Internet-Draft Composite ML-DSA November 2025
Ounsworth, et al. Expires 23 May 2026 [Page]
Workgroup:
LAMPS
Internet-Draft:
draft-ietf-lamps-pq-composite-sigs-latest
Published:
Intended Status:
Standards Track
Expires:
Authors:
M. Ounsworth
Entrust
J. Gray
Entrust
M. Pala
OpenCA Labs
J. Klaussner
Bundesdruckerei GmbH
S. Fluhrer
Cisco Systems

Composite ML-DSA for use in X.509 Public Key Infrastructure

Abstract

This document defines combinations of ML-DSA [FIPS.204] in hybrid with traditional algorithms RSASSA-PKCS1-v1.5, RSASSA-PSS, ECDSA, Ed25519, and Ed448. These combinations are tailored to meet regulatory guidelines. Composite ML-DSA is applicable in applications that uses 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 EUF-CMA-level security is acceptable.

About This Document

This note is to be removed before publishing as an RFC.

The latest revision of this draft can be found at https://lamps-wg.github.io/draft-composite-sigs/draft-ietf-lamps-pq-composite-sigs.html. Status information for this document may be found at https://datatracker.ietf.org/doc/draft-ietf-lamps-pq-composite-sigs/.

Discussion of this document takes place on the LAMPS Working Group mailing list (mailto:spams@ietf.org), which is archived at https://datatracker.ietf.org/wg/lamps/about/. Subscribe at https://www.ietf.org/mailman/listinfo/spams/.

Source for this draft and an issue tracker can be found at https://github.com/lamps-wg/draft-composite-sigs.

Status of This Memo

This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.

Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.

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This Internet-Draft will expire on 23 May 2026.

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Table of Contents

1. Changes since -07 (WGLC)

Interop-affecting changes:

Editorial changes:

A full review was performed of the encoding of each component:

2. Introduction

The advent of quantum computing poses a significant threat to current cryptographic systems. Traditional cryptographic signature algorithms such as RSA, DSA and its elliptic curve variants are vulnerable to quantum attacks. During the transition to post-quantum cryptography (PQC), there is considerable uncertainty regarding the robustness of both existing and new cryptographic algorithms. While we can no longer fully trust traditional cryptography, we also cannot immediately place complete trust in post-quantum replacements until they have undergone extensive scrutiny and real-world testing to uncover and rectify both algorithmic weaknesses as well as implementation flaws across all the new implementations.

Unlike previous migrations between cryptographic algorithms, this migration gives us the foresight that Traditional cryptographic algorithms will be broken in the future, with the Traditional algorithms remaining strong in the interim, the only uncertainty is around the timing. But there are also some novel challenges. For instance, the aggressive migration timelines may require deploying PQC algorithms before their implementations have been fully hardened or certified, and dual-algorithm data protection may be desirable over a longer time period to hedge against security vulnerabilities and other implementation flaws in the new implementations.

Cautious implementers may opt to combine cryptographic algorithms in such a way that an adversary would need to break all of them simultaneously to compromise the protected data. These mechanisms are referred to as Post-Quantum/Traditional (PQ/T) Hybrids [RFC9794].

Certain jurisdictions are already recommending or mandating that PQC lattice schemes be used exclusively within a PQ/T hybrid framework. The use of a composite scheme provides a straightforward implementation of hybrid solutions compatible with (and advocated by) some governments and cybersecurity agencies [BSI2021], [ANSSI2024].

Another motivation for using PQ/T Hybrids is regulatory compliance; for example, in some situations it might be possible to add Post-Quantum, via a PQ/T Hybrid, to an already audited and compliant solution without invalidating the existing certification, whereas a full replacement of the Traditional cryptography would almost certainly incur regulatory and compliance delays. In other words, PQ/T Hybrids can allow for deploying Post-Quantum before the PQ modules and operational procedures are fully audited and certified. This, more than any other requirement, is what motivates the large number of algorithm combinations in this specification: the intention is to provide a stepping-stone off of which ever cryptographic algorithm(s) an organization might have deployed today.

This specification defines a specific instantiation of the PQ/T Hybrid paradigm called "composite" where multiple cryptographic algorithms are combined to form a single signature algorithm presenting a single public key and signature value such that it can be treated as a single atomic algorithm at the protocol level; a property referred to as "protocol backwards compatibility" since it can be applied to protocols that are not explicitly hybrid-aware. Composite algorithms address algorithm strength uncertainty because the composite algorithm remains some security so long as one of its components remains strong. Concrete instantiations of composite ML-DSA algorithms are provided based on ML-DSA, RSASSA-PKCS1-v1.5, RSASSA-PSS, ECDSA, Ed25519, and Ed448. Backwards compatibility in the sense of upgraded systems continuing to inter-operate with legacy systems is not directly covered in this specification, but is the subject of Section 11.2. The idea of a composite was first presented in [Bindel2017].

Composite ML-DSA is applicable in PKIX-related applications that would otherwise use ML-DSA and where EUF-CMA-level security is acceptable.

2.1. Conventions and Terminology

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. These words may also appear in this document in lower case as plain English words, absent their normative meanings.

This specification is consistent with the terminology defined in [RFC9794]. In addition, the following terminology is used throughout this specification:

ALGORITHM: The usage of the term "algorithm" within this specification generally refers to any function which has a registered Object Identifier (OID) for use within an ASN.1 AlgorithmIdentifier. This loosely, but not precisely, aligns with the definitions of "cryptographic algorithm" and "cryptographic scheme" given in [RFC9794].

COMPONENT / PRIMITIVE: The words "component" or "primitive" are used interchangeably to refer to an asymmetric cryptographic algorithm that is used internally within a composite algorithm. For example this could be an asymmetric algorithm such as "ML-DSA-65" or "RSASSA-PSS".

DER: Distinguished Encoding Rules as defined in [X.690].

PKI: Public Key Infrastructure, as defined in [RFC5280].

SIGNATURE: A digital cryptographic signature, making no assumptions about which algorithm.

Notation: The algorithm descriptions use python-like syntax. The following symbols deserve special mention:

  • || represents concatenation of two byte arrays.

  • [:] represents byte array slicing.

  • (a, b) represents a pair of values a and b. Typically this indicates that a function returns multiple values; the exact conveyance mechanism -- tuple, struct, output parameters, etc. -- is left to the implementer.

  • (a, _): represents a pair of values where one -- the second one in this case -- is ignored.

  • Func<TYPE>(): represents a function that is parameterized by <TYPE> meaning that the function's implementation will have minor differences depending on the underlying TYPE. Typically this means that a function will need to look up different constants or use different underlying cryptographic primitives depending on which composite algorithm it is implementing.

2.2. Composite Design Philosophy

[RFC9794] defines composites as:

  • Composite Cryptographic Element: A cryptographic element that incorporates multiple component cryptographic elements of the same type in a multi-algorithm scheme.

Composite algorithms, as defined in this specification, follow this definition and should be regarded as a single key that performs a single cryptographic operation typical of a digital signature algorithm, such as key generation, signing, or verifying -- using its internal sequence of component keys as if they form a single key. This generally means that the complexity of combining algorithms can and should be handled by the cryptographic library or cryptographic module, and the single composite public key, private key, and signature value can be carried in existing fields in protocols such as PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], the CMS [RFC5652], and the Trust Anchor Format [RFC5914]. In this way, composites achieve "protocol backwards-compatibility" in that they will drop cleanly into any protocol that accepts an analogous single-algorithm cryptographic scheme without requiring any modification of the protocol to handle multiple algorithms.

Discussion of the specific choices of algorithm pairings can be found in Section 7.2.

In terms of security properties, Composite ML-DSA will be EUF-CMA secure if at least one of its component algorithms is EUF-CMA secure and the message hash PH is collision resistant. SUF-CMA security of Composite ML-DSA is more complicated. While some of the algorithm combinations defined in this specification are likely to be SUF-CMA secure against classical adversaries, none are SUF-CMA secure against a quantum adversary. This means that replacing an ML-DSA signature with a Composite ML-DSA signature is a reduction in security and should not be used in applications sensitive to the difference between SUF-CMA and EUF-CMA security. Composite ML-DSA is NOT RECOMMENDED for use in applications where it is has not been shown that EUF-CMA is acceptable. Further discussion can be found in Section 10.2.

3. Overview of the Composite ML-DSA Signature Scheme

Composite ML-DSA is a Post-Quantum / Traditional hybrid signature scheme which combines ML-DSA as specified in [FIPS.204] and [RFC9881] with one of RSASSA-PKCS1-v1_5 or RSASSA-PSS algorithms defined in [RFC8017], the Elliptic Curve Digital Signature Algorithm ECDSA scheme defined in section 6 of [FIPS.186-5], or Ed25519 / Ed448 defined in [RFC8410]. The two component signatures are combined into a composite algorithm via a "signature combiner" function which performs pre-hashing and prepends several signature label values to the message prior to passing it to the component algorithms. Composite ML-DSA achieves weak non-separability as well as several other security properties which are described in the Security Considerations in Section 10.

Composite signature schemes are defined as cryptographic primitives that match the API of a generic signature scheme, which consists of three algorithms:

The following algorithms are defined for serializing and deserializing component values and are provided as internal functions for use by the public functions KeyGen(), Sign(), and Verify(). These algorithms are inspired by similar algorithms in [RFC9180].

Full definitions of serialization and deserialization algorithms can be found in Section 5.

3.1. Pre-hashing

In [FIPS.204] NIST defines separate algorithms for pure and pre-hashed modes of ML-DSA, referred to as "ML-DSA" and "HashML-DSA" respectively. This specification defines a single mode which is similar in construction to HashML-DSA. This design provides a compromised balance between performance and security. Since pre-hashing is done at the composite level, "pure" ML-DSA is used as the underlying ML-DSA primitive.

The primary design motivation behind pre-hashing is to perform only a single pass over the potentially large input message M, compared to passing the full message to both component primitives, and to allow for optimizations in cases such as signing the same message digest with multiple keys. The actual length of the to-be-signed message M' depends on the application context ctx provided at runtime but since ctx has a maximum length of 255 bytes, M' has a fixed maximum length which depends on the output size of the hash function chosen as PH, but can be computed per composite algorithm.

This simplification into a single strongly-pre-hashed algorithm avoids the need for duplicate sets of "Composite-ML-DSA" and "Hash-Composite-ML-DSA" algorithms.

See Section 11.4 for a discussion of externalizing the pre-hashing step.

3.2. Prefix, Label and CTX

The to-be-signed message representative M' is created by concatenating several values, including the pre-hashed message.

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

A fixed octet string which is the byte encoding of the ASCII string "CompositeAlgorithmSignatures2025" which in hex is: 436F6D706F73697465416C676F726974686D5369676E61747572657332303235 See Section 10.4 for more information on the prefix.

Label:

A signature label which is specific to each composite algorithm. The signature label binds the signature to the specific composite algorithm. Signature label values for each algorithm are listed in Section 7.

len(ctx):

A single unsigned byte encoding the length of the context.

ctx:

The context bytes, which allows for applications to bind the signature to an application context.

PH( M ):

The hash of the message to be signed.

Each Composite ML-DSA algorithm has a unique signature label value which is used in constructing the message representative M' in the Composite-ML-DSA.Sign() (Section 4.2) and Composite-ML-DSA.Verify() (Section 4.3). This helps protect against component signature values being removed from the composite and used out of context of X.509, or if the prohibition on reusing key material between a composite and a non-composite, or between two composites is not adhered to.

Note that there are two different context strings ctx at play: the first is the application context that is passed in to Composite-ML-DSA.Sign and bound to the to-be-signed message M'. The second is the ctx that is passed down into the underlying ML-DSA.Sign and here Composite ML-DSA itself is the application that we wish to bind and so per-algorithm Label is used as the ctx for the underlying ML-DSA primitive. The EdDSA component primitive can also expose a ctx parameter, but this is not used by Composite ML-DSA.

