



LAMPS                                                       M. Ounsworth
Internet-Draft                                                   J. Gray
Intended status: Standards Track                                 Entrust
Expires: 8 January 2026                                          M. Pala
                                                             OpenCA Labs
                                                            J. Klaussner
                                                    Bundesdruckerei GmbH
                                                              S. Fluhrer
                                                           Cisco Systems
                                                             7 July 2025


      Composite ML-DSA for use in X.509 Public Key Infrastructure
                 draft-ietf-lamps-pq-composite-sigs-07

Abstract

   This document defines combinations of ML-DSA [FIPS.204] in hybrid
   with traditional algorithms RSASSA-PKCS1-v1_5, RSASSA-PSS, ECDSA,
   Ed25519, and Ed448.  These combinations are tailored to meet security
   best practices and regulatory guidelines.  Composite ML-DSA is
   applicable in any application 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.

About This Document

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

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

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

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

Status of This Memo

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





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Table of Contents

   1.  Changes in -07  . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   4
     2.1.  Conventions and Terminology . . . . . . . . . . . . . . .   5
     2.2.  Composite Design Philosophy . . . . . . . . . . . . . . .   6
   3.  Overview of the Composite ML-DSA Signature Scheme . . . . . .   7
     3.1.  Pre-hashing and Randomizer  . . . . . . . . . . . . . . .   8
     3.2.  Prefix, Domain Separators and CTX . . . . . . . . . . . .   9
   4.  Composite ML-DSA Functions  . . . . . . . . . . . . . . . . .   9
     4.1.  Key Generation  . . . . . . . . . . . . . . . . . . . . .   9
     4.2.  Sign  . . . . . . . . . . . . . . . . . . . . . . . . . .  11
     4.3.  Verify  . . . . . . . . . . . . . . . . . . . . . . . . .  14
   5.  Serialization . . . . . . . . . . . . . . . . . . . . . . . .  16
     5.1.  SerializePublicKey and DeserializePublicKey . . . . . . .  17
     5.2.  SerializePrivateKey and DeserializePrivateKey . . . . . .  20
     5.3.  SerializeSignatureValue and DeserializeSignatureValue . .  21
   6.  Use within X.509 and PKIX . . . . . . . . . . . . . . . . . .  23
     6.1.  Encoding to DER . . . . . . . . . . . . . . . . . . . . .  24
     6.2.  Key Usage Bits  . . . . . . . . . . . . . . . . . . . . .  24
     6.3.  ASN.1 Definitions . . . . . . . . . . . . . . . . . . . .  25
   7.  Algorithm Identifiers . . . . . . . . . . . . . . . . . . . .  27



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     7.1.  Domain Separator Values . . . . . . . . . . . . . . . . .  29
     7.2.  Rationale for choices . . . . . . . . . . . . . . . . . .  31
     7.3.  RSASSA-PSS Parameters . . . . . . . . . . . . . . . . . .  31
   8.  ASN.1 Module  . . . . . . . . . . . . . . . . . . . . . . . .  32
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  39
     9.1.  Object Identifier Allocations . . . . . . . . . . . . . .  39
       9.1.1.  Module Registration . . . . . . . . . . . . . . . . .  39
       9.1.2.  Object Identifier Registrations . . . . . . . . . . .  39
   10. Security Considerations . . . . . . . . . . . . . . . . . . .  43
     10.1.  Why Hybrids? . . . . . . . . . . . . . . . . . . . . . .  43
     10.2.  Non-separability, EUF-CMA and SUF  . . . . . . . . . . .  43
       10.2.1.  Implications of multiple encodings . . . . . . . . .  45
     10.3.  Key Reuse  . . . . . . . . . . . . . . . . . . . . . . .  45
     10.4.  Use of Prefix for attack mitigation  . . . . . . . . . .  47
     10.5.  Implications of signature randomizer . . . . . . . . . .  47
     10.6.  Policy for Deprecated and Acceptable Algorithms  . . . .  47
   11. Implementation Considerations . . . . . . . . . . . . . . . .  48
     11.1.  FIPS certification . . . . . . . . . . . . . . . . . . .  48
     11.2.  Backwards Compatibility  . . . . . . . . . . . . . . . .  49
     11.3.  Profiling down the number of options . . . . . . . . . .  49
     11.4.  External Pre-hashing . . . . . . . . . . . . . . . . . .  50
   12. References  . . . . . . . . . . . . . . . . . . . . . . . . .  52
     12.1.  Normative References . . . . . . . . . . . . . . . . . .  52
     12.2.  Informative References . . . . . . . . . . . . . . . . .  55
   Appendix A.  Approximate Key and Signature Sizes  . . . . . . . .  57
   Appendix B.  Component Algorithm Reference  . . . . . . . . . . .  59
   Appendix C.  Component AlgorithmIdentifiers for Public Keys and
           Signatures  . . . . . . . . . . . . . . . . . . . . . . .  61
   Appendix D.  Message Representative Examples  . . . . . . . . . .  69
   Appendix E.  Test Vectors . . . . . . . . . . . . . . . . . . . .  72
   Appendix F.  Intellectual Property Considerations . . . . . . . . 196
   Appendix G.  Contributors and Acknowledgements  . . . . . . . . . 196
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . . 197

1.  Changes in -07

   Interop-affecting changes:

   *  Fixed the ASN.1 module for the pk-CompositeSignature and sa-
      CompositeSignature to indicate no ASN.1 wrapping is used.

   Editorial changes:

   *  Added back MLDSA65-RSA3072-PKCS15-SHA512 which was missing from
      table 3, table 6 and the test vectors.

   *  Fixed a few problems with the test vectors (incorrect private
      keys).



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   *  Fixed a number of editorial issues.

2.  Introduction

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

   Unlike previous migrations between cryptographic algorithms, the
   decision of when to migrate and which algorithms to adopt is far from
   straightforward.  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 CVEs and other implementation flaws in the new
   implementations.

   Cautious implementers may opt to combine cryptographic algorithms in
   such a way that an attacker 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
   [I-D.ietf-pquip-pqt-hybrid-terminology].

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

   This specification defines a specific instantiation of the PQ/T
   Hybrid paradigm called "composite" where multiple cryptographic
   algorithms are combined to form a single signature algorithm
   presenting a single public key and signature value such that it can
   be treated as a single atomic algorithm at the protocol level; a
   property referred to as "protocol backwards compatibility" since it
   can be applied to protocols that are not explicitly hybrid-aware.
   Composite algorithms address algorithm strength uncertainty because
   the composite algorithm remains strong so long as one of its
   components remains strong.  Concrete instantiations of composite ML-
   DSA algorithms are provided based on ML-DSA, RSASSA-PKCS1-v1_5,



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   RSASSA-PSS, ECDSA, Ed25519, and Ed448.  Backwards compatibility in
   the sense of upgraded systems continuing to inter-operate with legacy
   systems is not directly covered in this specification, but is the
   subject of Section 11.2.

   Composite ML-DSA is applicable in any PKIX-related application that
   would otherwise use ML-DSA.

