Composite FN-DSA and LMS Digital Signature Algorithm for use in X.509 Public Key Infrastructure

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Table of Contents

1. Introduction

This document defines a composite signature scheme combining:¶

• FN-DSA (Falcon), a lattice-based signature algorithm¶

• LMS, a stateful hash-based signature algorithm [RFC8554]¶

The reason for this choice of algorithm combination:¶

• Both FN-DSA and LMS are believed to be quantum resistant algorithms (PQ/PQ Hybrid).¶

• They use completely different hardness problems (lattice based versus stateful hash based).¶

• If relevent attacks or implementations bugs are found in either algorithm there is resiliency.¶

• FN-DSA can help mitigate the risk of operational errors that lead to state failure in LMS.¶

• Combined together they produce a compact PQ/PQ composite signature ideally suited for high value assets in constrained environments.¶

The composite construction presents a single algorithm interface while internally invoking both primitives.¶

This specification follows the composite design framework described in [I-D.ietf-lamps-pq-composite-sigs].¶

2. Conventions and Definitions

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.¶

3. Overview of the Composite FN-DSA-LMS Scheme

Composite FN-DSA-LMS is a hybrid signature scheme formed by combining FN-DSA and LMS.¶

The construction follows the composite signature combiner approach:¶

M' := Prefix || Label || len(ctx) || ctx || PH(M) ¶

Both component algorithms independently sign M'.¶

4. Composite Functions

Composite-FNDSA-LMS.KeyGen() -> (pk, sk)

Steps:

1. Generate component keys:

(fndsaPK, fndsaSK) = FNDSA.KeyGen()
(lmsPK, lmsSK)     = LMS.KeyGen()

2. Output:

pk = SerializePublicKey(fndsaPK, lmsPK)
sk = SerializePrivateKey(fndsaSK, lmsSK)

Composite-FNDSA-LMS.Sign(sk, M, ctx) -> s

Steps:

1. Check:
   if len(ctx) > 255: error

2. Compute:
   M' := Prefix || Label || len(ctx) || ctx || PH(M)

3. Deserialize keys:
  (fndsaSK, lmsSK) = DeserializePrivateKey(sk)

4. Sign:
  fndsaSig = FNDSA.Sign(fndsaSK, M')
  lmsSig   = LMS.Sign(lmsSK, M')

5. Output:
  s = SerializeSignatureValue(fndsaSig, lmsSig)

Composite-FNDSA-LMS.Verify(pk, M, s, ctx) -> boolean

Steps:

1. Deserialize:
   (fndsaPK, lmsPK) = DeserializePublicKey(pk)
   (fndsaSig, lmsSig) = DeserializeSignatureValue(s)

2. Compute:
   M' := Prefix || Label || len(ctx) || ctx || PH(M)

3. Verify:
  FNDSA.Verify(fndsaPK, M', fndsaSig)
  LMS.Verify(lmsPK, M', lmsSig)

Both FNDSA.Verify() and LMS.Verify() MUST verify correctly.

SerializePublicKey(fndsaPK, lmsPK):
return fndsaPK || lmsPK

SerializePrivateKey(fndsaSK, lmsSK):
return fndsaSK || lmsSK

SerializeSignatureValue(fndsaSig, lmsSig):
return fndsaSig || lmsSig

5. Use within X.509 and PKIX

Composite FN-DSA-LMS is used identically to other composite algorithms.¶

• Public key encoded as BIT STRING¶

• Signature encoded as BIT STRING¶

• Raw serialized values used without ASN.1 wrapping¶

6. Algorithm Identifiers

7. Security Considerations

8. IANA Considerations

IANA is requested to assign OIDs under:¶

1.3.6.1.5.5.7.6¶

TODO for each combination¶

9. Normative References

[I-D.ietf-lamps-fn-dsa-certificates]

Massimo, J., Kampanakis, P., Turner, S., and B. Westerbaan, "Internet X.509 Public Key Infrastructure -- Algorithm Identifiers for the Fast-Fourier Transform over NTRU-Lattice-Based Digital Signature Algorithm (FN-DSA)", Work in Progress, Internet-Draft, draft-ietf-lamps-fn-dsa-certificates-00, 20 May 2026, <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-fn-dsa-certificates-00>.

[I-D.ietf-lamps-pq-composite-sigs]

Ounsworth, M., Gray, J., Pala, M., Klaußner, J., and S. Fluhrer, "Composite Module-Lattice-Based Digital Signature Algorithm (ML-DSA) for use in X.509 Public Key Infrastructure", Work in Progress, Internet-Draft, draft-ietf-lamps-pq-composite-sigs-19, 21 April 2026, <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-pq-composite-sigs-19>.

[RFC2119]

Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997, <https://www.rfc-editor.org/rfc/rfc2119>.

[RFC8174]

Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, May 2017, <https://www.rfc-editor.org/rfc/rfc8174>.

[RFC8554]

McGrew, D., Curcio, M., and S. Fluhrer, "Leighton-Micali Hash-Based Signatures", RFC 8554, DOI 10.17487/RFC8554, April 2019, <https://www.rfc-editor.org/rfc/rfc8554>.

[RFC9858]

Fluhrer, S. and Q. Dang, "Additional Parameter Sets for HSS/LMS Hash-Based Signatures", RFC 9858, DOI 10.17487/RFC9858, October 2025, <https://www.rfc-editor.org/rfc/rfc9858>.

Acknowledgments

TODO acknowledge.¶

Authors' Addresses