



LAMPS                                                       M. Ounsworth
Internet-Draft                                                   J. Gray
Intended status: Standards Track                                 Entrust
Expires: 25 July 2026                                            M. Pala
                                                             OpenCA Labs
                                                            J. Klaussner
                                                    Bundesdruckerei GmbH
                                                              S. Fluhrer
                                                           Cisco Systems
                                                         21 January 2026


      Composite ML-DSA for use in X.509 Public Key Infrastructure
               draft-ietf-lamps-pq-composite-sigs-latest

Abstract

   This document defines combinations of US NIST ML-DSA in hybrid with
   traditional algorithms RSASSA-PKCS1-v1.5, RSASSA-PSS, ECDSA, Ed25519,
   and Ed448.  These combinations are tailored to meet regulatory
   guidelines.  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

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   provisions of BCP 78 and BCP 79.

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   This Internet-Draft will expire on 25 July 2026.

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Table of Contents

   1.  Introduction
     1.1.  Conventions and Terminology
     1.2.  Notation
     1.3.  Composite Design Philosophy
   2.  Overview of the Composite ML-DSA Signature Scheme
     2.1.  Pre-hashing
     2.2.  Prefix, Label and CTX
   3.  Composite ML-DSA Functions
     3.1.  Key Generation
       3.1.1.  Allowed Modifications to the Key Generation Process
     3.2.  Sign
     3.3.  Verify
   4.  Serialization
     4.1.  SerializePublicKey and DeserializePublicKey
     4.2.  SerializePrivateKey and DeserializePrivateKey
     4.3.  SerializeSignatureValue and DeserializeSignatureValue
   5.  Use within X.509 and PKIX
     5.1.  Encoding to DER
     5.2.  Key Usage Bits
     5.3.  ASN.1 Definitions
   6.  Algorithm Identifiers and Parameters
     6.1.  RSASSA-PSS Parameters
     6.2.  Rationale for choices
   7.  ASN.1 Module
   8.  IANA Considerations
     8.1.  Object Identifier Allocations
       8.1.1.  Module Registration
       8.1.2.  Object Identifier Registrations
   9.  Security Considerations
     9.1.  Why Hybrids?
     9.2.  EUF-CMA, SUF-CMA and non-separability
       9.2.1.  EUF-CMA
       9.2.2.  SUF-CMA
       9.2.3.  Non-separability
     9.3.  Key Reuse
     9.4.  Use of Prefix for attack mitigation
     9.5.  Policy for Deprecated and Acceptable Algorithms
   10. Implementation Considerations
     10.1.  FIPS certification
     10.2.  Backwards Compatibility
     10.3.  Profiling down the number of options
     10.4.  External Pre-hashing
   11. References
     11.1.  Normative References
     11.2.  Informative References
   Appendix A.  Maximum Key and Signature Sizes
   Appendix B.  Component Algorithm Reference
   Appendix C.  Component AlgorithmIdentifiers for Public Keys and
           Signatures
   Appendix D.  Message Representative Examples
   Appendix E.  Test Vectors
   Appendix F.  Intellectual Property Considerations
   Appendix G.  Contributors and Acknowledgements
   Authors' Addresses

1.  Introduction

   The advent of quantum computing poses a significant threat to current
   cryptographic systems because traditional cryptographic signature
   algorithms such as RSA, DSA and its elliptic curve variants will
   become vulnerable to quantum attacks.  Unlike previous migrations
   between cryptographic algorithms, this migration gives us the
   foresight that traditional cryptographic algorithms will be broken in
   the future, but will remain 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].

   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.  The
   composite algorithm presents a single public key and signature value
   such that it can be treated as a single atomic algorithm at the
   protocol level.  This provides a property referred to as "protocol
   backwards compatibility" since it can be applied to protocols that
   are not explicitly hybrid-aware.  The idea of a composite was first
   presented in [Bindel2017].  Composite algorithms retain some security
   even if one of their component algorithms is broken, which is
   discussed in detail in Section 9.  This specification creates PQ/T
   Hybrids with ML-DSA, defined in [FIPS.204] as the PQ component.
   Instantiations of the composite ML-DSA scheme are provided based on
   ML-DSA, RSA-PSS, RSA-PKCS#1v1.5, ECDSA, Ed25519 and Ed448.  The full
   list of algorithms registered by this specification is in Section 6.
   Backwards compatibility in the sense of upgraded systems continuing
   to interoperate with legacy systems is not directly covered in this
   specification, but is the subject of Section 10.2.

   Certain jurisdictions have recommended that ML-DSA 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].

   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 Cryptography 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 from which any cryptographic algorithm an
   organization has deployed today can evolve or transition.

   While this specification registers a large number of composite
   algorithms, it is expected that organizations will choose to deploy a
   single composite algorithm, or a small number of composite
   algorithms, that meets the needs of their environment, and very few
   implementers will need concern themselves with the entire list.  This
   specification does not specify any mandatory-to-implement algorithms,
   but Section 10.3 provides a short-list of recommended composite
   algorithms for common use-cases.

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

1.1.  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.

   *APPLICATION BACKWARDS COMPATIBILITY*: The usual definition of
   backwards compatibility, meaning whether an upgraded and non-upgraded
   application can successfully establish communication.

   *COMPOSITE CRYPTOGRAPHIC ELEMENT*: [RFC9794] defines composites as: A
   cryptographic element that incorporates multiple component
   cryptographic elements of the same type in a multi-algorithm scheme.

   *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].

   *Post-Quantum Traditional (PQ/T) hybrid scheme*: A multi-algorithm
   scheme where at least one component algorithm is a post-quantum
   algorithm and at least one is a traditional algorithm.

   *PROTOCOL BACKWARDS COMPATIBILITY*: A property whereby a new feature
   can be added to a protocol without requiring any changes to the
   protocol's specification and only minimal changes to its
   implementations (such as adding new identifiers).  This is notable
   because many PQ/T Hybrids require modification of the protocol to
   make it "hybrid aware", whereas this specification presents as a
   standalone algorithm and thus can take advantage of existing
   cryptographic agility mechanisms.

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

1.2.  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.

1.3.  Composite Design Philosophy

   Composite algorithms, as defined in this specification, follow the
   definition in [RFC9794] and should be regarded as a single algorithm
   that performs a single cryptographic operation typical of a digital
   signature algorithm.  This generally means that the complexity of
   combining algorithms can and should be handled by the cryptographic
   library or cryptographic module.  The design intent is that protocols
   such as PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], the CMS
   [RFC5652], and the Trust Anchor Format [RFC5914] can treat composite
   algorithms as they would any other algorithm without the protocol
   layer to have any "hybrid-awareness".  This is a property referred to
   as "protocol backwards-compatibility".

   Discussion of the specific choices of algorithm pairings can be found
   in Section 6.2.

   In terms of security properties, we consider the two security
   properties EUF-CMA and SUF-CMA, which are treated more rigorously in
   Section 9.2.1 and Section 9.2.2.  As a simplified summary; 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 9.2.

2.  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 9.

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

   *  KeyGen() -> (pk, sk): A probabilistic key generation algorithm
      which generates a public key pk and a secret key sk.  Some
      cryptographic modules may also expose a KeyGen(seed) -> (pk, sk),
      which generates pk and sk deterministically from a seed.  This
      specification assumes a seed-based keygen for ML-DSA.

   *  Sign(sk, M) -> s: A signing algorithm which takes as input a
      secret key sk and a message M, and outputs a signature s.  Signing
      routines may take additional parameters such as a context string
      or a hash function to use for pre-hashing the message.

   *  Verify(pk, M, s) -> true or false: A verification algorithm which
      takes as input a public key pk, a message M and a signature s, and
      outputs true if the signature verifies correctly and false or an
      error otherwise.  Verification routines may take additional
      parameters such as a context string or a hash function to use for
      pre-hashing the message.

   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].

   *  SerializePublicKey(mldsaPK, tradPK) -> bytes: Produce a byte
      string encoding of the component public keys.

   *  DeserializePublicKey(bytes) -> (mldsaPK, tradPK): Parse a byte
      string to recover the component public keys.

   *  SerializePrivateKey(mldsaSeed, tradSK) -> bytes: Produce a byte
      string encoding of the component private keys.  Note that the
      keygen seed is used as the interoperable private key format for
      ML-DSA.

   *  DeserializePrivateKey(bytes) -> (mldsaSeed, tradSK): Parse a byte
      string to recover the component private keys.

   *  SerializeSignatureValue(mldsaSig, tradSig) -> bytes: Produce a
      byte string encoding of the component signature values.

   *  DeserializeSignatureValue(bytes) -> (mldsaSig, tradSig): Parse a
      byte string to recover the component signature values.

   Full definitions of serialization and deserialization algorithms can
   be found in Section 4.

