



LAMPS                                                       M. Ounsworth
Internet-Draft                                                   J. Gray
Intended status: Standards Track                                 Entrust
Expires: 13 April 2026                                           M. Pala
                                                             OpenCA Labs
                                                            J. Klaussner
                                                    Bundesdruckerei GmbH
                                                              S. Fluhrer
                                                           Cisco Systems
                                                         10 October 2025


      Composite ML-DSA for use in X.509 Public Key Infrastructure
                 draft-ietf-lamps-pq-composite-sigs-12

Abstract

   This document defines combinations of ML-DSA [FIPS.204] in hybrid
   with traditional algorithms RSASSA-PKCS1-v1.5, RSASSA-PSS, ECDSA,
   Ed25519, and Ed448.  These combinations are tailored to meet
   regulatory guidelines.  Composite ML-DSA is applicable in
   applications that uses X.509 or PKIX data structures that accept ML-
   DSA, but where the operator wants extra protection against breaks or
   catastrophic bugs in ML-DSA, and where EUF-CMA-level security is
   acceptable.

About This Document

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

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

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

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

Status of This Memo

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




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Table of Contents

   1.  Changes since -07 (WGLC)  . . . . . . . . . . . . . . . . . .   3
   2.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   5
     2.1.  Conventions and Terminology . . . . . . . . . . . . . . .   7
     2.2.  Composite Design Philosophy . . . . . . . . . . . . . . .   8
   3.  Overview of the Composite ML-DSA Signature Scheme . . . . . .   9
     3.1.  Pre-hashing . . . . . . . . . . . . . . . . . . . . . . .  10
     3.2.  Prefix, Label and CTX . . . . . . . . . . . . . . . . . .  11
   4.  Composite ML-DSA Functions  . . . . . . . . . . . . . . . . .  12
     4.1.  Key Generation  . . . . . . . . . . . . . . . . . . . . .  12
     4.2.  Sign  . . . . . . . . . . . . . . . . . . . . . . . . . .  14
     4.3.  Verify  . . . . . . . . . . . . . . . . . . . . . . . . .  16
   5.  Serialization . . . . . . . . . . . . . . . . . . . . . . . .  19
     5.1.  SerializePublicKey and DeserializePublicKey . . . . . . .  20
     5.2.  SerializePrivateKey and DeserializePrivateKey . . . . . .  23
     5.3.  SerializeSignatureValue and DeserializeSignatureValue . .  24
   6.  Use within X.509 and PKIX . . . . . . . . . . . . . . . . . .  27
     6.1.  Encoding to DER . . . . . . . . . . . . . . . . . . . . .  27
     6.2.  Key Usage Bits  . . . . . . . . . . . . . . . . . . . . .  27
     6.3.  ASN.1 Definitions . . . . . . . . . . . . . . . . . . . .  28
   7.  Algorithm Identifiers and Parameters  . . . . . . . . . . . .  30



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     7.1.  RSASSA-PSS Parameters . . . . . . . . . . . . . . . . . .  37
     7.2.  Rationale for choices . . . . . . . . . . . . . . . . . .  38
   8.  ASN.1 Module  . . . . . . . . . . . . . . . . . . . . . . . .  39
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  46
     9.1.  Object Identifier Allocations . . . . . . . . . . . . . .  46
       9.1.1.  Module Registration . . . . . . . . . . . . . . . . .  46
       9.1.2.  Object Identifier Registrations . . . . . . . . . . .  46
   10. Security Considerations . . . . . . . . . . . . . . . . . . .  49
     10.1.  Why Hybrids? . . . . . . . . . . . . . . . . . . . . . .  50
     10.2.  EUF-CMA, SUF-CMA and non-separability  . . . . . . . . .  50
       10.2.1.  EUF-CMA  . . . . . . . . . . . . . . . . . . . . . .  51
       10.2.2.  SUF-CMA  . . . . . . . . . . . . . . . . . . . . . .  52
       10.2.3.  Non-separability . . . . . . . . . . . . . . . . . .  52
     10.3.  Key Reuse  . . . . . . . . . . . . . . . . . . . . . . .  53
     10.4.  Use of Prefix for attack mitigation  . . . . . . . . . .  54
     10.5.  Policy for Deprecated and Acceptable Algorithms  . . . .  55
   11. Implementation Considerations . . . . . . . . . . . . . . . .  55
     11.1.  FIPS certification . . . . . . . . . . . . . . . . . . .  55
     11.2.  Backwards Compatibility  . . . . . . . . . . . . . . . .  56
     11.3.  Profiling down the number of options . . . . . . . . . .  57
     11.4.  External Pre-hashing . . . . . . . . . . . . . . . . . .  58
   12. References  . . . . . . . . . . . . . . . . . . . . . . . . .  59
     12.1.  Normative References . . . . . . . . . . . . . . . . . .  59
     12.2.  Informative References . . . . . . . . . . . . . . . . .  62
   Appendix A.  Maximum Key and Signature Sizes  . . . . . . . . . .  64
   Appendix B.  Component Algorithm Reference  . . . . . . . . . . .  66
   Appendix C.  Component AlgorithmIdentifiers for Public Keys and
           Signatures  . . . . . . . . . . . . . . . . . . . . . . .  68
   Appendix D.  Message Representative Examples  . . . . . . . . . .  76
   Appendix E.  Test Vectors . . . . . . . . . . . . . . . . . . . .  78
   Appendix F.  Intellectual Property Considerations . . . . . . . . 201
   Appendix G.  Contributors and Acknowledgements  . . . . . . . . . 201
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . . 202

1.  Changes since -07 (WGLC)

   Interop-affecting changes:

   *  Removed the randomizer, reverting the signature combiner
      construction to be similar to the HashComposite construction from
      -05.

   *  Fixed the ASN.1 module for the pk-CompositeSignature and sa-
      CompositeSignature to indicate no ASN.1 wrapping is used.  This
      simply clarifies the intended encoding but could be an interop-
      affecting change for implementations that built encoders /
      decoders from the ASN.1 and ended up with a non-intended encoding.




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   *  Aligned the hash function used for the RSA component to the RSA
      key size (Thanks Dan!).

   *  Changed the OID-based Domain Separators into HPKE-style signature
      label strings to match draft-irtf-cfrg-concrete-hybrid-kems-00.

   *  Updated to new prototype OIDs since it is not binary compatible
      with the previous release.