Within Composite ML-DSA, values of Label are fully specified, and runtime-variable Label values are not allowed. For authors of follow-on specifications that allow Label to be runtime-variable, it should be pre-fixed with the length, len(Label) || Label to prevent using this as an injection site that could enable various cryptographic attacks.

4. Composite ML-DSA Functions

This section describes the composite ML-DSA functions needed to instantiate the public API of a digital signature scheme as defined in Section 3.

4.1. Key Generation

In order to maintain security properties of the composite, applications that use composite keys MUST always perform fresh key generations of both component keys and MUST NOT reuse existing key material. See Section 10.3 for a discussion.

To generate a new key pair for composite schemes, the KeyGen() -> (pk, sk) function is used. The KeyGen() function calls the two key generation functions of the component algorithms independently. Multi-threaded, multi-process, or multi-module applications might choose to execute the key generation functions in parallel for better key generation performance or architectural modularity.

The following describes how to instantiate a KeyGen() function for a given composite algorithm represented by <OID>.

Composite-ML-DSA<OID>.KeyGen() -> (pk, sk)

Explicit inputs:

  None

Implicit inputs mapped from <OID>:

  ML-DSA     The underlying ML-DSA algorithm and
             parameter set, for example "ML-DSA-65".

  Trad       The underlying traditional algorithm and
             parameter set, for example "RSASSA-PSS"
             or "Ed25519".

Output:

  (pk, sk)   The composite key pair.


Key Generation Process:

  1. Generate component keys

     mldsaSeed = Random(32)
     (mldsaPK, mldsaSK) = ML-DSA.KeyGen_internal(mldsaSeed)
     (tradPK, tradSK) = Trad.KeyGen()

  2. Check for component key gen failure

     if NOT (mldsaPK, mldsaSK) or NOT (tradPK, tradSK):
       output "Key generation error"

  3. Output the composite public and private keys

     pk = SerializePublicKey(mldsaPK, tradPK)
     sk = SerializePrivateKey(mldsaSeed, tradSK)
     return (pk, sk)

This keygen routine make use of the seed-based ML-DSA.KeyGen_internal(𝜉), which is defined in Algorithm 6 of [FIPS.204]. For FIPS-certification implications, see Section 11.1.

In order to ensure fresh keys, the key generation functions MUST be executed for both component algorithms. Compliant parties MUST NOT use, import or export component keys that are used in other contexts, combinations, or by themselves as keys for standalone algorithm use. For more details on the security considerations around key reuse, see Section 10.3.

Note that this keygen routine outputs a serialized composite key, which contains only the ML-DSA seed. Implementations should feel free to modify this routine to additionally output the expanded mldsaSK or to make free use of ML-DSA.KeyGen_internal(mldsaSeed) as needed to expand the ML-DSA seed into an expanded key prior to performing a signing operation.

The above algorithm MAY be modified to expose an interface of Composite-ML-DSA<OID>.KeyGen(seed) if it is desirable to have a deterministic KeyGen that derives both component keys from a shared seed. Details of implementing this variation are not included in this document.

Variations in the keygen process above and signature processes below to accommodate particular private key storage mechanisms or alternate interfaces to the underlying cryptographic modules are considered to be conformant to this specification so long as they produce the same output and error handling. For example, component private keys stored in separate software or hardware modules where it is not possible to do a joint simultaneous keygen would be considered compliant so long as both keys are freshly generated. It is also possible that the underlying cryptographic module does not expose a ML-DSA.KeyGen_internal(seed) that accepts an externally-generated seed, and instead an alternate keygen interface must be used. Note however that cryptographic modules that do not support seed-based ML-DSA key generation will be incapable of importing or exporting composite keys in the standard format since the private key serialization routines defined in Section 5.2 only support ML-DSA keys as seeds.

4.2. Sign

The Sign() algorithm of Composite ML-DSA mirrors the construction of ML-DSA.Sign(sk, M, ctx) defined in Algorithm 3 of Section 5.2 of [FIPS.204]. Composite ML-DSA exposes an API similar to that of ML-DSA, despite the fact that it includes pre-hashing in a similar way to HashML-DSA. Internally it uses pure ML-DSA as the component algorithm since there is no advantage to pre-hashing twice.

The following describes how to instantiate a Sign() function for a given Composite ML-DSA algorithm represented by <OID>. See Section 3.1 for a discussion of the pre-hash function PH. See Section 3.2 for a discussion on the signature label Label and application context ctx. See Section 11.4 for a discussion of externalizing the pre-hashing step.

Composite-ML-DSA<OID>.Sign(sk, M, ctx) -> s

Explicit inputs:

  sk      Composite private key consisting of signing private keys
          for each component.

  M       The message to be signed, an octet string.

  ctx     The application context string used in the composite
          signature combiner, which defaults to the empty string.

Implicit inputs mapped from <OID>:

  ML-DSA  The underlying ML-DSA algorithm and parameter set, for
          example "ML-DSA-65".

  Trad    The underlying traditional algorithm and
          parameter set, for example "sha256WithRSAEncryption"
          or "Ed25519".

  Prefix  The prefix octet string.

  Label   A signature label which is specific to each composite
          algorithm. Additionally, the composite label is passed
          into the underlying ML-DSA primitive as the ctx.
          Signature Label values are defined in the "Signature Label Values"
          section below.

  PH      The function used to pre-hash M.


Output:

  s       The composite signature value.


Signature Generation Process:

  1. If len(ctx) > 255:
      return error

  2. Compute the Message representative M'.
     As in FIPS 204, len(ctx) is encoded as a single unsigned byte.

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

  3. Separate the private key into component keys
     and re-generate the ML-DSA key from seed.

       (mldsaSeed, tradSK) = DeserializePrivateKey(sk)
       (_, mldsaSK) = ML-DSA.KeyGen_internal(mldsaSeed)

  4. Generate the two component signatures independently by
     calculating the signature over M' according to their algorithm
     specifications.

       mldsaSig = ML-DSA.Sign( mldsaSK, M', ctx=Label )
       tradSig = Trad.Sign( tradSK, M' )

  5. If either ML-DSA.Sign() or Trad.Sign() return an error, then
     this process MUST return an error.

      if NOT mldsaSig or NOT tradSig:
        output "Signature generation error"

  6. Output the encoded composite signature value.

      s = SerializeSignatureValue(mldsaSig, tradSig)
      return s

Note that in step 4 above, both component signature processes are invoked, and no indication is given about which one failed. This SHOULD be done in a timing-invariant way to prevent side-channel attackers from learning which component algorithm failed.

It is possible to use component private keys stored in separate software or hardware keystores. Variations in the process to accommodate particular private key storage mechanisms are considered to be conformant to this specification so long as it produces the same output and error handling as the process sketched above.

4.3. Verify

The Verify() algorithm of Composite ML-DSA mirrors the construction of ML-DSA.Verify(pk, M, s, ctx) defined in Algorithm 3 Section 5.3 of [FIPS.204]. Composite ML-DSA exposes an API similar to that of ML-DSA, despite the fact that it includes pre-hashing in a similar way to HashML-DSA. Internally it uses pure ML-DSA as the component algorithm since there is no advantage to pre-hashing twice.

Compliant applications MUST output "Valid signature" (true) if and only if all component signatures were successfully validated, and "Invalid signature" (false) otherwise.

The following describes how to instantiate a Verify() function for a given composite algorithm represented by <OID>. See Section 3.1 for a discussion of the pre-hash function PH. See Section 3.2 for a discussion on the signature label Label and application context ctx. See Section 11.4 for a discussion of externalizing the pre-hashing step.

Composite-ML-DSA<OID>.Verify(pk, M, s, ctx) -> true or false

Explicit inputs:

  pk      Composite public key consisting of verification public
          keys for each component.

  M       Message whose signature is to be verified, an octet
          string.

  s       A composite signature value to be verified.

  ctx     The application context string used in the composite
          signature combiner, which defaults to the empty string.

Implicit inputs mapped from <OID>:

  ML-DSA  The underlying ML-DSA algorithm and parameter set, for
          example "ML-DSA-65".

  Trad    The underlying traditional algorithm and
          parameter set, for example "sha256WithRSAEncryption"
          or "Ed25519".

  Prefix  The prefix octet string.

  Label   A signature label which is specific to each composite
          algorithm. Additionally, the composite label is passed
          into the underlying ML-DSA primitive as the ctx.
          Signature Label values are defined in the "Signature Label Values"
          section below.

  PH      The function used to pre-hash M.

Output:

  Validity (bool)   "Valid signature" (true) if the composite
                    signature is valid, "Invalid signature"
                    (false) otherwise.

Signature Verification Process:

  1. If len(ctx) > 255
       return error

  2. Separate the keys and signatures

     (mldsaPK, tradPK)       = DeserializePublicKey(pk)
     (mldsaSig, tradSig)  = DeserializeSignatureValue(s)

   If Error during deserialization, or if any of the component
   keys or signature values are not of the correct type or
   length for the given component algorithm then output
   "Invalid signature" and stop.

  3. Compute a Hash of the Message.
     As in FIPS 204, len(ctx) is encoded as a single unsigned byte.

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

  4. Check each component signature individually, according to its
     algorithm specification.
     If any fail, then the entire signature validation fails.

      if not ML-DSA.Verify( mldsaPK, M', mldsaSig, ctx=Label ) then
          output "Invalid signature"

      if not Trad.Verify( tradPK, M', tradSig ) then
          output "Invalid signature"

      if all succeeded, then
         output "Valid signature"

Note that in step 4 above, the function fails early if the first component fails to verify. Since no private keys are involved in a signature verification, there are no timing attacks to consider, so this is ok.

5. Serialization

This section presents routines for serializing and deserializing composite public keys, private keys, and signature values to bytes via simple concatenation of the underlying encodings of the component algorithms. The functions defined in this section are considered internal implementation details and are referenced from within the public API definitions in Section 4.

Deserialization is possible because ML-DSA has fixed-length public keys, private keys (seeds), and signature values as shown in the following table.

Table 1: ML-DSA Sizes
Algorithm Public key Private key Signature
ML-DSA-44 1312 32 2420
ML-DSA-65 1952 32 3309
ML-DSA-87 2592 32 4627

While ML-DSA has a single fixed-size representation for each of public key, private key (seed), and signature, a traditional component algorithm might allow multiple valid encodings. For example, a stand-alone RSA private key can be encoded in Chinese Remainder Theorem form. In order to obtain interoperability, composite algorithms MUST use the following encodings of the underlying components:

All ASN.1 objects SHALL be encoded using DER on serialization. For all serialization routines below, when their output values are required to be carried in an ASN.1 structure, they are wrapped as described in Section 6.1.

Even with fixed encodings for the traditional component, there might be slight differences in size of the encoded value due to, for example, encoding rules that drop leading zeroes. See Appendix A for a table of maximum sizes for each composite algorithm and further discussion of the reason for variations in these sizes.

The deserialization routines described below do not check for well-formedness of the cryptographic material they are recovering. It is assumed that underlying cryptographic primitives will catch malformed values and raise an appropriate error.

5.1. SerializePublicKey and DeserializePublicKey

The serialization routine for keys simply concatenates the public keys of the component signature algorithms, as defined below:

Composite-ML-DSA.SerializePublicKey(mldsaPK, tradPK) -> bytes

Explicit inputs:

  mldsaPK The ML-DSA public key, which is bytes.

  tradPK  The traditional public key in the appropriate
          encoding for the underlying component algorithm.

Implicit inputs:

  None

Output:

  bytes   The encoded composite public key.

Serialization Process:

  1. Combine and output the encoded public key

     output mldsaPK || tradPK

Deserialization reverses this process. Each component key is deserialized according to their respective specification as shown in Appendix B.

The following describes how to instantiate a DeserializePublicKey(bytes) function for a given composite algorithm represented by <OID>.

Composite-ML-DSA<OID>.DeserializePublicKey(bytes)
                                    -> (mldsaPK, tradPK)

Explicit inputs:

  bytes    An encoded composite public key.