2.1.  Pre-hashing

   The ML-DSA algorithm as specified in [FIPS.204] is not pre-hashed,
   meaning that the entire to-be-signed message is passed into ML-
   DSA.Sign(sk, M, ctx) ([FIPS.204] Algorithm 2).  While there are some
   cryptographic advantages to designing a signature algorithm this way,
   it also has some operational drawbacks; namely the performance and
   privacy implications of needing to stream the entire to-be-signed
   message to the signing module or service, which is doubled in the
   context of a composite since the to-be-signed message needs to be
   streamed to both underlying component algorithms.  Also, "pure" (aka
   non-pre-hashed) modes lack support for digesting the message once and
   signing it with multiple different keys.

   Composite ML-DSA takes a design approach which mirrors that of
   [FIPS.204] Algorithm 2 in that the to-be-signed message
   representative M' in contains a hash of the message PH( M ) instead
   of the full message M.

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

   which closely mirrors the construction of M' in [FIPS.204] Algorithm
   4.

   Given this design of Composite ML-DSA, it is possible to split the
   pre-hashing step out from the signature generation process -- see
   {#impl-cons-external-ph} for further discussion and sample
   algorithms.

   Note that while the overall construction of Composite ML-DSA is
   similar to that of HashML-DSA, the ML-DSA component inside the
   composite is "pure" ML-DSA; implementing this specification does not
   require an implementation of HashML-DSA.

2.2.  Prefix, Label and CTX

   The to-be-signed message representative M', defined in Section 3.2 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 9.4 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 6.

   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 3.2) and Composite-ML-DSA.Verify()
   (Section 3.3).  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.

   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.

   The 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.

3.  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 2.

3.1.  Key Generation

   In order to maintain security properties of the composite, this
   specification strictly forbids re-using component key material
   between composite and non-composite keys, or between multiple
   composite keys.  This means that an invocation of Composite-ML-
   DSA.KeyGen() MUST perform, or otherwise guarantee, fresh generation
   of the key material for both underlying algorithms and MUST NOT reuse
   existing key material.  See Section 9.3 for further discussion of the
   security implications.

   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 process 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 10.1.

   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 9.3.

   Errors produced by the component KeyGen() routines MUST be forwarded
   on to the calling application.

3.1.1.  Allowed Modifications to the Key Generation Process

   Key generation is a process that is entirely internal to a
   cryptographic module, and as such it is often customized to fit the
   performance or operational requirements of the module.  In cases
   where the private keys never leave the module or are otherwise not
   required to interoperate with other cryptographic modules, it is not
   required for interoperability for the private keys to match the
   format described in this specification.  Therefore, in general,
   implementations of Composite ML-DSA MAY use an alternate key
   generation process so long as it generates compatible public keys,
   and so long as both component keys are freshly-generated and not re-
   used in a standalone key or within another composite key.  Below are
   some examples of modifications that an implementer MAY make to the
   key generation process.

   Implementations MAY modify this process to additionally output the
   expanded mldsaSK or to make 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.

   In cases where it is desirable to have a deterministic KeyGen of one
   or both component keys from a seed, this process MAY be modified to
   expose an interface of Composite-ML-DSA<OID>.KeyGen(seed) such that
   one component algorithm is generated from the seed and the other from
   random, or the input seed is cryptographically expanded to produce
   seeds for both components.  Implementation details and security
   analysis of such a modified key generation process is outside the
   scope of this document.

   Where interoperable private keys are not required, implementations
   MAY choose to use a different private key representation than the one
   given in Section 4.2.  For example, the component keys MAY be stored
   in separate cryptographic modules, or MAY be stored in separate
   PKCS#8 objects, or MAY be stored in a format that preserves the ML-
   DSA expanded key instead of the ML-DSA seed.  The required
   modifications to the key generation process, as well as the signature
   generation process below, to support these private key
   representations are considered compliant with this specification so
   long as they generate compatible public keys, and so long as both
   component keys are freshly-generated.  Note that when implementing
   Composite ML-DSA with a private key format that does not preserve the
   ML-DSA seed, especially when implementing on top of a cryptographic
   module that does not support seeds, it will be impossible to
   reconstruct a compliant seed-based private key as described in
   Section 4.2

3.2.  Sign

   The Sign() algorithm of Composite ML-DSA mirrors the construction of
   ML-DSA.Sign(sk, M, ctx) defined in Algorithm 2 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 2.1 for a discussion of the pre-hash function PH.  See
   Section 2.2 for a discussion on the signature label Label and
   application context ctx.  See Section 10.4 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', mldsa_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.

   Note that there are two different context strings ctx at play: the
   first is the application context ctx that is passed in to Composite-
   ML-DSA.Sign and bound to the to-be-signed message M' in Step 2.  The
   second is the mldsa-ctx that is passed down into the underlying ML-
   DSA.Sign(sk, M, ctx) as defined in [FIPS.204] Algorithm 2, in Step 4
   and here Composite ML-DSA itself is the application that we wish to
   bind and so the per-algorithm Label is used as the ctx for the
   underlying ML-DSA primitive.  Some implementations of the EdDSA
   component primitive can also expose a ctx parameter, but even if
   present, this is not used by Composite ML-DSA.

   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.

3.3.  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 2.1 for
   a discussion of the pre-hash function PH.  See Section 2.2 for a
   discussion on the signature label Label and application context ctx.
   See Section 10.4 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, mldsa_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.

   Note that there are two different context strings ctx at play: the
   first is the application context ctx that is passed in to Composite-
   ML-DSA.Sign and bound to the to-be-signed message M' in Step 3.  The
   second is the mldsa-ctx that is passed down into the underlying ML-
   DSA.Verify(pk, M, sigma, ctx) as defined in [FIPS.204] Algorithm 3,
   in Step 4 and here Composite ML-DSA itself is the application that we
   wish to bind and so the per-algorithm Label is used as the ctx for
   the underlying ML-DSA primitive.  Some implementations of the EdDSA
   component primitive can also expose a ctx parameter, but even if
   present, this is not used by Composite ML-DSA.

4.  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 3.

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

           +===========+============+=============+===========+
           | Algorithm | Public key | Private key | Signature |
           +===========+============+=============+===========+
           | ML-DSA-44 | 1312       | 32          | 2420      |
           +-----------+------------+-------------+-----------+
           | ML-DSA-65 | 1952       | 32          | 3309      |
           +-----------+------------+-------------+-----------+
           | ML-DSA-87 | 2592       | 32          | 4627      |
           +-----------+------------+-------------+-----------+

                      Table 1: ML-DSA Sizes in bytes

   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:

   *  *ML-DSA*: MUST be encoded as specified in section 7.2 of
      [FIPS.204], using a 32-byte seed as the private key.  The
      signature and public key format are encoded as specified in
      section 7.2 of [FIPS.204].

   *  *RSA*: the public key MUST be encoded as RSAPublicKey with the
      (n,e) public key representation as specified in A.1.1 of [RFC8017]
      and the private key representation as RSAPrivateKey specified in
      A.1.2 of [RFC8017] with version 0 and 'otherPrimeInfos' absent.
      An RSA signature MUST be encoded as specified in section 8.1.1
      (for RSASSA-PSS-SIGN) or 8.2.1 (for RSASSA-PCKS1-V1_5-SIGN) of
      [RFC8017].

   *  *ECDSA*: public key MUST be encoded as an uncompressed X9.62
      [X9.62_2005], including the leading byte 0x04 indicating
      uncompressed.  This is consistent with the encoding of ECPoint as
      specified in section 2.2 of [RFC5480] when no ASN.1 OCTET STRING
      wrapping is present.  A signature MUST be encoded as an Ecdsa-Sig-
      Value as specified in section 2.2.3 of [RFC3279].  The private key
      MUST be encoded as ECPrivateKey specified in [RFC5915] with the
      'NamedCurve' parameter set to the OID of the curve, but without
      the 'publicKey' field.

   *  *EdDSA*: public key and signature MUST be encoded as per section 3
      of [RFC8032] and the private key is a 32 or 57 byte raw value for
      Ed25519 and Ed448 respectively, which can be converted to a
      CurvePrivateKey specified in [RFC8410] by the addition of an OCTET
      STRING wrapper.

   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 5.1.

   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.

4.1.  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)

4.2.  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)

4.3.  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)

5.  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.

5.1.  Encoding to DER

   The serialization routines presented in Section 4 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 4 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.

5.2.  Key Usage Bits

   The intended application for the key is indicated in the keyUsage
   certificate extension; see Section 4.2.1.3 of [RFC5280].  If the
   keyUsage extension is present in a certificate that includes an OID
   indicating a composite ML-DSA algorithm in the SubjectPublicKeyInfo,
   then the subject public key can only be used for verifying digital
   signatures on certificates or CRLs, or those used in an entity
   authentication service, a data origin authentication service, an
   integrity service, and/or a non-repudiation service that protects
   against the signing entity falsely denying some action.  This means
   that the keyUsage extention MUST have at least one of the following
   bits set:

     digitalSignature
     nonRepudiation
     keyCertSign
     cRLSign

   ML-DSA subject public keys cannot be used to establish keys or
   encrypt data, so the keyUsage extention MUST NOT have any of
   following bits set:

      keyEncipherment,
      dataEncipherment,
      keyAgreement,
      encipherOnly, and
      decipherOnly.