   *  Dan Van Geest correctly pointed out that in ECPrivateKey
      (RFC5915), the parameters are not optional.  They have been added
      to the private keys in the test vectors.

   *  The Ed25519 and Ed448 private keys had been wrapped in OCTET
      STRING to match CurvePrivateKey (RFC8410).  This has been changed
      to 32/57 byte raw.

   Editorial changes:

   *  Incorporated the feedback from IETF 123, clarifying the pubic,
      private key and signature encodings.

   *  Many minor editorial fixes based on comments from the working
      group.

   *  Adjusted the Security Considerations about EUF-CMA and Non-
      Separability to match the removal of the randomizer.

   *  Clarified that the ECDSA public key is raw X9.62 with no OCTET
      STRING wrapping.  Test vectors were already correct.

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

   *  ML-DSA:

      -  pub key, priv key, sig value: Raw, according to FIPS 204.  Test
         vectors appear to match.

   *  RSA:

      -  pub key: ASN.1 RSAPublicKey.  Test vectors appear to match
         (manually inspected "id-MLDSA44-RSA2048-PSS-SHA256").

      -  priv key: RSAPrivateKey (CRT).  Test vectors appear to match
         (manually inspected "id-MLDSA44-RSA2048-PSS-SHA256").






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      -  sig value: length of sig for "id-MLDSA44-RSA2048-PSS-SHA256"
         and "id-MLDSA44-RSA2048-PKCS15-SHA256" verified to be 256
         bytes, format hard to manually inspect.

   *  ECDSA: Inspecting test vectors for "id-MLDSA44-ECDSA-P256-SHA256"

      -  pub key: The wording of the pub key format in Section 2.2 of
         RFC5480 is extremely confusing in how it would apply outside of
         a SubjectPublicKeyInfo.  The Composite author's interpretation
         was for it to be raw X9.62, which is what is already in the
         test vectors: verified to be raw X9.62 with a leading byte of
         0x04 (uncompressed).  Normative text in Section 5 is incorrect
         and has been changed.

      -  priv key: This is the ASN.1 structure ECPrivateKey [RFC5915] as
         intended, however, as Dan Van Geest points out, the parameters
         field, while marked OPTIONAL is actually required by Section 3
         of RFC5915.  That means the private keys here are invalid.
         This has been corrected in the test vectors.

      -  sig value: This is an ASN.1 Ecdsa-Sig-Value [RFC3279] as
         intended.

   *  EdDSA:

      -  pub key: 32 byte raw.

      -  priv key: Had been wrapped in OCTET STRING to match
         CurvePrivateKey (RFC8410).  This has been changed to 32/57 byte
         raw.

      -  sig value: 64 byte raw.

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.





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

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

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

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

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



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   systems is not directly covered in this specification, but is the
   subject of Section 11.2.  The idea of a composite was first presented
   in [Bindel2017].

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

2.1.  Conventions and Terminology

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

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

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

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

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

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

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

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

   *  || represents concatenation of two byte arrays.

   *  [:] represents byte array slicing.



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

2.2.  Composite Design Philosophy

   [RFC9794] defines composites as:

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

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

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

   In terms of security properties, Composite ML-DSA will be EUF-CMA
   secure if at least one of its component algorithms is EUF-CMA secure
   and the message hash PH is collision resistant.  SUF-CMA security of
   Composite ML-DSA is more complicated.  While some of the algorithm
   combinations defined in this specification are likely to be SUF-CMA
   secure against classical adversaries, none are SUF-CMA secure against



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   a quantum adversary.  This means that replacing an ML-DSA signature
   with a Composite ML-DSA signature is a reduction in security and
   should not be used in applications sensitive to the difference
   between SUF-CMA and EUF-CMA security.  Composite ML-DSA is NOT
   RECOMMENDED for use in applications where it is has not been shown
   that EUF-CMA is acceptable.  Further discussion can be found in
   Section 10.2.

3.  Overview of the Composite ML-DSA Signature Scheme

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

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

   *  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.







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

   *  SerializePublicKey(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.

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

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

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

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

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

3.1.  Pre-hashing

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

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




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

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

3.2.  Prefix, Label and CTX

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

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

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

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

   len(ctx):  A single unsigned byte encoding the length of the context.

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

   PH( M ):  The hash of the message to be signed.

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

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




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

4.  Composite ML-DSA Functions

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

4.1.  Key Generation

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

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

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






















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

   Explicit inputs:

     None

   Implicit inputs mapped from <OID>:

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

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

   Output:

     (pk, sk)   The composite key pair.


   Key Generation Process:

     1. Generate component keys

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

     2. Check for component key gen failure

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

     3. Output the composite public and private keys

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

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









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

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

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

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

4.2.  Sign

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






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

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

Explicit inputs:

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

  M       The message to be signed, an octet string.

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

Implicit inputs mapped from <OID>:

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

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

  Prefix  The prefix octet string.

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

  PH      The function used to pre-hash M.


Output:

  s       The composite signature value.


Signature Generation Process:

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



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

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

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

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

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

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

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

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

  6. Output the encoded composite signature value.

      s = SerializeSignatureValue(mldsaSig, tradSig)
      return s

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

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

4.3.  Verify

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



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

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

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

Explicit inputs:

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

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

  s       A composite signature value to be verified.

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

Implicit inputs mapped from <OID>:

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

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

  Prefix  The prefix octet string.

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

  PH      The function used to pre-hash M.

Output:

  Validity (bool)   "Valid signature" (true) if the composite



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                    signature is valid, "Invalid signature"
                    (false) otherwise.

Signature Verification Process:

  1. If len(ctx) > 255
       return error

  2. Separate the keys and signatures

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

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

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

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

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

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

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

      if all succeeded, then
         output "Valid signature"

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











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5.  Serialization

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

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

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

                          Table 1: ML-DSA Sizes

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

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

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






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

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

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

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

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

5.1.  SerializePublicKey and DeserializePublicKey

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
















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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

   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 "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)






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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

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

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














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

   Explicit inputs:

     bytes      An encoded composite private key.

   Implicit inputs:

     None

   Output:

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

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

   Deserialization Process:

     1. Parse each constituent encoded key.

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

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

     2. Output the component private keys

        output (mldsaSeed, tradSK)

5.3.  SerializeSignatureValue and DeserializeSignatureValue

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














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

   Explicit inputs:

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

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

   Implicit inputs:

     None

   Output:

     bytes     The encoded composite signature value.

