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Security Limited Additional Mechanisms for PKIX and SMIME composite fn-dsa lms This document defines a composite signature scheme combining the FN-DSA (Falcon) digital signature algorithm with the Leighton-Micali Signature (LMS) scheme defined in RFC 8554. This construction is designed for use within X.509 Public Key Infrastructure (PKI) and follows the composite signature paradigm defined in . About This Document The latest revision of this draft can be found at . Status information for this document may be found at . Discussion of this document takes place on the Limited Additional Mechanisms for PKIX and SMIME Working Group mailing list (), which is archived at . Subscribe at . Source for this draft and an issue tracker can be found at .

Introduction This document defines a composite signature scheme combining:

• FN-DSA (Falcon), a lattice-based signature algorithm
• LMS, a stateful hash-based signature algorithm

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 .

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 when, and only when, they appear in all capitals, as shown here.

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'.

Pre-hashing Composite FN-DSA-LMS uses a pre-hash function PH: PH(M) This is incorporated into the message representative: M' := Prefix || Label || len(ctx) || ctx || PH(M)

Prefix, Label, and Context Prefix: Always set to "CompositeAlgorithmSignatures2025" as in . Label: Unique per algorithm OID (defined in Algorithm Identifier section below) ctx: Application-defined context (0–255 bytes).

Composite Functions

Key Generation (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) ]]>

Sign Signing follows a similar procedure as in . 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) ]]>

Verify 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. ]]>

Serialization of Public and Privates Keys and Sigantures

Public Key

Private Key

Signature LMS signatures are variable length. Parsing relies on the fixed size of the FN-DSA signature.

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

Algorithm Identifiers

id-FNDSA512-LMS_M24-SHAKE

• Label: COMPSIG-FNDSA512-LMS_M24-SHAKE
• PH: SHAKE256
• FN-DSA: FN-DSA-512
• LMS: LMS_SHAKE_M24_H10

id-FNDSA512-LMS_M32-SHAKE

• Label: COMPSIG-FNDSA512-LMS_M32-SHAKE
• PH: SHAKE256
• FN-DSA: FN-DSA-512
• LMS: LMS_SHAKE_M32_H10

id-FNDSA1024-LMS_M32-SHAKE

• Label: COMPSIG-FNDSA1024-LMS_M32-SHAKE
• PH: SHAKE256
• FN-DSA: FN-DSA-1024
• LMS: LMS_SHAKE_M32_H15

TODO: Define other combinations here. We want to keep the list as small as possible.

Security Considerations

LMS Statefulness Requirement LMS private keys are stateful. Each invocation of LMS.Sign MUST use a unique leaf index. Reuse of a leaf index results in catastrophic loss of security.

Hybrid Security Composite FN-DSA-LMS is EUF-CMA secure if at least one component remains secure.

SUF-CMA Composite FN-DSA-LMS is NOT SUF-CMA secure.

Key Reuse Component keys MUST NOT be reused between:

• composite vs standalone
• multiple composites

IANA Considerations IANA is requested to assign OIDs under: 1.3.6.1.5.5.7.6 TODO for each combination

Normative References Entrust Limited Entrust Limited OpenCA Labs Bundesdruckerei GmbH Cisco Systems This document defines combinations of US NIST Module-Lattice-Based Digital Signature Algorithm (ML-DSA) in hybrid with traditional algorithms RSASSA-PKCS1-v1.5, RSASSA-PSS, ECDSA, Ed25519, and Ed448. These combinations are tailored to meet regulatory guidelines in certain regions. Composite ML-DSA is applicable in applications that use X.509 or PKIX data structures that accept ML-DSA, but where the operator wants extra protection against breaks or catastrophic bugs in ML-DSA, and where existential unforgeability (EUF-CMA) level security is acceptable. AWS AWS sn3rd Cloudflare Digital signatures are used within X.509 certificates and Certificate Revocation Lists (CRLs), and to sign messages. This document specifies the conventions for using, the forthcoming, FIPS 206, the Fast-Fourier Transform over NTRU-Lattice-Based Digital Signature Algorithm (FN-DSA), in Internet X.509 certificates and CRLs. The conventions for the associated signatures, subject public keys, and private key are also described. This note describes a digital-signature system based on cryptographic hash functions, following the seminal work in this area of Lamport, Diffie, Winternitz, and Merkle, as adapted by Leighton and Micali in 1995. It specifies a one-time signature scheme and a general signature scheme. These systems provide asymmetric authentication without using large integer mathematics and can achieve a high security level. They are suitable for compact implementations, are relatively simple to implement, and are naturally resistant to side-channel attacks. Unlike many other signature systems, hash-based signatures would still be secure even if it proves feasible for an attacker to build a quantum computer. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. This has been reviewed by many researchers, both in the research group and outside of it. The Acknowledgements section lists many of them. This document extends HSS/LMS (RFC 8554) by defining parameter sets that use alternative hash functions. These include hash functions that result in signatures with significantly smaller sizes than the signatures that use the RFC 8554 parameter sets and should have sufficient security. This document is a product of the Internet Research Task Force (IRTF). The IRTF publishes the results of Internet-related research and development activities. These results might not be suitable for deployment. This RFC represents the consensus of the Crypto Forum Research Group of the Internet Research Task Force (IRTF). Documents approved for publication by the IRSG are not candidates for any level of Internet Standard; see Section 2 of RFC 7841. In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings.

Acknowledgments TODO acknowledge.