Implicit inputs mapped from <OID>:

  ML-DSA   The underlying ML-DSA algorithm and
           parameter set to use, for example "ML-DSA-65".

Output:

  mldsaPK  The ML-DSA public key, which is bytes.

  tradPK   The traditional public key in the appropriate
           encoding for the underlying component algorithm.

Deserialization Process:

  1. Parse each constituent encoded public key.
     The length of the mldsaKey is known based on the
     size of the ML-DSA component key length specified
     by the Object ID.

     switch ML-DSA do
        case ML-DSA-44:
          mldsaPK = bytes[:1312]
          tradPK  = bytes[1312:]
        case ML-DSA-65:
          mldsaPK = bytes[:1952]
          tradPK  = bytes[1952:]
        case ML-DSA-87:
          mldsaPK = bytes[:2592]
          tradPK  = bytes[2592:]

     Note that while ML-DSA has fixed-length keys, RSA and
     ECDSA may not, depending on encoding, so rigorous
     length-checking of the overall composite key is not
     always possible.

  2. Output the component public keys

     output (mldsaPK, tradPK)

5.2. SerializePrivateKey and DeserializePrivateKey

The serialization routine for keys simply concatenates the private keys of the component signature algorithms, as defined below:

Composite-ML-DSA.SerializePrivateKey(mldsaSeed, tradSK) -> bytes

Explicit inputs:

  mldsaSeed  The ML-DSA private key, which is the bytes of the seed.

  tradSK     The traditional private key in the appropriate
             encoding for the underlying component algorithm.

Implicit inputs:

  None

Output:

  bytes      The encoded composite private key.


Serialization Process:

  1. Combine and output the encoded private key.

     output mldsaSeed || tradSK

Deserialization reverses this process. Each component key is deserialized according to their respective specification as shown in Appendix B.

The following describes how to instantiate a DeserializePrivateKey(bytes) function. Since ML-DSA private keys are 32 bytes for all parameter sets, this function does not need to be parameterized.

Composite-ML-DSA.DeserializePrivateKey(bytes) -> (mldsaSeed, tradSK)

Explicit inputs:

  bytes      An encoded composite private key.

Implicit inputs:

  None

Output:

  mldsaSeed  The ML-DSA private key, which is the bytes of the seed.

  tradSK     The traditional private key in the appropriate
             encoding for the underlying component algorithm.

Deserialization Process:

  1. Parse each constituent encoded key.

     mldsaSeed = bytes[:32]
     tradSK  = bytes[32:]

     Note that while ML-DSA has fixed-length keys, RSA and ECDSA
     may not, depending on encoding, so rigorous length-checking
     of the overall composite key is not always possible.

  2. Output the component private keys

     output (mldsaSeed, tradSK)

5.3. SerializeSignatureValue and DeserializeSignatureValue

The serialization routine for the composite signature value simply concatenates the fixed-length ML-DSA signature value with the signature value from the traditional algorithm, as defined below:

Composite-ML-DSA.SerializeSignatureValue(mldsaSig, tradSig) -> bytes

Explicit inputs:

  mldsaSig  The ML-DSA signature value, which is bytes.

  tradSig   The traditional signature value in the appropriate
            encoding for the underlying component algorithm.

Implicit inputs:

  None

Output:

  bytes     The encoded composite signature value.

Serialization Process:

  1. Combine and output the encoded composite signature

     output mldsaSig || tradSig

Deserialization reverses this process, raising an error in the event that the input is malformed. Each component signature is deserialized according to their respective specification as shown in Appendix B.

The following describes how to instantiate a DeserializeSignatureValue(bytes) function for a given composite algorithm represented by <OID>.

Composite-ML-DSA<OID>.DeserializeSignatureValue(bytes)
                                            -> (mldsaSig, tradSig)

Explicit inputs:

  bytes   An encoded composite signature value.

Implicit inputs mapped from <OID>:

  ML-DSA  The underlying ML-DSA algorithm and parameter set,
          for example "ML-DSA-65".

Output:

  mldsaSig  The ML-DSA signature value, which is bytes.

  tradSig   The traditional signature value in the appropriate
            encoding for the underlying component algorithm.

Deserialization Process:

  1. Parse each constituent encoded signature.
     The length of the mldsaSig is known based on the size of
     the ML-DSA component signature length specified by the
     Object ID.

     switch ML-DSA do
        case ML-DSA-44:
          mldsaSig = bytes[:2420]
          tradSig  = bytes[2420:]
        case ML-DSA-65:
          mldsaSig = bytes[:3309]
          tradSig  = bytes[3309:]
        case ML-DSA-87:
          mldsaSig = bytes[:4627]
          tradSig  = bytes[4627:]

     Note that while ML-DSA has fixed-length signatures,
     RSA and ECDSA may not, depending on encoding, so rigorous
     length-checking is not always possible here.

  3. Output the component signature values

     output (mldsaSig, tradSig)

6. Use within X.509 and PKIX

The following sections provide processing logic and the ASN.1 modules necessary to use composite ML-DSA within X.509 and PKIX protocols. Use within the Cryptographic Message Syntax (CMS) will be covered in a separate specification.

While composite ML-DSA keys and signature values MAY be used raw, the following sections provide conventions for using them within X.509 and other PKIX protocols such that Composite ML-DSA can be used as a drop-in replacement for existing digital signature algorithms in PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], and related protocols.

6.1. Encoding to DER

The serialization routines presented in Section 5 produce raw binary values. When these values are required to be carried within a DER-encoded message format such as an X.509's subjectPublicKey and signatureValue BIT STRING [RFC5280] or a OneAsymmetricKey.privateKey OCTET STRING [RFC5958], then the BIT STRING or OCTET STRING contains this raw byte string output of the appropriate serialization routine from Section 5 without further encoding.

When a Composite ML-DSA public key appears outside of a SubjectPublicKeyInfo type in an environment that uses ASN.1 encoding, it could be encoded as an OCTET STRING by using the Composite-ML-DSA-PublicKey type defined below.

Composite-ML-DSA-PublicKey ::= OCTET STRING

Size constraints MAY be enforced, as appropriate as per Appendix A.

6.2. Key Usage Bits

When any Composite ML-DSA Object Identifier appears within the SubjectPublicKeyInfo.AlgorithmIdentifier field of an X.509 certificate [RFC5280], the key usage certificate extension MUST only contain signing-type key usages.

The normal keyUsage rules for signing-type keys from [RFC5280] apply, and are reproduced here for completeness.

For Certification Authority (CA) certificates that carry a Composite ML-DSA public key, any combination of the following values MAY be present and any other values MUST NOT be present:

digitalSignature;
nonRepudiation;
keyCertSign; and
cRLSign.

For End Entity certificates, any combination of the following values MAY be present and any other values MUST NOT be present:

digitalSignature;
nonRepudiation; and
cRLSign.

Composite ML-DSA keys MUST NOT be used in a "dual usage" mode because even if the traditional component key supports both signing and encryption, the post-quantum algorithms do not and therefore the overall composite algorithm does not. Implementations MUST NOT use one component of the composite for the purposes of digital signature and the other component for the purposes of encryption or key establishment.

6.3. ASN.1 Definitions

Composite ML-DSA uses a substantially non-ASN.1 based encoding, as specified in Section 5. However, as composite algorithms will be used within ASN.1-based X.509 and PKIX protocols, some conventions for ASN.1 wrapping are necessary.

The following ASN.1 Information Object Classes are defined to allow for compact definitions of each composite algorithm, leading to a smaller overall ASN.1 module.

pk-CompositeSignature {OBJECT IDENTIFIER:id}
    PUBLIC-KEY ::= {
      IDENTIFIER id
      -- KEY no ASN.1 wrapping --
      PARAMS ARE absent
      CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign,
                                                             cRLSign}
      -- PRIVATE-KEY no ASN.1 wrapping --
    }

sa-CompositeSignature{OBJECT IDENTIFIER:id,
   PUBLIC-KEY:publicKeyType }
      SIGNATURE-ALGORITHM ::=  {
         IDENTIFIER id
         -- VALUE no ASN.1 wrapping --
         PARAMS ARE absent
         PUBLIC-KEYS {publicKeyType}
      }
Figure 1: ASN.1 Object Information Classes for Composite ML-DSA

As an example, the public key and signature algorithm types associated with id-MLDSA44-ECDSA-P256-SHA256 are defined as:

pk-MLDSA44-ECDSA-P256-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-ECDSA-P256-SHA256 }

sa-MLDSA44-ECDSA-P256-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA44-ECDSA-P256-SHA256,
       pk-MLDSA44-ECDSA-P256-SHA256 }

The full set of key types defined by this specification can be found in the ASN.1 Module in Section 8.

Use cases that require an interoperable encoding for composite private keys will often need to place a composite private key inside a OneAsymmetricKey structure defined in [RFC5958], such as when private keys are carried in PKCS #12 [RFC7292], CMP [RFC4210] or CRMF [RFC4211]. The definition of OneAsymmetricKey is copied here for convenience:

 OneAsymmetricKey ::= SEQUENCE {
       version                   Version,
       privateKeyAlgorithm       PrivateKeyAlgorithmIdentifier,
       privateKey                PrivateKey,
       attributes            [0] Attributes OPTIONAL,
       ...,
       [[2: publicKey        [1] PublicKey OPTIONAL ]],
       ...
     }
  ...
  PrivateKey ::= OCTET STRING
                        -- Content varies based on type of key.  The
                        -- algorithm identifier dictates the format of
                        -- the key.
Figure 2: OneAsymmetricKey as defined in [RFC5958]

When a composite private key is conveyed inside a OneAsymmetricKey structure (version 1 of which is also known as PrivateKeyInfo) [RFC5958], the privateKeyAlgorithm field SHALL be set to the corresponding composite algorithm identifier defined according to Section 7 and its parameters field MUST be absent. The privateKey field SHALL contain the OCTET STRING representation of the serialized composite private key as per Section 5.2. The publicKey field remains OPTIONAL. If the publicKey field is present, it MUST be a composite public key as per Section 5.1.

Some applications might need to reconstruct the SubjectPublicKeyInfo or OneAsymmetricKey objects corresponding to each component key individually, for example if this is required for invoking the underlying primitive. Section 7 provides the necessary mapping between composite and their component algorithms for doing this reconstruction.

Component keys of a composite MUST NOT be used in any other type of key or as a standalone key. For more details on the security considerations around key reuse, see Section 10.3.

7. Algorithm Identifiers and Parameters

This section lists the algorithm identifiers and parameters for all Composite ML-DSA algorithms.

Full specifications for the referenced algorithms can be found in Appendix B.

As the number of algorithms can be daunting, implementers who wish to implement only a single composite algorithm should see Section 11.3 for a discussion of the best algorithm for the most common use cases.

Labels are represented here as ASCII strings, but implementers MUST convert them to byte strings using the obvious ASCII conversions prior to concatenating them with other byte values as described in Section 3.2.

For all RSA key types and sizes, the exponent is RECOMMENDED to be 65537. Implementations MAY support only 65537 and reject other exponent values. Legacy RSA implementations that use other values for the exponent MAY be used within a composite, but need to be careful when interoperating with other implementations.

**Note: The pre-hash functions were chosen to roughly match the security level of the stronger component. In the case of Ed25519 and Ed448 they match the hash function defined in [RFC8032]; SHA512 for Ed25519ph and SHAKE256(x, 64), which is SHAKE256 producing 64 bytes (512 bits) of output, for Ed448ph.

7.1. RSASSA-PSS Parameters

Use of RSASSA-PSS [RFC8017] requires extra parameters to be specified.