   Serialization Process:

     1. Combine and output the encoded composite signature

        output mldsaSig || tradSig

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

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




















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

   Explicit inputs:

     bytes   An encoded composite signature value.

   Implicit inputs mapped from <OID>:

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

   Output:

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

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

   Deserialization Process:

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

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

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

     3. Output the component signature values

        output (mldsaSig, tradSig)







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6.  Use within X.509 and PKIX

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

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

6.1.  Encoding to DER

   The serialization routines presented in Section 5 produce raw binary
   values.  When these values are required to be carried within a DER-
   encoded message format such as an X.509's subjectPublicKey and
   signatureValue BIT STRING [RFC5280] or a OneAsymmetricKey.privateKey
   OCTET STRING [RFC5958], then the BIT STRING or OCTET STRING contains
   this raw byte string encoding of the public key.

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

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

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

6.2.  Key Usage Bits

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

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

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






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   digitalSignature;
   nonRepudiation;
   keyCertSign; and
   cRLSign.

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

   digitalSignature;
   nonRepudiation; and
   cRLSign.

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

6.3.  ASN.1 Definitions

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

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





















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

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

      Figure 1: ASN.1 Object Information Classes for Composite ML-DSA

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

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

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

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

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










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

             Figure 2: OneAsymmetricKey as defined in [RFC5958]

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

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

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

7.  Algorithm Identifiers and Parameters

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

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






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

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

   EDNOTE: the OIDs listed below are prototyping OIDs defined in
   Entrust's 2.16.840.1.114027.80.9.1 arc but will be replaced by IANA.

   *  id-MLDSA44-RSA2048-PSS-SHA256

      -  OID: 2.16.840.1.114027.80.9.1.20

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

      -  Pre-Hash function (PH): SHA256

      -  ML-DSA variant: ML-DSA-44

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: id-RSASSA-PSS

         o  RSA size: 2048

         o  RSASSA-PSS parameters: See Table 2

   *  id-MLDSA44-RSA2048-PKCS15-SHA256

      -  OID: 2.16.840.1.114027.80.9.1.21

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

      -  Pre-Hash function (PH): SHA256

      -  ML-DSA variant: ML-DSA-44

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: sha256WithRSAEncryption

         o  RSA size: 2048

   *  id-MLDSA44-Ed25519-SHA512




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      -  OID: 2.16.840.1.114027.80.9.1.22

      -  Label: COMPSIG-MLDSA44-Ed25519-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-44

      -  Traditional Algorithm: Ed25519

         o  Traditional Signature Algorithm: id-Ed25519

   *  id-MLDSA44-ECDSA-P256-SHA256

      -  OID: 2.16.840.1.114027.80.9.1.23

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

      -  Pre-Hash function (PH): SHA256

      -  ML-DSA variant: ML-DSA-44

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA256

         o  ECDSA curve: secp256r1

   *  id-MLDSA65-RSA3072-PSS-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.24

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

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: id-RSASSA-PSS

         o  RSA size: 3072

         o  RSASSA-PSS parameters: See Table 2

   *  id-MLDSA65-RSA3072-PKCS15-SHA512




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      -  OID: 2.16.840.1.114027.80.9.1.25

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

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: sha256WithRSAEncryption

         o  RSA size: 3072

   *  id-MLDSA65-RSA4096-PSS-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.26

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

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: id-RSASSA-PSS

         o  RSA size: 4096

         o  RSASSA-PSS parameters: See Table 3

   *  id-MLDSA65-RSA4096-PKCS15-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.27

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

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: sha384WithRSAEncryption

         o  RSA size: 4096




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   *  id-MLDSA65-ECDSA-P256-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.28

      -  Label: COMPSIG-MLDSA65-P256-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA256

         o  ECDSA curve: secp256r1

   *  id-MLDSA65-ECDSA-P384-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.29

      -  Label: COMPSIG-MLDSA65-P384-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA384

         o  ECDSA curve: secp384r1

   *  id-MLDSA65-ECDSA-brainpoolP256r1-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.30

      -  Label: COMPSIG-MLDSA65-BP256-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA256

         o  ECDSA curve: brainpoolP256r1




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   *  id-MLDSA65-Ed25519-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.31

      -  Label: COMPSIG-MLDSA65-Ed25519-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-65

      -  Traditional Algorithm: Ed25519

         o  Traditional Signature Algorithm: id-Ed25519

   *  id-MLDSA87-ECDSA-P384-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.32

      -  Label: COMPSIG-MLDSA87-P384-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA384

         o  ECDSA curve: secp384r1

   *  id-MLDSA87-ECDSA-brainpoolP384r1-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.33

      -  Label: COMPSIG-MLDSA87-BP384-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA384

         o  ECDSA curve: brainpoolP384r1

   *  id-MLDSA87-Ed448-SHAKE256




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      -  OID: 2.16.840.1.114027.80.9.1.34

      -  Label: COMPSIG-MLDSA87-Ed448-SHAKE256

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

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: Ed448

         o  Traditional Signature Algorithm: id-Ed448

   *  id-MLDSA87-RSA3072-PSS-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.35

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

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: id-RSASSA-PSS

         o  RSA size: 3072

         o  RSASSA-PSS parameters: See Table 2

   *  id-MLDSA87-RSA4096-PSS-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.36

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

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: RSA

         o  Traditional Signature Algorithm: id-RSASSA-PSS

         o  RSA size: 4096

         o  RSASSA-PSS parameters: See Table 3




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   *  id-MLDSA87-ECDSA-P521-SHA512

      -  OID: 2.16.840.1.114027.80.9.1.37

      -  Label: COMPSIG-MLDSA87-P521-SHA512

      -  Pre-Hash function (PH): SHA512

      -  ML-DSA variant: ML-DSA-87

      -  Traditional Algorithm: ECDSA

         o  Traditional Signature Algorithm: ecdsa-with-SHA512

         o  ECDSA curve: secp521r1

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

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

7.1.  RSASSA-PSS Parameters

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

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

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










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

                     Table 2: RSASSA-PSS 2048 and 3072
                                 Parameters

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

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

                    Table 3: RSASSA-PSS 4096 Parameters

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



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   attempting to exactly match the security level of the post-quantum
   and traditional components -- which in general is difficult to do
   since there is no academic consensus on how to compare the "bits of
   security" against classical adversaries and "qubits of security"
   against quantum adversaries.