   Requirements about the keyUsage extension bits defined in [RFC5280]
   still apply.

   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.

5.3.  ASN.1 Definitions

   Composite ML-DSA uses a substantially non-ASN.1 based encoding, as
   specified in Section 4.  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 7.

   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 6 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 4.2.  The publicKey field
   remains OPTIONAL.  If the publicKey field is present, it MUST be a
   composite public key as per Section 4.1.

   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 6 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 9.3.

6.  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 10.3
   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 2.2.

   *  id-MLDSA44-RSA2048-PSS-SHA256

      -  OID: 1.3.6.1.5.5.7.6.37

      -  Label: COMPSIG-MLDSA44-RSA2048-PSS-SHA256

      -  Pre-Hash function (PH): SHA256

      -  ML-DSA variant: ML-DSA-44

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: id-RSASSA-PSS

         o  RSA size: 2048

         o  RSASSA-PSS parameters: See Table 2

   *  id-MLDSA44-RSA2048-PKCS15-SHA256

      -  OID: 1.3.6.1.5.5.7.6.38

      -  Label: COMPSIG-MLDSA44-RSA2048-PKCS15-SHA256

      -  Pre-Hash function (PH): SHA256

      -  ML-DSA variant: ML-DSA-44

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: sha256WithRSAEncryption

         o  RSA size: 2048

   *  id-MLDSA44-Ed25519-SHA512

      -  OID: 1.3.6.1.5.5.7.6.39

      -  Label: COMPSIG-MLDSA44-Ed25519-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-44

      -  Traditional Algorithm: Ed25519

         o  Traditional Signature Algorithm: id-Ed25519

   *  id-MLDSA44-ECDSA-P256-SHA256

      -  OID: 1.3.6.1.5.5.7.6.40

      -  Label: COMPSIG-MLDSA44-ECDSA-P256-SHA256

      -  Pre-Hash function (PH): SHA256

      -  ML-DSA variant: ML-DSA-44

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA256

         o  ECDSA curve: secp256r1

   *  id-MLDSA65-RSA3072-PSS-SHA512

      -  OID: 1.3.6.1.5.5.7.6.41

      -  Label: COMPSIG-MLDSA65-RSA3072-PSS-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: id-RSASSA-PSS

         o  RSA size: 3072

         o  RSASSA-PSS parameters: See Table 2

   *  id-MLDSA65-RSA3072-PKCS15-SHA512

      -  OID: 1.3.6.1.5.5.7.6.42

      -  Label: COMPSIG-MLDSA65-RSA3072-PKCS15-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: sha256WithRSAEncryption

         o  RSA size: 3072

   *  id-MLDSA65-RSA4096-PSS-SHA512

      -  OID: 1.3.6.1.5.5.7.6.43

      -  Label: COMPSIG-MLDSA65-RSA4096-PSS-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: id-RSASSA-PSS

         o  RSA size: 4096

         o  RSASSA-PSS parameters: See Table 3

   *  id-MLDSA65-RSA4096-PKCS15-SHA512

      -  OID: 1.3.6.1.5.5.7.6.44

      -  Label: COMPSIG-MLDSA65-RSA4096-PKCS15-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: sha384WithRSAEncryption

         o  RSA size: 4096

   *  id-MLDSA65-ECDSA-P256-SHA512

      -  OID: 1.3.6.1.5.5.7.6.45

      -  Label: COMPSIG-MLDSA65-ECDSA-P256-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA256

         o  ECDSA curve: secp256r1

   *  id-MLDSA65-ECDSA-P384-SHA512

      -  OID: 1.3.6.1.5.5.7.6.46

      -  Label: COMPSIG-MLDSA65-ECDSA-P384-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA384

         o  ECDSA curve: secp384r1

   *  id-MLDSA65-ECDSA-brainpoolP256r1-SHA512

      -  OID: 1.3.6.1.5.5.7.6.47

      -  Label: COMPSIG-MLDSA65-ECDSA-BP256-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA256

         o  ECDSA curve: brainpoolP256r1

   *  id-MLDSA65-Ed25519-SHA512

      -  OID: 1.3.6.1.5.5.7.6.48

      -  Label: COMPSIG-MLDSA65-Ed25519-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: Ed25519

         o  Traditional Signature Algorithm: id-Ed25519

   *  id-MLDSA87-ECDSA-P384-SHA512

      -  OID: 1.3.6.1.5.5.7.6.49

      -  Label: COMPSIG-MLDSA87-ECDSA-P384-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA384

         o  ECDSA curve: secp384r1

   *  id-MLDSA87-ECDSA-brainpoolP384r1-SHA512

      -  OID: 1.3.6.1.5.5.7.6.50

      -  Label: COMPSIG-MLDSA87-ECDSA-BP384-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA384

         o  ECDSA curve: brainpoolP384r1

   *  id-MLDSA87-Ed448-SHAKE256

      -  OID: 1.3.6.1.5.5.7.6.51

      -  Label: COMPSIG-MLDSA87-Ed448-SHAKE256

      -  Pre-Hash function (PH): SHAKE256/64**

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: Ed448

         o  Traditional Signature Algorithm: id-Ed448

   *  id-MLDSA87-RSA3072-PSS-SHA512

      -  OID: 1.3.6.1.5.5.7.6.52

      -  Label: COMPSIG-MLDSA87-RSA3072-PSS-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: id-RSASSA-PSS

         o  RSA size: 3072

         o  RSASSA-PSS parameters: See Table 2

   *  id-MLDSA87-RSA4096-PSS-SHA512

      -  OID: 1.3.6.1.5.5.7.6.53

      -  Label: COMPSIG-MLDSA87-RSA4096-PSS-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: id-RSASSA-PSS

         o  RSA size: 4096

         o  RSASSA-PSS parameters: See Table 3

   *  id-MLDSA87-ECDSA-P521-SHA512

      -  OID: 1.3.6.1.5.5.7.6.54

      -  Label: COMPSIG-MLDSA87-ECDSA-P521-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA512

         o  ECDSA curve: secp521r1

   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.

6.1.  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:

                +=============================+===========+
                | RSASSA-PSS-params field     | Value     |
                +=============================+===========+
                | hashAlgorithm               | id-sha256 |
                +-----------------------------+-----------+
                | maskGenAlgorithm.algorithm  | id-mgf1   |
                +-----------------------------+-----------+
                | maskGenAlgorithm.parameters | id-sha256 |
                +-----------------------------+-----------+
                | saltLength                  | 32        |
                +-----------------------------+-----------+
                | trailerField                | 1         |
                +-----------------------------+-----------+

                     Table 2: RSASSA-PSS 2048 and 3072
                                 Parameters

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

                +=============================+===========+
                | RSASSA-PSS-params field     | Value     |
                +=============================+===========+
                | hashAlgorithm               | id-sha384 |
                +-----------------------------+-----------+
                | maskGenAlgorithm.algorithm  | id-mgf1   |
                +-----------------------------+-----------+
                | maskGenAlgorithm.parameters | id-sha384 |
                +-----------------------------+-----------+
                | saltLength                  | 48        |
                +-----------------------------+-----------+
                | trailerField                | 1         |
                +-----------------------------+-----------+

                    Table 3: RSASSA-PSS 4096 Parameters

6.2.  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.

7.  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}
            SMIME-CAPS { IDENTIFIED BY id }
         }


   -- Composite ML-DSA

   id-MLDSA44-RSA2048-PSS-SHA256 OBJECT IDENTIFIER ::= {
      iso(1) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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) identified-organization(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>

8.  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.

8.1.  Object Identifier Allocations

   EDNOTE to IANA: OIDs will need to be replaced in both the ASN.1
   module and in Section 6.

8.1.1.  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

8.1.2.  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 6 and Section 7.

   *  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

9.  Security Considerations

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

9.1.  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 9.2
   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 application 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 10.1.

9.2.  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.

9.2.1.  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.

9.2.2.  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.

9.2.3.  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 2.2 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 2.2 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 9.4 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 9.3 further strengthens the non-separability in practice.

9.3.  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 9.2 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.

9.4.  Use of Prefix for attack mitigation

   The Prefix value specified in Section 2.2 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.

9.5.  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.

10.  Implementation Considerations

10.1.  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 3.1 invokes ML-DSA.KeyGen_internal(seed) which
   might not be available in a cryptographic module running in FIPS-
   mode, but Section 3.1 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 4.2.  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 3.1 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.

10.2.  Backwards Compatibility

   The term "application 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 application backwards compatibility, only upgraded
   systems will understand the OIDs defined in this specification.

   If application 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.

10.3.  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

10.4.  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.

