LAMPS WG                                                      J. Massimo
Internet-Draft                                             P. Kampanakis
Intended status: Standards Track                                     AWS
Expires: 6 August 2025                                         S. Turner
                                                                   sn3rd
                                                        B. E. Westerbaan
                                                              Cloudflare
                                                         2 February 2025


Internet X.509 Public Key Infrastructure: Algorithm Identifiers for ML-
                                  DSA
               draft-ietf-lamps-dilithium-certificates-07

Abstract

   Digital signatures are used within X.509 certificates, Certificate
   Revocation Lists (CRLs), and to sign messages.  This document
   describes the conventions for using FIPS 204, the Module-Lattice-
   Based Digital Signature Algorithm (ML-DSA) in Internet X.509
   certificates and certificate revocation lists.  The conventions for
   the associated signatures, subject public keys, and private key are
   also described.

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/dilithium-certificates/#go.draft-ietf-lamps-dilithium-
   certificates.html.  Status information for this document may be found
   at https://datatracker.ietf.org/doc/draft-ietf-lamps-dilithium-
   certificates/.

   Discussion of this document takes place on the Limited Additional
   Mechanisms for PKIX and SMIME (lamps) Working Group mailing list
   (mailto:spasm@ietf.org), which is archived at
   https://mailarchive.ietf.org/arch/browse/spasm/.  Subscribe at
   https://www.ietf.org/mailman/listinfo/spasm/.

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

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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   Copyright (c) 2025 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Requirements Language . . . . . . . . . . . . . . . . . .   3
   2.  Identifiers . . . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  ML-DSA Signatures in PKIX . . . . . . . . . . . . . . . . . .   4
   4.  ML-DSA Public Keys in PKIX  . . . . . . . . . . . . . . . . .   5
   5.  Key Usage Bits  . . . . . . . . . . . . . . . . . . . . . . .   7
   6.  Private Key Format  . . . . . . . . . . . . . . . . . . . . .   7
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   8
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
     8.1.  Rationale for disallowing HashML-DSA  . . . . . . . . . .  10
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  11
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  11
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  12
   Appendix A.  ASN.1 Module . . . . . . . . . . . . . . . . . . . .  13
   Appendix B.  Security Strengths . . . . . . . . . . . . . . . . .  15
   Appendix C.  Examples . . . . . . . . . . . . . . . . . . . . . .  16
     C.1.  Example Private Key . . . . . . . . . . . . . . . . . . .  16
     C.2.  Example Public Key  . . . . . . . . . . . . . . . . . . .  17
     C.3.  Example Certificates  . . . . . . . . . . . . . . . . . .  25
   Appendix D.  Pre-hashing (ExternalMu-ML-DSA)  . . . . . . . . . .  49



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   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  51
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  51

1.  Introduction

   The Module-Lattice-Based Digital Signature Algorithm (ML-DSA) is a
   quantum-resistant digital signature scheme standardized by the US
   National Institute of Standards and Technology (NIST) PQC project
   [NIST-PQC] in [FIPS204].  This document specifies the use of the ML-
   DSA in Public Key Infrastructure X.509 (PKIX) certificates and
   Certificate Revocation Lists (CRLs) at three security levels: ML-DSA-
   44, ML-DSA-65, and ML-DSA-87.

   [FIPS204] defines two variants of ML-DSA: a pure and a prehash
   variant.  Only the former is specified in this document.  See
   Section 8.1 for the rationale.  The pure variant of ML-DSA supports
   the typical prehash flow, see Appendix D.  In short: one
   cryptographic module can compute the hash _mu_ on line 6 of algorithm
   7 of [FIPS204] and pass it to a second module to finish the
   signature.  The first module only needs access to the full message
   and the public key, whereas the second module only needs access to
   hash _mu_ and the private key.

   Prior to standardisation, ML-DSA was known as Dilithium.  ML-DSA and
   Dilithium are not compatible.

1.1.  Requirements Language

   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.

2.  Identifiers

   The AlgorithmIdentifier type is defined in [RFC5912] as follows:

    AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::=
      SEQUENCE {
        algorithm   ALGORITHM-TYPE.id({AlgorithmSet}),
        parameters  ALGORITHM-TYPE.
                      Params({AlgorithmSet}{@algorithm}) OPTIONAL
     }

      |  NOTE: The above syntax is from [RFC5912] and is compatible with
      |  the 2021 ASN.1 syntax [X680].  See [RFC5280] for the 1988 ASN.1
      |  syntax.



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   The fields in AlgorithmIdentifier have the following meanings:

   *  algorithm identifies the cryptographic algorithm with an object
      identifier.

   *  parameters, which are optional, are the associated parameters for
      the algorithm identifier in the algorithm field.

   The OIDs are:

      id-ml-dsa-44 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
               country(16) us(840) organization(1) gov(101) csor(3)
               nistAlgorithm(4) sigAlgs(3) id-ml-dsa-44(17) }

      id-ml-dsa-65 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
               country(16) us(840) organization(1) gov(101) csor(3)
               nistAlgorithm(4) sigAlgs(3) id-ml-dsa-65(18) }

      id-ml-dsa-87 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
               country(16) us(840) organization(1) gov(101) csor(3)
               nistAlgorithm(4) sigAlgs(3) id-ml-dsa-87(19) }

   The contents of the parameters component for each algorithm MUST be
   absent.  The ctx value used in the ML-DSA signing and verification
   [FIPS204] of ML-DSA signatures defined in this specification (X.509
   certificates, CRLs) is the empty string.

3.  ML-DSA Signatures in PKIX

   ML-DSA is a digital signature scheme built upon the Fiat-Shamir-with-
   aborts framework [Fiat-Shamir].  The security is based upon the
   hardness of lattice problems over module lattices [Dilithium].  ML-
   DSA provides three parameter sets for the NIST PQC security
   categories 2, 3 and 5.

   Signatures are used in a number of different ASN.1 structures.  As
   shown in the ASN.1 representation from [RFC5280] below, in an X.509
   certificate, a signature is encoded with an algorithm identifier in
   the signatureAlgorithm attribute and a signatureValue attribute that
   contains the actual signature.











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     Certificate  ::=  SIGNED{ TBSCertificate }

     SIGNED{ToBeSigned} ::= SEQUENCE {
        toBeSigned           ToBeSigned,
        algorithmIdentifier  SEQUENCE {
            algorithm        SIGNATURE-ALGORITHM.
                               &id({SignatureAlgorithms}),
            parameters       SIGNATURE-ALGORITHM.
                               &Params({SignatureAlgorithms}
                                 {@algorithmIdentifier.algorithm})
                                   OPTIONAL
        },
        signature BIT STRING (CONTAINING SIGNATURE-ALGORITHM.&Value(
                                 {SignatureAlgorithms}
                                 {@algorithmIdentifier.algorithm}))
     }

   Signatures are also used in the CRL list ASN.1 representation from
   [RFC5280] below.  In a X.509 CRL, a signature is encoded with an
   algorithm identifier in the signatureAlgorithm attribute and a
   signatureValue attribute that contains the actual signature.

      CertificateList  ::=  SIGNED{ TBSCertList }

   The identifiers defined in Section 2 can be used as the
   AlgorithmIdentifier in the signatureAlgorithm field in the sequence
   Certificate/CertificateList and the signature field in the sequence
   TBSCertificate/TBSCertList in certificates and CRLs, respectively,
   [RFC5280].  The parameters of these signature algorithms MUST be
   absent, as explained in Section 2.  That is, the AlgorithmIdentifier
   SHALL be a SEQUENCE of one component, the OID id-ml-dsa-*.

   The signatureValue field contains the corresponding ML-DSA signature
   computed upon the ASN.1 DER encoded tbsCertificate/tbsCertList
   [RFC5280].

   Conforming Certification Authority (CA) implementations MUST specify
   the algorithms explicitly by using the OIDs specified in Section 2
   when encoding ML-DSA signatures in certificates and CRLs.  Conforming
   client implementations that process certificates and CRLs using ML-
   DSA MUST recognize the corresponding OIDs.  Encoding rules for ML-DSA
   signature values are specified Section 2.

4.  ML-DSA Public Keys in PKIX

   In the X.509 certificate, the subjectPublicKeyInfo field has the
   SubjectPublicKeyInfo type, which has the following ASN.1 syntax:




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     SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE {
         algorithm        AlgorithmIdentifier {PUBLIC-KEY, {IOSet}},
         subjectPublicKey BIT STRING
     }

      |  NOTE: The above syntax is from [RFC5912] and is compatible with
      |  the 2021 ASN.1 syntax [X680].  See [RFC5280] for the 1988 ASN.1
      |  syntax.

   The fields in SubjectPublicKeyInfo have the following meaning:

   *  algorithm is the algorithm identifier and parameters for the
      public key (see above).

   *  subjectPublicKey contains the byte stream of the public key.

   The PUBLIC-KEY ASN.1 types for ML-DSA are defined here:

     pk-ml-dsa-44 PUBLIC-KEY ::= {
       IDENTIFIER id-ml-dsa-44
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

     pk-ml-dsa-65 PUBLIC-KEY ::= {
       IDENTIFIER id-ml-dsa-65
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

     pk-ml-dsa-87 PUBLIC-KEY ::= {
       IDENTIFIER id-ml-dsa-87
       -- KEY no ASN.1 wrapping --
       CERT-KEY-USAGE
         { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
       -- PRIVATE-KEY no ASN.1 wrapping -- }

     ML-DSA-PublicKey ::= OCTET STRING (SIZE (1312 | 1952 | 2592))

     ML-DSA-PrivateKey ::= OCTET STRING (SIZE (32))

   Algorithm 22 in Section 7.2 of [FIPS204] defines the raw byte string
   encoding of an ML-DSA public key.  When used in a
   SubjectPublicKeyInfo type, the subjectPublicKey BIT STRING contains
   the raw byte string encoding of the public key.




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

   [RFC5958] describes the Asymmetric Key Package's OneAsymmetricKey
   type for encoding asymmetric keypairs.  When an ML-DSA private key or
   keypair is encoded as a OneAsymmetricKey, it follows the description
   in Section 6.

   When the ML-DSA private key appears outside of an Asymmetric Key
   Package in an environment that uses ASN.1 encoding, it can be encoded
   as an OCTET STRING by using the ML-DSA-PrivateKey type.

   Appendix C contains example ML-DSA public keys encoded using the
   textual encoding defined in [RFC7468].

5.  Key Usage Bits

   The intended application for the key is indicated in the keyUsage
   certificate extension; see Section 4.2.1.3 of [RFC5280].  If the
   keyUsage extension is present in a certificate that indicates id-ml-
   dsa-* in the SubjectPublicKeyInfo, then the at least one of following
   MUST be present:

     digitalSignature; or
     nonRepudiation; or
     keyCertSign; or
     cRLSign.

   If the keyUsage extension is present in a certificate that indicates
   id-ml-dsa-* in the SubjectPublicKeyInfo, then the following MUST NOT
   be present:

      keyEncipherment; or
      dataEncipherment; or
      keyAgreement; or
      encipherOnly; or
      decipherOnly.

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

6.  Private Key Format

   An ML-DSA private key is encoded by storing its 32-octet seed in the
   privateKey field as follows.





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   [FIPS204] specifies two formats for an ML-DSA private key: a 32-octet
   seed (xi) and an (expanded) private key.  The expanded private key
   (and public key) is computed from the seed using ML-
   DSA.KeyGen_internal(xi) (algorithm 6).

   "Asymmetric Key Packages" [RFC5958] describes how to encode a private
   key in a structure that both identifies what algorithm the private
   key is for and allows for the public key and additional attributes
   about the key to be included as well.  For illustration, the ASN.1
   structure OneAsymmetricKey is replicated below.

     OneAsymmetricKey ::= SEQUENCE {
       version                  Version,
       privateKeyAlgorithm      SEQUENCE {
       algorithm                PUBLIC-KEY.&id({PublicKeySet}),
       parameters               PUBLIC-KEY.&Params({PublicKeySet}
                                  {@privateKeyAlgorithm.algorithm})
                                     OPTIONAL}
       privateKey               OCTET STRING (CONTAINING
                                  PUBLIC-KEY.&PrivateKey({PublicKeySet}
                                    {@privateKeyAlgorithm.algorithm})),
       attributes           [0] Attributes OPTIONAL,
       ...,
       [[2: publicKey       [1] BIT STRING (CONTAINING
                                  PUBLIC-KEY.&Params({PublicKeySet}
                                    {@privateKeyAlgorithm.algorithm})
                                    OPTIONAL,
       ...
     }

      |  NOTE: The above syntax is from [RFC5958] and is compatible with
      |  the 2021 ASN.1 syntax [X680].

   When used in a OneAsymmetricKey type, the privateKey OCTET STRING
   contains the raw octet string encoding of the 32-octet seed.  The
   publicKey field SHOULD be omitted because the public key can be
   computed as noted earlier in this section.