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

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

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

8.  ASN.1 Module

   <CODE STARTS>

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


   DEFINITIONS IMPLICIT TAGS ::= BEGIN

   EXPORTS ALL;

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

   --



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   -- Object Identifiers
   --

   --
   -- Information Object Classes
   --

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

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


   -- Composite ML-DSA 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) 20 }

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

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

   -- 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) 21 }

   pk-MLDSA44-RSA2048-PKCS15-SHA256 PUBLIC-KEY ::=



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     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) 22 }

   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) 23 }

   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) 24 }

   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 }



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   -- 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) 25 }

   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) 26 }

   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) 27 }

   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 }


   -- 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) 28 }

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



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   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) 29 }

   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) 30 }

   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) 31 }

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

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





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   -- 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) 32 }

   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) 33 }

   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) 34 }

   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 }


   -- 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) 35 }

   pk-MLDSA87-RSA3072-PSS-SHA512 PUBLIC-KEY ::=



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     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) 36 }

   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) 37 }

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

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


   SignatureAlgorithmSet SIGNATURE-ALGORITHM ::= {
     sa-MLDSA44-RSA2048-PSS-SHA256 |
     sa-MLDSA44-RSA2048-PKCS15-SHA256 |
     sa-MLDSA44-Ed25519-SHA512 |
     sa-MLDSA44-ECDSA-P256-SHA256 |
     sa-MLDSA65-RSA3072-PSS-SHA512 |
     sa-MLDSA65-RSA3072-PKCS15-SHA512 |
     sa-MLDSA65-RSA4096-PSS-SHA512 |
     sa-MLDSA65-RSA4096-PKCS15-SHA512 |
     sa-MLDSA65-ECDSA-P256-SHA512 |
     sa-MLDSA65-ECDSA-P384-SHA512 |
     sa-MLDSA65-ECDSA-brainpoolP256r1-SHA512 |



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

   END

   <CODE ENDS>

9.  IANA Considerations

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

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

9.1.  Object Identifier Allocations

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

9.1.1.  Module Registration

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

   *  Decimal: IANA Assigned - *Replace TBDMOD*

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

   *  References: This Document

9.1.2.  Object Identifier Registrations

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

   *  id-MLDSA44-RSA2048-PSS-SHA256




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      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA44-RSA2048-PKCS15-SHA256

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA44-Ed25519-SHA512

      -  Decimal: IANA Assigned

      -  Description: id-MLDSA44-Ed25519-SHA512

      -  References: This Document

   *  id-MLDSA44-ECDSA-P256-SHA256

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA65-RSA3072-PSS-SHA512

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA65-RSA3072-PKCS15-SHA512

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA65-RSA4096-PSS-SHA512




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      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA65-RSA4096-PKCS15-SHA512

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA65-ECDSA-P256-SHA512

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA65-ECDSA-P384-SHA512

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA65-ECDSA-brainpoolP256r1-SHA512

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA65-Ed25519-SHA512

      -  Decimal: IANA Assigned

      -  Description: id-MLDSA65-Ed25519-SHA512

      -  References: This Document

   *  id-MLDSA87-ECDSA-P384-SHA512




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      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA87-ECDSA-brainpoolP384r1-SHA512

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA87-Ed448-SHAKE256

      -  Decimal: IANA Assigned

      -  Description: id-MLDSA87-Ed448-SHAKE256

      -  References: This Document

   *  id-MLDSA87-RSA3072-PSS-SHA512

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA87-RSA4096-PSS-SHA512

      -  Decimal: IANA Assigned

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

      -  References: This Document

   *  id-MLDSA87-ECDSA-P521-SHA512

      -  Decimal: IANA Assigned

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

      -  References: This Document

10.  Security Considerations




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10.1.  Why Hybrids?

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

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

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

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

   First, a note about the security model under which this analysis is
   performed.  This specification strictly forbids re-using component
   key material between composite and non-composite keys, or between
   multiple composite keys.  This specification also exists within the
   X.509 PKI architecture where trust in a public verification key is
   assumed to be established either directly via a trust store or via a



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   certificate chain.  That said, these are both policy mechanisms that
   are outside the formal definitions of EUF-CMA and SUF-CMA under which
   a signature primitive must be analysed, therefore this section
   considers attacks that may be mitigated partially or completely
   within a strictly-implemented PKI setting, but which need to be
   considered when considering Composite ML-DSA as a general-purpose
   signature primitive that could be used outside of the X.509 setting.

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

10.2.1.  EUF-CMA

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

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

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

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

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

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






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10.2.2.  SUF-CMA

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

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

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

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

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

10.2.3.  Non-separability

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

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

   Composite ML-DSA signs a message M by passing M' as defined in
   Section 3.2 to the component signature primitives.  Consider an
   adversary that takes a composite signature (M, (mldsaSig, tradSig))
   and splits it into the component signatures (M', mldsaSig) and (M',



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

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

10.3.  Key Reuse

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

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
















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

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

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

10.4.  Use of Prefix for attack mitigation

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



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10.5.  Policy for Deprecated and Acceptable Algorithms

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

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

11.  Implementation Considerations

11.1.  FIPS certification

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

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

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

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

   The composite algorithm has been designed to treat the underlying
   primitives as "black-box implementations" and not impose any
   additional requirements on them that could require an existing
   implementation of an underlying primitive to run in a mode different
   from the one under which it was certified.  For example, the KeyGen
   defined in Section 4.1 invokes ML-DSA.KeyGen_internal(seed) which
   might not be available in a cryptographic module running in FIPS-



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   mode, but Section 4.1 is only a suggested implementation and the
   composite KeyGen MAY be implemented using a different available
   interface for ML-DSA.KeyGen.  However, using an interface which
   doesn't support a seed will prevent the implementation from encoding
   the private key according to Section 5.2.  Another example is pre-
   hashing; a pre-hash is inherent to RSA, ECDSA, and ML-DSA (μ), and
   composite makes no assumptions or requirements about whether
   component-specific pre-hashing is done locally as part of the
   composite, or remotely as part of the component primitive.

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

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

11.2.  Backwards Compatibility

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

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









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11.3.  Profiling down the number of options

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

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

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

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

   id-MLDSA65-ECDSA-P256-SHA512

   Below we list a few other recommendations for specific scenarios.