11.  References

11.1.  Normative References

   [FIPS.186-5]
              National Institute of Standards and Technology (NIST),
              "Digital Signature Standard (DSS)", February 2023,
              <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", August 2015,
              <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, August 2024,
              <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, March 1997,
              <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, November 2000,
              <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, April
              2002, <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, September 2005,
              <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, September 2005,
              <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, May 2008,
              <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, March 2009,
              <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, March 2010,
              <https://www.rfc-editor.org/info/rfc5639>.

   [RFC5652]  Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
              RFC 5652, DOI 10.17487/RFC5652, September 2009,
              <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, January 2010,
              <https://www.rfc-editor.org/info/rfc5758>.

   [RFC5915]  Turner, S. and D. Brown, "Elliptic Curve Private Key
              Structure", RFC 5915, DOI 10.17487/RFC5915, June 2010,
              <https://www.rfc-editor.org/info/rfc5915>.

   [RFC5958]  Turner, S., "Asymmetric Key Packages", RFC 5958,
              DOI 10.17487/RFC5958, August 2010,
              <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, February 2011,
              <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, May 2011,
              <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, November 2016,
              <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, January 2017,
              <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,
              May 2017, <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, August 2018,
              <https://www.rfc-editor.org/info/rfc8410>.

   [SEC1]     Certicom Research, "SEC 1: Elliptic Curve Cryptography",
              May 2009, <https://www.secg.org/sec1-v2.pdf>.

   [SEC2]     Certicom Research, "SEC 2: Recommended Elliptic Curve
              Domain Parameters", January 2010,
              <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, November 2015.

   [X9.62_2005]
              American National Standards Institute, "Public Key
              Cryptography for the Financial Services Industry The
              Elliptic Curve Digital Signature Algorithm (ECDSA)",
              November 2005.

11.2.  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", 2017, <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", January 2023,
              <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", October 2021,
              <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-07, 20 June
              2025, <https://datatracker.ietf.org/doc/html/draft-ietf-
              pquip-hybrid-signature-spectrums-07>.

   [RFC5914]  Housley, R., Ashmore, S., and C. Wallace, "Trust Anchor
              Format", RFC 5914, DOI 10.17487/RFC5914, June 2010,
              <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, July 2014,
              <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, October
              2014, <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, August 2018,
              <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, August 2018,
              <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,
              April 2019, <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,
              February 2022, <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, June 2025,
              <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, October 2025,
              <https://www.rfc-editor.org/info/rfc9881>.

   [TestVectors]
              "Test vectors for Composite-ML-DSA", n.d.,
              <https://github.com/lamps-wg/draft-composite-
              sigs/tree/main/src>.

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:

   *  Compressed vs uncompressed EC point.

   *  The RSA public key (n, e) allows e to vary is size between 3 and n
      - 1 [RFC8017].  Note that the size table below assumes the
      recommended value of e = 65537, so for RSA combinations it is in
      fact not a true maximum.

   *  When the underlying RSA or EC value is itself DER-encoded, integer
      values could occasionally be shorter than expected due to leading
      zeros being dropped from the encoding.

   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.

   +=========================================+======+=======+=========+
   | Algorithm                               |Public|Private|Signature|
   |                                         |key   |key    |         |
   +=========================================+======+=======+=========+
   | 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*    |
   +-----------------------------------------+------+-------+---------+

             Table 4: Maximum size values of composite ML-DSA

Appendix B.  Component Algorithm Reference

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

    +=========================+=========================+=============+
    | Component Signature     | OID                     |Specification|
    | Algorithm ID            |                         |             |
    +=========================+=========================+=============+
    | 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 5: Component Signature Algorithms 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 6: Elliptic Curves used in Composite Constructions

         +=============+=========================+===============+
         | 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]     |
         +-------------+-------------------------+---------------+

           Table 7: Hash algorithms used in pre-hashed Composite
                     Constructions to build PH element

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 48
         }
       }

   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 30

   *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.

   *  Prefix is the fixed constant defined in Section 2.2.

   *  Label is the specific signature label for this composite
      algorithm, as defined in Section 6.

   *  len(ctx) is the length of the Message context String which is 00
      when no context is used.

   *  ctx is the Message context string used in the composite signature
      combiner.  It is empty in this example.

   *  PH(M) is the output of hashing the message M.

   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."

   For all test vectors, a sample signature is provided computer over an
   empty ctx string, and also computed over the ctx string "The
   lethargic, colorless dog sat beneath the energetic, stationary fox.".

   Within each test case there are the following values:

   *  tcId the name of the algorithm.

   *  pk the raw verification public key.

   *  x5c a self-signed X.509 certificate of the public key.

   *  sk the raw signature private key.

   *  sk_pkcs8 the signature private key in a PKCS#8 object.

   *  s the signature value computed over m with an empty ctx string.

   *  sWithContext the signature value computed over m with the provided
      ctx string.

   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 [TestVectors].  The
   reference implementation written in python that generated them is
   also available.