2.1.  Conventions and Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.  These words may also appear in this
   document in lower case as plain English words, absent their normative
   meanings.

   This specification is consistent with the terminology defined in
   [I-D.ietf-pquip-pqt-hybrid-terminology].  In addition, the following
   terminology is used throughout this specification:

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

   *COMPONENT / PRIMITIVE*: The words "component" or "primitive" are
   used interchangeably to refer to a 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", or a
   Hash such as "SHA256".

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

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

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

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

   *  || represents concatenation of two byte arrays.

   *  [:] represents byte array slicing.



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

2.2.  Composite Design Philosophy

   [I-D.ietf-pquip-pqt-hybrid-terminology] defines composites as:

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

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

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










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3.  Overview of the Composite ML-DSA Signature Scheme

   Composite ML-DSA is a Post-Quantum / Traditional hybrid signature
   scheme which combines ML-DSA as specified in [FIPS.204] and
   [I-D.ietf-lamps-dilithium-certificates] 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 randomized pre-hashing
   and prepends several domain separator values to the message prior to
   passing it to the component algorithms.  Composite ML-DSA achieves
   weak non-separability as well as several other security properties
   which are described in the Security Considerations in Section 10.

   Composite signature schemes are defined as cryptographic primitives
   that consist 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.  These algorithms are inspired by
   similar algorithms in [RFC9180].

   *  SerializePublicKey(mlkdsaPK, 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.






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   *  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(r, mldsaSig, tradSig) -> bytes: Produce a
      byte string encoding of the component signature values.  The
      randomizer r is explained in Section 3.1.

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

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

3.1.  Pre-hashing and Randomizer

   In [FIPS.204] NIST defines separate algorithms for pure and pre-
   hashed modes of ML-DSA, referred to as "ML-DSA" and "HashML-DSA"
   respectively.  This specification defines a single mode which is
   similar in construction to HashML-DSA with the addition of a pre-hash
   randomizer inspired by [BonehShoup].  See Section 10.5 for detailed
   discussion of the security properties of the randomized pre-hash.
   This design provides a compromised balance between performance and
   security.  Since pre-hashing is done at the composite level, "pure"
   ML-DSA is used as the underlying ML-DSA primitive.

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

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

   See Section 10.5 for a discussion of security implications of the
   randomized pre-hash.




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

3.2.  Prefix, Domain Separators and CTX

   When constructing the to-be-signed message representative M', several
   domain separator values are pre-pended to the message pre-hash prior
   to signing.

   M' :=  Prefix || Domain || len(ctx) || ctx || r || PH( M )

   First a fixed prefix string is pre-pended which is the byte encoding
   of the ASCII string "CompositeAlgorithmSignatures2025" which in hex
   is:

    436F6D706F73697465416C676F726974686D5369676E61747572657332303235

   Additional discussion of the prefix can be found in Section 10.4.

   Next, the Domain separator defined in Section 7.1 which is the DER
   encoding of the OID of the specific composite algorithm is
   concatenated with the length of the context in bytes, the context,
   the randomizer r, and finally the hash of the message to be signed.
   The Domain separator serves to bind the signature to the specific
   composite algorithm used.  The context string allows for applications
   to bind the signature to some application context.  The randomizer is
   described in detail in Section 3.1.

   Note that there are two different context strings ctx at play: the
   first is the application context that is passed in to Composite-ML-
   DSA.Sign and bound to the to-be-signed message M'.  The second is the
   ctx that is passed down into the underlying ML-DSA.Sign and here
   Composite ML-DSA itself is the application that we wish to bind and
   so the DER-encoded OID of the composite algorithm, called Domain, is
   used as the ctx for the underlying ML-DSA primitive.

4.  Composite ML-DSA Functions

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

4.1.  Key Generation

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



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   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-process or multi-threaded applications might choose to execute
   the key generation functions in parallel for better key generation
   performance.

   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, could be "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, _) = ML-DSA.KeyGen(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)



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            Figure 1: Composite-ML-DSA<OID>.KeyGen() -> (pk, sk)

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

   Note that in step 2 above, both component key generation 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.

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

4.2.  Sign

   The Sign() algorithm of Composite ML-DSA mirrors the construction of
   ML-DSA.Sign(sk, M, ctx) defined in Algorithm 3 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.

   See Section 3.1 for a discussion of the pre-hashed design and
   randomizer r.

   See Section 3.2 for a discussion on the domain separator and context
   values.

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




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   The following describes how to instantiate a Sign() function for a
   given Composite ML-DSA algorithm represented by <OID>.

 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, could be "ML-DSA-65".

   Trad    The underlying traditional algorithm and
           parameter set, for example "RSASSA-PSS with id-sha256"
           or "Ed25519".

   Prefix  The prefix String which is the byte encoding of the String
           "CompositeAlgorithmSignatures2025" which in hex is
       436F6D706F73697465416C676F726974686D5369676E61747572657332303235

   Domain  Domain separator value for binding the signature to the
           Composite ML-DSA OID. Additionally, the composite Domain
           is passed into the underlying ML-DSA primitive as the ctx.
           Domain values are defined in the "Domain Separator Values"
           section below.

   PH      The hash function to use for pre-hashing.


 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.



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      Randomize the message representative

         r = Random(32)
         M' :=  Prefix || Domain || len(ctx) || ctx || r
                                             || 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(mldsaSeed)

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

        mldsaSig = ML-DSA.Sign( mldsaSK, M', ctx=Domain )
        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(r, mldsaSig, tradSig)
       return s

         Figure 2: Composite-ML-DSA<OID>.Sign(sk, M, ctx) -> s

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

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










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4.3.  Verify

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

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

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

  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, could be "ML-DSA-65".

    Trad    The underlying traditional algorithm and
            parameter set, for example "RSASSA-PSS with id-sha256"
            or "Ed25519".

    Prefix  The prefix String which is the byte encoding of the String
            "CompositeAlgorithmSignatures2025" which in hex is
        436F6D706F73697465416C676F726974686D5369676E61747572657332303235

    Domain  Domain separator value for binding the signature to the
            Composite ML-DSA OID. Additionally, the composite Domain
            is passed into the underlying ML-DSA primitive as the ctx.
            Domain values are defined in the "Domain Separators"



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            section below.

    PH      The Message Digest Algorithm for pre-hashing. See
            section on pre-hashing the message below.

  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)
       (r, 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 || Domain || len(ctx) || ctx || r
                                          || PH( M )

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

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

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

        if all succeeded, then
           output "Valid signature"

      Figure 3: Composite-ML-DSA<OID>.Verify(pk, M, signature, ctx)





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

5.  Serialization

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

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

           +===========+============+=============+===========+
           | 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 Key and Signature Sizes in bytes

   For all serialization routines below, when these values are required
   to be carried in an ASN.1 structure, they are wrapped as described in
   Section 6.1.