   Appendix C contains example ML-DSA private keys encoded using the
   textual encoding defined in [RFC7468].

7.  IANA Considerations

   For the ASN.1 module in Appendix A, IANA is requested to assign an
   object identifier (OID) for the module identifier (TBD1) with a
   Description of "id-mod-x509-ml-dsa-2024".  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).



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8.  Security Considerations

   The Security Considerations section of [RFC5280] applies to this
   specification as well.

   The digital signature scheme defined within this document are modeled
   under strongly existentially unforgeable under chosen message attack
   (SUF-CMA).  For the purpose of estimating security strength, it has
   been assumed that the attacker has access to signatures for no more
   than 2^{64} chosen messages.

   ML-DSA offers both deterministic and randomized signing.  By default
   ML-DSA signatures are non-deterministic.  The private random seed
   (rho') for the signature is pseudorandomly derived from the signer’s
   private key, the message, and a 256-bit string, rnd - where rnd
   should be generated by an approved RBG.  In the deterministic
   version, rng is instead a 256-bit constant string.  The source of
   randomness in the randomized mode has been "hedged" against sources
   of poor entropy, by including the signers private key and message
   into the derivation.  The primary purpose of rnd is to facilitate
   countermeasures to side-channel attacks and fault attacks on
   deterministic signatures.

   In the design of ML-DSA, care has been taken to make side-channel
   resilience easier to achieve.  For instance, ML-DSA does not depend
   on Gaussian sampling.  Implementations must still take great care not
   to leak information via various side channels.  While deliberate
   design decisions such as these can help to deliver a greater ease of
   secure implementation - particularly against side-channel attacks -
   it does not necessarily provide resistance to more powerful attacks
   such as differential power analysis.  Some amount of side-channel
   leakage has been demonstrated in parts of the signing algorithm
   (specifically the bit-unpacking function), from which a demonstration
   of key recovery has been made over a large sample of signatures.
   Masking countermeasures exist for ML-DSA, but come with a performance
   overhead.

   A fundamental security property also associated with digital
   signatures is non-repudiation.  Non-repudiation refers to the
   assurance that the owner of a signature key pair that was capable of
   generating an existing signature corresponding to certain data cannot
   convincingly deny having signed the data.  The digital signature
   scheme ML-DSA possess three security properties beyond
   unforgeability, that are associated with non-repudiation.  These are
   exclusive ownership, message-bound signatures, and non-resignability.
   These properties are based tightly on the assumed collision
   resistance of the hash function used (in this case SHAKE-256).




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   Exclusive ownership is a property in which a signature sigma uniquely
   determines the public key and message for which it is valid.
   Message-bound signatures is the property that a valid signature
   uniquely determines the message for which it is valid, but not
   necessarily the public key.  Non-resignability is the property in
   which one cannot produce a valid signature under another key given a
   signature sigma for some unknown message m.  These properties are not
   provided by classical signature schemes such as DSA or ECDSA, and
   have led to a variety of attacks such as Duplicate-Signature Key
   Selection (DSKS) attacks , and attacks on the protocols for secure
   routing.  A full discussion of these properties in ML-DSA can be
   found at [CDFFJ21].

   These properties are dependent, in part, on unambiguous public key
   serialization.  It for this reason the public key structure defined
   in Section 4 is intentionally encoded as a single OCTET STRING.

8.1.  Rationale for disallowing HashML-DSA

   The HashML-DSA mode defined in Section 5.4 of [FIPS204] MUST NOT be
   used; in other words, public keys identified by id-hash-ml-dsa-44-
   with-sha512, id-hash-ml-dsa-65-with-sha512, and id-hash-ml-dsa-87-
   with-sha512 MUST NOT be in X.509 certificates used for CRLs, OCSP,
   certificate issuance and related PKIX protocols (e.g. TLS).  The use
   of HashML-DSA public keys within end entity certificates is not
   prohibited, but conventions for doing so are outside the scope of
   this document.

   This restriction is for both implementation and security reasons.

   The implementation reason for disallowing HashML-DSA stems from the
   fact that ML-DSA and HashML-DSA are incompatible algorithms that
   require different Verify() routines.  This forwards to the protocol
   the complexity of informing the client whether to use ML-DSA.Verify()
   or HashML-DSA.Verify() along with the hash algorithm to use.
   Additionally, since the same OIDs are used to identify the ML-DSA
   public keys and ML-DSA signature algorithms, an implementation would
   need to commit a given public key to be either of type ML-DSA or
   HashML-DSA at the time of certificate creation.  This is anticipated
   to cause operational issues in contexts where the operator does not
   know at key generation time whether the key will need to produce pure
   or pre-hashed signatures.  ExternalMu-ML-DSA avoids all of these
   operational concerns by virtue of having keys and signatures that are
   indistinguishable from ML-DSA (i.e., ML-DSA and ExternalMu-ML-DSA are
   mathematically equivalent algorithms).  The difference between ML-DSA
   and ExternalMu-ML-DSA is merely an internal implementation detail of
   the signer and has no impact on the verifier or network protocol.




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   The security reason for disallowing HashML-DSA is that the design of
   the ML-DSA algorithm provides enhanced resistance against signature
   collision attacks, compared with conventional RSA or ECDSA signature
   algorithms.  Specifically, ML-DSA binds the hash of the public key tr
   to the message to-be-signed prior to hashing, as described in line 6
   of Algorithm 7 of [FIPS204].  In practice, this provides binding to
   the indended verification public key, preventing some attacks that
   would otherwise allow a signature to be successfully verified against
   a non-intended public key.  Also, this unlikely, theoretical binding
   means that in the unlikely discovery of a collision attack against
   SHA-3, an attacker would have to perform a public-key-specific
   collision search in order to find message pairs such that H(tr || m1)
   = H(tr || m2) since a direct hash collision H(m1) = H(m2) will not
   suffice.  HashML-DSA removes both of these enhanced security
   properties.

9.  References

9.1.  Normative References

   [FIPS204]  National Institute of Standards and Technology (NIST),
              "Module-Lattice-based Digital Signature Standard", FIPS
              PUB 204, August 2023, <https://csrc.nist.gov/projects/
              post-quantum-cryptography>.

   [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/rfc/rfc2119>.

   [RFC3647]  Chokhani, S., Ford, W., Sabett, R., Merrill, C., and S.
              Wu, "Internet X.509 Public Key Infrastructure Certificate
              Policy and Certification Practices Framework", RFC 3647,
              DOI 10.17487/RFC3647, November 2003,
              <https://www.rfc-editor.org/rfc/rfc3647>.

   [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/rfc/rfc5280>.

   [RFC5912]  Hoffman, P. and J. Schaad, "New ASN.1 Modules for the
              Public Key Infrastructure Using X.509 (PKIX)", RFC 5912,
              DOI 10.17487/RFC5912, June 2010,
              <https://www.rfc-editor.org/rfc/rfc5912>.





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

   [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/rfc/rfc8174>.

   [X680]     ITU-T, "Information Technology -- Abstract Syntax Notation
              One (ASN.1): Specification of basic notation", ITU-T
              Recommendation X.680, ISO/IEC 8824-1:2021, February 2021,
              <https://www.itu.int/rec/T-REC-X.680>.

   [X690]     ITU-T, "Information Technology -- Abstract Syntax Notation
              One (ASN.1): ASN.1 encoding rules: Specification of Basic
              Encoding Rules (BER), Canonical Encoding Rules (CER) and
              Distinguished Encoding Rules (DER)", ITU-T
              Recommendation X.690, ISO/IEC 8825-1:2021, February 2021,
              <https://www.itu.int/rec/T-REC-X.690>.

9.2.  Informative References

   [CDFFJ21]  Cremers, C., Düzlü, S., Fiedler, R., Fischlin, M., and C.
              Janson, "BUFFing signature schemes beyond unforgeability
              and the case of post-quantum signatures", In Proceedings
              of the 42nd IEEE Symposium on Security and Privacy , 2021,
              <https://eprint.iacr.org/2020/1525.pdf>.

   [Dilithium]
              Bai, S., Ducas, L., Lepoint, T., Lyubashevsky, V.,
              Schwabe, P., Seiler, G., and D. Stehlé, "CRYSTALS-
              Dilithium Algorithm Specifications and Supporting
              Documentation", 2021, <https://pq-
              crystals.org/dilithium/data/dilithium-specification-
              round3-20210208.pdf>.

   [Fiat-Shamir]
              Lyubashevsky, V., "Fiat-Shamir with aborts: Applications
              to lattice and factoring-based signatures", International
              Conference on the Theory and Application of Cryptology and
              Information Security , 2009,
              <https://www.iacr.org/archive/
              asiacrypt2009/59120596/59120596.pdf>.

   [NIST-PQC] National Institute of Standards and Technology (NIST),
              "Post-Quantum Cryptography Project", 20 December 2016,
              <https://csrc.nist.gov/Projects/post-quantum-
              cryptography>.



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   [RFC7468]  Josefsson, S. and S. Leonard, "Textual Encodings of PKIX,
              PKCS, and CMS Structures", RFC 7468, DOI 10.17487/RFC7468,
              April 2015, <https://www.rfc-editor.org/rfc/rfc7468>.

Appendix A.  ASN.1 Module

   This appendix includes the ASN.1 module [X680] for the ML-DSA.  Note
   that as per [RFC5280], certificates use the Distinguished Encoding
   Rules; see [X690].  This module imports objects from [RFC5912].

   <CODE BEGINS>
   X509-ML-DSA-2024
   { iso(1) identified-organization(3) dod(6)
     internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
     id-mod-x509-ml-dsa-2024(TBD1) }

   DEFINITIONS IMPLICIT TAGS ::=

   BEGIN

   -- EXPORTS ALL;

   IMPORTS

   PUBLIC-KEY, SIGNATURE-ALGORITHM
     FROM AlgorithmInformation-2009 -- From [RFC5912]
       { iso(1) identified-organization(3) dod(6) internet(1)
         security(5) mechanisms(5) pkix(7) id-mod(0)
         id-mod-algorithmInformation-02(58) } ;

   --
   -- Object Identifiers
   --

   sigAlgs OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) country(16)
       us(840) organization(1) gov(101) csor(3) nistAlgorithms(4) 3 }

   id-ml-dsa-44 OBJECT IDENTIFIER ::= { sigAlgs 17 }

   id-ml-dsa-65 OBJECT IDENTIFIER ::= { sigAlgs 18 }

   id-ml-dsa-87 OBJECT IDENTIFIER ::= { sigAlgs 19 }

   --
   -- Signature Algorithm Identifiers
   --

   sa-ml-dsa-44 SIGNATURE-ALGORITHM ::= {



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     IDENTIFIER id-ml-dsa-44
     PARAMS ARE absent
     PUBLIC-KEYS { pk-ml-dsa-44 }
     SMIME-CAPS { IDENTIFIED BY id-ml-dsa-44 } }

   sa-ml-dsa-65 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-ml-dsa-65
     PARAMS ARE absent
     PUBLIC-KEYS { pk-ml-dsa-65 }
     SMIME-CAPS { IDENTIFIED BY id-ml-dsa-65 } }

   sa-ml-dsa-87 SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-ml-dsa-87
     PARAMS ARE absent
     PUBLIC-KEYS { pk-ml-dsa-87 }
     SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 } }

   --
   -- Public Keys
   --

   pk-ml-dsa-44 PUBLIC-KEY ::= {
     IDENTIFIER id-ml-dsa-44
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
       { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-ml-dsa-65 PUBLIC-KEY ::= {
     IDENTIFIER id-ml-dsa-65
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
       { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   pk-ml-dsa-87 PUBLIC-KEY ::= {
     IDENTIFIER id-ml-dsa-87
     -- KEY no ASN.1 wrapping --
     CERT-KEY-USAGE
       { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
     -- PRIVATE-KEY no ASN.1 wrapping -- }

   ML-DSA-PublicKey ::= OCTET STRING (SIZE (1312 | 1952 | 2592))

   ML-DSA-PrivateKey ::= OCTET STRING (SIZE (32))

   --
   -- Expand SignatureAlgorithms from RFC 5912



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   --
   SignatureAlgorithms SIGNATURE-ALGORITHM ::= {
     sa-ml-dsa-44 |
     sa-ml-dsa-65 |
     sa-ml-dsa-87,
     ... }

   --
   -- Expand SignatureAlgorithms from RFC 5912
   --
   PublicKeys PUBLIC-KEY ::= {
     pk-ml-dsa-44 |
     pk-ml-dsa-65 |
     pk-ml-dsa-87,
     ...
   }

   END
   <CODE ENDS>

Appendix B.  Security Strengths

   Instead of defining the strength of a quantum algorithm in a
   traditional manner using the imprecise notion of bits of security,
   NIST has instead elected to define security levels by picking a
   reference scheme, which NIST expects to offer notable levels of
   resistance to both quantum and classical attack.  To wit, an
   algorithm that achieves NIST PQC security level 1 must require
   computational resources to break the relevant security property,
   which are greater than those required for a brute-force key search on
   AES-128.  Levels 3 and 5 use AES-192 and AES-256 as reference
   respectively.  Levels 2 and 4 use collision search for SHA-256 and
   SHA-384 as reference.