The RSASSA-PSS-params ASN.1 type defined in [RFC8017] is not used in Composite ML-DSA encodings since the parameter values are fixed by this specification. However, below refer to the named fields of the RSASSA-PSS-params ASN.1 type in order to provide a mapping between the use of RSASSA-PSS in Composite ML-DSA and [RFC8017]

When RSA-PSS is used at the 2048-bit or 3072-bit security level, RSASSA-PSS SHALL be instantiated with the following parameters:

Table 2: RSASSA-PSS 2048 and 3072 Parameters
RSASSA-PSS-params field Value
hashAlgorithm id-sha256
maskGenAlgorithm.algorithm id-mgf1
maskGenAlgorithm.parameters id-sha256
saltLength 32
trailerField 1

When RSA-PSS is used at the 4096-bit security level, RSASSA-PSS SHALL be instantiated with the following parameters:

Table 3: RSASSA-PSS 4096 Parameters
RSASSA-PSS-params field Value
hashAlgorithm id-sha384
maskGenAlgorithm.algorithm id-mgf1
maskGenAlgorithm.parameters id-sha384
saltLength 48
trailerField 1

7.2. Rationale for choices

In generating the list of composite algorithms, the idea was to provide composite algorithms at various security levels with varying performance characteristics.

The main design consideration in choosing pairings is to prioritize providing pairings of each ML-DSA security level with commonly-deployed traditional algorithms. This supports the design goal of using composites as a stepping stone to efficiently deploy post-quantum on top of existing hardened and certified traditional algorithm implementations. This was prioritized rather than attempting to exactly match the security level of the post-quantum and traditional components -- which in general is difficult to do since there is no academic consensus on how to compare the "bits of security" against classical adversaries and "qubits of security" against quantum adversaries.

SHA2 is prioritized over SHA3 in order to facilitate implementations that do not have easy access to SHA3 outside of the ML-DSA module. However SHAKE256 is used with Ed448 since this is already the recommended hash functions chosen for ED448ph in [RFC8032].

In some cases, multiple hash functions are used within the same composite algorithm. Consider for example id-MLDSA65-ECDSA-P256-SHA512 which requires SHA512 as the overall composite pre-hash in order to maintain the security level of ML-DSA-65, but uses SHA256 within the ecdsa-with-SHA256 with secp256r1 traditional component. While this increases the implementation burden of needing to carry multiple hash functions for a single composite algorithm, this aligns with the design goal of choosing commonly-implemented traditional algorithms since ecdsa-with-SHA256 with secp256r1 is far more common than, for example, ecdsa-with-SHA512 with secp256r1.

Full specifications for the referenced algorithms can be found in Appendix B.

8. ASN.1 Module 

<CODE STARTS>

Composite-MLDSA-2025
  { iso(1) identified-organization(3) dod(6) internet(1)
        security(5) mechanisms(5) pkix(7) id-mod(0)
        id-mod-composite-mldsa-2025(TBDMOD) }


DEFINITIONS IMPLICIT TAGS ::= BEGIN

EXPORTS ALL;

IMPORTS
  PUBLIC-KEY, SIGNATURE-ALGORITHM, SMIME-CAPS, AlgorithmIdentifier{}
    FROM AlgorithmInformation-2009  -- RFC 5912 [X509ASN1]
      { iso(1) identified-organization(3) dod(6) internet(1)
        security(5) mechanisms(5) pkix(7) id-mod(0)
        id-mod-algorithmInformation-02(58) }
;

--
-- Object Identifiers
--

--
-- Information Object Classes
--

pk-CompositeSignature {OBJECT IDENTIFIER:id}
    PUBLIC-KEY ::= {
      IDENTIFIER id
      -- KEY no ASN.1 wrapping --
      PARAMS ARE absent
      CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign,
                                                            cRLSign}
      -- PRIVATE-KEY no ASN.1 wrapping --
    }

sa-CompositeSignature{OBJECT IDENTIFIER:id,
   PUBLIC-KEY:publicKeyType }
      SIGNATURE-ALGORITHM ::=  {
         IDENTIFIER id
         -- VALUE no ASN.1 wrapping --
         PARAMS ARE absent
         PUBLIC-KEYS {publicKeyType}
      }


-- Composite ML-DSA

id-MLDSA44-RSA2048-PSS-SHA256 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 37 }

pk-MLDSA44-RSA2048-PSS-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-RSA2048-PSS-SHA256}

sa-MLDSA44-RSA2048-PSS-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA44-RSA2048-PSS-SHA256,
       pk-MLDSA44-RSA2048-PSS-SHA256 }


id-MLDSA44-RSA2048-PKCS15-SHA256 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 38 }

pk-MLDSA44-RSA2048-PKCS15-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-RSA2048-PKCS15-SHA256}

sa-MLDSA44-RSA2048-PKCS15-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA44-RSA2048-PKCS15-SHA256,
       pk-MLDSA44-RSA2048-PKCS15-SHA256 }


id-MLDSA44-Ed25519-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 39 }

pk-MLDSA44-Ed25519-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-Ed25519-SHA512}

sa-MLDSA44-Ed25519-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA44-Ed25519-SHA512,
       pk-MLDSA44-Ed25519-SHA512 }


id-MLDSA44-ECDSA-P256-SHA256 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 40 }

pk-MLDSA44-ECDSA-P256-SHA256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA44-ECDSA-P256-SHA256}

sa-MLDSA44-ECDSA-P256-SHA256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA44-ECDSA-P256-SHA256,
       pk-MLDSA44-ECDSA-P256-SHA256 }


id-MLDSA65-RSA3072-PSS-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 41 }

pk-MLDSA65-RSA3072-PSS-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-RSA3072-PSS-SHA512}

sa-MLDSA65-RSA3072-PSS-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-RSA3072-PSS-SHA512,
       pk-MLDSA65-RSA3072-PSS-SHA512 }


id-MLDSA65-RSA3072-PKCS15-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 42 }

pk-MLDSA65-RSA3072-PKCS15-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-RSA3072-PKCS15-SHA512}

sa-MLDSA65-RSA3072-PKCS15-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-RSA3072-PKCS15-SHA512,
       pk-MLDSA65-RSA3072-PKCS15-SHA512 }


id-MLDSA65-RSA4096-PSS-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 43 }

pk-MLDSA65-RSA4096-PSS-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-RSA4096-PSS-SHA512}

sa-MLDSA65-RSA4096-PSS-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-RSA4096-PSS-SHA512,
       pk-MLDSA65-RSA4096-PSS-SHA512 }


id-MLDSA65-RSA4096-PKCS15-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 44 }

pk-MLDSA65-RSA4096-PKCS15-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-RSA4096-PKCS15-SHA512}

sa-MLDSA65-RSA4096-PKCS15-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-RSA4096-PKCS15-SHA512,
       pk-MLDSA65-RSA4096-PKCS15-SHA512 }


id-MLDSA65-ECDSA-P256-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 45 }

pk-MLDSA65-ECDSA-P256-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-ECDSA-P256-SHA512}

sa-MLDSA65-ECDSA-P256-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-ECDSA-P256-SHA512,
       pk-MLDSA65-ECDSA-P256-SHA512 }


id-MLDSA65-ECDSA-P384-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 46 }

pk-MLDSA65-ECDSA-P384-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-ECDSA-P384-SHA512}

sa-MLDSA65-ECDSA-P384-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-ECDSA-P384-SHA512,
       pk-MLDSA65-ECDSA-P384-SHA512 }


id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 47 }

pk-MLDSA65-ECDSA-brainpoolP256r1-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-ECDSA-brainpoolP256r1-SHA512}

sa-MLDSA65-ECDSA-brainpoolP256r1-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-ECDSA-brainpoolP256r1-SHA512,
       pk-MLDSA65-ECDSA-brainpoolP256r1-SHA512 }


id-MLDSA65-Ed25519-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 48 }

pk-MLDSA65-Ed25519-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA65-Ed25519-SHA512}

sa-MLDSA65-Ed25519-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA65-Ed25519-SHA512,
       pk-MLDSA65-Ed25519-SHA512 }


id-MLDSA87-ECDSA-P384-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 49 }

pk-MLDSA87-ECDSA-P384-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-ECDSA-P384-SHA512}

sa-MLDSA87-ECDSA-P384-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-ECDSA-P384-SHA512,
       pk-MLDSA87-ECDSA-P384-SHA512 }


id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 50 }

pk-MLDSA87-ECDSA-brainpoolP384r1-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-ECDSA-brainpoolP384r1-SHA512}

sa-MLDSA87-ECDSA-brainpoolP384r1-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-ECDSA-brainpoolP384r1-SHA512,
       pk-MLDSA87-ECDSA-brainpoolP384r1-SHA512 }


id-MLDSA87-Ed448-SHAKE256 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 51 }

pk-MLDSA87-Ed448-SHAKE256 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-Ed448-SHAKE256}

sa-MLDSA87-Ed448-SHAKE256 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-Ed448-SHAKE256,
       pk-MLDSA87-Ed448-SHAKE256 }


id-MLDSA87-RSA3072-PSS-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 52 }

pk-MLDSA87-RSA3072-PSS-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-RSA3072-PSS-SHA512}

sa-MLDSA87-RSA3072-PSS-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-RSA3072-PSS-SHA512,
       pk-MLDSA87-RSA3072-PSS-SHA512 }


id-MLDSA87-RSA4096-PSS-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 53 }

pk-MLDSA87-RSA4096-PSS-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-RSA4096-PSS-SHA512}

sa-MLDSA87-RSA4096-PSS-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-RSA4096-PSS-SHA512,
       pk-MLDSA87-RSA4096-PSS-SHA512 }


id-MLDSA87-ECDSA-P521-SHA512 OBJECT IDENTIFIER ::= {
   iso(1) org(3) dod(6) internet(1) security(5) mechanisms(5)
   pkix(7) alg(6) 54 }

pk-MLDSA87-ECDSA-P521-SHA512 PUBLIC-KEY ::=
  pk-CompositeSignature{ id-MLDSA87-ECDSA-P521-SHA512}

sa-MLDSA87-ECDSA-P521-SHA512 SIGNATURE-ALGORITHM ::=
    sa-CompositeSignature{
       id-MLDSA87-ECDSA-P521-SHA512,
       pk-MLDSA87-ECDSA-P521-SHA512 }


SignatureAlgorithmSet SIGNATURE-ALGORITHM ::= {
  sa-MLDSA44-RSA2048-PSS-SHA256 |
  sa-MLDSA44-RSA2048-PKCS15-SHA256 |
  sa-MLDSA44-Ed25519-SHA512 |
  sa-MLDSA44-ECDSA-P256-SHA256 |
  sa-MLDSA65-RSA3072-PSS-SHA512 |
  sa-MLDSA65-RSA3072-PKCS15-SHA512 |
  sa-MLDSA65-RSA4096-PSS-SHA512 |
  sa-MLDSA65-RSA4096-PKCS15-SHA512 |
  sa-MLDSA65-ECDSA-P256-SHA512 |
  sa-MLDSA65-ECDSA-P384-SHA512 |
  sa-MLDSA65-ECDSA-brainpoolP256r1-SHA512 |
  sa-MLDSA65-Ed25519-SHA512 |
  sa-MLDSA87-ECDSA-P384-SHA512 |
  sa-MLDSA87-ECDSA-brainpoolP384r1-SHA512 |
  sa-MLDSA87-Ed448-SHAKE256 |
  sa-MLDSA87-RSA3072-PSS-SHA512 |
  sa-MLDSA87-RSA4096-PSS-SHA512 |
  sa-MLDSA87-ECDSA-P521-SHA512,
  ... }

END

<CODE ENDS>

9. IANA Considerations

IANA is requested to assign an object identifier (OID) for the module identifier (TBDMOD) with a Description of "id-mod-composite-mldsa-2025". The OID for the module should be allocated in the "SMI Security for PKIX Module Identifier" registry (1.3.6.1.5.5.7.0).

IANA is also requested to allocate values from the "SMI Security for PKIX Algorithms" registry (1.3.6.1.5.5.7.6) to identify the eighteen algorithms defined within.

9.1. Object Identifier Allocations

EDNOTE to IANA: OIDs will need to be replaced in both the ASN.1 module and in Section 7.