   While ML-DSA has a single fixed-size representation for each of
   public key, private key (seed), and signature, the traditional
   component might allow multiple valid encodings; for example an
   elliptic curve public key might be validly encoded as either
   compressed or uncompressed [SEC1], or an RSA private key could be
   encoded in Chinese Remainder Theorem form [RFC8017].  In order to
   obtain interoperability, composite algorithms MUST use the following
   encodings of the underlying components:

   *  *ML-DSA*: MUST be encoded as specified in [FIPS.204], using a
      32-byte seed as the private key.






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   *  *RSA*: MUST be encoded with the (n,e) public key representation as
      specified in A.1.1 of [RFC8017] and the private key representation
      as specified in A.1.2 of [RFC8017].

   *  *ECDSA*: public key MUST be encoded as an ECPoint as specified in
      section 2.2 of [RFC5480], with both compressed and uncompressed
      keys supported.  For maximum interoperability, it is RECOMMENDED
      to use uncompressed points.  A signature MUST be DER encoded as an
      Ecdsa-Sig-Value as specified in section 2.2.3 of [RFC3279].

   *  *EdDSA*: MUST be encoded as per section 3 of [RFC8032].

   Even with fixed encodings for the traditional component, there may be
   slight differences in size of the encoded value due to, for example,
   encoding rules that drop leading zeroes.  See Appendix A for further
   discussion of encoded size of each composite algorithm.

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

5.1.  SerializePublicKey and DeserializePublicKey

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

























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   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

     Figure 4: Composite-ML-DSA.SerializePublicKey(mldsaPK, tradPK) ->
                                   bytes

   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>.

















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  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, could be "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)

      Figure 5: Composite-ML-DSA<OID>.DeserializePublicKey(bytes) ->
                            (mldsaPK, tradPK)






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5.2.  SerializePrivateKey and DeserializePrivateKey

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

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

   Explicit inputs:

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

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

   Implicit inputs:

     None

   Output:

     bytes   The encoded composite private key.


   Serialization Process:

     1. Combine and output the encoded private key.

        output mldsaSeed || tradSK

     Figure 6: Composite-ML-DSA.SerializePrivateKey(mldsaSeed, tradSK)
                                  -> bytes

   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
   parametrized.











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

   Explicit inputs:

     bytes   An encoded composite private key.

   Implicit inputs:

     That an ML-DSA private key is 32 bytes for all parameter sets.

   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.
        The length of an ML-DSA private key is always a 32 byte seed
        for all parameter sets.

        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)

         Figure 7: Composite-ML-DSA.DeserializePrivateKey(bytes) ->
                            (mldsaSeed, tradSK)

5.3.  SerializeSignatureValue and DeserializeSignatureValue

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









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

 Explicit inputs:

   r         The 32 byte signature randomizer.

   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 r || mldsaSig || tradSig

    Figure 8: Composite-ML-DSA.SerializeSignatureValue(r, mldsaSig,
                           tradSig) -> bytes

   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)
                                              -> (r, 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 to use, for example, could be "ML-DSA-65".



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  Output:

    r         The 32 byte signature randomizer.

    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 the randomizer r.

       r = bytes[:32]
       sigs = bytes[32:]  # truncate off the randomizer

    2. 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 = sigs[:2420]
            tradSig  = sigs[2420:]
          case ML-DSA-65:
            mldsaSig = sigs[:3309]
            tradSig  = sigs[3309:]
          case ML-DSA-87:
            mldsaSig = sigs[:4627]
            tradSig  = sigs[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 (r, mldsaSig, tradSig)

     Figure 9: Composite-ML-DSA<OID>.DeserializeSignatureValue(bytes)
                        -> (r, mldsaSig, tradSig)

6.  Use within X.509 and PKIX

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



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

6.1.  Encoding to DER

   The serialization routines presented in Section 5 produce raw binary
   values.  When these values are required to be carried within a DER-
   encoded message format such as an X.509's subjectPublicKey and
   signatureValue BIT STRING [RFC5280] or a CMS SignerInfo.signature
   OCTET STRING [RFC5652], then the composite value MUST be wrapped into
   a DER BIT STRING or OCTET STRING in the obvious ways.

   When a BIT STRING is required, the octets of the composite data value
   SHALL be used as the bits of the bit string, with the most
   significant bit of the first octet becoming the first bit, and so on,
   ending with the least significant bit of the last octet becoming the
   last bit of the bit string.

   When an OCTET STRING is required, the DER encoding of the composite
   data value SHALL be used directly.

6.2.  Key Usage Bits

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

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

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

   digitalSignature;
   nonRepudiation;
   keyCertSign; and
   cRLSign.

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





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   digitalSignature; and
   nonRepudiation;

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

6.3.  ASN.1 Definitions

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

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

   pk-CompositeSignature {OBJECT IDENTIFIER:id}
       PUBLIC-KEY ::= {
         IDENTIFIER id
         -- KEY without ASN.1 wrapping --
         PARAMS ARE absent
         CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign,
                                                                cRLSign}
       }

   sa-CompositeSignature{OBJECT IDENTIFIER:id,
      PUBLIC-KEY:publicKeyType }
         SIGNATURE-ALGORITHM ::=  {
            IDENTIFIER id
            -- VALUE without ASN.1 wrapping --
            PARAMS ARE absent
            PUBLIC-KEYS {publicKeyType}
         }

      Figure 10: 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:







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

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

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

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

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

            Figure 11: OneAsymmetricKey as defined in [RFC5958]

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

   Some applications might need to reconstruct the SubjectPublicKeyInfo
   or OneAsymmetricKey objects corresponding to each component key
   individually, for example if this is required for invoking the



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   underlying primitive.  Section 7 provides the necessary mapping
   between composite and their component algorithms for doing this
   reconstruction.

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

7.  Algorithm Identifiers

   This table summarizes the OID and the component algorithms for each
   Composite ML-DSA algorithm.

   EDNOTE: these are prototyping OIDs to be replaced by IANA.

   <CompSig> is equal to 2.16.840.1.114027.80.9.1

   +=============================+============+====+=======================+=============+
   |Composite Signature Algorithm|OID         |ML- |Trad                   |Pre-Hash     |
   |                             |            |DSA |                       |             |
   +=============================+============+====+=======================+=============+
   |id-MLDSA44-RSA2048-PSS-SHA256|<CompSig>.0 |ML-D|RSASSA-PSS with SHA256 |SHA256       |
   |                             |            |SA-4|                       |             |
   |                             |            |4   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-                          |<CompSig>.1 |ML-D|sha256WithRSAEncryption|SHA256       |
   |MLDSA44-RSA2048-PKCS15-SHA256|            |SA-4|                       |             |
   |                             |            |4   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA44-Ed25519-SHA512    |<CompSig>.2 |ML-D|Ed25519                |SHA512       |
   |                             |            |SA-4|                       |             |
   |                             |            |4   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA44-ECDSA-P256-SHA256 |<CompSig>.3 |ML-D|ecdsa-with-SHA256 with |SHA256       |
   |                             |            |SA-4|secp256r1              |             |
   |                             |            |4   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA65-RSA3072-PSS-SHA512|<CompSig>.4 |ML-D|RSASSA-PSS with SHA256 |SHA512       |
   |                             |            |SA-6|                       |             |
   |                             |            |5   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-                          |<CompSig>.5 |ML-D|sha256WithRSAEncryption|SHA512       |
   |MLDSA65-RSA3072-PKCS15-SHA512|            |SA-6|                       |             |
   |                             |            |5   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA65-RSA4096-PSS-SHA512|<CompSig>.6 |ML-D|RSASSA-PSS with SHA384 |SHA512       |
   |                             |            |SA-6|                       |             |
   |                             |            |5   |                       |             |