   The parameter sets defined for NIST security levels 2, 3 and 5 are
   listed in the Figure 1, along with the resulting signature size,
   public key, and private key sizes in bytes.  Note that these are the
   sizes of the plain private and public keys; and not the sizes of the
   resultant OneAsymmetricKey and SubjectPublicKeyInfo objects in which
   they are wrapped.











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   |=======+=======+=====+========+========+========|
   | Level | (k,l) | eta |  Sig.  | Public | Private|
   |       |       |     |  (B)   | Key(B) | Key(B) |
   |=======+=======+=====+========+========+========|
   |   2   | (4,4) |  2  |  2420  |  1312  |  32    |
   |   3   | (6,5) |  4  |  3309  |  1952  |  32    |
   |   5   | (8,7) |  2  |  4627  |  2592  |  32    |
   |=======+=======+=====+========+========+========|

                        Figure 1: ML-DSA Parameters

Appendix C.  Examples

   This appendix contains examples of ML-DSA public keys, private keys
   and certificates.

C.1.  Example Private Key

   The following is an example of a ML-DSA-44 private key with hex seed
   000102…1e1f:

   -----BEGIN PRIVATE KEY-----
   MDICAQAwCwYJYIZIAWUDBAMRBCAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
   HB0eHw==
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
     }
     OCTET_STRING { `000102030405060708090a0b0c0d0e0f10111213141516
   1718191a1b1c1d1e1f` }
   }

   The following is an example of a ML-DSA-65 private key with hex seed
   000102…1e1f:

   -----BEGIN PRIVATE KEY-----
   MDICAQAwCwYJYIZIAWUDBAMSBCAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
   HB0eHw==
   -----END PRIVATE KEY-----









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   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
     }
     OCTET_STRING { `000102030405060708090a0b0c0d0e0f10111213141516
   1718191a1b1c1d1e1f` }
   }

   The following is an example of a ML-DSA-87 private key with hex seed
   000102…1e1f:

   -----BEGIN PRIVATE KEY-----
   MDICAQAwCwYJYIZIAWUDBAMTBCAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
   HB0eHw==
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
     }
     OCTET_STRING { `000102030405060708090a0b0c0d0e0f10111213141516
   1718191a1b1c1d1e1f` }
   }

   NOTE: The private key is the seed and all three examples keys use the
   same seed; therefore, the private above are the same except for the
   OID used to represent the ML-DSA algorithm's security strength.

C.2.  Example Public Key

   The following is the ML-DSA-44 public key corresponding to the
   private key in the previous section.

















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   -----BEGIN PUBLIC KEY-----
   MIIFMjALBglghkgBZQMEAxEDggUhANeytHJUquDbReeTDUqY0sl9jxOX0Xidr6Fw
   JLMW6b7JT8mUbULxm3mnQTu6oz5xSctC7VEVaTrAQfrLmIretf4OHYYxGEmVtZLD
   l9IpTi4U+QqkFLo4JomaxD9MzKy8JumoMrlRGNXLQzy++WYLABOOCBf2HnYsonTD
   atVU6yKqwRYuSrAay6HjjE79j4C2WzM9D3LlXf5xzpweu5iJ58VhBsD9c4A6Kuz+
   r97XqjyyztpU0SvYzTanjPl1lDtHq9JeiArEUuV0LtHo0agq+oblkMdYwVrk0oQN
   kryhpQkPQElll/yn2LlRPxob2m6VCqqY3kZ1B9Sk9aTwWZIWWCw1cvYu2okFqzWB
   ZwxKAnd6M+DKcpX9j0/20aCjp2g9ZfX19/xg2gI+gmxfkhRMAvfRuhB1mHVT6pNn
   /NdtmQt/qZzUWv24g21D5Fn1GH3wWEeXCaAepoNZNfpwRgmQzT3BukAbqUurHd5B
   rGerMxncrKBgSNTE7vJ+4TqcF9BTj0MPLWQtwkFWYN54h32NirxyUjl4wELkKF9D
   GYRsRBJiQpdoRMEOVWuiFbWnGeWdDGsqltOYWQcf3MLN51JKe+2uVOhbMY6FTo/i
   svPt+slxkSgnCq/R5QRMOk/a/Z/zH5B4S46ORZYUSg2vWGUR09mWK56pWvGXtOX8
   YPKx7RXeOlvvX4m9x52RBR2bKBbnT6VFMe/cHL501EiFf0drzVjyHAtlOzt2pOB2
   plWaMCcYVVzGP3SFmqurkl8COGHKjND3utsocfZ9VTJtdFETWtRfShumkRj7ssij
   DuyTku8/l3Bmya3VxxDMZHsVFNIX2VjHAXw+kP0gwE5nS5BIbpNwoxoAHTL0c5ee
   SQZ0nn5Hf6C3RQj4pfI3gxK4PCW9OIygsP/3R4uvQrcWZ+2qyXxGsSlkPlhuWwVa
   DCEZRtTzbmdb7Vhg+gQqMV2YJhZNapI3w1pfv0lUkKW9TfJIuVxKrneEtgVnMWas
   QkW1tLCCoJ6TI+YvIHjFt2eDRG3v1zatOjcC1JsImESQCmGDM5e8RBmzDXqXoLOH
   wZEUdMTUG1PjKpd6y28Op122W7OeWecB52lX3vby1EVZwxp3EitSBOO1whnxaIsU
   7QvAuAGz5ugtzUPpwOn0F0TNmBW9G8iCDYuxI/BPrNGxtoXdWisbjbvz7ZM2cPCV
   oYC08ZLQixC4+rvfzCskUY4y7qCl4MkEyoRHgAg/OwzS0Li2r2e8NVuUlAJdx7Cn
   j6gOOi2/61EyiFHWB4GY6Uk2Ua54fsAlH5Irow6fUd9iptcnhM890gU5MXbfoySl
   Er2Ulwo23TSlFKhnkfDrNvAUWwmrZGUbSgMTsplhGiocSIkWJ1mHaKMRQGC6RENI
   bfUVIqHOiLMJhcIW+ObtF43VZ7MEoNTK+6iCooNC8XqaomrljbYwCD0sNY/fVmw/
   XWKkKFZ7yeqM6VyqDzVHSwv6jzOaJQq0388gg76O77wQVeGP4VNw7ssmBWbYP/Br
   IRquxDyim1TM0A+IFaJGXvC0ZRXMfkHzEk8J7/9zkwmrWLKaFFmgC85QOOk4yWeP
   cusOTuX9quZtn4Vz/Jf8QrSVn0v4th14Qz6GsDNdbpGRxNi/SHs5BcEIz9asJLDO
   t9y3z1H4TQ7Wh7lerrHFM8BvDZcCPZKnCCWDe1m6bLfU5WsKh8IDhiro8xW6WSXo
   7e+meTaaIgJ2YVHxapZfn4Hs52zAcLVYaeTbl4TPBcgwsyQsgxI=
   -----END PUBLIC KEY-----





















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   SEQUENCE {
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
     }
     BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d17
   89dafa17024b316e9bec94fc9946d42f19b79a7413bbaa33e7149cb42ed51156
   93ac041facb988adeb5fe0e1d8631184995b592c397d2294e2e14f90aa414ba3
   826899ac43f4cccacbc26e9a832b95118d5cb433cbef9660b00138e0817f61e7
   62ca274c36ad554eb22aac1162e4ab01acba1e38c4efd8f80b65b333d0f72e55
   dfe71ce9c1ebb9889e7c56106c0fd73803a2aecfeafded7aa3cb2ceda54d12bd
   8cd36a78cf975943b47abd25e880ac452e5742ed1e8d1a82afa86e590c758c15
   ae4d2840d92bca1a5090f40496597fca7d8b9513f1a1bda6e950aaa98de46750
   7d4a4f5a4f0599216582c3572f62eda8905ab3581670c4a02777a33e0ca7295f
   d8f4ff6d1a0a3a7683d65f5f5f7fc60da023e826c5f92144c02f7d1ba1075987
   553ea9367fcd76d990b7fa99cd45afdb8836d43e459f5187df058479709a01ea
   6835935fa70460990cd3dc1ba401ba94bab1dde41ac67ab3319dcaca06048d4c
   4eef27ee13a9c17d0538f430f2d642dc2415660de78877d8d8abc72523978c04
   2e4285f4319846c44126242976844c10e556ba215b5a719e59d0c6b2a96d3985
   9071fdcc2cde7524a7bedae54e85b318e854e8fe2b2f3edfac9719128270aafd
   1e5044c3a4fdafd9ff31f90784b8e8e4596144a0daf586511d3d9962b9ea95af
   197b4e5fc60f2b1ed15de3a5bef5f89bdc79d91051d9b2816e74fa54531efdc1
   cbe74d448857f476bcd58f21c0b653b3b76a4e076a6559a302718555cc63f748
   59aabab925f023861ca8cd0f7badb2871f67d55326d7451135ad45f4a1ba6911
   8fbb2c8a30eec9392ef3f977066c9add5c710cc647b1514d217d958c7017c3e9
   0fd20c04e674b90486e9370a31a001d32f473979e4906749e7e477fa0b74508f
   8a5f2378312b83c25bd388ca0b0fff7478baf42b71667edaac97c46b129643e5
   86e5b055a0c211946d4f36e675bed5860fa042a315d9826164d6a9237c35a5fb
   f495490a5bd4df248b95c4aae7784b605673166ac4245b5b4b082a09e9323e62
   f2078c5b76783446defd736ad3a3702d49b089844900a61833397bc4419b30d7
   a97a0b387c1911474c4d41b53e32a977acb6f0ea75db65bb39e59e701e76957d
   ef6f2d44559c31a77122b5204e3b5c219f1688b14ed0bc0b801b3e6e82dcd43e
   9c0e9f41744cd9815bd1bc8820d8bb123f04facd1b1b685dd5a2b1b8dbbf3ed9
   33670f095a180b4f192d08b10b8fabbdfcc2b24518e32eea0a5e0c904ca84478
   0083f3b0cd2d0b8b6af67bc355b9494025dc7b0a78fa80e3a2dbfeb51328851d
   6078198e9493651ae787ec0251f922ba30e9f51df62a6d72784cf3dd20539317
   6dfa324a512bd94970a36dd34a514a86791f0eb36f0145b09ab64651b4a0313b
   299611a2a1c48891627598768a3114060ba4443486df51522a1ce88b30985c21
   6f8e6ed178dd567b304a0d4cafba882a28342f17a9aa26ae58db630083d2c358
   fdf566c3f5d62a428567bc9ea8ce95caa0f35474b0bfa8f339a250ab4dfcf208
   3be8eefbc1055e18fe15370eecb260566d83ff06b211aaec43ca29b54ccd00f8
   815a2465ef0b46515cc7e41f3124f09efff739309ab58b29a1459a00bce5038e
   938c9678f72eb0e4ee5fdaae66d9f8573fc97fc42b4959f4bf8b61d78433e86b
   0335d6e9191c4d8bf487b3905c108cfd6ac24b0ceb7dcb7cf51f84d0ed687b95
   eaeb1c533c06f0d97023d92a70825837b59ba6cb7d4e56b0a87c203862ae8f31
   5ba5925e8edefa679369a2202766151f16a965f9f81ece76cc070b55869e4db9
   784cf05c830b3242c8312` }
   }




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   The following is the ML-DSA-65 public key corresponding to the
   private key in the previous section.