9.1.1. Module Registration

The following is to be registered in "SMI Security for PKIX Module Identifier":

  • Decimal: IANA Assigned - Replace TBDMOD

  • Description: Composite-Signatures-2025 - id-mod-composite-signatures

  • References: This Document

9.1.2. Object Identifier Registrations

The following are to be registered in "SMI Security for PKIX Algorithms":

Note to IANA / RPC: these were all early allocated on 2025-10-20, so they should all already be assigned to the values used above in Section 7 and Section 8.

  • id-MLDSA44-RSA2048-PSS-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLDSA44-RSA2048-PSS-SHA256

    • References: This Document

  • id-MLDSA44-RSA2048-PKCS15-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLDSA44-RSA2048-PKCS15-SHA256

    • References: This Document

  • id-MLDSA44-Ed25519-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA44-Ed25519-SHA512

    • References: This Document

  • id-MLDSA44-ECDSA-P256-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLDSA44-ECDSA-P256-SHA256

    • References: This Document

  • id-MLDSA65-RSA3072-PSS-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-RSA3072-PSS-SHA512

    • References: This Document

  • id-MLDSA65-RSA3072-PKCS15-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-RSA3072-PKCS15-SHA512

    • References: This Document

  • id-MLDSA65-RSA4096-PSS-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-RSA4096-PSS-SHA512

    • References: This Document

  • id-MLDSA65-RSA4096-PKCS15-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-RSA4096-PKCS15-SHA512

    • References: This Document

  • id-MLDSA65-ECDSA-P256-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-ECDSA-P256-SHA512

    • References: This Document

  • id-MLDSA65-ECDSA-P384-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-ECDSA-P384-SHA512

    • References: This Document

  • id-MLDSA65-ECDSA-brainpoolP256r1-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-ECDSA-brainpoolP256r1-SHA512

    • References: This Document

  • id-MLDSA65-Ed25519-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA65-Ed25519-SHA512

    • References: This Document

  • id-MLDSA87-ECDSA-P384-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-ECDSA-P384-SHA512

    • References: This Document

  • id-MLDSA87-ECDSA-brainpoolP384r1-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-ECDSA-brainpoolP384r1-SHA512

    • References: This Document

  • id-MLDSA87-Ed448-SHAKE256

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-Ed448-SHAKE256

    • References: This Document

  • id-MLDSA87-RSA3072-PSS-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-RSA3072-PSS-SHA512

    • References: This Document

  • id-MLDSA87-RSA4096-PSS-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-RSA4096-PSS-SHA512

    • References: This Document

  • id-MLDSA87-ECDSA-P521-SHA512

    • Decimal: IANA Assigned

    • Description: id-MLDSA87-ECDSA-P521-SHA512

    • References: This Document

10. Security Considerations

As this specification uses ML-DSA as a component of all composite algorithms, all security considerations from [RFC9881] apply.

10.1. Why Hybrids?

In broad terms, a PQ/T Hybrid can be used either to provide dual-algorithm security or to provide migration flexibility. Let's quickly explore both.

Dual-algorithm security. The general idea is that the data is protected by two algorithms such that an adversary would need to break both in order to compromise the data. As with most of cryptography, this property is easy to state in general terms, but becomes more complicated when expressed in formalisms. Section 10.2 goes into more detail here. One common counter-argument against PQ/T hybrid signatures is that if an adversary can forge one of the component algorithms, then why attack the hybrid-signed message at all when they could simply forge a completely new message? The answer to this question must be found outside the cryptographic primitives themselves, and instead in policy; once an algorithm is known to be broken it ought to be disallowed for single-algorithm use by cryptographic policy, while hybrids involving that algorithm may continue to be used and to provide value, and also in the fact that the composite public key could be trusted by the verifier while the component keys in isolation are not, thus requiring the adversary to forge a whole composite signature.

Migration flexibility. Some PQ/T hybrids exist to provide a sort of "OR" mode where the application can choose to use one algorithm or the other or both. The intention is that the PQ/T hybrid mechanism builds in backwards compatibility to allow legacy and upgraded applications to co-exist and communicate. The composites presented in this specification do not provide this since they operate in a strict "AND" mode. They do, however, provide codebase migration flexibility. Consider that an organization has today a mature, validated, certified, hardened implementation of RSA or ECC; composites allow them to add an ML-DSA implementation which immediately starts providing benefits against long-term document integrity attacks even if that ML-DSA implementation is still an experimental, non-validated, non-certified, non-hardened implementation. More details of obtaining FIPS certification of a composite algorithm can be found in Section 11.1.

10.2. EUF-CMA, SUF-CMA and non-separability

First, a note about the security model under which this analysis is performed. This specification strictly forbids re-using component key material between composite and non-composite keys, or between multiple composite keys. This specification also exists within the X.509 PKI architecture where trust in a public verification key is assumed to be established either directly via a trust store or via a certificate chain. That said, these are both policy mechanisms that are outside the formal definitions of EUF-CMA and SUF-CMA under which a signature primitive must be analysed, therefore this section considers attacks that may be mitigated partially or completely within a strictly-implemented PKI setting, but which need to be considered when considering Composite ML-DSA as a general-purpose signature primitive that could be used outside of the X.509 setting.

The second securtiy model considiration is that composites are designed to provide value even if one algorithm is broken, even if you do not know which. However, the security properties offered by the composite signature can differ based on which algorithm you consider to be broken.

10.2.1. EUF-CMA

A signature algorithm is Existentially Unforgeable under Chosen-Message Attack (EUF-CMA) if an adversary that has access to a signing oracle cannot create a message-signature pair (M, Sig) that would be accepted by the verifier for any message M that was not an input to a signing oracle query.

In general, Composite ML-DSA will be EUF-CMA secure if at least one of the component algorithms is EUF-CMA secure and PH is collision resistant. Any algorithm that creates an existential forgery (M, (mldsaSig, tradSig)) for Composite ML-DSA can be converted into a pair of algorithms that will either create existential forgeries (M', mldsaSig) and (M', tradSig) for the component algorithms or a collision in PH.

However, the nature of the EUF-CMA security guarantee can still change if one of the component algorithms is broken:

  • If the traditional component is broken, then Composite ML-DSA will remain EUF-CMA secure against quantum adversaries.

  • If ML-DSA is broken, then Composite ML-DSA will only be EUF-CMA secure against classical adversaries.

The same properties will hold for X.509 certificates that use Composite ML-DSA: a classical adversary cannot forge a Composite ML-DSA signed certificate if at least one component algorithm is classically EUF-CMA secure, and a quantum adversary cannot forge a Composite ML-DSA signed certificate if ML-DSA remains quantumly EUF-CMA secure.

10.2.2. SUF-CMA

A signature algorithm is Strongly Unforgeable under Chosen-Message Attack (SUF-CMA) if an adversary that has access to a signing oracle cannot create a message-signature pair (M, Sig) that was not an output of a signing oracle query. This is a stronger property than EUF-CMA since the message M does not need to be different. SUF-CMA security is also more complicated for Composite ML-DSA than EUF-CMA.

A SUF-CMA failure in one component algorithm can lead to a SUF-CMA failure in the composite. For example, an ECDSA signature can be trivially modified to produce a different signature that is still valid for the same message and this property passes directly through to Composite ML-DSA with ECDSA.

Unfortunately, it is not generally sufficient for both component algorithms to be SUF-CMA secure. If repeated calls to the signing oracle produce two valid message-signature pairs (M, (mldsaSig1, tradSig1)) and (M, (mldsaSig2, tradSig2)) for the same message M, but where mldsaSig1 =/= mldsaSig2 and tradSig1 =/= tradSig2, then the adversary can construct a third pair (M, (mldsaSig1, tradSig2)) that will also be valid.

Nevertheless, Composite ML-DSA will not be SUF-CMA secure, and Composite ML-DSA signed X.509 certificates will not be strongly unforgeable, against quantum adversaries since a quantum adversary will be able to break the SUF-CMA security of the traditional component.

Consequently, applications where SUF-CMA security is critical SHOULD NOT use Composite ML-DSA.

10.2.3. Non-separability

Weak Non-Separability (WNS) of a hybrid signature is defined in [I-D.ietf-pquip-hybrid-signature-spectrums] as the guarantee that an adversary cannot simply "remove" one of the component signatures without evidence left behind.

Strong Non-Separability (SNS) is the stronger notion that an adversary cannot take a hybrid signature and produce a component signature, with a potentially different message, that will be accepted by the component verifier.

Composite ML-DSA signs a message M by passing M' as defined in Section 3.2 to the component signature primitives. Consider an adversary that takes a composite signature (M, (mldsaSig, tradSig)) and splits it into the component signatures (M', mldsaSig) and (M', tradSig). On the traditional side, (M', tradSig) will verify correctly, but the static Prefix defined in Section 3.2 remains as evidence of the original composite. On the ML-DSA side, (M', mldsaSig) is signed with ML-DSA's context value equal to the composite algorithm's Label so will fail to verify under ML-DSA.Verify(M', ctx=""). Consequently, Composite ML-DSA will provide WNS for both components and a limited form of SNS for the ML-DSA component. It can achieve stronger non-separability in practice for both components if the prefix-based mitigation described in Section 10.4 is applied.

When used within X.509, the Label representing the signature algorithm is included in the signed object so if one of the component signatures is removed from the Composite ML-DSA signature then the signed-over Label will still indicate the composite algorithm, and this will fail at the X.509 processing layer. Composite ML-DSA therefore provides a version of SNS for X.509. The prohibition on key reuse between composite and single-algorithm contexts discussed in Section 10.3 further strengthens the non-separability in practice.

10.3. Key Reuse

While conformance with this specification requires that both components of a composite key MUST be freshly generated, the designers are aware that some implementers may be forced to break this rule due to operational constraints. This section documents the implications of doing so.

When using single-algorithm cryptography, the best practice is to always generate fresh key material for each purpose, for example when renewing a certificate, or obtaining both a TLS and S/MIME certificate for the same device. However, in practice key reuse in such scenarios is not always catastrophic to security and therefore often tolerated. However this reasoning does not hold in the PQ/T hybrid setting.

Within the broader context of PQ/T hybrids, we need to consider new attack surfaces that arise due to the hybrid constructions that did not exist in single-algorithm contexts. One of these is key reuse where the component keys within a hybrid are also used by themselves within a single-algorithm context. For example, it might be tempting for an operator to take an already-deployed RSA key pair and combine it with an ML-DSA key pair to form a hybrid key pair for use in a hybrid algorithm. Within a hybrid signature context this leads to a class of attacks referred to as "stripping attacks" discussed in Section 10.2 and may also open up risks from further cross-protocol attacks. Despite the weak non-separability property offered by the composite signature combiner, key reuse MUST be avoided to prevent the introduction of EUF-CMA vulnerabilities.

In addition, there is a further implication to key reuse regarding certificate revocation. Upon receiving a new certificate enrolment request, many certification authorities will check if the requested public key has been previously revoked due to key compromise. Often a CA will perform this check by using the public key hash. Therefore, if one, or even both, components of a composite have been previously revoked, the CA may only check the hash of the combined composite key and not find the revocations. Therefore, because the possibility of key reuse exists even though forbidden in this specification, CAs performing revocation checks on a composite key SHOULD also check both component keys independently to verify that the component keys have not been revoked.

Some application might disregard the requirements of this specification to not reuse key material between single-algorithm and composite contexts. While doing so is still a violation of this specification, the weakening of security from doing so can be mitigated by using an appropriate ctx value, such as ctx=Foobar-dual-cert-sig to indicate that this signature belongs to the Foobar protocol where two certificates were used to create a single composite signature. This specification does not endorse such uses, and per-application security analysis is needed.

10.4. Use of Prefix for attack mitigation

The Prefix value specified in Section 3.2 allows for cautious implementers to wrap their existing Traditional Verify() implementations with a guard that looks for messages starting with this string and fail with an error -- i.e. this can act as an extra protection against taking a composite signature and splitting it back into components. However, an implementation that does this will be unable to perform a Traditional signature and verification on a message which happens to start with this string. The designers accepted this trade-off.