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   +-----------------------------+------------+----+-----------------------+-------------+
   |id-                          |<CompSig>.7 |ML-D|sha384WithRSAEncryption|SHA512       |
   |MLDSA65-RSA4096-PKCS15-SHA512|            |SA-6|                       |             |
   |                             |            |5   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA65-ECDSA-P256-SHA512 |<CompSig>.8 |ML-D|ecdsa-with-SHA256 with |SHA512       |
   |                             |            |SA-6|secp256r1              |             |
   |                             |            |5   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA65-ECDSA-P384-SHA512 |<CompSig>.9 |ML-D|ecdsa-with-SHA384 with |SHA512       |
   |                             |            |SA-6|secp384r1              |             |
   |                             |            |5   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA65-ECDSA-            |<CompSig>.10|ML-D|ecdsa-with-SHA256 with |SHA512       |
   |brainpoolP256r1-SHA512       |            |SA-6|brainpoolP256r1        |             |
   |                             |            |5   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA65-Ed25519-SHA512    |<CompSig>.11|ML-D|Ed25519                |SHA512       |
   |                             |            |SA-6|                       |             |
   |                             |            |5   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA87-ECDSA-P384-SHA512 |<CompSig>.12|ML-D|ecdsa-with-SHA384 with |SHA512       |
   |                             |            |SA-8|secp384r1              |             |
   |                             |            |7   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA87-ECDSA-            |<CompSig>.13|ML-D|ecdsa-with-SHA384 with |SHA512       |
   |brainpoolP384r1-SHA512       |            |SA-8|brainpoolP384r1        |             |
   |                             |            |7   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA87-Ed448-SHAKE256    |<CompSig>.14|ML-D|Ed448                  |SHAKE256/512*|
   |                             |            |SA-8|                       |             |
   |                             |            |7   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA87-RSA3072-PSS-SHA512|<CompSig>.15|ML-D|RSASSA-PSS with SHA384 |SHA512       |
   |                             |            |SA-8|                       |             |
   |                             |            |7   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA87-RSA4096-PSS-SHA512|<CompSig>.16|ML-D|RSASSA-PSS with SHA384 |SHA512       |
   |                             |            |SA-8|                       |             |
   |                             |            |7   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+
   |id-MLDSA87-ECDSA-P521-SHA512 |<CompSig>.17|ML-D|ecdsa-with-SHA512 with |SHA512       |
   |                             |            |SA-8|secp521r1              |             |
   |                             |            |7   |                       |             |
   +-----------------------------+------------+----+-----------------------+-------------+

               Table 2: ML-DSA Composite Signature Algorithms




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   *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.

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

   As the number of algorithms can be daunting to implementers, see
   Section 11.3 for a discussion of choosing a subset to support.

7.1.  Domain Separator Values

   Each Composite ML-DSA algorithm has a unique domain separator value
   which is used in constructing the message representative M' in the
   Composite-ML-DSA.Sign() (Section 4.2) and Composite-ML-DSA.Verify()
   (Section 4.3).  This helps protect against component signature values
   being removed from the composite and used out of context.

   The domain separator is simply the DER encoding of the OID.  The
   following table shows the HEX-encoded domain separator value for each
   Composite ML-DSA algorithm.




























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   +=======================================+==========================+
   |Composite Signature Algorithm          |Domain Separator (in Hex  |
   |                                       |encoding)                 |
   +=======================================+==========================+
   |id-MLDSA44-RSA2048-PSS-SHA256          |060B6086480186FA6B50090100|
   +---------------------------------------+--------------------------+
   |id-MLDSA44-RSA2048-PKCS15-SHA256       |060B6086480186FA6B50090101|
   +---------------------------------------+--------------------------+
   |id-MLDSA44-Ed25519-SHA512              |060B6086480186FA6B50090102|
   +---------------------------------------+--------------------------+
   |id-MLDSA44-ECDSA-P256-SHA256           |060B6086480186FA6B50090103|
   +---------------------------------------+--------------------------+
   |id-MLDSA65-RSA3072-PSS-SHA512          |060B6086480186FA6B50090104|
   +---------------------------------------+--------------------------+
   |id-MLDSA65-RSA3072-PKCS15-SHA512       |060B6086480186FA6B50090105|
   +---------------------------------------+--------------------------+
   |id-MLDSA65-RSA4096-PSS-SHA512          |060B6086480186FA6B50090106|
   +---------------------------------------+--------------------------+
   |id-MLDSA65-RSA4096-PKCS15-SHA512       |060B6086480186FA6B50090107|
   +---------------------------------------+--------------------------+
   |id-MLDSA65-ECDSA-P256-SHA512           |060B6086480186FA6B50090108|
   +---------------------------------------+--------------------------+
   |id-MLDSA65-ECDSA-P384-SHA512           |060B6086480186FA6B50090109|
   +---------------------------------------+--------------------------+
   |id-MLDSA65-ECDSA-brainpoolP256r1-SHA512|060B6086480186FA6B5009010A|
   +---------------------------------------+--------------------------+
   |id-MLDSA65-Ed25519-SHA512              |060B6086480186FA6B5009010B|
   +---------------------------------------+--------------------------+
   |id-MLDSA87-ECDSA-P384-SHA512           |060B6086480186FA6B5009010C|
   +---------------------------------------+--------------------------+
   |id-MLDSA87-ECDSA-brainpoolP384r1-SHA512|060B6086480186FA6B5009010D|
   +---------------------------------------+--------------------------+
   |id-MLDSA87-Ed448-SHAKE256              |060B6086480186FA6B5009010E|
   +---------------------------------------+--------------------------+
   |id-MLDSA87-RSA3072-PSS-SHA512          |060B6086480186FA6B5009010F|
   +---------------------------------------+--------------------------+
   |id-MLDSA87-RSA4096-PSS-SHA512          |060B6086480186FA6B50090110|
   +---------------------------------------+--------------------------+
   |id-MLDSA87-ECDSA-P521-SHA512           |060B6086480186FA6B50090111|
   +---------------------------------------+--------------------------+

          Table 3: ML-DSA Composite Signature Domain Separators

   EDNOTE: these domain separators are based on the prototyping OIDs
   assigned on the Entrust arc.  We will need to ask for IANA early
   assignment of these OIDs so that we can re-compute the domain
   separators over the final OIDs.




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7.2.  Rationale for choices

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

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

   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.