   -----BEGIN PUBLIC KEY-----
   MIIHsjALBglghkgBZQMEAxIDggehAEhoPZGXjjHrPd24sEc0gtK4il9iWUn9j1il
   YeaWvUwn0Fs427Lt8B5mTv2Bvh6ok2iM5oqi1RxZWPi7xutOie5n0sAyCVTVchLK
   xyKf8dbq8DkovVFRH42I2EdzbH3icw1ZeOVBBxMWCXiGdxG/VTmgv8TDUMK+Vyuv
   DuLi+xbM/qCAKNmaxJrrt1k33c4RHNq2L/886ouiIz0eVvvFxaHnJt5j+t0q8Bax
   GRd/o9lxotkncXP85VtndFrwt8IdWX2+uT5qMvNBxJpai+noJQiNHyqkUVXWyK4V
   Nn5OsAO4/feFEHGUlzn5//CQI+r0UQTSqEpFkG7tRnGkTcKNJ5h7tV32np6FYfYa
   gKcmmVA4Zf7Zt+5yqOF6GcQIFE9LKa/vcDHDpthXFhC0LJ9CEkWojxl+FoErAxFZ
   tluWh+Wz6TTFIlrpinm6c9Kzmdc1EO/60Z5TuEUPC6j84QEv2Y0mCnSqqhP64kmg
   BrHDT1uguILyY3giL7NvIoPCQ/D/618btBSgpw1V49QKVrbLyIrh8Dt7KILZje6i
   jhRcne39jq8c7y7ZSosFD4lk9G0eoNDCpD4N2mGCrb9PbtF1tnQiV4Wb8i86QX7P
   H52JMXteU51YevFrnhMT4EUU/6ZLqLP/K4Mh+IEcs/sCLI9kTnCkuAovv+5gSrtz
   eQkeqObFx038AoNma0DAeThwAoIEoTa/XalWjreY00kDi9sMEeA0ReeEfLUGnHXP
   KKxgHHeZ2VghDdvLIm5Rr++fHeR7Bzhz1tP5dFa+3ghQgudKKYss1I9LMJMVXzZs
   j6YBxq+FjfoywISRsqKYh/kDNZSaXW7apnmIKjqV1r9tlwoiH0udPYy/OEr4GqyV
   4rMpTgR4msg3J6XcBFWflq9B2KBTUW/u7rxSdG62qygZ4JEIcQ2DXwEfpjBlhyrT
   NNXN/7KyMQUH6S/Jk64xfal/TzCc2vD2ftmdkCFVdgg4SflTskbX/ts/22dnmFCl
   rUBOZBR/t89Pau3dBa+0uDSWjR/ogBSWDc5dlCI2Um4SpHjWnl++aXAxCzCMBoRQ
   GM/HsqtDChOmsax7sCzMuz2RGsLxEGhhP74Cm/3OAs9c04lQ7XLIOUTt+8dWFa+H
   +GTAUfPFVFbFQShjpAwG0dq1Yr3/BXG408ORe70wCIC7pemYI5uV+pG31kFtTzmL
   OtvNMJg+01krTZ731CNv0A9Q2YqlOiNaxBcnIPd9lhcmcpgM/o/3pacCeD7cK6Mb
   IlkBWhEvx/RoqcL5RkA5AC0w72eLTLeYvBFiFr96mnwYugO3tY/QdRXTEVBJ02FL
   56B+dEMAdQ3x0sWHUziQWer8PXhczdMcB2SL7cA6XDuK1G0GTVnBPVc3Ryn8TilT
   YuKlGRIEUwQovBUir6KP9f4WVeMEylvIwnrQ4MajndTfKJVsFLOMyTaCzv5AK71e
   gtKcRk5E6103tI/FaN/gzG6OFrrqBeUTVZDxkpTnPoNnsCFtu4FQMLneVZE/CAOc
   QjUcWeVRXdWvjgiaFeYl6Pbe5jk4bEZJfXomMoh3TeWBp96WKbQbRCQUH5ePuDMS
   CO/ew8bg3jm8VwY/Pc1sRwNzwIiR6inLx8xtZIO4iJCDrOhqp7UbHCz+birRjZfO
   NvvFbqQvrpfmp6wRSGRHjDZt8eux57EakJhQT9WXW98fSdxwACtjwXOanSY/utQH
   P2qfbCuK9LTDMqEDoM/6Xe6y0GLKPCFf02ACa+fFFk9KRCTvdJSIBNZvRkh3Msgg
   LHlUeGR7TqcdYnwIYCTMo1SkHwh3s48Zs3dK0glcjaU7Bp4hx2ri0gB+FnGe1ACA
   0zT32lLp9aWZBDnK8IOpW4M/Aq0QoIwabQ8mDAByhb1KL0dwOlrvRlKH0lOxisIl
   FDFiEP9WaBSxD4eik9bxmdPDlZmQ0MEmi09Q1fn877vyN70MKLgBgtZll0HxTxC/
   uyG7oSq2IKojlvVsBoa06pAXmQIkIWsv6K12xKkUju+ahqNjWmqne8Hc+2+6Wad9
   /am3Uw3AyoZIyNlzc44Burjwi0kF6EqkZBvWAkEM2XUgJl8vIx8rNeFesvoE0r2U
   1ad6uvHg4WEBCpkAh/W0bqmIsrwFEv2g+pI9rdbEXFMB0JSDZzJltasuEPS6Ug9r
   utVkpcPV4nvbCA99IOEylqMYGVTDnGSclD6+F99cH3quCo/hJsR3WFpdTWSKDQCL
   avXozTG+aakpbU8/0l7YbyIeS5P2X1kplnUzYkuSNXUMMHB1ULWFNtEJpxMcWlu+
   SlcVVnwSU0rsdmB2Huu5+uKJHHdFibgOVmrVV93vc2cZa3In6phw7wnd/seda5MZ
   poebUgXXa/erpazzOvtZ0X/FTmg4PWvloI6bZtpT3N4Ai7KUuFgr0TLNzEmVn9vC
   HlJyGIDIrQNSx58DpDu9hMTN/cbFKQBeHnzZo0mnFoo1Vpul3qgYlo1akUZr1uZO
   IL9iQXGYr8ToHCjdd+1AKCMjmLUvvehryE9HW5AWcQziqrwRoGtNuskB7BbPNlyj
   8tU4E5SKaToPk+ecRspdWm3KPSjKUK0YvRP8pVBZ3ZsYX3n5xHGWpOgbIQS8RgoF
   HgLy6ERP
   -----END PUBLIC KEY-----




Massimo, et al.           Expires 6 August 2025                [Page 20]

Internet-Draft           ML-DSA in Certificates            February 2025


   SEQUENCE {
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
     }
     BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f62594
   9fd8f58a561e696bd4c27d05b38dbb2edf01e664efd81be1ea893688ce68aa2d
   51c5958f8bbc6eb4e89ee67d2c0320954d57212cac7229ff1d6eaf03928bd515
   11f8d88d847736c7de2730d5978e5410713160978867711bf5539a0bfc4c350c
   2be572baf0ee2e2fb16ccfea08028d99ac49aebb75937ddce111cdab62fff3ce
   a8ba2233d1e56fbc5c5a1e726de63fadd2af016b119177fa3d971a2d9277173f
   ce55b67745af0b7c21d597dbeb93e6a32f341c49a5a8be9e825088d1f2aa4515
   5d6c8ae15367e4eb003b8fdf7851071949739f9fff09023eaf45104d2a84a459
   06eed4671a44dc28d27987bb55df69e9e8561f61a80a72699503865fed9b7ee7
   2a8e17a19c408144f4b29afef7031c3a6d8571610b42c9f421245a88f197e168
   12b031159b65b9687e5b3e934c5225ae98a79ba73d2b399d73510effad19e53b
   8450f0ba8fce1012fd98d260a74aaaa13fae249a006b1c34f5ba0b882f263782
   22fb36f2283c243f0ffeb5f1bb414a0a70d55e3d40a56b6cbc88ae1f03b7b288
   2d98deea28e145c9dedfd8eaf1cef2ed94a8b050f8964f46d1ea0d0c2a43e0dd
   a6182adbf4f6ed175b6742257859bf22f3a417ecf1f9d89317b5e539d587af16
   b9e1313e04514ffa64ba8b3ff2b8321f8811cb3fb022c8f644e70a4b80a2fbfe
   e604abb7379091ea8e6c5c74dfc0283666b40c0793870028204a136bf5da9568
   eb798d349038bdb0c11e03445e7847cb5069c75cf28ac601c7799d958210ddbc
   b226e51afef9f1de47b073873d6d3f97456bede085082e74a298b2cd48f4b309
   3155f366c8fa601c6af858dfa32c08491b2a29887f90335949a5d6edaa679882
   a3a95d6bf6d970a221f4b9d3d8cbf384af81aac95e2b3294e04789ac83727a5d
   c04559f96af41d8a053516feeeebc52746eb6ab2819e09108710d835f011fa63
   065872ad334d5cdffb2b2310507e92fc993ae317da97f4f309cdaf0f67ed99d9
   0215576083849f953b246d7fedb3fdb67679850a5ad404e64147fb7cf4f6aedd
   d05afb4b834968d1fe88014960dce5d942236526e12a478d69e5fbe6970310b3
   08c06845018cfc7b2ab430a13a6b1ac7bb02cccbb3d911ac2f11068613fbe029
   bfdce02cf5cd38950ed72c83944edfbc75615af87f864c051f3c55456c541286
   3a40c06d1dab562bdff0571b8d3c3917bbd300880bba5e998239b95fa91b7d64
   16d4f398b3adbcd30983ed3592b4d9ef7d4236fd00f50d98aa53a235ac417272
   0f77d96172672980cfe8ff7a5a702783edc2ba31b2259015a112fc7f468a9c2f
   9464039002d30ef678b4cb798bc116216bf7a9a7c18ba03b7b58fd07515d3115
   049d3614be7a07e744300750df1d2c58753389059eafc3d785ccdd31c07648be
   dc03a5c3b8ad46d064d59c13d57374729fc4e295362e2a5191204530428bc152
   2afa28ff5fe1655e304ca5bc8c27ad0e0c6a39dd4df28956c14b38cc93682cef
   e402bbd5e82d29c464e44eb5d37b48fc568dfe0cc6e8e16baea05e5135590f19
   294e73e8367b0216dbb815030b9de55913f08039c42351c59e5515dd5af8e089
   a15e625e8f6dee639386c46497d7a263288774de581a7de9629b41b4424141f9
   78fb8331208efdec3c6e0de39bc57063f3dcd6c470373c08891ea29cbc7cc6d6
   483b8889083ace86aa7b51b1c2cfe6e2ad18d97ce36fbc56ea42fae97e6a7ac1
   14864478c366df1ebb1e7b11a9098504fd5975bdf1f49dc70002b63c1739a9d2
   63fbad4073f6a9f6c2b8af4b4c332a103a0cffa5deeb2d062ca3c215fd360026
   be7c5164f4a4424ef74948804d66f46487732c8202c795478647b4ea71d627c0
   86024cca354a41f0877b38f19b3774ad2095c8da53b069e21c76ae2d2007e167
   19ed40080d334f7da52e9f5a5990439caf083a95b833f02ad10a08c1a6d0f260



Massimo, et al.           Expires 6 August 2025                [Page 21]

Internet-Draft           ML-DSA in Certificates            February 2025


   c007285bd4a2f47703a5aef465287d253b18ac22514316210ff566814b10f87a
   293d6f199d3c3959990d0c1268b4f50d5f9fcefbbf237bd0c28b80182d665974
   1f14f10bfbb21bba12ab620aa2396f56c0686b4ea9017990224216b2fe8ad76c
   4a9148eef9a86a3635a6aa77bc1dcfb6fba59a77dfda9b7530dc0ca8648c8d97
   3738e01bab8f08b4905e84aa4641bd602410cd97520265f2f231f2b35e15eb2f
   a04d2bd94d5a77abaf1e0e161010a990087f5b46ea988b2bc0512fda0fa923da
   dd6c45c5301d09483673265b5ab2e10f4ba520f6bbad564a5c3d5e27bdb080f7
   d20e13296a3181954c39c649c943ebe17df5c1f7aae0a8fe126c477585a5d4d6
   48a0d008b6af5e8cd31be69a9296d4f3fd25ed86f221e4b93f65f59299675336
   24b9235750c30707550b58536d109a7131c5a5bbe4a5715567c12534aec76607
   61eebb9fae2891c774589b80e566ad557ddef7367196b7227ea9870ef09ddfec
   79d6b9319a6879b5205d76bf7aba5acf33afb59d17fc54e68383d6be5a08e9b6
   6da53dcde008bb294b8582bd132cdcc49959fdbc21e52721880c8ad0352c79f0
   3a43bbd84c4cdfdc6c529005e1e7cd9a349a7168a35569ba5dea818968d5a914
   66bd6e64e20bf62417198afc4e81c28dd77ed4028232398b52fbde86bc84f475
   b9016710ce2aabc11a06b4dbac901ec16cf365ca3f2d53813948a693a0f93e79
   c46ca5d5a6dca3d28ca50ad18bd13fca55059dd9b185f79f9c47196a4e81b210
   4bc460a051e02f2e8444f` }
   }

   The following is the ML-DSA-87 public key corresponding to the
   private key in the previous section.

