures)
- XMSS (eXtended Merkle Signature Scheme)
- SLH-DSA (Stateless Hash-Based Digital Signature Standard)
The most important similarity of these three algorithms is that they are all hash-based signature schemes. Being hash-based, they are all quantum-safe signature schemes that rely on the tried and true security properties of proven battle-hardened hashing algorithms. They all use Merkle Trees to combine many data structure instances into a single public key.
These instances form the leaf nodes of the Merkle tree and are called WOTS (Winternitz One-Time Signature) in LMS and WOTS+ in XMSS. WOTS uses a “prefix construction” while WOTS+ uses a “prefix and bitmask construction” with random bitmasks to give it stronger security assumptions.
XMSS uses “L-trees” for compression, requiring more hashing operations. LMS does not have a corresponding compression scheme.
From the perspective of performance, LMS is consistently better (fewer clock cycles) for key generation, signing, and verification.
Generally speaking, XMSS has higher memory consumption, mostly during signing and verification.
While XMSS has various theoretical optimizations that would hamper interoperability, LMS remains more efficient in practice, but the difference is quite negligible. If security assurance via the bitmask constructions are important to you, then you should go with XMSS, but LMS is a better default.
The thing that LMS and XMSS both have in common is that they have a state and a limited number of available signatures; once that limit is hit, the private key must be discarded. The state is very important because if it is mismanaged, the signer might reuse a WOTS or WOTS+ which would then allow an attacker to forge signatures. With this formidable problem in mind, SLH-DSA was designed to eliminate this pitfall by not requiring state. SLH-DSA takes a randomized approach and makes conjectures on the probability of collisions. Note that the SLH-DSA equivalent of WOTS is a “few time signature”.
With the elimination of state, SLH-DSA opens the door to parallelization and distributed usage while LMS and XMSS would have signing operations tightly coupled to a single instance of the private key limiting it to serial signing operations.
Finally, one of the most important distinctions is that all three algorithms are standardized and recognized by NIST while only LMS and XMSS are approved for use under CNSA 2.0.
This concludes our comparison of LMS, XMSS and SLH-DSA. That said, this has only touched on the surface of these algorithms. Want deeper technical details? Looking to know which is most appropriate for your use-case? Have some more questions? Let us know by sending a message to facts@wolfSSL.com; we are always happy to continue the conversation!
If you have questions about any of the above, please contact us at facts@wolfssl.com or call us at +1 425 245 8247.
Download wolfSSL Now