7.3.  RSASSA-PSS Parameters

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

   As with the other composite signature algorithms, when a composite
   algorithm OID involving RSA-PSS is used in an AlgorithmIdentifier,
   the parameters MUST be absent.

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






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                +=============================+===========+
                | RSASSA-PSS Parameter        | Value     |
                +=============================+===========+
                | MaskGenAlgorithm.algorithm  | id-mgf1   |
                +-----------------------------+-----------+
                | MaskGenAlgorithm.parameters | id-sha256 |
                +-----------------------------+-----------+
                | Message Digest Algorithm    | id-sha256 |
                +-----------------------------+-----------+
                | Salt Length in bits         | 256       |
                +-----------------------------+-----------+

                    Table 4: RSASSA-PSS 2048 Parameters

   When RSA-PSS is used at the 3072-bit or 4096-bit security level,
   RSASSA-PSS SHALL be instantiated with the following parameters:

                +=============================+===========+
                | RSASSA-PSS Parameter        | Value     |
                +=============================+===========+
                | MaskGenAlgorithm.algorithm  | id-mgf1   |
                +-----------------------------+-----------+
                | MaskGenAlgorithm.parameters | id-sha512 |
                +-----------------------------+-----------+
                | Message Digest Algorithm    | id-sha512 |
                +-----------------------------+-----------+
                | Salt Length in bits         | 512       |
                +-----------------------------+-----------+

                     Table 5: RSASSA-PSS 3072 and 4096
                                 Parameters

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

8.  ASN.1 Module

   <CODE STARTS>

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


   DEFINITIONS IMPLICIT TAGS ::= BEGIN

   EXPORTS ALL;



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   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 without ASN.1 wrapping --
         PARAMS ARE absent
         CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign,
                                                               cRLSign}
       }

   sa-CompositeSignature{OBJECT IDENTIFIER:id,
      PUBLIC-KEY:publicKeyType }
         SIGNATURE-ALGORITHM ::=  {
            IDENTIFIER id
            -- VALUE without ASN.1 wrapping --
            PARAMS ARE absent
            PUBLIC-KEYS {publicKeyType}
         }


   -- Composite ML-DSA which uses a PreHash Message

   -- TODO: OID to be replaced by IANA
   id-MLDSA44-RSA2048-PSS-SHA256 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 0 }

   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,



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          pk-MLDSA44-RSA2048-PSS-SHA256 }

   -- TODO: OID to be replaced by IANA
   id-MLDSA44-RSA2048-PKCS15-SHA256 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 1 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA44-Ed25519-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 2 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA44-ECDSA-P256-SHA256 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 3 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA65-RSA3072-PSS-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 4 }



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   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA65-RSA3072-PKCS15-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 5 }

   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 }

   -- TODO: OID to be replaced by IANA
   id-MLDSA65-RSA4096-PSS-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 6 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA65-RSA4096-PKCS15-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 7 }

   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 }



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   -- TODO: OID to be replaced by IANA
   id-MLDSA65-ECDSA-P256-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 8 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA65-ECDSA-P384-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 9 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 10 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA65-Ed25519-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 11 }

   pk-MLDSA65-Ed25519-SHA512 PUBLIC-KEY ::=



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     pk-CompositeSignature{ id-MLDSA65-Ed25519-SHA512}

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


   -- TODO: OID to be replaced by IANA
   id-MLDSA87-ECDSA-P384-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 12 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 13 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA87-Ed448-SHAKE256 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 14 }

   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 }



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   -- TODO: OID to be replaced by IANA
   id-MLDSA87-RSA3072-PSS-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 15 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA87-RSA4096-PSS-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 16 }

   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 }


   -- TODO: OID to be replaced by IANA
   id-MLDSA87-ECDSA-P521-SHA512 OBJECT IDENTIFIER ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      entrust(114027) algorithm(80) composite-mldsa(9) signature(1) 17 }

   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 |



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     sa-MLDSA65-RSA3072-PKCS15-SHA512 |
     sa-MLDSA65-RSA4096-PSS-SHA512 |
     sa-MLDSA65-RSA4096-PKCS15-SHA512 |
     sa-MLDSA65-ECDSA-P256-SHA512 |
     sa-MLDSA65-ECDSA-P384-SHA512 |
     sa-MLDSA65-ECDSA-brainpoolP256r1-SHA512 |
     sa-MLDSA65-Ed25519-SHA512 |
     sa-MLDSA87-ECDSA-P384-SHA512 |
     sa-MLDSA87-ECDSA-brainpoolP384r1-SHA512 |
     sa-MLDSA87-Ed448-SHAKE256 |
     sa-MLDSA87-RSA3072-PSS-SHA512 |
     sa-MLDSA87-RSA4096-PSS-SHA512 |
     sa-MLDSA87-ECDSA-P521-SHA512,
     ... }

   END

   <CODE ENDS>

9.  IANA Considerations

   IANA is requested to allocate a value from the "SMI Security for PKIX
   Module Identifier" registry [RFC7299] for the included ASN.1 module,
   and allocate values from "SMI Security for PKIX Algorithms" to
   identify the eighteen algorithms defined within.

9.1.  Object Identifier Allocations

   EDNOTE to IANA: OIDs will need to be replaced in both the ASN.1
   module and in Table 2.

9.1.1.  Module Registration

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

   *  Decimal: IANA Assigned - *Replace TBDMOD*

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

   *  References: This Document

9.1.2.  Object Identifier Registrations

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




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   *  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




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   *  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




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   *  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




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10.  Security Considerations

10.1.  Why Hybrids?

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

   Dual-algorithm security.  The general idea is that the data is
   protected by two algorithms such that an attacker would need to break
   both in order to compromise the data.  As with most of cryptography,
   this property is easy to state in general terms, but becomes more
   complicated when expressed in formalisms.  Section 10.2 goes into
   more detail here.  One common counter-argument against PQ/T hybrid
   signatures is that if an attacker 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.

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

10.2.  Non-separability, EUF-CMA and SUF

   The signature combiner defined in this specification is Weakly Non-
   Separable (WNS), as defined in
   [I-D.ietf-pquip-hybrid-signature-spectrums], since the forged message
   M’ will include the composite domain separator as evidence.  The
   prohibition on key reuse between composite and single-algorithm
   contexts discussed in Section 10.3 further strengthens the non-
   separability in practice, but does not achieve Strong Non-



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   Separability (SNS) since policy mechanisms such as this are outside
   the definition of SNS.

   Unforgeability properties are somewhat more nuanced.  We recall first
   the definitions of Existential Unforgeability under Chosen Message
   Attack (EUF-CMA) and Strong Unforgeability (SUF).  The classic EUF-
   CMA game is in reference to a pair of algorithms ( Sign(), Verify() )
   where the attacker has access to a signing oracle using the Sign()
   and must produce a message-signature pair (m', s') that is accepted
   by the verifier using Verify() and where m' was never signed by the
   oracle.  SUF is similar but requires only that (m', s') != (m, s) for
   any honestly-generated (m, s), i.e. that the attacker cannot
   construct a new signature to an already-signed message.