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

   id-MLDSA65-RSA3072-PSS-SHA512

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

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

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

   id-MLDSA87-ECDSA-P384-SHA512





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

   id-MLDSA65-Ed25519-SHA512

11.4.  External Pre-hashing

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

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

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

   Explicit inputs:

     M       The message to be signed, an octet string.

   Implicit inputs mapped from <OID>:

     PH      The hash function to use for pre-hashing.

   Output:

      ph     The pre-hash which equals PH ( M )

   Process:


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

      ph = PH ( M )

   2. Output ph











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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 "ML-DSA-65".

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

  Prefix  The prefix octet string.

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

Process:

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

12.  References

12.1.  Normative References

   [FIPS.186-5]
              National Institute of Standards and Technology (NIST),
              "Digital Signature Standard (DSS)", 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>.

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

   [RFC5958]  Turner, S., "Asymmetric Key Packages", RFC 5958,
              DOI 10.17487/RFC5958, August 2010,
              <https://www.rfc-editor.org/info/rfc5958>.

   [RFC6090]  McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic
              Curve Cryptography Algorithms", RFC 6090,
              DOI 10.17487/RFC6090, February 2011,
              <https://www.rfc-editor.org/info/rfc6090>.

   [RFC6234]  Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms
              (SHA and SHA-based HMAC and HKDF)", RFC 6234,
              DOI 10.17487/RFC6234, May 2011,
              <https://www.rfc-editor.org/info/rfc6234>.

   [RFC8017]  Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch,
              "PKCS #1: RSA Cryptography Specifications Version 2.2",
              RFC 8017, DOI 10.17487/RFC8017, November 2016,
              <https://www.rfc-editor.org/info/rfc8017>.

   [RFC8032]  Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
              Signature Algorithm (EdDSA)", RFC 8032,
              DOI 10.17487/RFC8032, January 2017,
              <https://www.rfc-editor.org/info/rfc8032>.




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

   [RFC8410]  Josefsson, S. and J. Schaad, "Algorithm Identifiers for
              Ed25519, Ed448, X25519, and X448 for Use in the Internet
              X.509 Public Key Infrastructure", RFC 8410,
              DOI 10.17487/RFC8410, August 2018,
              <https://www.rfc-editor.org/info/rfc8410>.

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

   [SEC2]     Certicom Research, "SEC 2: Recommended Elliptic Curve
              Domain Parameters", January 2010,
              <https://www.secg.org/sec2-v2.pdf>.

   [X.690]    ITU-T, "Information technology - ASN.1 encoding Rules:
              Specification of Basic Encoding Rules (BER), Canonical
              Encoding Rules (CER) and Distinguished Encoding Rules
              (DER)", ISO/IEC 8825-1:2015, November 2015.

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

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>.







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   [BonehShoup]
              Boneh, D. and V. Shoup, "A Graduate Course in Applied
              Cryptography v0.6", January 2023,
              <https://crypto.stanford.edu/~dabo/cryptobook/
              BonehShoup_0_6.pdf>.

   [BSI2021]  Federal Office for Information Security (BSI), "Quantum-
              safe cryptography - fundamentals, current developments and
              recommendations", October 2021,
              <https://www.bsi.bund.de/SharedDocs/Downloads/EN/BSI/
              Publications/Brochure/quantum-safe-cryptography.pdf>.

   [codesigningbrsv3.8]
              CA/Browser Forum, "Baseline Requirements for the Issuance
              and Management of Publicly‐Trusted Code Signing
              Certificates Version 3.8.0", n.d., <https://cabforum.org/
              working-groups/code-signing/documents/>.

   [eIDAS2014]
              European Parliament and Council, "Regulation (EU) No
              910/2014 of the European Parliament and of the Council of
              23 July 2014 on electronic identification and trust
              services for electronic transactions in the internal
              market and repealing Directive 1999/93/EC", n.d.,
              <https://eur-lex.europa.eu/eli/reg/2014/910/oj/eng>.

   [I-D.ietf-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>.

   [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>.






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   [RFC7292]  Moriarty, K., Ed., Nystrom, M., Parkinson, S., Rusch, A.,
              and M. Scott, "PKCS #12: Personal Information Exchange
              Syntax v1.1", RFC 7292, DOI 10.17487/RFC7292, July 2014,
              <https://www.rfc-editor.org/info/rfc7292>.

   [RFC7296]  Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T.
              Kivinen, "Internet Key Exchange Protocol Version 2
              (IKEv2)", STD 79, RFC 7296, DOI 10.17487/RFC7296, October
              2014, <https://www.rfc-editor.org/info/rfc7296>.

   [RFC8411]  Schaad, J. and R. Andrews, "IANA Registration for the
              Cryptographic Algorithm Object Identifier Range",
              RFC 8411, DOI 10.17487/RFC8411, August 2018,
              <https://www.rfc-editor.org/info/rfc8411>.

   [RFC8446]  Rescorla, E., "The Transport Layer Security (TLS) Protocol
              Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
              <https://www.rfc-editor.org/info/rfc8446>.

   [RFC8551]  Schaad, J., Ramsdell, B., and S. Turner, "Secure/
              Multipurpose Internet Mail Extensions (S/MIME) Version 4.0
              Message Specification", RFC 8551, DOI 10.17487/RFC8551,
              April 2019, <https://www.rfc-editor.org/info/rfc8551>.

   [RFC9180]  Barnes, R., Bhargavan, K., Lipp, B., and C. Wood, "Hybrid
              Public Key Encryption", RFC 9180, DOI 10.17487/RFC9180,
              February 2022, <https://www.rfc-editor.org/info/rfc9180>.

   [RFC9794]  Driscoll, F., Parsons, M., and B. Hale, "Terminology for
              Post-Quantum Traditional Hybrid Schemes", RFC 9794,
              DOI 10.17487/RFC9794, June 2025,
              <https://www.rfc-editor.org/info/rfc9794>.

Appendix A.  Maximum Key and Signature Sizes

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

   *  Compressed vs uncompressed EC point.

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






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

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

   Non-hybrid ML-DSA is included for reference.