   {
   "m": "VGhlIHF1aWNrIGJyb3duIGZveCBqdW1wcyBvdmVyIHRoZSBsYXp5IGRvZy4=",
   "ctx": "VGhlIGxldGhhcmdpYywgY29sb3JsZXNzIGRvZyBzYXQgYmVuZWF0aCB0aGUg
   ZW5lcmdldGljLCBzdGF0aW9uYXJ5IGZveC4=",
   "tests": [
   {
   "tcId": "id-ML-DSA-44",
   "pk": "EWoNgliCgU7GOoTqJ1BCV4WR/izOHNrm717rEbJ0FfMMH+38K7zEVhsZrm00b
   meyCTBWP8kXrZeL6150vChktTXTgpfnN1hLvZwpgxoHrq2I9MIZZNcai7SHDHjCppBkN
   dRImWi9mOCGBtZwuZGgMvlEmyvmQadCMLxyrhJMueR19UphKics/8UzPWk0Fw6tEI1Ft
   PHgM264OPzE9km31VXI0IvYASwC8ypsVyrEgQWQyUgBlyxG4ZZyhrV0PJzXcZ+pSM6s0
   R+5HrC3O7YaeU6Bw0blkZOFJAmHDBjJXKCYIrZtM5BIaQyyaFTAqEQgkZ9EpGsT4auU8
   yFFtEYUdAWfqeyGGY8g85jebjj+2sYkqoOHnxKTRPDL0CN4FIzwohJqu0KZ4AzMMHd4p
   a01xok05M8Gt14DzPSpIr+UDZ8Nf59bc/6xC4vDnup0KaUWrWT8xcq3oxB3nZ/eoRlLh
   SxgtaGBosFS4xYO3o0z9iknrnEWQz8YjkIJM5M3WoVeYjvtOK/yw8yNqnGbRtCY3uuy+
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   Xi/buhq19PlAgGACKxfXXbjlFfL1zOnR8Mjd0LmdR0odtAVQmrZPFF/afaH+efgrxV0Q
   a/TbH5O21QyR1X4cy1KSMtiCYSg9zCzITX7fvT7WGhZiZw/qcvCKwHj0uQ+VxyXBUS9T
   uDOltCYavxC00+uMm0N2YtEdTxcRsoHtooMiKgpUnM851/zp87VwjDslQ/huwalKVNbO
   B/GyQfeDBAz8glnJZu5pgC2TJC13t/OiIRRs6ebguXd6sWib/sD4gaU+ZXS8Pm2u7ESj
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   FtB2Q8HyuRyTRYisciNCXW7a4G3WFZqEbN3sQoBrgi4/1a6SZ9x4v2NB3Ylz/+5/K4Ic
   oXQ7YOIo6qsHFMOd2/zrcmmGUh+Apb/PM13ZB1l2KqGUjJiY8pxCQtij20hHKq2cN+Gr
   WaYwWmgvAk9wlxR7zK63dpQXKldykPhFDl+XqmfEFAEHq7mbgxMtv+auA==",
   "x5c": "MIIPjDCCBgKgAwIBAgIUfBL+fTjkvp10eezFK6d4FCUGw1gwCwYJYIZIAWUD
[encoded data, 5544 characters]
   AAAAAAAAAAAOHzRC",
   "sk": "HAhWcYP1/1xeu2cmwHGCWrGMgF/TTzR4yppE/s8z6Y4=",
   "sk_pkcs8": "MDQCAQAwCwYJYIZIAWUDBAMRBCKAIBwIVnGD9f9cXrtnJsBxglqxjIB
   f0080eMqaRP7PM+mO",
   "s": "mt5kaIWbf8VC4wDBAnw2jUaffnfmaRLp9H/cMh2YyF135hzMM5xJA2JQGQ+0Qu
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   fh7wAAAAAAAAAAAAAAAAAAAAAAAAAAABEcLDs=",
   "sWithContext": "d2nRH/bO4tcl+7DaA4NpHXJ+QVnL2WQKk0svtjjiVCdBqnDut24
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   },
   {
   "tcId": "id-ML-DSA-65",
   "pk": "CehMzdl/hDYK2onXrTgctj5b/N3QrpXfkrhTSPsKRSHelQgjO4IaoK3COkZaO
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   0b8ua+JPX3NyAKLbyM9ZlpF1+E=",
   "x5c": "MIIVhTCCCIKgAwIBAgIUOcHM7EB9Nopgm7PXwUMUYUlvbZkwCwYJYIZIAWUD
[encoded data, 7704 characters]
   AAAAAAAGCQ8XHiU=",
   "sk": "J99savK3IWkld8k0UedxNuQCpLDv96cdJKkXIKo6pXE=",
   "sk_pkcs8": "MDQCAQAwCwYJYIZIAWUDBAMSBCKAICffbGrytyFpJXfJNFHncTbkAqS
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   "s": "UFXqB7QFgN9SMrRUJaSkvGyTDank52coI4S/4hEI9kmViUwuV9bk/4ag7yGOjZ
[encoded data, 4536 characters]
   5jsMjTQn+bo7voCSssfb7h/v8Rhrm9eX+JpbXV1wAAAAAAAAAAAAAAAAAADBAWHiIp",
   "sWithContext": "+nMdTXRmExDbJUOaFgkLd5FA7jR57z/PGLNcX6XBNT4Si+/rXkc
[encoded data, 4608 characters]
   ABQ0RFyMn"
   },
   {
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   "x5c": "MIIdKzCCCwKgAwIBAgIUU8Ew8WFOWPrYs6ypxZhy9ygyUhEwCwYJYIZIAWUD
[encoded data, 10440 characters]
   xsoAAAAAAAAAAAAAAAAAAAAAAAAAAAAEDhEWISk0Ng==",
   "sk": "B/jrKc1CGwOK3CY7/k9Q/Ish38dPTfzzXQ2rMLaF3Ok=",
   "sk_pkcs8": "MDQCAQAwCwYJYIZIAWUDBAMTBCKAIAf46ynNQhsDitwmO/5PUPyLId/
   HT038810NqzC2hdzp",
   "s": "XcWjJfq92g6Y4B69ANNPZEmQVr16ior6tkJm7osNwdTcSm8rGGAt8/Oa7Q4xOF
[encoded data, 6408 characters]
   4KDhwmNUFFbqkVRVuIkaLhAAAAAAAAAAAAAAAAAAAAAAAKERYbIiozOg==",
   "sWithContext": "bQNOjVn48qkgJAgN8JCBTP3fJUYpT1d16Wbd2fkHE9RcEw5tRKh
[encoded data, 6480 characters]
   ="
   },
   {
   "tcId": "id-MLDSA44-RSA2048-PSS-SHA256",
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   5cCAwEAAQ==",
   "x5c": "MIIRuTCCBzCgAwIBAgIUTTHWFAYUq8fnjKZrFARLHi1GsmQwCgYIKwYBBQUH
[encoded data, 6336 characters]
   /pKq0AcxISI=",
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   Dtrz1s=",
   "sk_pkcs8": "MIIE2gIBADAKBggrBgEFBQcGJQSCBMc0+QGb0VTZNfUJqKMoSGewn3J
   Fs/46/7UT5+M+q+SLHTCCBKMCAQACggEBANRYZQ7Neqmh3FZdij9alH6M3fo+08nlYYR
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[encoded data, 5112 characters]
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[encoded data, 5112 characters]
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[encoded data, 9216 characters]
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   "s": "ytsOXnfqoclXD0Qcx4LYbq39OVYPKr0W970e6wb99Puj9GlA+AIVTe0wBE46F0
[encoded data, 5328 characters]
   Q=",
   "sWithContext": "ezPjM2/DxLRvCkyilJ1jR1tTu+in1HuJ6HwSeJf+u9rvqf88jdP
[encoded data, 5328 characters]
   k4fr380CyuDI="
   },
   {
   "tcId": "id-MLDSA65-ECDSA-P256-SHA512",
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   "x5c": "MIIWKzCCCOGgAwIBAgIUW0MoLO0np7/Ch09mfDIxAm9wH3AwCgYIKwYBBQUH
[encoded data, 7920 characters]
   srtQ355qdpx78+SId1hKHTnxSRdeRYHr",
   "sk": "bsdcWusLmyFNumCKr944e8i+AxpGXddgx9fH69Yo49owMQIBAQQgmEOXvMQ5w
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   "sk_pkcs8": "MGQCAQAwCgYIKwYBBQUHBi0EU27HXFrrC5shTbpgiq/eOHvIvgMaRl3
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   "s": "Z2cXSmyeY+LB6sYY3fPKYRjhisbdrjPXpdWnbLpB9vCyqNnHDvOa2/gL+FpGcj
[encoded data, 4680 characters]
   nnV57SD9jlFuGe1Ll0N/g6oSA=",
   "sWithContext": "oHXylglVknUKV5ZzGdY29ZcVAruptT8vnoOzTl7F0ryNbDC8Rxy
[encoded data, 4680 characters]