10.5. Policy for Deprecated and Acceptable Algorithms

Traditionally, a public key or certificate contains a single cryptographic algorithm. If and when an algorithm becomes deprecated (for example, RSA-512, or SHA1), the path to deprecating it through policy and removing it from operational environments is, at least is principle, straightforward.

In the composite model this is less obvious since a PQ/T hybrid is expected to still be considered valid after the traditional component is deprecated for individual use. As such, a single composite public key or certificate may contain a mixture of deprecated and non-deprecated algorithms. In general this should be manageable through policy by removing OIDs for the standalone component algorithms while still allowing OIDs for composite algorithms. However, complications may arise when the composite implementation needs to invoke the cryptographic module for a deprecated component algorithm. In particular, this could lead to complex Cryptographic Bills of Materials that show implementations of deprecated algorithms still present and being used.

11. Implementation Considerations

11.1. FIPS certification

The following sections give guidance to implementers wishing to FIPS-certify a composite implementation.

This guidance is not authoritative and has not been endorsed by NIST.

One of the primary design goals of this specification is for the overall composite algorithm to be able to be considered FIPS-approved even when one of the component algorithms is not.

Implementers seeking FIPS certification of a composite signature algorithm where only one of the component algorithms has been FIPS-validated or FIPS-approved should credit the FIPS-validated component algorithm with full security strength, the non-FIPS-validated component algorithm with zero security, and the overall composite should be considered at least as strong and thus FIPS-approved.

The composite algorithm has been designed to treat the underlying primitives as "black-box implementations" and not impose any additional requirements on them that could require an existing implementation of an underlying primitive to run in a mode different from the one under which it was certified. For example, the KeyGen defined in Section 4.1 invokes ML-DSA.KeyGen_internal(seed) which might not be available in a cryptographic module running in FIPS-mode, but Section 4.1 is only a suggested implementation and the composite KeyGen MAY be implemented using a different available interface for ML-DSA.KeyGen. However, using an interface which doesn't support a seed will prevent the implementation from encoding the private key according to Section 5.2. Another example is pre-hashing; a pre-hash is inherent to RSA, ECDSA, and ML-DSA (μ), and composite makes no assumptions or requirements about whether component-specific pre-hashing is done locally as part of the composite, or remotely as part of the component primitive.

Note also that also that Section 4.1 depicts the generation of the seed as mldsaSeed = Random(), when implementing this for FIPS certification, this MUST be the direct output of a FIPS-approved DRBG.

The authors wish to note that composite algorithms provide a design pattern to provide utility in future situations that require care to remain FIPS-compliant, such as future cryptographic migrations as well as bridging across jurisdictions with non-intersecting cryptographic requirements.

11.2. Backwards Compatibility

The term "backwards compatibility" is used here to mean that existing systems as they are deployed today can interoperate with the upgraded systems of the future. This document explicitly does not provide backwards compatibility, only upgraded systems will understand the OIDs defined in this specification.

If backwards compatibility is required, then additional mechanisms will be needed. Migration and interoperability concerns need to be thought about in the context of various types of protocols that make use of X.509 and PKIX with relation to digital signature objects, from online negotiated protocols such as TLS 1.3 [RFC8446] and IKEv2 [RFC7296], to non-negotiated asynchronous protocols such as S/MIME signed email [RFC8551], document signing such as in the context of the European eIDAS regulations [eIDAS2014], and publicly trusted code signing [codesigningbrsv3.8], as well as myriad other standardized and proprietary protocols and applications that leverage CMS [RFC5652] signed structures. Composite simplifies the protocol design work because it can be implemented as a signature algorithm that fits into existing systems.

11.3. Profiling down the number of options

One daunting aspect of this specification is the number of composite algorithm combinations. Each option has been specified because there is a community that has a direct application for it; typically because the traditional component is already deployed in a change-managed environment, or because that specific traditional component is required for regulatory reasons.

However, this large number of combinations leads either to fracturing of the ecosystem into non-interoperable sub-groups when different communities choose non-overlapping subsets to support, or on the other hand it leads to spreading development resources too thin when trying to support all options.

This specification does not list any particular composite algorithm as mandatory-to-implement, however organizations that operate within specific application domains are encouraged to define profiles that select a small number of composites appropriate for that application domain.

For applications that do not have any regulatory requirements or legacy implementations to consider, it is RECOMMENDED to focus implementation effort on as it provides the best overall balance of performance and security.

id-MLDSA65-ECDSA-P256-SHA512

Below we list a few other recommendations for specific scenarios.

In applications that require RSA, it is RECOMMENDED to focus implementation effort on:

id-MLDSA65-RSA3072-PSS-SHA512

In applications that are performance and bandwidth-sensitive, it is RECOMMENDED to focus implementation effort on:

id-MLDSA44-ECDSA-P256-SHA256
or
id-MLDSA44-Ed25519-SHA512

In applications that only allow NIST PQC Level 5, it is RECOMMENDED to focus implementation effort on:

id-MLDSA87-ECDSA-P384-SHA512

In applications that require the signature primitive to provide SUF-CMA, it is RECOMMENDED to focus implementation effort on:

id-MLDSA65-Ed25519-SHA512

11.4. External Pre-hashing

Implementers MAY externalize the pre-hash computation outside the module that computes Composite-ML-DSA.Sign() in an analogous way to how pre-hash signing is used for RSA, ECDSA or HashML-DSA. Such a modification to the Composite-ML-DSA.Sign() algorithm is considered compliant to this specification so long as it produces the same output and error conditions.

Below is a suggested implementation for splitting the pre-hashing and signing between two parties.

Composite-ML-DSA<OID>.Prehash(M) ->  ph

Explicit inputs:

  M       The message to be signed, an octet string.

Implicit inputs mapped from <OID>:

  PH      The hash function to use for pre-hashing.

Output:

   ph     The pre-hash which equals PH ( M )

Process:


1. Compute the Prehash of the message using the Hash function
    defined by PH

   ph = PH ( M )

2. Output ph

Composite-ML-DSA<OID>.Sign_ph(sk, ph, ctx) -> s

Explicit inputs:

  sk      Composite private key consisting of signing private keys
          for each component.

  ph      The pre-hash digest over the message

  ctx     The Message context string used in the composite
          signature combiner, which defaults to the empty string.


Implicit inputs mapped from <OID>:

  ML-DSA  The underlying ML-DSA algorithm and parameter set, for
          example "ML-DSA-65".

  Trad    The underlying traditional algorithm and
          parameter set, for example "sha256WithRSAEncryption"
          or "Ed25519".

  Prefix  The prefix octet string.

  Label   A signature label which is specific to each composite
          algorithm. Additionally, the composite label is passed
          into the underlying ML-DSA primitive as the ctx.
          Signature Label values are defined in the "Signature Label Values"
          section below.

Process:

   1.  Identical to Composite-ML-DSA<OID>.Sign (sk, M, ctx) but
       replace the internally generated PH( M ) from step 2 of
       Composite-ML-DSA<OID>.Sign (sk, M, ctx) with ph which is
       input into this function.

12. References

12.1. Normative References

[FIPS.186-5]
National Institute of Standards and Technology (NIST), "Digital Signature Standard (DSS)", , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-5.pdf>.
[FIPS.202]
National Institute of Standards and Technology (NIST), "SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions", , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf>.
[FIPS.204]
National Institute of Standards and Technology (NIST), "Module-Lattice-Based Digital Signature Standard", FIPS PUB 204, , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.204.pdf>.
[RFC2119]
Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <https://www.rfc-editor.org/info/rfc2119>.
[RFC2986]
Nystrom, M. and B. Kaliski, "PKCS #10: Certification Request Syntax Specification Version 1.7", RFC 2986, DOI 10.17487/RFC2986, , <https://www.rfc-editor.org/info/rfc2986>.
[RFC3279]
Bassham, L., Polk, W., and R. Housley, "Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 3279, DOI 10.17487/RFC3279, , <https://www.rfc-editor.org/info/rfc3279>.
[RFC4210]
Adams, C., Farrell, S., Kause, T., and T. Mononen, "Internet X.509 Public Key Infrastructure Certificate Management Protocol (CMP)", RFC 4210, DOI 10.17487/RFC4210, , <https://www.rfc-editor.org/info/rfc4210>.
[RFC4211]
Schaad, J., "Internet X.509 Public Key Infrastructure Certificate Request Message Format (CRMF)", RFC 4211, DOI 10.17487/RFC4211, , <https://www.rfc-editor.org/info/rfc4211>.
[RFC5280]
Cooper, D., Santesson, S., Farrell, S., Boeyen, S., Housley, R., and W. Polk, "Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, , <https://www.rfc-editor.org/info/rfc5280>.
[RFC5480]
Turner, S., Brown, D., Yiu, K., Housley, R., and T. Polk, "Elliptic Curve Cryptography Subject Public Key Information", RFC 5480, DOI 10.17487/RFC5480, , <https://www.rfc-editor.org/info/rfc5480>.
[RFC5639]
Lochter, M. and J. Merkle, "Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation", RFC 5639, DOI 10.17487/RFC5639, , <https://www.rfc-editor.org/info/rfc5639>.
[RFC5652]
Housley, R., "Cryptographic Message Syntax (CMS)", STD 70, RFC 5652, DOI 10.17487/RFC5652, , <https://www.rfc-editor.org/info/rfc5652>.
[RFC5758]
Dang, Q., Santesson, S., Moriarty, K., Brown, D., and T. Polk, "Internet X.509 Public Key Infrastructure: Additional Algorithms and Identifiers for DSA and ECDSA", RFC 5758, DOI 10.17487/RFC5758, , <https://www.rfc-editor.org/info/rfc5758>.
[RFC5915]
Turner, S. and D. Brown, "Elliptic Curve Private Key Structure", RFC 5915, DOI 10.17487/RFC5915, , <https://www.rfc-editor.org/info/rfc5915>.
[RFC5958]
Turner, S., "Asymmetric Key Packages", RFC 5958, DOI 10.17487/RFC5958, , <https://www.rfc-editor.org/info/rfc5958>.
[RFC6090]
McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic Curve Cryptography Algorithms", RFC 6090, DOI 10.17487/RFC6090, , <https://www.rfc-editor.org/info/rfc6090>.
[RFC6234]
Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)", RFC 6234, DOI 10.17487/RFC6234, , <https://www.rfc-editor.org/info/rfc6234>.
[RFC8017]
Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch, "PKCS #1: RSA Cryptography Specifications Version 2.2", RFC 8017, DOI 10.17487/RFC8017, , <https://www.rfc-editor.org/info/rfc8017>.
[RFC8032]
Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital Signature Algorithm (EdDSA)", RFC 8032, DOI 10.17487/RFC8032, , <https://www.rfc-editor.org/info/rfc8032>.
[RFC8174]
Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, , <https://www.rfc-editor.org/info/rfc8174>.
[RFC8410]
Josefsson, S. and J. Schaad, "Algorithm Identifiers for Ed25519, Ed448, X25519, and X448 for Use in the Internet X.509 Public Key Infrastructure", RFC 8410, DOI 10.17487/RFC8410, , <https://www.rfc-editor.org/info/rfc8410>.
[SEC1]
Certicom Research, "SEC 1: Elliptic Curve Cryptography", , <https://www.secg.org/sec1-v2.pdf>.
[SEC2]
Certicom Research, "SEC 2: Recommended Elliptic Curve Domain Parameters", , <https://www.secg.org/sec2-v2.pdf>.
[X.690]
ITU-T, "Information technology - ASN.1 encoding Rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)", ISO/IEC 8825-1:2015, .
[X9.62_2005]
American National Standards Institute, "Public Key Cryptography for the Financial Services Industry The Elliptic Curve Digital Signature Algorithm (ECDSA)", .