   +=========================================+======+=======+=========+
   | Algorithm                               |Public|Private|Signature|
   |                                         |key   |key    |         |
   +=========================================+======+=======+=========+
   | id-ML-DSA-44                            |1312  |32     |2420     |
   +-----------------------------------------+------+-------+---------+
   | id-ML-DSA-65                            |1952  |32     |3309     |
   +-----------------------------------------+------+-------+---------+
   | id-ML-DSA-87                            |2592  |32     |4627     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA44-RSA2048-PSS-SHA256           |1582* |1226*  |2676     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA44-RSA2048-PKCS15-SHA256        |1582* |1226*  |2676     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA44-Ed25519-SHA512               |1344  |64     |2484     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA44-ECDSA-P256-SHA256            |1377  |83     |2492*    |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-RSA3072-PSS-SHA512           |2350* |1802*  |3693     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-RSA3072-PKCS15-SHA512        |2350* |1802*  |3693     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-RSA4096-PSS-SHA512           |2478* |2383*  |3821     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-RSA4096-PKCS15-SHA512        |2478* |2383*  |3821     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-ECDSA-P256-SHA512            |2017  |83     |3381*    |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-ECDSA-P384-SHA512            |2049  |96     |3413*    |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 |2017  |84     |3381*    |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA65-Ed25519-SHA512               |1984  |64     |3373     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-ECDSA-P384-SHA512            |2689  |96     |4731*    |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 |2689  |100    |4731*    |



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   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-Ed448-SHAKE256               |2649  |89     |4741     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-RSA3072-PSS-SHA512           |2990* |1802*  |5011     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-RSA4096-PSS-SHA512           |3118* |2383*  |5139     |
   +-----------------------------------------+------+-------+---------+
   | id-MLDSA87-ECDSA-P521-SHA512            |2725  |114    |4766*    |
   +-----------------------------------------+------+-------+---------+

             Table 4: Maximum size values of composite ML-DSA

Appendix B.  Component Algorithm Reference

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



































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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     |[RFC3279],   |
    |                         |                         |[RFC5915],   |
    |                         |                         |[RFC5758],   |
    |                         |                         |[RFC5480],   |
    |                         |                         |[SEC1],      |
    |                         |                         |[X9.62_2005] |
    +-------------------------+-------------------------+-------------+
    | ecdsa-with-SHA384       | 1.2.840.10045.4.3.3     |[RFC3279],   |
    |                         |                         |[RFC5915],   |
    |                         |                         |[RFC5758],   |
    |                         |                         |[RFC5480],   |
    |                         |                         |[SEC1],      |
    |                         |                         |[X9.62_2005] |
    +-------------------------+-------------------------+-------------+
    | ecdsa-with-SHA512       | 1.2.840.10045.4.3.4     |[RFC3279],   |
    |                         |                         |[RFC5915],   |
    |                         |                         |[RFC5758],   |
    |                         |                         |[RFC5480],   |
    |                         |                         |[SEC1],      |
    |                         |                         |[X9.62_2005] |
    +-------------------------+-------------------------+-------------+
    | sha256WithRSAEncryption | 1.2.840.113549.1.1.11   |[RFC8017]    |
    +-------------------------+-------------------------+-------------+
    | sha384WithRSAEncryption | 1.2.840.113549.1.1.12   |[RFC8017]    |
    +-------------------------+-------------------------+-------------+
    | id-RSASSA-PSS           | 1.2.840.113549.1.1.10   |[RFC8017]    |
    +-------------------------+-------------------------+-------------+

         Table 5: Component Signature Algorithms used in Composite
                               Constructions





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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 6: Elliptic Curves used in Composite Constructions

         +=============+=========================+===============+
         | HashID      | OID                     | Specification |
         +=============+=========================+===============+
         | id-sha256   | 2.16.840.1.101.3.4.2.1  | [RFC6234]     |
         +-------------+-------------------------+---------------+
         | id-sha384   | 2.16.840.1.101.3.4.2.2  | [RFC6234]     |
         +-------------+-------------------------+---------------+
         | id-sha512   | 2.16.840.1.101.3.4.2.3  | [RFC6234]     |
         +-------------+-------------------------+---------------+
         | id-shake256 | 2.16.840.1.101.3.4.2.18 | [FIPS.202]    |
         +-------------+-------------------------+---------------+
         | id-mgf1     | 1.2.840.113549.1.1.8    | [RFC8017]     |
         +-------------+-------------------------+---------------+

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

Appendix C.  Component AlgorithmIdentifiers for Public Keys and
             Signatures

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





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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 & 3072*

   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 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-sha384,   -- (2.16.840.1.101.3.4.2.2)
           parameters NULL
           },
         AlgorithmIdentifier ::= {
           algorithm id-mgf1,       -- (1.2.840.113549.1.1.8)
           parameters AlgorithmIdentifier ::= {
             algorithm id-sha384,   -- (2.16.840.1.101.3.4.2.2)
             parameters NULL
             }
           },
         saltLength 64
         }
       }

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

   *RSASSA-PKCS1-v1_5 2048 & 3072*

   AlgorithmIdentifier of Public Key

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

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



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   AlgorithmIdentifier of Signature

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

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

   *RSASSA-PKCS1-v1_5 4096*

   AlgorithmIdentifier of Public Key

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

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

   AlgorithmIdentifier of Signature

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

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

   *ECDSA NIST P256*

   AlgorithmIdentifier of Public Key













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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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   *  Label is the specific signature label for this composite
      algorithm, as defined in Section 7.

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

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

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

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

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

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

   # Inputs:

   M: 00010203040506070809
   ctx: <empty>

   # Components of M':

   Prefix:
   436f6d706f73697465416c676f726974686d5369676e61747572657332303235

   Label: COMPSIG-MLDSA65-P256-SHA512

   len(ctx): 00

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


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

   M': 436f6d706f73697465416c676f726974686d5369676e6174757265733230323
   5434f4d505349472d4d4c44534136352d503235362d534841353132000f89ee1fcb
   7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f9a3f202f56fadba4c
   d9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f903533





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

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

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

   # Inputs:

   M: 00010203040506070809
   ctx: 0813061205162623

   # Components of M':

   Prefix:
   436f6d706f73697465416c676f726974686d5369676e61747572657332303235

   Label: COMPSIG-MLDSA65-P256-SHA512

   len(ctx): 08

   ctx: 0813061205162623

   PH(M): 0f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f
   9a3f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f90353
   3


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

   M': 436f6d706f73697465416c676f726974686d5369676e6174757265733230323
   5434f4d505349472d4d4c44534136352d503235362d534841353132080813061205
   1626230f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f9
   a3f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f903533

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:




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   *  tcId the name of the algorithm.

   *  pk the verification public key.

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

   *  sk the raw signature private key.