   6z38ZZfLNEuXI6m3Ul6X8l+mK8L+Aowzbxl/n"
   },
   {
   "tcId": "id-MLDSA65-ECDSA-P384-SHA512",
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   bLOVtrutejeW48xwSRK",
   "x5c": "MIIWazCCCQGgAwIBAgIUEjaXBZrvZZ10VCdx0cYv3mUxs/MwCgYIKwYBBQUH
[encoded data, 7992 characters]
   pFQ9i1eB9geBYxkV8jWRwiHkz77/tBugRe2KkWXjQNXMGGKmMQ==",
   "sk": "GBzZVGrgCtjNd7FtNzoxmzXVEcHki9NScm7fSsJokqAwPgIBAQQwHgigRN8us
   gijZwZRq9Xo0wu5aeauYgfkTTKGmPFfoomz4FJBpwmk5oRVHB8eyrtHoAcGBSuBBAAi"
   ,
   "sk_pkcs8": "MHECAQAwCgYIKwYBBQUHBi4EYBgc2VRq4ArYzXexbTc6MZs11RHB5Iv
   TUnJu30rCaJKgMD4CAQEEMB4IoETfLrIIo2cGUavV6NMLuWnmrmIH5E0yhpjxX6KJs+B
   SQacJpOaEVRwfHsq7R6AHBgUrgQQAIg==",
   "s": "h/1YyBhPhCx/bWXDY27cLN4ZRI1MrusyQk2799YY5fSt1PH7sXIoIAG2pSMtm+
[encoded data, 4680 characters]
   Iwfo+AL2BOc34rmYPgy24oeq0JJKR5MW1BumbGwhBK9fSVd1zjFGpCgJqbYXMvwFqx",
   "sWithContext": "AKQJEKdrDu1G9LiA9Fh8kJUWaH0sFV7fU+u4X6lXou95UiU8FTO
[encoded data, 4752 characters]
   Quz5+PYTF6w=="
   },
   {
   "tcId": "id-MLDSA65-ECDSA-brainpoolP256r1-SHA512",
   "pk": "qy+xBiomV+u6zDyLzKjPr0M3O2lFQYKU0Z9r7kzSW258fB8I/HQXpP/4c5P/T
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   X3UcEZFBajbwo/dttTek7HVK24rfZpvBX2+n8gslBIsdPRXhkA0gPE25RhwcShamc983
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   YNETy33x+JOvnrRKVb3UcxjrxkEc74boGWo/cK6r+wq0OgquUB2F7ysoU5DKCtbIMuUk
   iYrlf8ETZEAK7zNvwACz4hCi6k/5/Ln/QZVfhDft63BnQ==",
   "x5c": "MIIWQDCCCPegAwIBAgIUaEnQXbeVQ5cZoJuYJoXe3oEO3QAwCgYIKwYBBQUH
[encoded data, 7920 characters]
   vch1/n2Dm3rxVg0CIBOhaqs8PUqoYeKo4vPKA45kdAmyCA4OzJZlX3ZpogRl",
   "sk": "IQp1j8gIDkGwD9GlIF6cLzcN9dKeIsr2xb4KW/c4JUcwMgIBAQQgjnC6/VN7S
   McIVUeJpWVqOH7vHMWSEKQLTUzah+w9mnqgCwYJKyQDAwIIAQEH",
   "sk_pkcs8": "MGUCAQAwCgYIKwYBBQUHBi8EVCEKdY/ICA5BsA/RpSBenC83DfXSniL
   K9sW+Clv3OCVHMDICAQEEII5wuv1Te0jHCFVHiaVlajh+7xzFkhCkC01M2ofsPZp6oAs
   GCSskAwMCCAEBBw==",
   "s": "ZKI2hFc1lbxDhRrx5+TXisGUHhi3ey3CJdWqvWz9wPLB+ARqBxX04GN8s3yCak
[encoded data, 4680 characters]
   3ulgABbqfmBkkkTPgmoQB0kvs=",
   "sWithContext": "7Ds2ERU8mBQqrWNqH1RAwVceZv86rkxCBnYyC65X+iOLPKXDA6D
[encoded data, 4680 characters]
   vx6meMLICUobuP/dndzdMYrFAfqsOalDQgA=="
   },
   {
   "tcId": "id-MLDSA65-Ed25519-SHA512",
   "pk": "lJHqFchj4m+jxLow4ARGz/Vgrwa0hpIrPMgTOBx6DouPmdO0P88unCWMDtG4Z
   FkRAkghkdXzsNTNqXzNws/PypD4w86l+KOGB/DrAJMZZK/Y3ndi6P+GQPbsOu/yoaHbi
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   z3+fiIUIvsWwlWyxHk3P86gKZJCyBTqGIGD+DYnsTyWMDrhIcjcHh8brfzIP/vV2FBP2
   g==",
   "x5c": "MIIV/DCCCLqgAwIBAgIUZqRb5vWjxJFTRqlAjlz+D3KeciwwCgYIKwYBBQUH
[encoded data, 7848 characters]
   bGLEHriTw9B4pk65K3TO/EiKsLqOBmZK8vXUDg==",
   "sk": "I6V4IFKJVV5l3fVnYBy0cV+1k6d5ao9x1mjDvKh22Tdg6XQfX7imizxJC5Pkq
   g5dgiBu87jiJC4bz0cp8uFGqg==",
   "sk_pkcs8": "MFECAQAwCgYIKwYBBQUHBjAEQCOleCBSiVVeZd31Z2ActHFftZOneWq
   PcdZow7yodtk3YOl0H1+4pos8SQuT5KoOXYIgbvO44iQuG89HKfLhRqo=",
   "s": "Fxh/AyW+vDUEOBaRjZgvhcgBJWxZG7F3srk+MQFAn86a2iNyE4ao4VordDdnee
[encoded data, 4680 characters]
   W1gNehm0bSGvlKBQ==",
   "sWithContext": "r3ma4PVEUN3jyVhD0ZKc5dSZ0fBvPveY7Tj5MeNZi/qtUpQKdyT
[encoded data, 4680 characters]
   aQDL09qlDv33xnH83QYFqsx1iAw=="
   },
   {
   "tcId": "id-MLDSA87-ECDSA-P384-SHA512",
   "pk": "VJ3mQ7kwpzVTIf9jMh3pRI1y+baUMFVfm9czHDJ/yqV9m797G/ARvNXDFf+s1
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   YetpKu0ZLsHndm3xXR56r2MARjUQ22tYhERK/2vK2Cfw9y0nBf/0PLVQhxoM5kzrryMh
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   "x5c": "MIIeETCCC4GgAwIBAgIUC20XzvAlMLTtLgJIn+JJDvhn9c8wCgYIKwYBBQUH
[encoded data, 10800 characters]
   PyhuRDyh",
   "sk": "yCBUZVCkA6UiJYJdYS8gXsRQEnbPGZbvvVQWeWE9UoMwPgIBAQQwSCmFoWj68
   Zr/KCGPh/W9yQwiv0/Sa0HIqKhYdA0S5Nt4Kg+FjcZGjUJNK3aSxtGPoAcGBSuBBAAi"
   ,
   "sk_pkcs8": "MHECAQAwCgYIKwYBBQUHBjEEYMggVGVQpAOlIiWCXWEvIF7EUBJ2zxm
   W771UFnlhPVKDMD4CAQEEMEgphaFo+vGa/yghj4f1vckMIr9P0mtByKioWHQNEuTbeCo
   PhY3GRo1CTSt2ksbRj6AHBgUrgQQAIg==",
   "s": "x8ta9TIW7+Abwj8OIpW6c2JCg7ad/oBYMDimauy/0v0Qu9VZQMWWC9XIGMrU2Q
[encoded data, 6552 characters]
   e3NB2TVdnGsD2Is5WvxzZIjppz3JY7jKiCJY3kXvdK28RJWGdqUYmhT44=",
   "sWithContext": "imPui7FJsM9p7AiJTlb9ep5FlXQXFAIgl6eRkhbCKTfFsE+95Ii
[encoded data, 6624 characters]
   ="
   },
   {
   "tcId": "id-MLDSA87-ECDSA-brainpoolP384r1-SHA512",
   "pk": "HAN2zXLF0r9XxXuEsPY7T8D8fXk+S3yuSM1pHW1L4hBGfWgTHMGxljPzsDO0s
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   Bxq474uyTBkg8N4hDp1WBhiVYX0FAZgIvv66z3ebEr7PKxRmK0q+we8q7xziJEAiIT3N
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   lFqFec3XV0j9FcnV45d+kJ8kDU+YWnmTmyCGkeEZQtDArYbpaiLdYcNnFhS2apQjejhj
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   SoN7tA5+HHpnr8VF4Fk9S5Bq/ZBnfYlAMPtbjSlVqQt1gScaSKzmzXyqXNjaPSyBbVTi
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   YZ1HDFwV5iFamGdNawvTghQ+BYUMrUUYCgIzDUaNWXsEIr1Ts2hQ7GPU5KoAP8MFOS4C
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   345jQKn6zt9yR9GvtFCIc9iAgYBUkPy8rgYrWxr95PO8jZ9m8w412RUUbSmuFEKMiOLZ
   mdZkMyIt8Da8xF8KBHNtAp63LpvAQZhYQbwVZpYAg02nKKYTp5DJ/0w9QeNxbLMFOIzq
   IpZWuRzLiHsyh6kZafSVb07K6m63F+GDkTWeGdQoXOMpZAnIk6Aj5hkJi8Gj3pOnybtz
   F8vSmqH63IvRh3jSm3lSHRqySY08Uh988rUq3ldY2M2pkrJ6PHJ/QAz5tLm7Z6pSsr7N
   6VSeYAJONL5z2ZhOWTFc/JKgWZE2WwIThnu3j5FCQffq2P2NV4TO9GoELH46k7IvuOq5