12.2. Informative References

[ANSSI2024]
French Cybersecurity Agency (ANSSI), Federal Office for Information Security (BSI), Netherlands National Communications Security Agency (NLNCSA), and Swedish National Communications Security Authority, Swedish Armed Forces, "Position Paper on Quantum Key Distribution", n.d., <https://cyber.gouv.fr/sites/default/files/document/Quantum_Key_Distribution_Position_Paper.pdf>.
[Bindel2017]
Bindel, N., Herath, U., McKague, M., and D. Stebila, "Transitioning to a quantum-resistant public key infrastructure", , <https://link.springer.com/chapter/10.1007/978-3-319-59879-6_22>.
[BonehShoup]
Boneh, D. and V. Shoup, "A Graduate Course in Applied Cryptography v0.6", , <https://crypto.stanford.edu/~dabo/cryptobook/BonehShoup_0_6.pdf>.
[BSI2021]
Federal Office for Information Security (BSI), "Quantum-safe cryptography - fundamentals, current developments and recommendations", , <https://www.bsi.bund.de/SharedDocs/Downloads/EN/BSI/Publications/Brochure/quantum-safe-cryptography.pdf>.
[codesigningbrsv3.8]
CA/Browser Forum, "Baseline Requirements for the Issuance and Management of Publicly‐Trusted Code Signing Certificates Version 3.8.0", n.d., <https://cabforum.org/working-groups/code-signing/documents/>.
[eIDAS2014]
European Parliament and Council, "Regulation (EU) No 910/2014 of the European Parliament and of the Council of 23 July 2014 on electronic identification and trust services for electronic transactions in the internal market and repealing Directive 1999/93/EC", n.d., <https://eur-lex.europa.eu/eli/reg/2014/910/oj/eng>.
[I-D.ietf-pquip-hybrid-signature-spectrums]
Bindel, N., Hale, B., Connolly, D., and F. D, "Hybrid signature spectrums", Work in Progress, Internet-Draft, draft-ietf-pquip-hybrid-signature-spectrums-06, , <https://datatracker.ietf.org/doc/html/draft-ietf-pquip-hybrid-signature-spectrums-06>.
[RFC5914]
Housley, R., Ashmore, S., and C. Wallace, "Trust Anchor Format", RFC 5914, DOI 10.17487/RFC5914, , <https://www.rfc-editor.org/info/rfc5914>.
[RFC7292]
Moriarty, K., Ed., Nystrom, M., Parkinson, S., Rusch, A., and M. Scott, "PKCS #12: Personal Information Exchange Syntax v1.1", RFC 7292, DOI 10.17487/RFC7292, , <https://www.rfc-editor.org/info/rfc7292>.
[RFC7296]
Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T. Kivinen, "Internet Key Exchange Protocol Version 2 (IKEv2)", STD 79, RFC 7296, DOI 10.17487/RFC7296, , <https://www.rfc-editor.org/info/rfc7296>.
[RFC8411]
Schaad, J. and R. Andrews, "IANA Registration for the Cryptographic Algorithm Object Identifier Range", RFC 8411, DOI 10.17487/RFC8411, , <https://www.rfc-editor.org/info/rfc8411>.
[RFC8446]
Rescorla, E., "The Transport Layer Security (TLS) Protocol Version 1.3", RFC 8446, DOI 10.17487/RFC8446, , <https://www.rfc-editor.org/info/rfc8446>.
[RFC8551]
Schaad, J., Ramsdell, B., and S. Turner, "Secure/Multipurpose Internet Mail Extensions (S/MIME) Version 4.0 Message Specification", RFC 8551, DOI 10.17487/RFC8551, , <https://www.rfc-editor.org/info/rfc8551>.
[RFC9180]
Barnes, R., Bhargavan, K., Lipp, B., and C. Wood, "Hybrid Public Key Encryption", RFC 9180, DOI 10.17487/RFC9180, , <https://www.rfc-editor.org/info/rfc9180>.
[RFC9794]
Driscoll, F., Parsons, M., and B. Hale, "Terminology for Post-Quantum Traditional Hybrid Schemes", RFC 9794, DOI 10.17487/RFC9794, , <https://www.rfc-editor.org/info/rfc9794>.
[RFC9881]
Massimo, J., Kampanakis, P., Turner, S., and B. E. Westerbaan, "Internet X.509 Public Key Infrastructure -- Algorithm Identifiers for the Module-Lattice-Based Digital Signature Algorithm (ML-DSA)", RFC 9881, DOI 10.17487/RFC9881, , <https://www.rfc-editor.org/info/rfc9881>.

Appendix A. Maximum Key and Signature Sizes

The sizes listed below are maximas. Several factors could cause fluctuations in the size of the traditional component. For example, this could be due to:

Size values marked with an asterisk (*) in the table are not fixed but maximum possible values for the composite key or ciphertext. Implementations should be careful when performing length checking based on such values.

Non-hybrid ML-DSA is included for reference.

Table 4: Maximum size values of composite ML-DSA
Algorithm Public key Private key Signature
id-ML-DSA-44 1312 32 2420
id-ML-DSA-65 1952 32 3309
id-ML-DSA-87 2592 32 4627
id-MLDSA44-RSA2048-PSS-SHA256 1582* 1226* 2676
id-MLDSA44-RSA2048-PKCS15-SHA256 1582* 1226* 2676
id-MLDSA44-Ed25519-SHA512 1344 64 2484
id-MLDSA44-ECDSA-P256-SHA256 1377 83 2492*
id-MLDSA65-RSA3072-PSS-SHA512 2350* 1802* 3693
id-MLDSA65-RSA3072-PKCS15-SHA512 2350* 1802* 3693
id-MLDSA65-RSA4096-PSS-SHA512 2478* 2383* 3821
id-MLDSA65-RSA4096-PKCS15-SHA512 2478* 2383* 3821
id-MLDSA65-ECDSA-P256-SHA512 2017 83 3381*
id-MLDSA65-ECDSA-P384-SHA512 2049 96 3413*
id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 2017 84 3381*
id-MLDSA65-Ed25519-SHA512 1984 64 3373
id-MLDSA87-ECDSA-P384-SHA512 2689 96 4731*
id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 2689 100 4731*
id-MLDSA87-Ed448-SHAKE256 2649 89 4741
id-MLDSA87-RSA3072-PSS-SHA512 2990* 1802* 5011
id-MLDSA87-RSA4096-PSS-SHA512 3118* 2383* 5139
id-MLDSA87-ECDSA-P521-SHA512 2725 114 4766*

Appendix B. Component Algorithm Reference

This section provides references to the full specification of the algorithms used in the composite constructions.

Table 5: Component Signature Algorithms used in Composite Constructions
Component Signature Algorithm ID OID Specification
id-ML-DSA-44 2.16.840.1.101.3.4.3.17 [FIPS.204]
id-ML-DSA-65 2.16.840.1.101.3.4.3.18 [FIPS.204]
id-ML-DSA-87 2.16.840.1.101.3.4.3.19 [FIPS.204]
id-Ed25519 1.3.101.112 [RFC8032], [RFC8410]
id-Ed448 1.3.101.113 [RFC8032], [RFC8410]
ecdsa-with-SHA256 1.2.840.10045.4.3.2 [RFC3279], [RFC5915], [RFC5758], [RFC5480], [SEC1], [X9.62_2005]
ecdsa-with-SHA384 1.2.840.10045.4.3.3 [RFC3279], [RFC5915], [RFC5758], [RFC5480], [SEC1], [X9.62_2005]
ecdsa-with-SHA512 1.2.840.10045.4.3.4 [RFC3279], [RFC5915], [RFC5758], [RFC5480], [SEC1], [X9.62_2005]
sha256WithRSAEncryption 1.2.840.113549.1.1.11 [RFC8017]
sha384WithRSAEncryption 1.2.840.113549.1.1.12 [RFC8017]
id-RSASSA-PSS 1.2.840.113549.1.1.10 [RFC8017]
Table 6: Elliptic Curves used in Composite Constructions
Elliptic CurveID OID Specification
secp256r1 1.2.840.10045.3.1.7 [RFC6090], [SEC2]
secp384r1 1.3.132.0.34 [RFC5480], [RFC6090], [SEC2]
secp521r1 1.3.132.0.35 [RFC5480], [RFC6090], [SEC2]
brainpoolP256r1 1.3.36.3.3.2.8.1.1.7 [RFC5639]
brainpoolP384r1 1.3.36.3.3.2.8.1.1.11 [RFC5639]
Table 7: Hash algorithms used in pre-hashed Composite Constructions to build PH element
HashID OID Specification
id-sha256 2.16.840.1.101.3.4.2.1 [RFC6234]
id-sha384 2.16.840.1.101.3.4.2.2 [RFC6234]
id-sha512 2.16.840.1.101.3.4.2.3 [RFC6234]
id-shake256 2.16.840.1.101.3.4.2.18 [FIPS.202]
id-mgf1 1.2.840.113549.1.1.8 [RFC8017]

Appendix C. Component AlgorithmIdentifiers for Public Keys and Signatures

Many cryptographic libraries are X.509-focused and do not expose interfaces to instantiate a public key from raw bytes, but only from a SubjectPublicKeyInfo structure as you would find in an X.509 certificate, therefore implementing composite in those libraries requires reconstructing the SPKI for each component algorithm. In order to aid implementers and reduce interoperability issues, this section lists out the full public key and signature AlgorithmIdentifiers for each component algorithm.

For newer Algorithms like Ed25519 or ML-DSA the AlgorithmIdentifiers are the same for Public Key and Signature. Older Algorithms have different AlgorithmIdentifiers for keys and signatures and are specified separately here for each component.

ML-DSA-44

AlgorithmIdentifier of Public Key and Signature

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ML-DSA-44   -- (2 16 840 1 101 3 4 3 17)
   }

DER:
  30 0B 06 09 60 86 48 01 65 03 04 03 11

ML-DSA-65

AlgorithmIdentifier of Public Key and Signature

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ML-DSA-65   -- (2 16 840 1 101 3 4 3 18)
   }

DER:
  30 0B 06 09 60 86 48 01 65 03 04 03 12

ML-DSA-87

AlgorithmIdentifier of Public Key and Signature

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ML-DSA-87   -- (2 16 840 1 101 3 4 3 19)
   }

DER:
  30 0B 06 09 60 86 48 01 65 03 04 03 13

RSASSA-PSS 2048 & 3072

AlgorithmIdentifier of Public Key

Note that we suggest here to use id-RSASSA-PSS (1.2.840.113549.1.1.10) as the public key OID for RSA-PSS, although most implementations also would accept rsaEncryption (1.2.840.113549.1.1.1), and some might in fact prefer or require it.