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

   *  s the signature value.

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

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

   2.  Validate the self-signed certificate x5c.

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

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

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

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

   {
   "m":
   "VGhlIHF1aWNrIGJyb3duIGZveCBqdW1wcyBvdmVyIHRoZSBsYXp5IGRvZy4=",

   "tests": [
   {
   "tcId": "id-ML-DSA-44",
   "pk": "G3anHRfMi5t8ZaM+2bv8lvdD
   JaCnSayGHVU4ZE3553Xd04JleJlixI+nh/mtzHleg3DEfbA4pMUMr/04StF+aLVREqI+
   6P+j4P6kPCGRfaAVHQG5gsoKo5qGySOlxLKHtgEeae1YyB8P/AZbEtQtB6qr9Lld2gX7
   wd4w+WO1Cd0gA+pYaG02B8KxKB2o9WXVJtfi7uv9/XeF0ldD+I+uGxgTB9un1aomnlcR
   DmbVieL/WoxSQP2nCxB2XhJ68BFqPTy0pc2zPW9l9Q9czXyM5iviPghNc3oySnuRBhS7
   GMGd3eQZVQVhEWlB6CYgNK2z5tQadmPGxre4emKAIubJ4CKi7ZLVTvLMq0FjnQVl2dN/
   G8xb9cyaxj0Y5BuiqGj/fuFN2Xxj34MmTIYPQl4zUSVZsKlC/kjhvP5Qmw3Sk4I7ovJw



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   DFNgKzOAkpJl+OgpfoITEBBWSQY3c3hqFxAfWr9/RnoGbBu/yDvnT7Mn+alChkCl0qu/
   MeR9qaxlskOFUs95lx1YPO1KUhaCftCZIC7jQeDSgNMG+Y28hSQaBSCqz73wopjAP7jW
   54hjiJ0vJcjbBwWWeNIlQtsc1Er924+1NtSYI8HvoKl6JJNMmslvikgklMnI+EbHOLWj
   7xoSZzJ3tkY6+KVHdRu3WKkttuXIDhsxexU8zTLQ+6Tbe/LY6fgaTeDMJOsBIUPSHs4t
   Rst9q0cS2bkX+ABpBnsoLdW4kS9RUsKF1wqVbfCM4GypxYj8x+yXNXWENANxachFItd1
   Gw7MbYEZxWvuAMjcyGepXDsQ8kHWKPWjF62pdPKHEZkTHOemXHfIbYQ2dJlrOcaJpeFm
   v9uLP0llxjJ94LyQd6HG9wVPwQ3kRTsQO9/GAauSbagaTTc8GKH2ZK3GRsLYD/DPOdRM
   uLExnr/Kvn8HrG/6NDm7dmdOhrVXx8zuLSg1Xbcl6CC90Gk+OY/M0voEKorALb/nRVW3
   FizUscqttMfRSIIkwY3dz8+wbPhLxQIhc7bSijXrM+NL685yumbQr5OfE1kNmewD/+M6
   6PeVRD/Jiu7a/jIrL8E0s6Azwivbcj+YlXzdjJNgACtsilUtJk/eTS+csnjyuOeRkeiz
   xOc2XKMZgrRtYM+17Hsmlk1x+yk2X5ybwRfkyBHkcDv16WrfhVmviPXoub5XDIhpox+e
   LULdKlhnaPEIMAATXyyDuXE5XODRQ1sgEuBlVx9VqcbKwnGkI20/xuePARyggWqi4uWF
   XyE0cBtd8jW7nEvYKuyngyI+owy5me5xsu42B8S6KKvpX+BvGgcC4SpkoH3l7XkrMrRG
   9Ds5onuJJS8ydixEUoN7gKiMKgpB1sPWfK2GLagtimsLngqwh0weVDU2ba8Gju8LpLwW
   rdWSOWeTPGwfyotNvlOhjZuwJJCDZE2G/z1rRlSMqt6tLrZ0GQBin5d55cJqIlYk8frV
   H0alqPoWmV3PRwsFChHC285Mykh9YiB/NNcX/fPZs938i53P5lz0VQy+3J8h271c0zXJ
   vVGyMX0YSiT6doODNxQnZd7wUwPPu3IEy7h6wONpwB8OWxR0oVXQ9BJSFrVNKM4zaUjK
   lKYiX4GZSMS1EJi/kCV2Pg3t70Gun8VWquHvkDnZJPuER3UmGUK2wgAN6eoYd1ubdBKg
   Rdb8NpkePEQNNh2GDlj+tMFT8VowvkipDOr0Yh6ujUu3IH7MZ173MzdScrgrRYOU55Dz
   SHYYKUaPXE5PaE8VjMNTD2mmTg==",
   "x5c": "MIIPjDCCBgKgAwIBAgIUJlQdv4mcH
   hc3/t8Q7z6J5fQH/BcwCwYJYIZIAWUDBAMRMDYxDTALBgNVBAoMBElFVEYxDjAMBgNVB
   AsMBUxBTVBTMRUwEwYDVQQDDAxpZC1NTC1EU0EtNDQwHhcNMjUxMDA5MTQxMDA2WhcNM
   zUxMDEwMTQxMDA2WjA2MQ0wCwYDVQQKDARJRVRGMQ4wDAYDVQQLDAVMQU1QUzEVMBMGA
   1UEAwwMaWQtTUwtRFNBLTQ0MIIFMjALBglghkgBZQMEAxEDggUhABt2px0XzIubfGWjP
   tm7/Jb3QyWgp0mshh1VOGRN+ed13dOCZXiZYsSPp4f5rcx5XoNwxH2wOKTFDK/9OErRf
   mi1URKiPuj/o+D+pDwhkX2gFR0BuYLKCqOahskjpcSyh7YBHmntWMgfD/wGWxLULQeqq
   /S5XdoF+8HeMPljtQndIAPqWGhtNgfCsSgdqPVl1SbX4u7r/f13hdJXQ/iPrhsYEwfbp
   9WqJp5XEQ5m1Yni/1qMUkD9pwsQdl4SevARaj08tKXNsz1vZfUPXM18jOYr4j4ITXN6M
   kp7kQYUuxjBnd3kGVUFYRFpQegmIDSts+bUGnZjxsa3uHpigCLmyeAiou2S1U7yzKtBY
   50FZdnTfxvMW/XMmsY9GOQboqho/37hTdl8Y9+DJkyGD0JeM1ElWbCpQv5I4bz+UJsN0
   pOCO6LycAxTYCszgJKSZfjoKX6CExAQVkkGN3N4ahcQH1q/f0Z6Bmwbv8g750+zJ/mpQ
   oZApdKrvzHkfamsZbJDhVLPeZcdWDztSlIWgn7QmSAu40Hg0oDTBvmNvIUkGgUgqs+98
   KKYwD+41ueIY4idLyXI2wcFlnjSJULbHNRK/duPtTbUmCPB76CpeiSTTJrJb4pIJJTJy
   PhGxzi1o+8aEmcyd7ZGOvilR3Ubt1ipLbblyA4bMXsVPM0y0Puk23vy2On4Gk3gzCTrA
   SFD0h7OLUbLfatHEtm5F/gAaQZ7KC3VuJEvUVLChdcKlW3wjOBsqcWI/MfslzV1hDQDc
   WnIRSLXdRsOzG2BGcVr7gDI3MhnqVw7EPJB1ij1oxetqXTyhxGZExznplx3yG2ENnSZa
   znGiaXhZr/biz9JZcYyfeC8kHehxvcFT8EN5EU7EDvfxgGrkm2oGk03PBih9mStxkbC2
   A/wzznUTLixMZ6/yr5/B6xv+jQ5u3ZnToa1V8fM7i0oNV23JeggvdBpPjmPzNL6BCqKw
   C2/50VVtxYs1LHKrbTH0UiCJMGN3c/PsGz4S8UCIXO20oo16zPjS+vOcrpm0K+TnxNZD
   ZnsA//jOuj3lUQ/yYru2v4yKy/BNLOgM8Ir23I/mJV83YyTYAArbIpVLSZP3k0vnLJ48
   rjnkZHos8TnNlyjGYK0bWDPtex7JpZNcfspNl+cm8EX5MgR5HA79elq34VZr4j16Lm+V
   wyIaaMfni1C3SpYZ2jxCDAAE18sg7lxOVzg0UNbIBLgZVcfVanGysJxpCNtP8bnjwEco
   IFqouLlhV8hNHAbXfI1u5xL2Crsp4MiPqMMuZnucbLuNgfEuiir6V/gbxoHAuEqZKB95
   e15KzK0RvQ7OaJ7iSUvMnYsRFKDe4CojCoKQdbD1nythi2oLYprC54KsIdMHlQ1Nm2vB
   o7vC6S8Fq3VkjlnkzxsH8qLTb5ToY2bsCSQg2RNhv89a0ZUjKrerS62dBkAYp+XeeXCa
   iJWJPH61R9Gpaj6Fpldz0cLBQoRwtvOTMpIfWIgfzTXF/3z2bPd/Iudz+Zc9FUMvtyfI
   du9XNM1yb1RsjF9GEok+naDgzcUJ2Xe8FMDz7tyBMu4esDjacAfDlsUdKFV0PQSUha1T