   QNug4uft36XRLMyPDfFvS58V25tnl+juSHgcVkL6Mo7pvt/ZXbRfhgVvd13o9fCBGMUL
   VJ+EyEjK423xEgOvtbseOo+SlujEP9J51t8/BcOUwla07+F+7iCaq4uYKy6G2hy82yiz
   IvcDCYN4DuX+q6hrps6N+us2UKr35n9gP2UNKqNxrSvddJhpbUaVg7Ryg==",
   "x5c": "MIIeJTCCC5egAwIBAgIUDRtlQRUouxHp3avudsNdVUAxuBwwCgYIKwYBBQUH
[encoded data, 10800 characters]
   pFhJykPVtbWi5dchsTy4kYncBq3eO9quxJc=",
   "sk": "LM7G+JMPMv0YNysC87onvWaSAygI0q8Ji+V5DMxYGW4wQgIBAQQwBMcCBKGKs
   IevLPveYvm+1f/Y4ZEejHTcEREm0qaXRqH/M4YmdUI6Y76/apBumRItoAsGCSskAwMCC
   AEBCw==",
   "sk_pkcs8": "MHUCAQAwCgYIKwYBBQUHBjIEZCzOxviTDzL9GDcrAvO6J71mkgMoCNK
   vCYvleQzMWBluMEICAQEEMATHAgShirCHryz73mL5vtX/2OGRHox03BERJtKml0ah/zO
   GJnVCOmO+v2qQbpkSLaALBgkrJAMDAggBAQs=",
   "s": "j8FNyt3W/zxqrcokGq0MxDk8ls0Nyo2aP+eyyibNNBniPRV3QFOM3h6kodOFo2
[encoded data, 6552 characters]
   s2D60PsMOpx9MOSrYEKIYs8yvHNshOUxg73QKlqnwRTqadzPxtYsUYtQ==",
   "sWithContext": "NYOAabWqQZXj+AFv1Im6mK+9lD7rfOQfYK9UUPuO2lO4Cl4MSlQ
[encoded data, 6624 characters]
   ="
   },
   {
   "tcId": "id-MLDSA87-Ed448-SHAKE256",
   "pk": "5DGvszcdLLQLBtD48ypskVo/XbbDl4h3If3xdulc+NqaPgokr2jFNfy64sDGh
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   VtKfmZkUVRWonsqIiQK9o4uJ8sO/aTnmLbNexchHoIWPF9iCyqzavfmJfnobLBnaCx9H
   q/hctpji0ZdPJ3Kbhlx/USxkpk+wygATsJUgOosRrOrfo4889yRU2k49mANg1hHE3gnq
   bUMb9eqE2W8HVuvezATaZOU5vuACQ80HRKHOQ6TrcWzQJpWupAznQKbF2YtGfWrP9Dum
   28NAfH1ckoeypV0OVP/Y0QRkqZGxQ25ETz379l5YC6tTKMPazabhRBP1MFjvms7jsbTI
   YalkqYv9sRSqKsn/JfWQf3NF0b3jioPbiRzPCC4myqr8T1Ii5hRdV55YpeNCOTDk1SHY
   ph/ylebJfHiWO72iLkXqXR1s1CxxXDWmqF3YSPLwXG6uSHyngzYIAG1hERHEVikY/nIN
   KraKRZRRRy56wB1OVeEs9OxBDuaYD7RcKzaJN3xw6fBLD8cuxWPe5Xuwp56HcSrnUmFc
   5JxHyI6ua6s3WTxj+sXk9H4MkWpkOV23ofxriiQSJYf9IJtqyLy9rkadW/uSyijqjS23
   qyxUiPwriwLdh6iD/bkN6SewVfraneLYrv+qLcaGBhCRd+DNvvz1qiUZeXcXdHQthIZk
   FEA",
   "x5c": "MIId7TCCC1OgAwIBAgIUF5v44A++VMkHZqL4o/3MbEQrBvMwCgYIKwYBBQUH
[encoded data, 10728 characters]
   XH4D1RMve4CAJtKbNxC6ctlOKy4A",
   "sk": "cvodaRlkcpyalK+R9rqUSD95CNbLedGQ/ls9u5sVo9fJE1xKda+msIkoZg7WZ
   IASEGW1KfueHwKx/i6G3jiIndchxOl12t7AiIaMupaEgZtneMHfuPKlFgY=",
   "sk_pkcs8": "MGoCAQAwCgYIKwYBBQUHBjMEWXL6HWkZZHKcmpSvkfa6lEg/eQjWy3n
   RkP5bPbubFaPXyRNcSnWvprCJKGYO1mSAEhBltSn7nh8Csf4uht44iJ3XIcTpddrewIi
   GjLqWhIGbZ3jB37jypRYG",
   "s": "6Ee2aGK+8ZebApp+wiRoszatM2NOG8hzOBAQeIi8fdIE15aP4PuO++JvWNKM0+
[encoded data, 6624 characters]
   IBAA==",
   "sWithContext": "e4JTJu+7qObp9YzFkcHh4JzYVDPMG24m2gOFm5RX+Vz4y2GA5+a
[encoded data, 6624 characters]
   9tnaePB3gS+w+AA=="
   },
   {
   "tcId": "id-MLDSA87-RSA3072-PSS-SHA512",
   "pk": "yNZ84X0bbi1CpYzeZ8pVWb7f/YBxxnCln1W6UAQDwEW8x+ESwyvvsrra18LFw
[encoded data, 4104 characters]
   fGsF9SdeZ/oZeuDM0VF/NX5hnlZV/ot31+t16To+7gRAgMBAAE=",
   "x5c": "MIIgWDCCDLCgAwIBAgIUCVCEiXXymVjwOLPlDj+o76qxuSgwCgYIKwYBBQUH
[encoded data, 11592 characters]
   qYfca65esSLVwBar/p11uWozdmEYAnITqxeCfA==",
   "sk": "FirLQx496w1zaUZUD4Q9/7sUv5V9W8kFXeLzqBLaDJcwggbjAgEAAoIBgQDjV
   81gk4POGyC3JUD9nFmJ5O6r5Mu4r/KnUGGb4jDpRh8mUEoYttOJoJcepE9qzr45bTPtK
   8IDxsxrtURxlpD9Y3CoYqaDGwtGwgtvfDMige29dLwt1Z5aXEPZGXlwWHkj7s+B5NCRU
   2wXXUW58xKkghkm5w34iTKObYNSg2oEXvS3oM2drUFPtGh2ppzYcQpGqhn4jGqi+QZES
   Ebmp0SxxgS+Nlw8HQXJE7jhaT3EnSaA68CBEmKnhuNgjYvIZpK06FVV1zEh5v8cH2bBX
   eJCkNFS55fi85HPpp4kBaGFp4ovzsYWwOMpM142zoZ7OpHqQzZ+Juky+FUT0lYKXmVgO
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[encoded data, 6984 characters]
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[encoded data, 6984 characters]
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   },
   {
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[encoded data, 4320 characters]
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[encoded data, 11952 characters]
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   6URw2S89hjikAK5/rDU/Q8fVj6nmkgYWHXeZQMgPtcECjkoOJwwPfFxPby2oILlhjSXu
   qwGVM8D8l78UmIa+YBrPvi8udBg8MUqN5ci554ujfRzMJb3boBAroOAk7wHfUFTP0Xec
   oQC99oQRIQnK2ppe0WYweVUU6Uym3i/txpzMjuXvpJljYRoX+0/7G1ezi/xfzQcChnzI
   q8M7A2ZkCggEAeWDlgbRiOAE3L3ofKoTNHKfkK5461woCkkcnlpmwcxU1rHr1UXwKXnM
   iWE7OhzPVDc7kajMaoZubdLDeiqdkfF9NLx5IfFn27nis/87cbMjlZWHnZtOmBowOeaH
   Y6mZY3p8/rZfz0nzjuhMokvoPn+lQqLHP9L2WFo7JDtiVkJvNbW88z4cnJyXO4sdV9sC
   QqpoR967wMunY4N11lTqU2TeV0uSDAHrejZ12urU7aIsdHoJz0p2dFrik1Ro/cGdmrF7
   t4ejKaMEBVlAYrjkyaJmNhAEmHSwW8T0Q+F6zNycbixAPsD7wgU5jhdfmEBYpg3MH7//
   EgvAn2eqspoEywQKCAQAH5VXWGDoQ1SxyYoHwhCdSCYWQKq8XCz7ydXka+dW5pJOIyN7
   8F1RkGO10s//GcTFwygmHNAUGQVfYOQP6azf8kM/CzGTtVN1b7Azzo16irJ9IV7gETwK
   tPPC4FKhY0hPYcJLfIW+BpSvHLKE4zb+CTPFCGEjTTQLqZXVozRPom2o+PSzH6+hNQKW
   trhx3TV/GqyyZPd9CbFiGAKsWLAsx9VJFmssFQZjD2oz5ql2TyYA6iQGzBkLmDMGwPQT
   QKsj2f8IkTacNAKDWVg3Ggq3VC3dGMEpQ88xw1XtZ5BF0tJVgCJnYMQvUB6Lx2VCSvzm
   AjelrXc6jPrYfENw/ZKzV",
   "s": "3OeU2Bcn1HUZC3DWtsJEOx5V8q0UojD7JVxvHqIZuzAQ+zE00GsmS0vXRL+SKY
[encoded data, 7128 characters]
   30+GrAMzoWZdPPjuBZuzAuqCnEh3Eya+Q5Wy6VKaI08+IesJ4TcZLxOqjg",
   "sWithContext": "ToOMhY5sKmKiTFLT19i/bD51irQUjIeKGJBBdrvwPXTc7YghCok
[encoded data, 7200 characters]
   n"
   },
   {
   "tcId": "id-MLDSA87-ECDSA-P521-SHA512",
   "pk": "Rq3lfdnHzXIJmWgpWqUxzFUCfO7HmrXG/EZOOD6qvKpYWmTzS8NWI/QtkYlyF
   oFPxj0/WxbQbv/pFiBkijuf6Ou6XpM7HZtUzyybNfUa1R9aN0HNVkLNPbb8M6Ricpe38