   -----BEGIN PUBLIC KEY-----
   MIIKMjALBglghkgBZQMEAxMDggohAJeSvOwvJDBoaoL8zzwvX/Zl53HXq0G5AljP
   p+kOyXEkpzsyO5uiGrZNdnxDP1pSHv/hj4bkahiJUsRGfgSLcp5/xNEV5+SNoYlt
   X+EZsQ3N3vYssweVQHS0IzblKDbeYdqUH4036misgQb6vhkHBnmvYAhTcSD3B5O4
   6pzA5ue3tMmlx0IcYPJEUboekz2xou4Wx5VZ8hs9G4MFhQqkKvuxPx9NW59INfnY
   ffzrFi0O9Kf9xMuhdDzRyHu0ln2hbMh2S2Vp347lvcv/6aTgV0jm/fIlr55O63dz
   ti6Phfm1a1SJRVUYRPvYmAakrDab7S0lYQD2iKatXgpwmCbcREnpHiPFUG5kI2Hv
   WjE3EvebxLMYaGHKhaS6sX5/lD0bijM6o6584WtEDWAY+eBNr1clx/GpP60aWie2
   eJW9JJqpFoXeIK8yyLfiaMf5aHfQyFABE1pPCo8bgmT6br5aNJ2K7K0aFimczy/Z
   x7hbrOLO06oSdrph7njtflyltnzdRYqTVAMOaru6v1agojFv7J26g7UdQv0xZ/Hg
   +QhV1cZlCbIQJl3B5U7ES0O6fPmu8Ri0TYCRLOdRZqZlHhFs6+SSKacGLAmTH3Gr
   0ik/dvfvwyFbqXgAA35Y5HC9u7Q8GwQ56vecVNk7RKrJ7+n74VGHTPsqZMvuKMxM
   D+d3Xl2HDxwC5bLjxQBMmV8kybd5y3U6J30Ocf1CXra8LKVs4SnbUfcHQPMeY5dr
   UMcxLpeX14xbGsJKX6NHzJFuCoP1w7Z1zTC4Hj+hC5NETgc5dXHM6Yso2lHbkFa8
   coxbCxGB4vvTh7THmrGl/v7ONxZ693LdrRTrTDmC2lpZ0OnrFz7GMVCRFwAno6te
   9qoSnLhYVye5NYooUB1xOnLz8dsxcUKG+bZAgBOvBgRddVkvwLfdR8c+2cdbEenX
   xp98rfwygKkGLFJzxDvhw0+HRIhkzqe1yX1tMvWb1fJThGU7tcT6pFvqi4lAKEPm
   Rba5Jp4r2YjdrLAzMo/7BgRQ998IAFPmlpslHodezsMs/FkoQNaatpp14Gs3nFNd
   lSZrCC9PCckxYrM7DZ9zB6TqqlIQRDf+1m+O4+q71F1nslqBM/SWRotSuv/b+tk+
   7xqYGLXkLscieIo9jTUp/Hd9K6VwgB364B7IgwKDfB+54DVXJ2Re4QRsP5Ffaugt
   rU+2sDVqRlGP/INBVcO0/m2vpsyKXM9TxzoISdjUT33PcnVOcOG337RHu070nRpx
   j2Fxu84gCVDgzpJhBrFRo+hx1c5JcxvWZQqbDKly2hxfE21Egg6mODwI87OEzyM4
   54nFE/YYzFaUpvDO4QRRHh7XxfI6Hr/YoNuEJFUyQBVtv2IoMbDGQ9HFUbbz96mN
   KbhcLeBaZfphXu4WSVvZBzdnIRW1PpHF2QAozz8ak5U6FT3lO0QITpzP9rc2aTkm
   2u/rstd6pa1om5LzFoZmnfFtFxXMWPeiz7ct0aUekvglmTp0Aivn6etgVGVEVwlN



Massimo, et al.           Expires 6 August 2025                [Page 22]

Internet-Draft           ML-DSA in Certificates            February 2025


   FJKPICFeeyIqxWtRrb7I2L22mDl5p+OiG0S10VGMqX0LUZX1HtaiQ1DIl0fh7epR
   tEjj6RRwVM6SeHPJDbOU2GiI4H3/F3WT1veeFSMCIErrA74jhq8+JAeL0CixaJ9e
   FHyfRSyM6wLsWcydtjoDV2zur+mCOQI4l9oCNmMKU8Def0NaGYaXkvqzbnueY1dg
   8JBp5kMucAA1rCoCh5//Ch4b7FIgRxk9lOtd8e/VPuoRRMp4lAhS9eyXJ5BLNm7e
   T14tMx+tX8KC6ixH6SMUJ3HD3XWoc1dIfe+Z5fGOnZ7WI8F10CiIxR+CwHqA1UcW
   s8PCvb4unwqbuq6+tNUpNodkBvXADo5LvQpewFeX5iB8WrbIjxpohCG9BaEU9Nfe
   KsJB+g6L7f9H92Ldy+qpEAT40x6FCVyBBUmUrTgm40S6lgQIEPwLKtHeSM+t4ALG
   LlpJoHMas4NEvBY23xa/YH1WhV5W1oQAPHGOS62eWgmZefzd7rHEp3ds03o0F8sO
   GE4p75vA6HR1umY74J4Aq1Yut8D3Fl+WmptCQUGYzPG/8qLI1omkFOznZiknZlaJ
   6U25YeuuxWFcvBp4lcaFGslhQy/xEY1GB9Mu+dxzLVEzO+S00OMN3qeE7Ki+R+dB
   vpwZYx3EcKUu9NwTpPNjP9Q014fBcJd7QX31mOHQ3eUGu3HW8LwX7HDjsDzcGWXL
   Npk/YzsEcuUNCSOsbGb98dPmRZzBIfD1+U0J6dvPXWkOIyM4OKC6y3xjjRsmUKQw
   jNFxtoVRJtHaZypu2FqNeMKG+1b0qz0hSXUoBFxjJiyKQq8vmALFO3u4vijnj+C1
   zkX7t6GvGjsoqNlLeJDjyILjm8mOnwrXYCW/DdLwApjnFBoiaz187kFPYE0eC6VN
   EdX+WLzOpq13rS6MHKrPMkWQFLe5EAGx76itFypSP7jjZbV3Ehv5/Yiixgwh6CHX
   tqy0elqZXkDKztXCI7j+beXhjp0uWJOu/rt6rn/xoUYmDi8RDpOVKCE6ACWjjsea
   q8hhsl68UJpGdMEyqqy34BRvFO/RHPyvTKpPd1pxbOMl4KQ1pNNJ1yC88TdFCvxF
   BG/Bofg6nTKXd6cITkqtrnEizpcAWTBSjrPH9/ESmzcoh6NxFVo7ogGiXL8dy2Tn
   ze4JLDFB+1VQ/j0N2C6HDleLK0ZQCBgRO49laXc8Z3OFtppCt33Lp6z/2V/URS4j
   qqHTfh2iFR6mWNQKNZayesn4Ep3GzwZDdyYktZ9PRhIw30ccomCHw5QtXGaH32CC
   g1k1o/h8t2Kww7HQ3aSmUzllvvG3uCkuJUwBTQkP7YV8RMGDnGlMCmTj+tkKEfU0
   citu4VdPLhSdVddE3kiHAk4IURQxwGJ1DhbHSrnzJC8ts/+xKo1hB/qiKdb2NzsH
   8205MrO9sEwZ3WTq3X+Tw8Vkw1ihyB3PHJwx5bBlaPl1RMF9wVaYxcs4mDqa/EJ4
   P6p3OlLJ2CYGkL6eMVaqW8FQneo/aVh2lc1v8XK6g+am2KfWu+u7zaNnJzGYP4m8
   WDHcN8PzxcVvrMaX88sgvV2629cC5UhErC9iaQH+FZ25Pf1Hc9j+c1YrhGwfyFbR
   gCdihA68cteYi951y8pw0xnTLODMAlO7KtRVcj7gx/RzbObmZlxayjKkgcU4Obwl
   kWewE9BCM5Xuuaqu4yBhSafVUNZ/xf3+SopcNdJRC2ZDeauPcoVaKvR6vOKmMgSO
   r4nly0qI3rxTpZUQOszk8c/xis/wev4etXFqoeQLYxNMOjrpV5+of1Fb4JPC0p22
   1rZck2YeAGNrWScE0JPMZxbCNC6xhT1IyFxjrIooVEYse3fn470erFvKKP+qALXT
   SfilR62HW5aowrKRDJMBMJo/kTilaTER9Vs8AJypR8Od/ILZjrHKpKnL6IX3hvqG
   5VvgYiIvi6kKl0BzMmsxISrs4KNKYA==
   -----END PUBLIC KEY-----

   SEQUENCE {
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
     }
     BIT_STRING { `00` `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab4
   1b90258cfa7e90ec97124a73b323b9ba21ab64d767c433f5a521effe18f86e46
   a188952c4467e048b729e7fc4d115e7e48da1896d5fe119b10dcddef62cb3079
   54074b42336e52836de61da941f8d37ea68ac8106fabe19070679af600853712
   0f70793b8ea9cc0e6e7b7b4c9a5c7421c60f24451ba1e933db1a2ee16c79559f
   21b3d1b8305850aa42afbb13f1f4d5b9f4835f9d87dfceb162d0ef4a7fdc4cba
   1743cd1c87bb4967da16cc8764b6569df8ee5bdcbffe9a4e05748e6fdf225af9
   e4eeb7773b62e8f85f9b56b548945551844fbd89806a4ac369bed2d256100f68
   8a6ad5e0a709826dc4449e91e23c5506e642361ef5a313712f79bc4b3186861c
   a85a4bab17e7f943d1b8a333aa3ae7ce16b440d6018f9e04daf5725c7f1a93fa
   d1a5a27b67895bd249aa91685de20af32c8b7e268c7f96877d0c85001135a4f0



Massimo, et al.           Expires 6 August 2025                [Page 23]

Internet-Draft           ML-DSA in Certificates            February 2025


   a8f1b8264fa6ebe5a349d8aecad1a16299ccf2fd9c7b85bace2ced3aa1276ba6
   1ee78ed7e5ca5b67cdd458a9354030e6abbbabf56a0a2316fec9dba83b51d42f
   d3167f1e0f90855d5c66509b210265dc1e54ec44b43ba7cf9aef118b44d80912
   ce75166a6651e116cebe49229a7062c09931f71abd2293f76f7efc3215ba9780
   0037e58e470bdbbb43c1b0439eaf79c54d93b44aac9efe9fbe151874cfb2a64c
   bee28cc4c0fe7775e5d870f1c02e5b2e3c5004c995f24c9b779cb753a277d0e7
   1fd425eb6bc2ca56ce129db51f70740f31e63976b50c7312e9797d78c5b1ac24
   a5fa347cc916e0a83f5c3b675cd30b81e3fa10b93444e07397571cce98b28da5
   1db9056bc728c5b0b1181e2fbd387b4c79ab1a5fefece37167af772ddad14eb4
   c3982da5a59d0e9eb173ec6315091170027a3ab5ef6aa129cb8585727b9358a2
   8501d713a72f3f1db31714286f9b6408013af06045d75592fc0b7dd47c73ed9c
   75b11e9d7c69f7cadfc3280a9062c5273c43be1c34f87448864cea7b5c97d6d3
   2f59bd5f25384653bb5c4faa45bea8b89402843e645b6b9269e2bd988ddacb03
   3328ffb060450f7df080053e6969b251e875ecec32cfc592840d69ab69a75e06
   b379c535d95266b082f4f09c93162b33b0d9f7307a4eaaa52104437fed66f8ee
   3eabbd45d67b25a8133f496468b52baffdbfad93eef1a9818b5e42ec722788a3
   d8d3529fc777d2ba570801dfae01ec88302837c1fb9e0355727645ee1046c3f9
   15f6ae82dad4fb6b0356a46518ffc834155c3b4fe6dafa6cc8a5ccf53c73a084
   9d8d44f7dcf72754e70e1b7dfb447bb4ef49d1a718f6171bbce200950e0ce926
   106b151a3e871d5ce49731bd6650a9b0ca972da1c5f136d44820ea6383c08f3b
   384cf2338e789c513f618cc5694a6f0cee104511e1ed7c5f23a1ebfd8a0db842
   4553240156dbf622831b0c643d1c551b6f3f7a98d29b85c2de05a65fa615eee1
   6495bd90737672115b53e91c5d90028cf3f1a93953a153de53b44084e9ccff6b
   736693926daefebb2d77aa5ad689b92f31686669df16d1715cc58f7a2cfb72dd
   1a51e92f825993a74022be7e9eb6054654457094d14928f20215e7b222ac56b5
   1adbec8d8bdb6983979a7e3a21b44b5d1518ca97d0b5195f51ed6a24350c8974
   7e1edea51b448e3e9147054ce927873c90db394d86888e07dff177593d6f79e1
   52302204aeb03be2386af3e24078bd028b1689f5e147c9f452c8ceb02ec59cc9
   db63a03576ceeafe98239023897da0236630a53c0de7f435a19869792fab36e7
   b9e635760f09069e6432e700035ac2a02879fff0a1e1bec522047193d94eb5df
   1efd53eea1144ca78940852f5ec9727904b366ede4f5e2d331fad5fc282ea2c4
   7e923142771c3dd75a87357487def99e5f18e9d9ed623c175d02888c51f82c07
   a80d54716b3c3c2bdbe2e9f0a9bbaaebeb4d52936876406f5c00e8e4bbd0a5ec
   05797e6207c5ab6c88f1a688421bd05a114f4d7de2ac241fa0e8bedff47f762d
   dcbeaa91004f8d31e85095c81054994ad3826e344ba96040810fc0b2ad1de48c
   fade002c62e5a49a0731ab38344bc1636df16bf607d56855e56d684003c718e4
   bad9e5a099979fcddeeb1c4a7776cd37a3417cb0e184e29ef9bc0e87475ba663
   be09e00ab562eb7c0f7165f969a9b42414198ccf1bff2a2c8d689a414ece7662
   927665689e94db961ebaec5615cbc1a7895c6851ac961432ff1118d4607d32ef
   9dc732d51333be4b4d0e30ddea784eca8be47e741be9c19631dc470a52ef4dc1
   3a4f3633fd434d787c170977b417df598e1d0dde506bb71d6f0bc17ec70e3b03
   cdc1965cb36993f633b0472e50d0923ac6c66fdf1d3e6459cc121f0f5f94d09e
   9dbcf5d690e23233838a0bacb7c638d1b2650a4308cd171b6855126d1da672a6
   ed85a8d78c286fb56f4ab3d21497528045c63262c8a42af2f9802c53b7bb8be2
   8e78fe0b5ce45fbb7a1af1a3b28a8d94b7890e3c882e39bc98e9f0ad76025bf0
   dd2f00298e7141a226b3d7cee414f604d1e0ba54d11d5fe58bccea6ad77ad2e8
   c1caacf32459014b7b91001b1efa8ad172a523fb8e365b577121bf9fd88a2c60
   c21e821d7b6acb47a5a995e40caced5c223b8fe6de5e18e9d2e5893aefebb7aa