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   SjOM2lIypSmIl+BmUjEtRCYv5Aldj4N7e9Brp/FVqrh75A52ST7hEd1JhlCtsIADenqG
   Hdbm3QSoEXW/DaZHjxEDTYdhg5Y/rTBU/FaML5IqQzq9GIero1LtyB+zGde9zM3UnK4K
   0WDlOeQ80h2GClGj1xOT2hPFYzDUw9ppk6jEjAQMA4GA1UdDwEB/wQEAwIHgDALBglgh
   kgBZQMEAxEDggl1AP5s7F6sK7v/M9ouMGUEgebraBklY8G+4vEbyM1rARhDx7s0XKVec
   HE0bh5WTekoLeMyslob2cIRaYSXY/Ai53DhoWkWKx3K9AcosiwgYZ2T266tFvgGkTpNG
   8xdRLELRVg1KikYhmlaH/I7I8DpEf8cvtFT1xwyNBoKdYNaRzkgkvW6zBXNQAqmgs4gY
   7OEyVTFMgMoW9ZfMndBqmkxQYcrdp5+CLxZjoWzfC/OmXHlVYNHm2BdsYeswKLpTvI22
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Ounsworth, et al.         Expires 13 April 2026                [Page 81]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 82]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 83]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 84]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 85]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 86]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 87]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 88]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 89]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 90]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 91]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 92]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 93]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 94]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 95]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 96]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 97]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 98]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026                [Page 99]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 100]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 101]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 102]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 103]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 104]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 105]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 106]

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Ounsworth, et al.         Expires 13 April 2026               [Page 107]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 108]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 109]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 110]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 111]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 112]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 113]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 114]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 115]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 116]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 117]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 118]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 119]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 120]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 121]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 122]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 123]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 124]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 125]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 126]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 127]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 128]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 129]

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Ounsworth, et al.         Expires 13 April 2026               [Page 130]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 131]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 132]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 133]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 134]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 135]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 136]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 137]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 138]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 139]

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Ounsworth, et al.         Expires 13 April 2026               [Page 140]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 141]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 142]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 143]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 144]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 145]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 146]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 147]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 148]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 149]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 150]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 151]

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Ounsworth, et al.         Expires 13 April 2026               [Page 152]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 153]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 154]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 155]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 156]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 157]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 158]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 159]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 160]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 161]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 162]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 163]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 164]

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Ounsworth, et al.         Expires 13 April 2026               [Page 165]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 166]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 167]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 168]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 169]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 170]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 171]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 172]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 173]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 174]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 175]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 176]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 177]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 178]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 179]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 180]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 181]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 182]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 183]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 184]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 185]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 186]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 187]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 188]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 189]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 190]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 191]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 192]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 193]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 194]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 195]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 196]

Internet-Draft              Composite ML-DSA                October 2025


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Ounsworth, et al.         Expires 13 April 2026               [Page 197]

Internet-Draft              Composite ML-DSA                October 2025


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   ]
   }

Appendix F.  Intellectual Property Considerations

   The following IPR Disclosure relates to this document:

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

Appendix G.  Contributors and Acknowledgements

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






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

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

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

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

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

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

Authors' Addresses

   Mike Ounsworth
   Entrust Limited
   2500 Solandt Road – Suite 100
   Ottawa, Ontario  K2K 3G5
   Canada
   Email: mike.ounsworth@entrust.com








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


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


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


   Scott Fluhrer
   Cisco Systems
   Email: sfluhrer@cisco.com

























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