   IBw+dt+5DIrgGq5PU86bCx1CTdDuNXTz/WxXxTMOjo7g2PDwLyaGCVl/8zd7Lyu9ZZHn
   JOX4UnmbgpZKpeLiXdKPhTqI87/0WxKNLFq/v4hrzYm38bdNU5qGu1whEc6KF6VG7WyT
   BKGRmXwtyyqgmRSkoUJvaiSdzDXJVNjCdzjVXGHA0/lSImcn63GoQhpZfpQVJk2OfZqJ
   6nnEvmcDfCt+eqVzdyVDlUh9i22yttU8ybMb5jg7DZy/BXOvyKhwjqjgglhf9A0aoPDi
   RScajbMgs2QVj2x0FSeukuKR+I976QYjMIbCvjchv1qmkPJKinTmOX3SB5zldkxVtWif
   vZo21hWNCT7H7P4r+nyWQEdPwJEaypsM0nR8WA2z3+wzqWeAMdDL4IFWY5wFwa7vpDEs
   ABeg/tUBf2FSDySpe286IiX+vKnRlpxU+0D0yNbmYpTDLDvXx2soUfMVLKdrbO343dlN
   pKr+1qfABc74+63kVTBj4kHStYlqJqSEKWsgTRY2rWJpQyIKCz3I4TVOP58XMwH1gpGw
   2mr0VcmdaU+S3Hpd5bIitmOf8MkvEm+Reo0fUo9iVsS2H/VBM4g8wQBD/1wdnLPXg5fp
   H2M2gbzeiJKi0rrdjif/1UcTKdNkLcS9/fH7PN0TD4aWQEbiUVrpK4RuzkMSe16XiL8B
   N4gD6Eg402SLLaOAoMNTmPpOo0b/plPyDx6MSdvF9YKlqKxw2X5rRXqzHSI2dCHxIHNq
   uEoNtpaNf1X8/u8D+QnCAQFCUFN4uQkKt9Abgi1AWWrXqULHJV+aR+Ft03m18Meawddu
   VZgdkAGuGwokGCrY9j81M4ejos6stURvB8ce8bMhojk+pQyeI4Vn3L4J4sNJkGYzTHfB
   0Yt1wCyFHS3XuUqM545zxgpwUlU46vnmsrRjG4koslTpZOXJf+MFdMXM2JzqaV8pTWWr
   xhgxx/Bxzq6i5S6YBXcSSgRzi0SWoCn6u+fhQjTUWA9TRMvTTCZdEMV6IrzVO1M7Y3g7
   F0dAGRR5I9fxYcdu99GqlA/CKv2OqzUHs3xX2k5OKprqlJpRPOuHW/L8ooVG+EWppm99
   2Nt+kP81+8be9nD0PM4sed+D7JJpy54ENBqztpJO6kr/hCnvIJUndl2sFTztEucDJUrR
   mOm6DUl0LItK0N6fEQnTCVboEFN1KRl+PUgMoIEByESqYmqnNx6W6gdvrAugik7ezQR2
   Ss9HtpdlleyBF34CxcajwK2RqsTEioLTSulJqoLZ0O3U7D/kuZfasbuh6Dy5gtPeDGpm
   E7ZDTGBjdpEfiJkeXPjcAzMPwHaTWFEIZHaa4nZ3KzEt3VbSkTz58d228XZ5pEnHlQ6I
   WyiRuwjRP+QZa0aJY/dXpYgwq5xAFXx7vqQr8QeyumLvtO2571i5ccD0ZOZcHbnyO0BD
   N2NhM4OS5G5JxwwoGfKjX+zi3d/Z3QhRD9AUYBW6xelIqN/LsEopw71SrnuZNIZKEJ/8
   WlaTYDcCurddmgJMvG2AlytV1y3EgyNCm70dmqlUsoMSJ+/hrr5p1yaHFpMiLCo4vLiq
   9YFqMiofw6FOrgzY8TdLQQOFoxOSNCwGjFNvb4kn3L7brhGz54fI68on/jltELSVnCUh
   Hl3T87WXjLo7imwT+GWb0O5vHZOwN3EBRtBQH4q1UVd/FpXV7HdSBaVC1Ppd3PAWjpnJ
   3WjA3r5CSAsiHhgnn5E/VbyVXQl8iQREJkEKkzA/bZzjCv1qTfMRu84xorAeJRqAZCI1
   ukfELg/x3/B7GFvqs2R7mgKiq/Z7p8VO9yuUt4yypvFm24Lju0X4NEhUP9Iydctm/+1P
   RWooJTnYWD0R1jPIhTrbCs52hJYIGCEmHiFJ1bXtTHLtTzvUMg7JXS/rloxs1gfuNJxF
   mfyvWSQ7UJQln3hgz2LTOSCyJ3vu8uiZ3XBdZtZZgMzB53mK/QfQz/VCZva3aHuc/kjW
   aDcWpi35FQjMFGtJE0kGMrem805NYgqhA3FUG6p5dieuFZvTgCZiRJqO9g6IuskEe8Iw
   0cx1Wa5uJkc8J5MOUf99EqqqKD+E/yv7lqJ6PdVCgGYLVDamC6FZ1YjdO3IgKG4PEx5G
   CSbBSDMU5xEFUrP+DmQmN0rNE4LMnea+5ZshkZZ2cpJx1Vkjt2zftGZXpckluRFdxSFC
   Y1HlFBGq+BhJexbGGXSyisgHFZktxQZLA/kDdFyUv+133hpvFl7HVNzBqWsqc6lTVkjS
   Z4DgEmJ641HWn8yUXhp4I07N5uF6+hj57D3f3Veqv+D+aOtLVXGXqNWDRFvH5Qz96eyz
   jR8dH1b3B4v2xouw5k7WHYBRc76LJsv5ECDtKtq/lO/SumjD3/e1Hcu6V+kcznW9xLLj
   VC7yPtoiH5lTA24kfFwufMdziYiJvkeucq2kRUPpP2W2fiQHnUp62VhGfpHYgF7yH45P
   rxtQlp8fHZuAEjgtEXaKmyr5H7jMtSqrY3ZX5xV4MW54W3U+vXOu9u5aMOqIrmzw7R+X
   OVwYr/tEnmg6MIpcYQqxfDu4zr0FVguHHYxjrbt2s5UgddmoyrIXCA04nG0eUrhT5t/V
   n3trifm0dyj/i1XEqpz5HBDFLZ8cwfQkpzrO7TzKbKrV9NzXVGbLvZ9YEXP70CGUUq8X
   o+3E1DquF9oou66v9ahWV/x1nw+rzN7FfcZAjbc/1Pgz9oRQ2ScFnR3qcSdtqaY3ugCG
   U0/a9GsD3iyST+UAI2AK1sqnG+aO/LLZskZ3S52R2eaSb+vUpqny8sowkoQnXaS6Urbi
   QAFxVCBxnBk76UroGvi4pjZyhkmCcypVUNn/mwyUFx8xcVWcLzUb2vfRw40u9fweeDH/
   CKnWTNHPw1390RdSpjE2/CF1RRjCUpjkJplEcKl6Z5t4+b0u84c20wZD3oblyU6KgpBw
   I308pMN6Stq3nqHCBE5YwShaESFTpzC4GRQslNDf9njc2lFFabnCYXAjRiOUyPqpCGRt
   ygnfMZ1uXQPn3rANTbaBx/9QbogI97l0SZGq+7UMVcr3/oYWnrd/rHZMwA5BYiqpIT6t
   6ZADkYG71jagitGS///jcS9etgp3AAOXu5fmhfhbz7U/89lE/M/tzUICqiSvJziUstaM
   Xb9mqrxkcLARVkVkaPTppFMTEhw2L1Ppgru2LA2zg6SxlOZHTJ0hkH3nDQgM7PTAzPmG
   y5ba0kUo5ph+kGqRTknOMmXrAZ48mL0XbAnMSV8iTm5b0ICEvGCyjPrF17L3+4i/Ygsg
   4/9wmIGQRR7/EeC/HA2lh/bTTSJXjDKZUsd5XdtiDABV+3na/PLq1qoe7Vim9spBAC9O
   /bSo2oOxjstlbpC12OMuhFn/RQ3GGwMkshzfJRoOmJgSqWnPH3ftZrCJY+SPTmzIhhNb
   YVvqqzv0L5HPowiOAGEbfx03z+8HoHNPHZ4Xhh5xYIQSOW12wf9/+QH4QfiALYFqFD+H
   iJQYAyHzigvCFUj53AzPaOCKMuVO2pfxUSEmQ==",
   "x5c": "MIIeWDCCC6WgAwIBAgIUM76USZRItUZBBqMZuFGKphhdSgcwCgYIKwYBBQUH
[encoded data, 10872 characters]
   oqI7zzUJARRD62rlN0/j6MBZQ0zzyIVyM8c=",
   "sk": "i6WXRYb3bZgYjyZTAkTzGOG3RxqlKx7H5mvjE4sASjAwUAIBAQRCAPV/kCyal
   JFpSWFTmSR7inkTFwk15OcdfGNDHROW9GWcbS45POp6wX9XWcPb423uihFk2484/dlTJ
   3sdDpCXGgFgoAcGBSuBBAAj",
   "sk_pkcs8": "MIGDAgEAMAoGCCsGAQUFBwY2BHKLpZdFhvdtmBiPJlMCRPMY4bdHGqU
   rHsfma+MTiwBKMDBQAgEBBEIA9X+QLJqUkWlJYVOZJHuKeRMXCTXk5x18Y0MdE5b0ZZx
   tLjk86nrBf1dZw9vjbe6KEWTbjzj92VMnex0OkJcaAWCgBwYFK4EEACM=",
   "s": "GrOwaKBqBUvkBKlG0qlu+fHXv8IZSoslHMRKgUeUIxJ9tHlDt5hnD4njfiS2Hs
[encoded data, 6624 characters]
   0Zzx1YGkYhboXZkUbUriRMlCMp9cWwIRc0nw==",
   "sWithContext": "aG/0H/RnureRTzIZhvAzuqS2Ke8e4bLNyBFXKCpXZWn+k+oa5Hs
[encoded data, 6624 characters]
   r99OhEFuD9oF8wlPRr7+HdgaYXnT2+AKsu2ptUlfX+FFd"
   }
   ]
   }

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), Chris Patton (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
   Email: mike.ounsworth@entrust.com


   John Gray
   Entrust Limited
   2500 Solandt Road – Suite 100
   Ottawa, Ontario  K2K 3G5
   Canada
   Email: john.gray@entrust.com


   Massimiliano Pala
   OpenCA Labs
   New York City, New York,
   United States of America
   Email: director@openca.org


   Jan Klaussner
   Bundesdruckerei GmbH
   Kommandantenstr. 18
   10969 Berlin
   Germany
   Email: jan.klaussner@bdr.de


   Scott Fluhrer
   Cisco Systems
   Email: sfluhrer@cisco.com