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   e7ff1a146260e2f110e939528213a0025a38ec79aabc861b25ebc509a4674c13
   2aaacb7e0146f14efd11cfcaf4caa4f775a716ce325e0a435a4d349d720bcf13
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   add7f93c3c564c358a1c81dcf1c9c31e5b06568f97544c17dc15698c5cb38983
   a9afc42783faa773a52c9d8260690be9e3156aa5bc1509dea3f69587695cd6ff
   172ba83e6a6d8a7d6bbebbbcda3672731983f89bc5831dc37c3f3c5c56facc69
   7f3cb20bd5dbadbd702e54844ac2f626901fe159db93dfd4773d8fe73562b846
   c1fc856d1802762840ebc72d7988bde75cbca70d319d32ce0cc0253bb2ad4557
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   ee3206149a7d550d67fc5fdfe4a8a5c35d2510b664379ab8f72855a2af47abce
   2a632048eaf89e5cb4a88debc53a595103acce4f1cff18acff07afe1eb5716aa
   1e40b63134c3a3ae9579fa87f515be093c2d29db6d6b65c93661e00636b59270
   4d093cc6716c2342eb1853d48c85c63ac8a2854462c7b77e7e3bd1eac5bca28f
   faa00b5d349f8a547ad875b96a8c2b2910c9301309a3f9138a5693111f55b3c0
   09ca947c39dfc82d98eb1caa4a9cbe885f786fa86e55be062222f8ba90a97407
   3326b31212aece0a34a60` }
   }

C.3.  Example Certificates

      |  The example certificates in this section have key usage bits
      |  set to digitalSignature, keyCertSign, and cRLSign to lessen the
      |  number of examples, i.e., brevity.  Certificate Policies (CPs)
      |  [RFC3647] for production CAs should consider whether this
      |  combination is appropriate.

   The following is a self-signed certificate for the ML-DSA-44 public
   key in the previous section.

   -----BEGIN CERTIFICATE-----
   MIIPlDCCBgqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMR
   MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
   MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
   TEFNUFMgV0cwggUyMAsGCWCGSAFlAwQDEQOCBSEA17K0clSq4NtF55MNSpjSyX2P
   E5fReJ2voXAksxbpvslPyZRtQvGbeadBO7qjPnFJy0LtURVpOsBB+suYit61/g4d
   hjEYSZW1ksOX0ilOLhT5CqQUujgmiZrEP0zMrLwm6agyuVEY1ctDPL75ZgsAE44I
   F/YediyidMNq1VTrIqrBFi5KsBrLoeOMTv2PgLZbMz0PcuVd/nHOnB67mInnxWEG
   wP1zgDoq7P6v3teqPLLO2lTRK9jNNqeM+XWUO0er0l6ICsRS5XQu0ejRqCr6huWQ
   x1jBWuTShA2SvKGlCQ9ASWWX/KfYuVE/GhvabpUKqpjeRnUH1KT1pPBZkhZYLDVy
   9i7aiQWrNYFnDEoCd3oz4Mpylf2PT/bRoKOnaD1l9fX3/GDaAj6CbF+SFEwC99G6
   EHWYdVPqk2f8122ZC3+pnNRa/biDbUPkWfUYffBYR5cJoB6mg1k1+nBGCZDNPcG6



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   QBupS6sd3kGsZ6szGdysoGBI1MTu8n7hOpwX0FOPQw8tZC3CQVZg3niHfY2KvHJS
   OXjAQuQoX0MZhGxEEmJCl2hEwQ5Va6IVtacZ5Z0MayqW05hZBx/cws3nUkp77a5U
   6FsxjoVOj+Ky8+36yXGRKCcKr9HlBEw6T9r9n/MfkHhLjo5FlhRKDa9YZRHT2ZYr
   nqla8Ze05fxg8rHtFd46W+9fib3HnZEFHZsoFudPpUUx79wcvnTUSIV/R2vNWPIc
   C2U7O3ak4HamVZowJxhVXMY/dIWaq6uSXwI4YcqM0Pe62yhx9n1VMm10URNa1F9K
   G6aRGPuyyKMO7JOS7z+XcGbJrdXHEMxkexUU0hfZWMcBfD6Q/SDATmdLkEhuk3Cj
   GgAdMvRzl55JBnSefkd/oLdFCPil8jeDErg8Jb04jKCw//dHi69CtxZn7arJfEax
   KWQ+WG5bBVoMIRlG1PNuZ1vtWGD6BCoxXZgmFk1qkjfDWl+/SVSQpb1N8ki5XEqu
   d4S2BWcxZqxCRbW0sIKgnpMj5i8geMW3Z4NEbe/XNq06NwLUmwiYRJAKYYMzl7xE
   GbMNepegs4fBkRR0xNQbU+Mql3rLbw6nXbZbs55Z5wHnaVfe9vLURVnDGncSK1IE
   47XCGfFoixTtC8C4AbPm6C3NQ+nA6fQXRM2YFb0byIINi7Ej8E+s0bG2hd1aKxuN
   u/PtkzZw8JWhgLTxktCLELj6u9/MKyRRjjLuoKXgyQTKhEeACD87DNLQuLavZ7w1
   W5SUAl3HsKePqA46Lb/rUTKIUdYHgZjpSTZRrnh+wCUfkiujDp9R32Km1yeEzz3S
   BTkxdt+jJKUSvZSXCjbdNKUUqGeR8Os28BRbCatkZRtKAxOymWEaKhxIiRYnWYdo
   oxFAYLpEQ0ht9RUioc6IswmFwhb45u0XjdVnswSg1Mr7qIKig0LxepqiauWNtjAI
   PSw1j99WbD9dYqQoVnvJ6ozpXKoPNUdLC/qPM5olCrTfzyCDvo7vvBBV4Y/hU3Du
   yyYFZtg/8GshGq7EPKKbVMzQD4gVokZe8LRlFcx+QfMSTwnv/3OTCatYspoUWaAL
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   n+VHd8D2WADpR/kEMpDhSwG2P44mwwE4CUKGbHS0qQLOSRwMlQVEzwxpOOrLMusw
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   3YqNKrEpTgVV7EmVpUjcVszjWgXcSKynVVsWQd3j0Zf83zXRLwmq8+anJ3XNGCSa
   IecO2sZxDbaiHhwFYRkt0BGRM2QM//IPMYeXhRa/1svmbOEHGxJG9LqTffkBs+01
   Bp7r3/9lRZ+5t3eukpinpJrCT0AgeV3l3ujbzyCiQbboFDaPS4+kKvi+iS2eHjiu
   S/WkfP1Go5jksxhkceJFNPsTmGCyXGPy2/haU9hkiMg9/wmuIKm/gxRfIBh/DoIr
   1HWZjTuWcBGWTu2NuXeAVO/MbMtpB0u6mWYktHQcVxA2LenU+N5LEPbbHp+AmPQC
   RZPqBziTyx/nuVnFD+/EAbPKzeqMKhcTW6nfkKt/Md4zmi1vhWxx7c+wDlo9cyAf
   vsS0p5uXKK1wzaC4mBIVdPYNlZtAjBCK8asKpH3/NyYJ8xhsBjxXLLiQifKiGOpA
   LLBy/LyJWmo4R4zkAtUILD4FcsIyLMIJlsqWjaNdey7bwGI75hZQkBIF8QJxFVtT
   n4HQBtuNe2ek7e72d+bayceJvlUAFXTu6oeX9/UuS7AhuY4giNzI1pNOgNwWXRxx
   REmwvPrzJatZZ7cwfsKTezSSQlv2O4q70+2X2h0VtUg/pkz3GknE07S3ggDR9Qkg
   bywQS/42luPIADbbAKXhHaBaX/TaD/uZVn+BOZ5sqWmxEbbHtvzlSea02J1Fk4Hq
   kWbpuzByCJ25SuDRr+Xyn84ZDnetumQ0lBkc2ro+rZKXw8YGMyt0aX8ZwJxL4qNB
   /WFFEproVsOru8G7iwXgt4QP8WRBSp2kTlQUbNTF3gxOTsslkUErTnvcRQ0GpK06



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   DRQG8wbjgewpHyw7O8Sfi34EjAzic0gwtIp501/MWmKpRUgAow9LPreiaLq2TBIQ
   DXEhUb9fEhY77QKeir8cpue3sShqcz9TLa5REJGqsP/8/URk7lZjiI+YWbRLp2U2
   D//0NPEq8fxrzNtacZRxSdx2id/yTWumtj5swjFA4yk0tunadltDMgEYuKgR+Jw9
   G3/yFTDnepHK41V6x8eE/4JjUAvIJWADDWxudO7oF/wsY0AnUuWe9DkW09g8IWhk
   NukDTdpsl08hCLF06qH3MSHJrdUAzs2GGLMCvtrXK2L3k70PcLqMXhbPSr7d1RGW
   gW0BlRfR4l+2LJ952SMv3xzuxgT43aX3FFVBxXk7nFrhWJWIpJpuYXRhTqASkzoZ
   KzsIRyW0ZbsaIsy0tgzzyhQvdoOoJn+2sKjcCzpfY6tgRD9sfucOm1sGet/cM5YP
   iJYei2qKMeYcvACWiI8GNGY37OzhlikbleO4xXnfJwEOYx66NjTHZqkz1/TiCBGU
   a7h+l/fnut6VfkxS1yZ2r5Gsdx7DUfNkEeKyzIMnYRA3zw3047lHqH714rV5VbE3
   yYEQWvdtYlHMFM2z9DDta59RRATOemm7AA1fYsfodrV/QPJi5qPmvpHtCvfItbdL
   Fg88Zh1zV5nV+0doUTXFVR9poJRE9fASlfU5qCJ9Jx5ISfvIkGz1fmfqXhUN9fE7
   C0Evl7IYQLguTXFznRvsXvnliwR9Ut/g85JtXUiku4F2ThCBMHBDbov6p128kP+2
   7LBgShM4IG80clxon8sWh6y0RLUz1MTamEYZKCXAPZzJoWhbzdNns/QTsjNP8wlu
   vBRtdkb6w4Vrm6GO2BXY6pQUBPcoDuymAhfAF9TxRn860OQeMcT/NRsU9Z/8nRnz
   3KbAuMTYsQ6qbjuLTDwfF9B4b4YUDQR22z8wlzCNLzgwFlGSI12xhf3ejRlwjGZJ
   J/11Up4pEegRS/c+Li2OUvQr9Jxi8XGIdEJZY1T8oVpzDJf3C29gpARWSDAXrFn0
   lgZHnqFyebeC1uDW8r/wGtYmI2EC53+FlOF5AFcH+3LzObZzerqwror4UMOA+B5c
   QMU5vDv1LFcWLzvJHMXJfCHL5nVSukXCMawr+DbeKjrkseG0UX0gpUbQy0vHIH1K
   2geD2xyl3TJ8jCaKOxb/Hu+KfkvtOCsh07TA+cnTV1WHR77svUcMErzHXWOFm8+U
   omIXALO1EiDbpu38gERRLkC84eMhRBQjKcdmlcBFsmilt3cfIofypuhMRiIFjIke
   00y2GEdQVsZGA/LX1HILqD4dEFDDQI2LPvCG5qe28HTfWspzsqK94IRESzm+Vmdp
   IjNzkTyrPI06yMvxaHGajwUtLWCReJOG/uXhswbX7EviVYyqCR4vzDLDVXAulxo/
   OsHaQhMX8xYOLXontx7SNCBlu/EEBww5QklKUldgd5igr7bDxsvZ6vHy/wcNIzY3
   RUdidnuDkpSm1hIoLz4/SW2Tm6C2u9La5evu7xAfIy1ul8LE3/P0AAAAAAAAAAAA
   AAAAABcmOEM=
   -----END CERTIFICATE-----