   The pair ( CompositeML-DSA.Sign(), CompositeML-DSA.Verify() ) is EUF-
   CMA secure so long as at least one component algorithm is EUF-CMA
   secure since any attempt to modify the message would cause the EUF-
   CMA secure component to fail its Verify() which in turn will cause
   CompositeML-DSA.Verify() to fail.

   Composite ML-DSA only achieves SUF security if both components are
   SUF secure, which is not a useful property; the argument is that if
   the first component algorithm is not SUF secure then by definition it
   admits at least one (m, s1') pair where s1' was not produced by the
   honest signer, and the attacker can then combine it with an honestly-
   signed (m, s2) signature produced by the second algorithm over the
   same message m to create (m, (s1', s2)) which violates SUF for the
   composite algorithm.  Of the traditional signature component
   algorithms used in this specification, only Ed25519 and Ed448 are SUF
   secure and therefore applications that require SUF security to be
   maintained even in the event that ML-DSA is broken SHOULD use it in
   composite with Ed25519 or Ed448.

   In addition to the classic EUF-CMA game, we also consider a “cross-
   protocol” version of the EUF-CMA game that is relevant to hybrids.
   Specifically, we want to consider a modified version of the EUF-CMA
   game where the attacker has access to either a signing oracle over
   the two component algorithms in isolation, Trad.Sign() and ML-
   DSA.Sign(), and attempts to fraudulently present them as a composite,
   or where the attacker has access to a composite signing oracle and
   then attempts to split the signature back into components and present
   them to either ML-DSA.Verify() or Trad.Verify().

   In the case of Composite ML-DSA, a specific message forgery exists
   for a cross-protocol EUF-CMA attack, namely introduced by the prefix
   construction used to construct the to-be-signed message
   representative M'.  This applies to use of individual component
   signing oracles with fraudulent presentation of the signature to a



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   composite verification oracle, and use of a composite signing oracle
   with fraudulent splitting of the signature for presentation to
   component verification oracle(s) of either ML-DSA.Verify() or
   Trad.Verify().  In the first case, an attacker with access to signing
   oracles for the two component algorithms can sign M’ and then
   trivially assemble a composite.  In the second case, the message M’
   (containing the composite domain separator) can be presented as
   having been signed by a standalone component algorithm.  However, use
   of the context string for domain separation enables Weak Non-
   Separability and auditable checks on hybrid use, which is deemed a
   reasonable trade-off.  Moreover and very importantly, the cross-
   protocol EUF-CMA attack in either direction is foiled if implementers
   strictly follow the prohibition on key reuse presented in
   Section 10.3 since there cannot exist simultaneously composite and
   non-composite signers and verifiers for the same keys.

10.2.1.  Implications of multiple encodings

   As noted in Section 5, this specification leaves some flexibility the
   choice of encoding of the traditional component.  As such it is
   possible for the same composite public key to carry multiple valid
   representations (mldsaPK, tradPK1) and (mldsaPK, tradPK2) where
   tradPK1 and tradPK2 are alternate encodings of the same key, for
   example compressed vs uncompressed EC points.  In theory alternate
   encodings of the traditional signature value are also possible,
   although the authors are not aware of any.

   In theory this introduces complications for EUF-CMA and SUF-CMA
   security proofs.  Implementers who are concerned with this SHOULD
   choose implementations of the traditional component that only accept
   a single encoding and performs appropriate length-checking, and
   reject composites which contain any other encodings.  This would
   reduce interoperability with other Composite ML-DSA implementations,
   but it is permitted by this specification.

10.3.  Key Reuse

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









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

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

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

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







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10.4.  Use of Prefix for attack mitigation

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

10.5.  Implications of signature randomizer

   The primary design motivation behind pre-hashing is to perform only a
   single pass over the potentially large input message M and to allow
   for optimizations in cases such as signing the same message digest
   with multiple different keys.

   Composite ML-DSA introduces a 32-byte randomizer into the signature
   representative M'.  This is to prevent a class of attacks unique to
   composites, which we define as a "mixed-key forgery attack": Take two
   composite keys (mldsaPK1, tradPK1) and (mldsaPK2, tradPK2) which do
   not share any key material and have them produce signatures (r1,
   mldsaSig1, tradSig1) and (r2, mldsaSig2, tradSig2) respectively over
   the same message M.  Consider whether it is possible to construct a
   forgery by swapping components and presenting (r, mldsaSig1,
   tradSig2) that verifies under a forged public key (mldsaPK1,
   tradPK2).  This forgery attack is blocked by the randomizer r so long
   as r1 != r2.

   A failure of randomness, for example r = 0, or a fixed value of 'r'
   effectively reduces r to a prefix that doesn't add value, but it is
   no worse than the security properties that Composite ML-DSA would
   have had without the randomizer.

   Introduction of the randomizer might introduce other beneficial
   security properties, but these are outside the scope of design
   consideration.

10.6.  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.




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

11.  Implementation Considerations

11.1.  FIPS certification

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

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

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

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

   The composite algorithm has been designed to treat the underlying
   primitives as "black-box implementations" and not impose any
   additional requirements on them that could require an existing
   implementation of an underlying primitive to run in a mode different
   from the one under which it was certified.  For example, the KeyGen
   defined in Section 4.1 invokes ML-DSA.KeyGen(seed) which might not be
   available in a cryptographic module running in FIPS-mode, but
   Section 4.1 is only a suggested implementation and the composite
   KeyGen MAY be implemented using a different available interface for
   ML-DSA.KeyGen.  Another example is pre-hashing; a pre-hash is
   inherent to RSA, ECDSA, and ML-DSA (mu), 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.




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   The signature randomizer r requires the composite implementation to
   have access to a cryptographic random number generator.  However, as
   noted in Section 10.5, this provides additional security properties
   on top of those provided by ML-DSA, RSA, ECDSA, and EdDSA, and
   failure of randomness does not compromise the Composite ML-DSA
   algorithm or the underlying primitives.  Therefore it should be
   possible to exclude this RNG invocation from the FIPS boundary if an
   implementation is not able to guarantee use of a FIPS-approved RNG.

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

11.2.  Backwards Compatibility

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

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

11.3.  Profiling down the number of options

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






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   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:

   id-MLDSA65-ECDSA-P256-SHA512

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

   id-MLDSA65-RSA3072-PSS-SHA512

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

   id-MLDSA87-ECDSA-P384-SHA512

11.4.  External Pre-hashing

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

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














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   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

               Figure 12: Generation of the external pre-hash


























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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, could be "ML-DSA-65".

  Trad      The underlying traditional algorithm and
            parameter set, for example "RSASSA-PSS with id-sha256"
            or "Ed25519".

  Prefix    The prefix String which is the byte encoding of the String
            "CompositeAlgorithmSignatures2025" which in hex is
            436F6D706F73697465416C676F726974686D5369676E61747572657332303235

  Domain    Domain separator value for binding the signature to the
            Composite OID. Additionally, the composite Domain is passed into
            the underlying ML-DSA primitive as the ctx.
            Domain values are defined in the "Domain Separators" 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.