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-RSASSA-PSS   -- (1.2.840.113549.1.1.10)
    }

DER:
  30 0B 06 09 2A 86 48 86 F7 0D 01 01 0A

AlgorithmIdentifier of Signature

ASN.1:
  signatureAlgorithm AlgorithmIdentifier ::= {
    algorithm id-RSASSA-PSS,   -- (1.2.840.113549.1.1.10)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm id-sha256,   -- (2.16.840.1.101.3.4.2.1)
        parameters NULL
        },
      AlgorithmIdentifier ::= {
        algorithm id-mgf1,       -- (1.2.840.113549.1.1.8)
        parameters AlgorithmIdentifier ::= {
          algorithm id-sha256,   -- (2.16.840.1.101.3.4.2.1)
          parameters NULL
          }
        },
      saltLength 32
      }
    }

DER:
  30 41 06 09 2A 86 48 86 F7 0D 01 01 0A 30 34 A0
  0F 30 0D 06 09 60 86 48 01 65 03 04 02 01 05 00
  A1 1C 30 1A 06 09 2A 86 48 86 F7 0D 01 01 08 30
  0D 06 09 60 86 48 01 65 03 04 02 01 05 00 A2 03
  02 01 20

RSASSA-PSS 4096

AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-RSASSA-PSS   -- (1.2.840.113549.1.1.10)
    }

DER:
  30 0B 06 09 2A 86 48 86 F7 0D 01 01 0A

AlgorithmIdentifier of Signature

ASN.1:
  signatureAlgorithm AlgorithmIdentifier ::= {
    algorithm id-RSASSA-PSS,   -- (1.2.840.113549.1.1.10)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm id-sha384,   -- (2.16.840.1.101.3.4.2.2)
        parameters NULL
        },
      AlgorithmIdentifier ::= {
        algorithm id-mgf1,       -- (1.2.840.113549.1.1.8)
        parameters AlgorithmIdentifier ::= {
          algorithm id-sha384,   -- (2.16.840.1.101.3.4.2.2)
          parameters NULL
          }
        },
      saltLength 64
      }
    }

DER:
  30 41 06 09 2A 86 48 86 F7 0D 01 01 0A 30 34 A0
  0F 30 0D 06 09 60 86 48 01 65 03 04 02 02 05 00
  A1 1C 30 1A 06 09 2A 86 48 86 F7 0D 01 01 08 30
  0D 06 09 60 86 48 01 65 03 04 02 02 05 00 A2 03
  02 01 40

RSASSA-PKCS1-v1_5 2048 & 3072

AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm rsaEncryption,   -- (1.2.840.113549.1.1.1)
    parameters NULL
    }

DER:
  30 0D 06 09 2A 86 48 86 F7 0D 01 01 01 05 00

AlgorithmIdentifier of Signature

ASN.1:
  signatureAlgorithm AlgorithmIdentifier ::= {
    algorithm sha256WithRSAEncryption,   -- (1.2.840.113549.1.1.11)
    parameters NULL
    }

DER:
  30 0D 06 09 2A 86 48 86 F7 0D 01 01 0D 05 00

RSASSA-PKCS1-v1_5 4096

AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm rsaEncryption,   -- (1.2.840.113549.1.1.1)
    parameters NULL
    }

DER:
  30 0D 06 09 2A 86 48 86 F7 0D 01 01 01 05 00

AlgorithmIdentifier of Signature

ASN.1:
  signatureAlgorithm AlgorithmIdentifier ::= {
    algorithm sha384WithRSAEncryption,   -- (1.2.840.113549.1.1.12)
    parameters NULL
    }

DER:
  30 0D 06 09 2A 86 48 86 F7 0D 01 01 0C 05 00

ECDSA NIST P256

AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ecPublicKey   -- (1.2.840.10045.2.1)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm secp256r1   -- (1.2.840.10045.3.1.7)
        }
      }
    }

DER:
  30 13 06 07 2A 86 48 CE 3D 02 01 06 08 2A 86 48 CE 3D 03 01 07

AlgorithmIdentifier of Signature

ASN.1:
  signature AlgorithmIdentifier ::= {
    algorithm ecdsa-with-SHA256   -- (1.2.840.10045.4.3.2)
    }

DER:
  30 0A 06 08 2A 86 48 CE 3D 04 03 02

ECDSA NIST P384

AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ecPublicKey   -- (1.2.840.10045.2.1)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm secp384r1   -- (1.3.132.0.34)
        }
      }
    }

DER:
  30 10 06 07 2A 86 48 CE 3D 02 01 06 05 2B 81 04 00 22

AlgorithmIdentifier of Signature

ASN.1:
  signature AlgorithmIdentifier ::= {
    algorithm ecdsa-with-SHA384   -- (1.2.840.10045.4.3.3)
    }

DER:
  30 0A 06 08 2A 86 48 CE 3D 04 03 03

ECDSA NIST P521

AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ecPublicKey   -- (1.2.840.10045.2.1)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm secp521r1   -- (1.3.132.0.35)
        }
      }
    }

DER:
  30 10 06 07 2A 86 48 CE 3D 02 01 06 05 2B 81 04 00 23

AlgorithmIdentifier of Signature

ASN.1:
  signature AlgorithmIdentifier ::= {
    algorithm ecdsa-with-SHA512   -- (1.2.840.10045.4.3.4)
    }

DER:
  30 0A 06 08 2A 86 48 CE 3D 04 03 04

ECDSA Brainpool-P256

AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ecPublicKey   -- (1.2.840.10045.2.1)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm brainpoolP256r1   -- (1.3.36.3.3.2.8.1.1.7)
        }
      }
    }

DER:
  30 14 06 07 2A 86 48 CE 3D 02 01 06 09 2B 24 03
  03 02 08 01 01 07

AlgorithmIdentifier of Signature

ASN.1:
  signature AlgorithmIdentifier ::= {
    algorithm ecdsa-with-SHA256   -- (1.2.840.10045.4.3.2)
    }

DER:
  30 0A 06 08 2A 86 48 CE 3D 04 03 02

ECDSA Brainpool-P384

AlgorithmIdentifier of Public Key

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-ecPublicKey   -- (1.2.840.10045.2.1)
    parameters ANY ::= {
      AlgorithmIdentifier ::= {
        algorithm brainpoolP384r1   -- (1.3.36.3.3.2.8.1.1.11)
        }
      }
    }

DER:
  30 14 06 07 2A 86 48 CE 3D 02 01 06 09 2B 24 03
  03 02 08 01 01 0B

AlgorithmIdentifier of Signature

ASN.1:
  signature AlgorithmIdentifier ::= {
    algorithm ecdsa-with-SHA384   -- (1.2.840.10045.4.3.3)
    }

DER:
  30 0A 06 08 2A 86 48 CE 3D 04 03 03

Ed25519

AlgorithmIdentifier of Public Key and Signature

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-Ed25519   -- (1.3.101.112)
    }

DER:
  30 05 06 03 2B 65 70

Ed448

AlgorithmIdentifier of Public Key and Signature

ASN.1:
  algorithm AlgorithmIdentifier ::= {
    algorithm id-Ed448   -- (1.3.101.113)
    }

DER:
  30 05 06 03 2B 65 71

Appendix D. Message Representative Examples

This section provides examples of constructing the message representative M', showing all intermediate values. This is intended to be useful for debugging purposes.

The input message for this example is the hex string "00 01 02 03 04 05 06 07 08 09".

Each input component is shown. Note that values are shown hex-encoded for display purposes only, they are actually raw binary values.

Finally, the fully assembled M' is given, which is simply the concatenation of the above values.

First is an example of constructing the message representative M' for MLDSA65-ECDSA-P256-SHA256 without a context string ctx.

Example of id-MLDSA65-ECDSA-P256-SHA512 construction of M'.

# Inputs:

M: 00010203040506070809
ctx: <empty>

# Components of M':

Prefix:
436f6d706f73697465416c676f726974686d5369676e61747572657332303235

Label: COMPSIG-MLDSA65-ECDSA-P256-SHA512

len(ctx): 00

ctx: <empty>
PH(M): 0f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f
9a3f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f90353
3


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

M': 436f6d706f73697465416c676f726974686d5369676e6174757265733230323
5434f4d505349472d4d4c44534136352d45434453412d503235362d534841353132
000f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f9a3f2
02f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f903533

Second is an example of constructing the message representative M' for MLDSA65-ECDSA-P256-SHA256 with a context string ctx.

The inputs are similar to the first example with the exception that there is an 8 byte context string 'ctx'.

Example of id-MLDSA65-ECDSA-P256-SHA512 construction of M'.

# Inputs:

M: 00010203040506070809
ctx: 0813061205162623

# Components of M':

Prefix:
436f6d706f73697465416c676f726974686d5369676e61747572657332303235

Label: COMPSIG-MLDSA65-ECDSA-P256-SHA512

len(ctx): 08

ctx: 0813061205162623

PH(M): 0f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f
9a3f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f90353
3


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

M': 436f6d706f73697465416c676f726974686d5369676e6174757265733230323
5434f4d505349472d4d4c44534136352d45434453412d503235362d534841353132
0808130612051626230f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c
3523a20974f9a3f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d85
4c342f903533

Appendix E. Test Vectors

The following test vectors are provided in a format similar to the NIST ACVP Known-Answer-Tests (KATs).

The structure is that a global message m is signed over in all test cases. m is the ASCII string "The quick brown fox jumps over the lazy dog."

Within each test case there are the following values:

Implementers should be able to perform the following tests using the test vectors below:

  1. Load the public key pk or certificate x5c and use it to verify the signature s over the message m.

  2. Validate the self-signed certificate x5c.

  3. Load the signing private key sk or sk_pkcs8 and use it to produce a new signature which can be verified using the provided pk or x5c.

Test vectors are provided for each underlying ML-DSA algorithm in isolation for the purposes of debugging.

Due to the length of the test vectors, some readers will prefer to retrieve the non-word-wrapped copy from GitHub. The reference implementation written in python that generated them is also available:

https://github.com/lamps-wg/draft-composite-sigs/tree/main/src

{
"m": "VGhlIHF1aWNrIGJyb3duIGZveCBqdW1wcyBvdmVyIHRoZSBsYXp5IGRvZy4=",
"tests": [
{
"tcId": "id-ML-DSA-44",
"pk": "trUzS5Q/s24OG+1jSoa3j4jwB73C2JqQrnShcKSupay4bSA3NTrUe8AfyaCjO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",
"x5c": "MIIPjDCCBgKgAwIBAgIUR9lXE54GlhGC+SsDTXh+1XrPgWkwCwYJYIZIAWUD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]
}

Appendix F. Intellectual Property Considerations

The following IPR Disclosure relates to this document:

https://datatracker.ietf.org/ipr/3588/

Appendix G. Contributors and Acknowledgements

This document incorporates contributions and comments from a large group of experts. The editors would especially like to acknowledge the expertise and tireless dedication of the following people, who attended many long meetings and generated millions of bytes of electronic mail and VOIP traffic over the past six years in pursuit of this document:

Serge Mister (Entrust), Felipe Ventura (Entrust), Richard Kettlewell (Entrust), Ali Noman (Entrust), Dr. Britta Hale (Naval Postgraduade School), Tim Hollebeek (Digicert), Panos Kampanakis (Amazon), Chris A. Wood (Apple), Christopher D. Wood (Apple), Sophie Schmieg (Google), Bas Westerbaan (Cloudflare), Deirdre Connolly (SandboxAQ), Richard Kisley (IBM), Piotr Popis (Enigma), François Rousseau, Falko Strenzke, Alexander Ralien (Siemens), José Ignacio Escribano, Jan Oupický, 陳志華 (Abel C. H. Chen, Chunghwa Telecom), 林邦曄 (Austin Lin, Chunghwa Telecom), Zhao Peiduo (Seventh Sense AI), Phil Hallin (Microsoft), Samuel Lee (Microsoft), Alicja Kario (Red Hat), Jean-Pierre Fiset (Crypto4A), Varun Chatterji (Seventh Sense AI), Mojtaba Bisheh-Niasar and Douglas Stebila (University of Waterloo).

We especially want to recognize the contributions of Dr. Britta Hale who has helped immensely with strengthening the signature combiner construction, and to Dr. Hale along with Peter C and John Preuß Mattsson with analyzing the scheme with respect to EUF-CMA, SUF-CMA and Non-Separability properties.

We wish to acknowledge particular effort from Carl Wallace and Daniel Van Geest (CryptoNext Security), who have put in sustained effort over multiple years both reviewing and implementing at the hackathon each iteration of this document.

Thanks to Giacomo Pope (github.com/GiacomoPope) whose ML-DSA and ML-KEM implementations were used to generate the test vectors.

We are grateful to all who have given feedback over the years, formally or informally, on mailing lists or in person, including any contributors who may have been inadvertently omitted from this list.

Finally, we wish to thank the authors of all the referenced documents upon which this specification was built. "Copying always makes things easier and less error prone" - [RFC8411].

Authors' Addresses

Mike Ounsworth
Entrust Limited
2500 Solandt Road – Suite 100
Ottawa, Ontario K2K 3G5
Canada
John Gray
Entrust Limited
2500 Solandt Road – Suite 100
Ottawa, Ontario K2K 3G5
Canada
Massimiliano Pala
OpenCA Labs
New York City, New York,
United States of America
Jan Klaussner
Bundesdruckerei GmbH
Kommandantenstr. 18
10969 Berlin
Germany
Scott Fluhrer
Cisco Systems