   SEQUENCE {
     SEQUENCE {
       [0] {
         INTEGER { 2 }
       }
       INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
       SEQUENCE {
         OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
       }
       SEQUENCE {
         SET {
           SEQUENCE {
             # organizationName
             OBJECT_IDENTIFIER { 2.5.4.10 }
             PrintableString { "IETF" }
           }
         }
         SET {
           SEQUENCE {
             # commonName
             OBJECT_IDENTIFIER { 2.5.4.3 }



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             PrintableString { "LAMPS WG" }
           }
         }
       }
       SEQUENCE {
         UTCTime { "200203043210Z" }
         UTCTime { "400129043210Z" }
       }
       SEQUENCE {
         SET {
           SEQUENCE {
             # organizationName
             OBJECT_IDENTIFIER { 2.5.4.10 }
             PrintableString { "IETF" }
           }
         }
         SET {
           SEQUENCE {
             # commonName
             OBJECT_IDENTIFIER { 2.5.4.3 }
             PrintableString { "LAMPS WG" }
           }
         }
       }
       SEQUENCE {
         SEQUENCE {
           OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
         }
         BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f139
   7d1789dafa17024b316e9bec94fc9946d42f19b79a7413bbaa33e7149cb42ed5
   115693ac041facb988adeb5fe0e1d8631184995b592c397d2294e2e14f90aa41
   4ba3826899ac43f4cccacbc26e9a832b95118d5cb433cbef9660b00138e0817f
   61e762ca274c36ad554eb22aac1162e4ab01acba1e38c4efd8f80b65b333d0f7
   2e55dfe71ce9c1ebb9889e7c56106c0fd73803a2aecfeafded7aa3cb2ceda54d
   12bd8cd36a78cf975943b47abd25e880ac452e5742ed1e8d1a82afa86e590c75
   8c15ae4d2840d92bca1a5090f40496597fca7d8b9513f1a1bda6e950aaa98de4
   67507d4a4f5a4f0599216582c3572f62eda8905ab3581670c4a02777a33e0ca7
   295fd8f4ff6d1a0a3a7683d65f5f5f7fc60da023e826c5f92144c02f7d1ba107
   5987553ea9367fcd76d990b7fa99cd45afdb8836d43e459f5187df058479709a
   01ea6835935fa70460990cd3dc1ba401ba94bab1dde41ac67ab3319dcaca0604
   8d4c4eef27ee13a9c17d0538f430f2d642dc2415660de78877d8d8abc7252397
   8c042e4285f4319846c44126242976844c10e556ba215b5a719e59d0c6b2a96d
   39859071fdcc2cde7524a7bedae54e85b318e854e8fe2b2f3edfac9719128270
   aafd1e5044c3a4fdafd9ff31f90784b8e8e4596144a0daf586511d3d9962b9ea
   95af197b4e5fc60f2b1ed15de3a5bef5f89bdc79d91051d9b2816e74fa54531e
   fdc1cbe74d448857f476bcd58f21c0b653b3b76a4e076a6559a302718555cc63
   f74859aabab925f023861ca8cd0f7badb2871f67d55326d7451135ad45f4a1ba
   69118fbb2c8a30eec9392ef3f977066c9add5c710cc647b1514d217d958c7017



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   c3e90fd20c04e674b90486e9370a31a001d32f473979e4906749e7e477fa0b74
   508f8a5f2378312b83c25bd388ca0b0fff7478baf42b71667edaac97c46b1296
   43e586e5b055a0c211946d4f36e675bed5860fa042a315d9826164d6a9237c35
   a5fbf495490a5bd4df248b95c4aae7784b605673166ac4245b5b4b082a09e932
   3e62f2078c5b76783446defd736ad3a3702d49b089844900a61833397bc4419b
   30d7a97a0b387c1911474c4d41b53e32a977acb6f0ea75db65bb39e59e701e76
   957def6f2d44559c31a77122b5204e3b5c219f1688b14ed0bc0b801b3e6e82dc
   d43e9c0e9f41744cd9815bd1bc8820d8bb123f04facd1b1b685dd5a2b1b8dbbf
   3ed933670f095a180b4f192d08b10b8fabbdfcc2b24518e32eea0a5e0c904ca8
   44780083f3b0cd2d0b8b6af67bc355b9494025dc7b0a78fa80e3a2dbfeb51328
   851d6078198e9493651ae787ec0251f922ba30e9f51df62a6d72784cf3dd2053
   93176dfa324a512bd94970a36dd34a514a86791f0eb36f0145b09ab64651b4a0
   313b299611a2a1c48891627598768a3114060ba4443486df51522a1ce88b3098
   5c216f8e6ed178dd567b304a0d4cafba882a28342f17a9aa26ae58db630083d2
   c358fdf566c3f5d62a428567bc9ea8ce95caa0f35474b0bfa8f339a250ab4dfc
   f2083be8eefbc1055e18fe15370eecb260566d83ff06b211aaec43ca29b54ccd
   00f8815a2465ef0b46515cc7e41f3124f09efff739309ab58b29a1459a00bce5
   038e938c9678f72eb0e4ee5fdaae66d9f8573fc97fc42b4959f4bf8b61d78433
   e86b0335d6e9191c4d8bf487b3905c108cfd6ac24b0ceb7dcb7cf51f84d0ed68
   7b95eaeb1c533c06f0d97023d92a70825837b59ba6cb7d4e56b0a87c203862ae
   8f315ba5925e8edefa679369a2202766151f16a965f9f81ece76cc070b55869e
   4db9784cf05c830b3242c8312` }
       }
       [3] {
         SEQUENCE {
           SEQUENCE {
             # keyUsage
             OBJECT_IDENTIFIER { 2.5.29.15 }
             BOOLEAN { TRUE }
             OCTET_STRING {
               BIT_STRING { b`1000011` }
             }
           }
           SEQUENCE {
             # basicConstraints
             OBJECT_IDENTIFIER { 2.5.29.19 }
             BOOLEAN { TRUE }
             OCTET_STRING {
               SEQUENCE {
                 BOOLEAN { TRUE }
               }
             }
           }
           SEQUENCE {
             # subjectKeyIdentifier
             OBJECT_IDENTIFIER { 2.5.29.14 }
             OCTET_STRING {
               OCTET_STRING { `329a07b1fabb48f52a309f11a1898f848e23



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   22ff` }
             }
           }
         }
       }
     }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
     }
     BIT_STRING { `00` `67a8951fc308e12f6867611fdc254bf4bcb514f7f5f
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Massimo, et al.           Expires 6 August 2025                [Page 30]

Internet-Draft           ML-DSA in Certificates            February 2025


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   beeef101f232d6e97c2c4dff3f40000000000000000000000000017263843` }
   }

   The following is a self-signed certificate for the ML-DSA-65 public
   key in the previous section.

   -----BEGIN CERTIFICATE-----
   MIIVjTCCCIqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMS
   MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
   MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
   TEFNUFMgV0cwggeyMAsGCWCGSAFlAwQDEgOCB6EASGg9kZeOMes93biwRzSC0riK
   X2JZSf2PWKVh5pa9TCfQWzjbsu3wHmZO/YG+HqiTaIzmiqLVHFlY+LvG606J7mfS



Massimo, et al.           Expires 6 August 2025                [Page 31]

Internet-Draft           ML-DSA in Certificates            February 2025


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Massimo, et al.           Expires 6 August 2025                [Page 32]

Internet-Draft           ML-DSA in Certificates            February 2025


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   MmzKH/pnAWl9UmOl/066Pz4g0XEX/jg8wPKHvnMyd6QbSud5Y1swOqcnperhhkVN



Massimo, et al.           Expires 6 August 2025                [Page 33]

Internet-Draft           ML-DSA in Certificates            February 2025


   +mJqTkSujjFr7EMdkUsG1SK0BeTVS9lSb6iu7bLa2rOha9l/zPI1Fp7WiHqANnOW
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   f4Bi0XC/I1E4xQ46UwTvGQKLTtRHyeg3vG+gX5raRK2Ny6IXDJj0scYE79q83TAc
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   KOo4Bpfj1etTFQAcU6E3weyVD9ROi7WtSBH4EFhFOfgfga1CHD8DHbwDdsa+dhIj
   9mORCp7dEUPjt5Qi5mimlqQwYFfCHI+ap6VYsrhpzWr3gPi8EENRsbTUEWWezM/n
   +BH4UnmFmQY7SGZyeHuDvFNzdNIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAYNDxMc
   IA==
   -----END CERTIFICATE-----

   SEQUENCE {
     SEQUENCE {
       [0] {
         INTEGER { 2 }
       }
       INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
       SEQUENCE {
         OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
       }
       SEQUENCE {
         SET {
           SEQUENCE {
             # organizationName
             OBJECT_IDENTIFIER { 2.5.4.10 }
             PrintableString { "IETF" }
           }
         }
         SET {
           SEQUENCE {
             # commonName
             OBJECT_IDENTIFIER { 2.5.4.3 }
             PrintableString { "LAMPS WG" }
           }
         }
       }
       SEQUENCE {
         UTCTime { "200203043210Z" }
         UTCTime { "400129043210Z" }
       }
       SEQUENCE {
         SET {



Massimo, et al.           Expires 6 August 2025                [Page 34]

Internet-Draft           ML-DSA in Certificates            February 2025


           SEQUENCE {
             # organizationName
             OBJECT_IDENTIFIER { 2.5.4.10 }
             PrintableString { "IETF" }
           }
         }
         SET {
           SEQUENCE {
             # commonName
             OBJECT_IDENTIFIER { 2.5.4.3 }
             PrintableString { "LAMPS WG" }
           }
         }
       }
       SEQUENCE {
         SEQUENCE {
           OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
         }
         BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f6
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   72720f77d96172672980cfe8ff7a5a702783edc2ba31b2259015a112fc7f468a



Massimo, et al.           Expires 6 August 2025                [Page 35]

Internet-Draft           ML-DSA in Certificates            February 2025


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   3e79c46ca5d5a6dca3d28ca50ad18bd13fca55059dd9b185f79f9c47196a4e81
   b2104bc460a051e02f2e8444f` }
       }
       [3] {
         SEQUENCE {
           SEQUENCE {
             # keyUsage
             OBJECT_IDENTIFIER { 2.5.29.15 }
             BOOLEAN { TRUE }
             OCTET_STRING {
               BIT_STRING { b`1000011` }
             }
           }
           SEQUENCE {
             # basicConstraints
             OBJECT_IDENTIFIER { 2.5.29.19 }
             BOOLEAN { TRUE }
             OCTET_STRING {



Massimo, et al.           Expires 6 August 2025                [Page 36]

Internet-Draft           ML-DSA in Certificates            February 2025


               SEQUENCE {
                 BOOLEAN { TRUE }
               }
             }
           }
           SEQUENCE {
             # subjectKeyIdentifier
             OBJECT_IDENTIFIER { 2.5.29.14 }
             OCTET_STRING {
               OCTET_STRING { `1b0563e3cd3346149c8c9ebcf23b0a4e5a90
   0eea` }
             }
           }
         }
       }
     }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
     }
     BIT_STRING { `00` `11816868a90c66934bdbb1d19c53a6a5dc30535ff6d
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   0cc95313a32a8f8b91f1f7a295380af2672571480b40b0ac8c033fc53d81dd11



Massimo, et al.           Expires 6 August 2025                [Page 37]

Internet-Draft           ML-DSA in Certificates            February 2025


   95512c785b6d6ad0560fcb82fd342c8a31f14e83cfb70a1982839bba5d82a771
   21e5b72a0413c5d50e010a83138dcb986e0983e90e8d3ceca7b500683a06be96
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   fd6c95cd4f3564b2581c2bf83f7447c52b501cc75aaa7ab1b4f117817f4e4561



Massimo, et al.           Expires 6 August 2025                [Page 38]

Internet-Draft           ML-DSA in Certificates            February 2025


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   3cdc5f242ab111f0c91e6910c180e2a9166992e309d99e7eb983c2b57ebee9ba
   48ae62c141917147f62014b945e6de6bb4769d2f70c28ce5b2bd3d2d3a1bd07d
   aa1e3a88e049aad8ae6e46cef0a5134485d4f3ec9ffaac158d2cf1fa63a553b0
   b94f84dea8b9f55e8b559078344627f31f2a4ec772799f99f9decb6e7b0f8abb
   d2154fabfd95024cff11cddd9e8c7f1a906a147a979782a5171ddaa2f3a8ef82
   84ddb3cbc7520ec4dce1a3047e26cbde1568dc7a3bc1c8121b58eb3ab65f5f08
   911bf05213bd74b21466a60d0200b99fff0d42bc51aa2898d11c49f5439bb5e7
   f962536c34da1798be2d5ef27d7ac30d4cc151e5b1cb9455b97697c77764c2cc
   064ac513de1abb8a435e0a1665dfbdc9b0d7cb55ed85cd4e2b4fb416fee68b22
   2485fc1811bdd5e8a9c4dcadc4afeaa15aafbdf8f2b527f8062d170bf235138c
   50e3a5304ef19028b4ed447c9e837bc6fa05f9ada44ad8dcba2170c98f4b1c60
   4efdabcdd301cb965c7ea62740f4e0475bfeeb7eda7e712f954375efeb5e5ce7
   b5b0984f0c5ae016c99988f040288a5730de9275dd323c6c57412ec373a49b70
   88429edb88fa3bd74f32e64789965e87129c7bb164f7ee634ea23e0015d9bbf7
   0cc4250865ea928ea380697e3d5eb5315001c53a137c1ec950fd44e8bb5ad481
   1f810584539f81f81ad421c3f031dbc0376c6be761223f663910a9edd1143e3b
   79422e668a696a4306057c21c8f9aa7a558b2b869cd6af780f8bc104351b1b4d
   411659ecccfe7f811f852798599063b486672787b83bc537374d200000000000
   00000000000000000000000000000000000060d0f131c20` }
   }

   The following is a self-signed certificate for the ML-DSA-87 public
   key in the previous section.