     Figure 13: Suggested implementation of external pre-hashing

12.  References

12.1.  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>.



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   [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>.







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   [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>.

   [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>.

   [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>.



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   [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.

12.2.  Informative References

   [ANSSI2024]
              French Cybersecurity Agency (ANSSI), Federal Office for
              Information Security (BSI), Netherlands National
              Communications Security Agency (NLNCSA), and Swedish
              National Communications Security Authority, Swedish Armed
              Forces, "Position Paper on Quantum Key Distribution",
              n.d., <https://cyber.gouv.fr/sites/default/files/document/
              Quantum_Key_Distribution_Position_Paper.pdf>.

   [Bindel2017]
              Bindel, N., Herath, U., McKague, M., and D. Stebila,
              "Transitioning to a quantum-resistant public key
              infrastructure", 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>.





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   [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-lamps-dilithium-certificates]
              Massimo, J., Kampanakis, P., Turner, S., and B.
              Westerbaan, "Internet X.509 Public Key Infrastructure -
              Algorithm Identifiers for the Module-Lattice-Based Digital
              Signature Algorithm (ML-DSA)", Work in Progress, Internet-
              Draft, draft-ietf-lamps-dilithium-certificates-11, 22 May
              2025, <https://datatracker.ietf.org/doc/html/draft-ietf-
              lamps-dilithium-certificates-11>.

   [I-D.ietf-pquip-hybrid-signature-spectrums]
              Bindel, N., Hale, B., Connolly, D., and F. D, "Hybrid
              signature spectrums", Work in Progress, Internet-Draft,
              draft-ietf-pquip-hybrid-signature-spectrums-06, 9 January
              2025, <https://datatracker.ietf.org/doc/html/draft-ietf-
              pquip-hybrid-signature-spectrums-06>.

   [I-D.ietf-pquip-pqt-hybrid-terminology]
              D, F., P, M., and B. Hale, "Terminology for Post-Quantum
              Traditional Hybrid Schemes", Work in Progress, Internet-
              Draft, draft-ietf-pquip-pqt-hybrid-terminology-06, 10
              January 2025, <https://datatracker.ietf.org/doc/html/
              draft-ietf-pquip-pqt-hybrid-terminology-06>.

   [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>.






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   [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>.

   [RFC7299]  Housley, R., "Object Identifier Registry for the PKIX
              Working Group", RFC 7299, DOI 10.17487/RFC7299, July 2014,
              <https://www.rfc-editor.org/info/rfc7299>.

   [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>.

   [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>.

Appendix A.  Approximate Key and Signature Sizes

   The sizes listed below are approximate: these values are measured
   from the test vectors, however, 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 in size between 3 and n
      - 1 [RFC8017].

   *  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.




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   By contrast, ML-DSA values are always fixed size, so composite values
   can always be correctly de-serialized based on the size of the ML-DSA
   component.  It is expected for the size values of RSA and ECDSA
   variants to fluctuate by a few bytes even between subsequent runs of
   the same composite implementation.

   Implementations MUST NOT perform strict length checking based on the
   values in this table except for ML-DSA + EdDSA; since these
   algorithms produce fixed-size outputs, the values in the table below
   for these variants MAY be treated as constants.

   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  |1222   |2708     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA44-RSA2048-PKCS15-SHA256        |1582  |1223   |2708     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA44-Ed25519-SHA512               |1344  |64     |2516     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA44-ECDSA-P256-SHA256            |1377  |153    |2522     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-RSA3072-PSS-SHA512           |2350  |1799   |3725     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-RSA3072-PKCS15-SHA512        |2350  |1800   |3725     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-RSA4096-PSS-SHA512           |2478  |2380   |3853     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-RSA4096-PKCS15-SHA512        |2478  |2380   |3853     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-ECDSA-P256-SHA512            |2017  |153    |3412     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-ECDSA-P384-SHA512            |2049  |199    |3444     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 |2017  |154    |3411     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-Ed25519-SHA512               |1984  |64     |3405     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-ECDSA-P384-SHA512            |2689  |199    |4763     |



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   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 |2689  |203    |4761     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-Ed448-SHAKE256               |2649  |89     |4773     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-RSA3072-PSS-SHA512           |2990  |1801   |5043     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-RSA4096-PSS-SHA512           |3118  |2381   |5171     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-ECDSA-P521-SHA512            |2725  |255    |4798     |
   +-----------------------------------------+------+-------+---------+

           Table 6: Approximate 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.

































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    +=========================+=========================+=============+
    | 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     |[RFC5758],   |
    |                         |                         |[RFC5480],   |
    |                         |                         |[SEC1],      |
    |                         |                         |[X9.62_2005] |
    +-------------------------+-------------------------+-------------+
    | ecdsa-with-SHA384       | 1.2.840.10045.4.3.3     |[RFC5758],   |
    |                         |                         |[RFC5480],   |
    |                         |                         |[SEC1],      |
    |                         |                         |[X9.62_2005] |
    +-------------------------+-------------------------+-------------+
    | ecdsa-with-SHA512       | 1.2.840.10045.4.3.4     |[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 7: Component Signature Algorithms used in Composite
                               Constructions











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     +==================+=======================+===================+
     | 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 8: Elliptic Curves used in Composite Constructions

         +=============+=========================+===============+
         | HashID      | OID                     | Specification |
         +=============+=========================+===============+
         | id-sha256   | 2.16.840.1.101.3.4.2.1  | [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 9: Hash algorithms used in pre-hashed Composite
                     Constructions to build PH element

Appendix C.  Component AlgorithmIdentifiers for Public Keys and
             Signatures

   The following sections list explicitly the DER encoded
   AlgorithmIdentifier that MUST be used when reconstructing
   SubjectPublicKeyInfo and Signature Algorithm objects for each
   component algorithm type, which may be required for example if
   cryptographic library requires the public key in this form in order
   to process each component algorithm.  The public key BIT STRING
   should be taken directly from the respective component of the
   Composite ML-DSA public key.







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   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*

   AlgorithmIdentifier of Public Key







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   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 3072 & 4096*

   AlgorithmIdentifier of Public Key









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   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-sha512,   -- (2.16.840.1.101.3.4.2.3)
          parameters NULL
          },
        AlgorithmIdentifier ::= {
          algorithm id-mgf1,       -- (1.2.840.113549.1.1.8)
          parameters AlgorithmIdentifier ::= {
            algorithm id-sha512,   -- (2.16.840.1.101.3.4.2.3)
            parameters NULL
            }
          },
        saltLength 64
        }
      }

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

   *RSASSA-PKCS1-v1_5 2048*

   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



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   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 3072 & 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 sha512WithRSAEncryption,   -- (1.2.840.113549.1.1.13)
       parameters NULL
       }

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

   *ECDSA NIST P256*

   AlgorithmIdentifier of Public Key















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   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










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   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













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   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










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   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 3.2.





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   *  Domain is the specific domain separator for this composite
      algorithm, as defined in Section 7.1.