   -----BEGIN CERTIFICATE-----
   MIIdMzCCCwqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMT
   MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
   MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
   TEFNUFMgV0cwggoyMAsGCWCGSAFlAwQDEwOCCiEAl5K87C8kMGhqgvzPPC9f9mXn
   cderQbkCWM+n6Q7JcSSnOzI7m6Iatk12fEM/WlIe/+GPhuRqGIlSxEZ+BItynn/E
   0RXn5I2hiW1f4RmxDc3e9iyzB5VAdLQjNuUoNt5h2pQfjTfqaKyBBvq+GQcGea9g
   CFNxIPcHk7jqnMDm57e0yaXHQhxg8kRRuh6TPbGi7hbHlVnyGz0bgwWFCqQq+7E/
   H01bn0g1+dh9/OsWLQ70p/3Ey6F0PNHIe7SWfaFsyHZLZWnfjuW9y//ppOBXSOb9
   8iWvnk7rd3O2Lo+F+bVrVIlFVRhE+9iYBqSsNpvtLSVhAPaIpq1eCnCYJtxESeke
   I8VQbmQjYe9aMTcS95vEsxhoYcqFpLqxfn+UPRuKMzqjrnzha0QNYBj54E2vVyXH
   8ak/rRpaJ7Z4lb0kmqkWhd4grzLIt+Jox/lod9DIUAETWk8KjxuCZPpuvlo0nYrs
   rRoWKZzPL9nHuFus4s7TqhJ2umHueO1+XKW2fN1FipNUAw5qu7q/VqCiMW/snbqD
   tR1C/TFn8eD5CFXVxmUJshAmXcHlTsRLQ7p8+a7xGLRNgJEs51FmpmUeEWzr5JIp
   pwYsCZMfcavSKT929+/DIVupeAADfljkcL27tDwbBDnq95xU2TtEqsnv6fvhUYdM
   +ypky+4ozEwP53deXYcPHALlsuPFAEyZXyTJt3nLdTonfQ5x/UJetrwspWzhKdtR



Massimo, et al.           Expires 6 August 2025                [Page 39]

Internet-Draft           ML-DSA in Certificates            February 2025


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   w6B7hE/ZvPUteNt674Mc2zqOyOAYWM6dWjDJMtKmfdLk2vA1ph0BubRHI9MHGzil



Massimo, et al.           Expires 6 August 2025                [Page 40]

Internet-Draft           ML-DSA in Certificates            February 2025


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Massimo, et al.           Expires 6 August 2025                [Page 41]

Internet-Draft           ML-DSA in Certificates            February 2025


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   yw0yMsWOanzDyh0y7OGhDgXiJS42y2XU0UH/JGGEZbZlEpfNNNOPYcYvMfuOlwww
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   rnVLSDqKkbgKCwwRPEiw8SU8WZu5zwG9ygURLGN4obLeSQU8UHyCteEbbpGrstXp
   AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQMEhUdHiUs
   -----END CERTIFICATE-----





Massimo, et al.           Expires 6 August 2025                [Page 42]

Internet-Draft           ML-DSA in Certificates            February 2025


   SEQUENCE {
     SEQUENCE {
       [0] {
         INTEGER { 2 }
       }
       INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
       SEQUENCE {
         OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
       }
       SEQUENCE {
         SET {
           SEQUENCE {
             # organizationName
             OBJECT_IDENTIFIER { 2.5.4.10 }
             PrintableString { "IETF" }
           }
         }
         SET {
           SEQUENCE {
             # commonName
             OBJECT_IDENTIFIER { 2.5.4.3 }
             PrintableString { "LAMPS WG" }
           }
         }
       }
       SEQUENCE {
         UTCTime { "200203043210Z" }
         UTCTime { "400129043210Z" }
       }
       SEQUENCE {
         SET {
           SEQUENCE {
             # organizationName
             OBJECT_IDENTIFIER { 2.5.4.10 }
             PrintableString { "IETF" }
           }
         }
         SET {
           SEQUENCE {
             # commonName
             OBJECT_IDENTIFIER { 2.5.4.3 }
             PrintableString { "LAMPS WG" }
           }
         }
       }
       SEQUENCE {
         SEQUENCE {
           OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }



Massimo, et al.           Expires 6 August 2025                [Page 43]

Internet-Draft           ML-DSA in Certificates            February 2025


         }
         BIT_STRING { `00` `9792bcec2f2430686a82fccf3c2f5ff665e771d
   7ab41b90258cfa7e90ec97124a73b323b9ba21ab64d767c433f5a521effe18f8
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   e48cfade002c62e5a49a0731ab38344bc1636df16bf607d56855e56d684003c7



Massimo, et al.           Expires 6 August 2025                [Page 44]

Internet-Draft           ML-DSA in Certificates            February 2025


   18e4bad9e5a099979fcddeeb1c4a7776cd37a3417cb0e184e29ef9bc0e87475b
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   abce2a632048eaf89e5cb4a88debc53a595103acce4f1cff18acff07afe1eb57
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   b3c009ca947c39dfc82d98eb1caa4a9cbe885f786fa86e55be062222f8ba90a9
   74073326b31212aece0a34a60` }
       }
       [3] {
         SEQUENCE {
           SEQUENCE {
             # keyUsage
             OBJECT_IDENTIFIER { 2.5.29.15 }
             BOOLEAN { TRUE }
             OCTET_STRING {
               BIT_STRING { b`1000011` }
             }
           }
           SEQUENCE {
             # basicConstraints



Massimo, et al.           Expires 6 August 2025                [Page 45]

Internet-Draft           ML-DSA in Certificates            February 2025


             OBJECT_IDENTIFIER { 2.5.29.19 }
             BOOLEAN { TRUE }
             OCTET_STRING {
               SEQUENCE {
                 BOOLEAN { TRUE }
               }
             }
           }
           SEQUENCE {
             # subjectKeyIdentifier
             OBJECT_IDENTIFIER { 2.5.29.14 }
             OCTET_STRING {
               OCTET_STRING { `89886750b57c24db3fc012e61ede59753337
   374f` }
             }
           }
         }
       }
     }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
     }
     BIT_STRING { `00` `08783d565efc7b97440f8bd9818b466be538dbccedb
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   85911997ab02a656c1f9f3b7c9fb043f811883fef3c05fb5a1703ce56776ee6f



Massimo, et al.           Expires 6 August 2025                [Page 46]

Internet-Draft           ML-DSA in Certificates            February 2025


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   3bf780ccc18586c5ab7d26a97c27348c1581f9aeeb0d76daaceb77e49b99bc49
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   140124ee215da5ce9a11d865bf83017cdfab6b4014e31f9da293078ddf7c5125



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   0000000000000000000000000000000000000000000040c12151d1e252c` }
   }

Appendix D.  Pre-hashing (ExternalMu-ML-DSA)

   Some applications require pre-hashing, where the signature generation
   process can be separated into a pre-hash step and a core signature
   step in order to ease operational requirements around large or
   inconsistently-sized payloads.  Pre-hashing can be performed at the
   protocol layer, but not all protocols support it.  Examples in
   [RFC5280] are certificates and CRLs; these do not include message
   digesting before signing.  This can make signing large CRLs or a high
   volume of certificates with large public keys challenging.

   As mentioned in the introduction, pure ML-DSA signing itself supports
   a pre-hashing flow by splitting the operation over two modules.  In
   this section, we make this "ExternalMu-ML-DSA" more explicit.

   There are two steps.  First an ExternalMu-ML-DSA.Prehash() followed
   by ExternalMu-ML-DSA.Sign().  Together these are functionally
   equivalent to ML-DSA.Sign() from [FIPS204] in that used in sequence
   they create exactly the same signatures as regular pure ML-DSA, which
   can be verified by the unmodified ML-DSA.Verify().






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   An ML-DSA key and certificate can be used with either ML-DSA or
   ExternalMu-ML-DSA interchangeably.  Note that ExternalMu-ML-DSA
   describes a different signature API from ML-DSA and therefore might
   require explicit support from hardware or software cryptographic
   modules.

   Note that the signing mode defined here is different from HashML-DSA
   defined in Section 5.4 of [FIPS204].  This specification uses
   exclusively ExternalMu-ML-DSA for pre-hashed use cases.  See
   Section 8.1 for additional discussion of why HashML-DSA is disallowed
   in PKIX.

   All functions and notation used in Figure 2 and Figure 3 are defined
   in [FIPS204].

   External operations:

 ExternalMu-ML-DSA.Prehash(pk, M, ctx):

   if |ctx| > 255 then
     return error  # return an error indication if the context string is
                   # too long
   end if

   M' = BytesToBits(IntegerToBytes(0, 1) ∥ IntegerToBytes(|ctx|, 1)
                                                         || ctx) || M
   mu = H(BytesToBits(H(pk, 64)) || M', 64)
   return mu

             Figure 2: External steps of ExternalMu-ML-DSA

   Internal operations:



















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ExternalMu-ML-DSA.Sign(sk, mu):

  if |mu| != 512 then
    return error  # return an error indication if the input mu is not
                  # 64 bytes (512 bits).
  end if

  rnd = rand(32)  # for the optional deterministic variant,
                  # set rnd to all zeroes
  if rnd = NULL then
    return error  # return an error indication if random bit
                  # generation failed
  end if

  sigma = ExternalMu-ML-DSA.Sign_internal(sk, mu, rnd)
  return sigma

ExternalMu-ML-DSA.Sign_internal(sk, mu, rnd): # mu is passed as argument instead of M'
   ... identical to FIPS 204 Algorithm 7, but with Line 6 removed.

            Figure 3: Internal steps of ExternalMu-ML-DSA

   ExternalMu-ML-DSA requires the public key, or its prehash, as input
   to the pre-digesting function.  This assumes the signer generating
   the pre-hash is in possession of the public key before signing and is
   different from conventional pre-hashing which only requires the
   message and the hash function as input.

   Security-wise, during the signing operation of pure (or "one-step")
   ML-DSA, the cryptographic module extracts the public key hash tr from
   the secret key object, and thus there is no possibility of mismatch
   between tr and sk.  In ExternalMu-ML-DSA, the public key or its hash
   needs to be provided to the Prehash() routine indpedendly of the
   secret key, and while the exact mechanism by which it is delivered
   will be implementation-specific, it does open a windown for
   mismatches between tr and sk.  First, this will produce a signature
   which will fail to verify under the intended public key since a
   compliant Verify() routine will independently compute tr from the
   public key.  Implementors should pay careful attention to how the
   public key or its hash is delivered to the ExternalMu-ML-
   DSA.Prehash() routine, and from where they are sourcing this data.

Acknowledgments

   We would like to thank ... for their insightful comments.

Authors' Addresses




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   Jake Massimo
   AWS
   United States of America
   Email: jakemas@amazon.com


   Panos Kampanakis
   AWS
   United States of America
   Email: kpanos@amazon.com


   Sean Turner
   sn3rd
   Email: sean@sn3rd.com


   Bas Westerbaan
   Cloudflare
   Email: bas@cloudflare.com































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