   *  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.

   *  r is a random 32-byte value chosen by the signer.

   *  PH(r||M) is the output of hashing the randomizer together with 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.
































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

  # Inputs:

  M: 00010203040506070809
  ctx: <empty>

  # Components of M':

  Prefix:
  436f6d706f73697465416c676f726974686d5369676e61747572657332303235

  Domain: 060b6086480186fa6b50090108

  len(ctx): 00

  ctx: <empty>
  r: 9b45a9e08f38cd31f7eaff5a05b572c763b81f2b6a802e3a4d1e0d86de049c22
  PH(M): 0f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f9a3
  f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f903533


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

  M': 436f6d706f73697465416c676f726974686d5369676e6174757265733230323506
  0b6086480186fa6b50090108009b45a9e08f38cd31f7eaff5a05b572c763b81f2b6a80
  2e3a4d1e0d86de049c220f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3
  523a20974f9a3f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c34
  2f903533

   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'.















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

  # Inputs:

  M: 00010203040506070809
  ctx: 0813061205162623

  # Components of M':

  Prefix:
  436f6d706f73697465416c676f726974686d5369676e61747572657332303235

  Domain: 060b6086480186fa6b50090108

  len(ctx): 08

  ctx: 0813061205162623

  r: ef7fcb00232f6229aee169e398d78ecc642ac02a7bc82bbe168021be945b4653
  PH(M): 0f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f9a3
  f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f903533


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

  M': 436f6d706f73697465416c676f726974686d5369676e6174757265733230323506
  0b6086480186fa6b50090108080813061205162623ef7fcb00232f6229aee169e398d7
  8ecc642ac02a7bc82bbe168021be945b46530f89ee1fcb7b0a4f7809d1267a02971900
  4c5a5e5ec323a7c3523a20974f9a3f202f56fadba4cd9e8d654ab9f2e96dc5c795ea17
  6fa20ede8d854c342f903533

Appendix E.  Test Vectors

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

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

   Within each test case there are the following values:

   *  tcId the name of the algorithm.

   *  pk the verification public key.

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



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   *  sk the raw signature private key.

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

   *  s the signature value.

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

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

   2.  Validate the self-signed certificate x5c.

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

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

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

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

   TODO: lock this to a specific commit.

   {
   "m":
   "VGhlIHF1aWNrIGJyb3duIGZveCBqdW1wcyBvdmVyIHRoZSBsYXp5IGRvZy4=",

   "tests": [
   {
   "tcId": "id-ML-DSA-44",
   "pk": "hkOk8B4qwY0tx6meGcqaSVRZ
   IeA9v3ceRDStgZuu/C1PCUKjQkTdjCYmc475HNVvveHJjKGo7aBO6VnDgd0vs9p8chiw
   QUnObVW+MpIBwKTVEaBi6BXSBt7Q2VfvZO8I4MEGV1gY0OEiTdu6Vb+JBCakJUgBlDg+
   HSiRUI5AYbOt77YP8/XrxUx2lsAIw1bKUyVMwJKuolbNNuJQ97M6sxqc6fwkXvVvOOvH
   p8bQBTT/kTaAqO4rSFnGE9fAVZCRlaG1bIIhxakL5xoMwAv48LdAYBGqBCMwW0JGsURO
   E1+QjaFxe7VE5ovdpcC8nV7HZZz7Jh38AquH7dd3qkmD0UsBgiGr+B9myMVVXgKtWZXt
   nWT9Xy1A+LtPTAmsGT1AK0feHgv6vLrbGAd6zoVvwRIB6OJJZzLBCH3i/vH+/CuB+SPY
   4Loy8y7fH3VTmWyovvZahzhrw2SqH9GflY2QvuAIjjHeb+WIGOc0aTpfGzLZk66Bn3QX
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   Rx3QgpaaGqyYFfUSu0wgTzpq0wHKQMseM8PnlAGx/u5FwLaIqpx4kAHDEDOZd93tH5Fy



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Ounsworth, et al.        Expires 8 January 2026                [Page 75]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 76]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 77]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 78]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 79]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 80]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 81]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 82]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 83]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 84]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 85]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 86]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 87]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 88]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 89]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 90]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 91]

Internet-Draft              Composite ML-DSA                   July 2025


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   {
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Ounsworth, et al.        Expires 8 January 2026                [Page 92]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 93]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 94]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 95]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 96]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 97]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 98]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026                [Page 99]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 100]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 101]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 102]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 103]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 104]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 105]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 106]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 107]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 108]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 109]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 110]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 111]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 112]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 113]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 114]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 115]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 116]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 117]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 118]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 119]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 120]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 121]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 122]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 123]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 124]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 125]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 126]

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Ounsworth, et al.        Expires 8 January 2026               [Page 127]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 128]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 129]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 130]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 131]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 132]

Internet-Draft              Composite ML-DSA                   July 2025


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   },
   {
   "tcId":
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Ounsworth, et al.        Expires 8 January 2026               [Page 133]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 134]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 135]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 136]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 137]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 138]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 139]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 140]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 141]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 142]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 143]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 144]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 145]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 146]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 147]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 148]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 149]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 150]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 151]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 152]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 153]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 154]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 155]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 156]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 157]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 158]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 159]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 160]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 161]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 162]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 163]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 164]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 165]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 166]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 167]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 168]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 169]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 170]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 171]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 172]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 173]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 174]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 175]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 176]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 177]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 178]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 179]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 180]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 181]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 182]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 183]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 184]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 185]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 186]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 187]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 188]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 189]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 190]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 191]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 192]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 193]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 194]

Internet-Draft              Composite ML-DSA                   July 2025


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Ounsworth, et al.        Expires 8 January 2026               [Page 195]

Internet-Draft              Composite ML-DSA                   July 2025


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   }
   ]
   }

Appendix F.  Intellectual Property Considerations

   The following IPR Disclosure relates to this draft:

   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), Daniel Van Geest (CryptoNext), Dr.
   Britta Hale (Naval Postgraduade School), Tim Hollebeek (Digicert),
   Panos Kampanakis (Amazon), Chris A.  Wood (Apple), Christopher D.



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   Wood (Apple), Sophie Schmieg (Google), Bas Westerbaan (Cloudflare),
   Deirdre Connolly (SandboxAQ), Richard Kisley (IBM), Piotr Popis
   (Enigma), François Rousseau, Falko Strenzke, Alexander Ralien
   (Siemens), José Ignacio Escribano, Jan Oupický, 陳志華 (Abel C.  H.
   Chen, Chunghwa Telecom), 林邦曄 (Austin Lin, Chunghwa Telecom), Zhao
   Peiduo (Seventh Sense AI), Phil Hallin (Microsoft), Samuel Lee
   (Microsoft), Alicja Kario (Red Hat), Jean-Pierre Fiset (Crypto4A),
   Varun Chatterji (Seventh Sense AI), Mojtaba Bisheh-Niasar and Douglas
   Stebila (University of Waterloo).

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

   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



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   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





































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