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Internet X.509 Public Key Infrastructure - Algorithm Identifiers for the Module-Lattice-Based Digital Signature Algorithm (ML-DSA)
draft-ietf-lamps-dilithium-certificates-12

Document Type Active Internet-Draft (lamps WG)
Authors Jake Massimo , Panos Kampanakis , Sean Turner , Bas Westerbaan
Last updated 2025-07-07 (Latest revision 2025-06-26)
Replaces draft-massimo-lamps-pq-sig-certificates
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draft-ietf-lamps-dilithium-certificates-12
LAMPS WG                                                      J. Massimo
Internet-Draft                                             P. Kampanakis
Intended status: Standards Track                                     AWS
Expires: 29 December 2025                                      S. Turner
                                                                   sn3rd
                                                        B. E. Westerbaan
                                                              Cloudflare
                                                            27 June 2025

Internet X.509 Public Key Infrastructure - Algorithm Identifiers for the
       Module-Lattice-Based Digital Signature Algorithm (ML-DSA)
               draft-ietf-lamps-dilithium-certificates-12

Abstract

   Digital signatures are used within X.509 certificates, Certificate
   Revocation Lists (CRLs), and to sign messages.  This document
   specifies 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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   This Internet-Draft will expire on 29 December 2025.

Copyright Notice

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

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents (https://trustee.ietf.org/
   license-info) in effect on the date of publication of this document.
   Please review these documents carefully, as they describe your rights
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   provided without warranty as described in the Revised BSD License.

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  . . . . . . . . . . . . . . . . .   6
   5.  Key Usage Bits  . . . . . . . . . . . . . . . . . . . . . . .   8
   6.  Private Key Format  . . . . . . . . . . . . . . . . . . . . .   8
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  11
   8.  Operational Considerations  . . . . . . . . . . . . . . . . .  11
     8.1.  Private Key Format  . . . . . . . . . . . . . . . . . . .  11
     8.2.  Private Key Consistency Testing . . . . . . . . . . . . .  12
     8.3.  Rationale for disallowing HashML-DSA  . . . . . . . . . .  12
   9.  Security Considerations . . . . . . . . . . . . . . . . . . .  13
   10. References  . . . . . . . . . . . . . . . . . . . . . . . . .  14
     10.1.  Normative References . . . . . . . . . . . . . . . . . .  14
     10.2.  Informative References . . . . . . . . . . . . . . . . .  15
   Appendix A.  ASN.1 Module . . . . . . . . . . . . . . . . . . . .  16
   Appendix B.  Security Strengths . . . . . . . . . . . . . . . . .  20
   Appendix C.  Examples . . . . . . . . . . . . . . . . . . . . . .  20
     C.1.  Example Private Keys  . . . . . . . . . . . . . . . . . .  21

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       C.1.1.  ML-DSA-44 Private Key Examples  . . . . . . . . . . .  21
       C.1.2.  ML-DSA-65 Private Key Examples  . . . . . . . . . . .  28
       C.1.3.  ML-DSA-87 Private Key Examples  . . . . . . . . . . .  38
     C.2.  Example Public Keys . . . . . . . . . . . . . . . . . . .  50
     C.3.  Example Certificates  . . . . . . . . . . . . . . . . . .  58
     C.4.  Example Inconsistent Seed and Expanded Private Keys . . .  82
   Appendix D.  Pre-hashing (ExternalMu-ML-DSA)  . . . . . . . . . .  87
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  89
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  89

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 pre-hash
   variant.  Only the former is specified in this document.  See
   Section 8.3 for the rationale.  The pure variant of ML-DSA supports
   the typical pre-hash flow.  Refer to Appendix D for more details.

   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
     }

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      |  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 AlgorithmIdentifier have the following meanings:

   *  algorithm identifies the cryptographic algorithm with an object
      identifier (OID).

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

   The NIST registered OIDs [CSOR] 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.

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 following SIGNATURE-ALGORITHM ASN.1 classes are for ML-DSA-44,
   ML-DSA-65, and ML-DSA-87:

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

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      |  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 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-*, where * is
   44, 65, or 87 - see Section 2.

   The signatureValue field contains the corresponding ML-DSA signature
   computed upon the ASN.1 DER encoded tbsCertificate/tbsCertList
   [RFC5280].  The optional context string (ctx) parameter as defined in
   Section 5.2 of [FIPS204] is left to its default value: the empty
   string.

   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 in 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:

     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 public key.

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   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
   this raw byte string encoding of the public key.  When an 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 ML-DSA-44-PublicKey, ML-DSA-65-PublicKey, and ML-
   DSA-87-PublicKey types corresponding to the correct key size defined
   below.

   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 ML-DSA-44-PrivateKey }  -- defined in Section 6

     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 ML-DSA-65-PrivateKey }  -- defined in Section 6

     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 ML-DSA-87-PrivateKey }  -- defined in Section 6

     ML-DSA-44-PublicKey ::= OCTET STRING (SIZE (1312))

     ML-DSA-65-PublicKey ::= OCTET STRING (SIZE (1952))

     ML-DSA-87-PublicKey ::= OCTET STRING (SIZE (2592))

      |  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.

   [RFC5958] specifies 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.

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   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
   using one of the the ML-DSA-PrivateKey CHOICE formats defined in
   Section 6.  The seed format is RECOMMENDED as it efficiently stores
   both the private and public key.

   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 includes id-ml-
   dsa-* (where * is 44, 65, or 87 - see Section 2) in the
   SubjectPublicKeyInfo, then the subject public key can only be used
   for verifying digital signatures on certificates or CRLs, or those
   used in an entity authentication service, a data origin
   authentication service, an integrity service, and/or a non-
   repudiation service that protects against the signing entity falsely
   denying some action.  This means that the keyUsage extention MUST
   have at least one of the following bits set:

     digitalSignature
     nonRepudiation
     keyCertSign
     cRLSign

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

      keyEncipherment,
      dataEncipherment,
      keyAgreement,
      encipherOnly, and
      decipherOnly.

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

6.  Private Key Format

   [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).

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   "Asymmetric Key Packages" [RFC5958] specifies 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].

   For ML-DSA private keys, the privateKey field in OneAsymmetricKey
   contains one of the following DER-encoded CHOICE structures.  The
   seed format is a fixed 32 byte OCTET STRING (34 bytes total with the
   0x8020 tag and length) for all security levels, while the expandedKey
   and both formats vary in size by security level:

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   ML-DSA-44-PrivateKey ::= CHOICE {
     seed [0] OCTET STRING (SIZE (32)),
     expandedKey OCTET STRING (SIZE (2560)),
     both SEQUENCE {
         seed OCTET STRING (SIZE (32)),
         expandedKey OCTET STRING (SIZE (2560))
         }
     }

   ML-DSA-65-PrivateKey ::= CHOICE {
     seed [0] OCTET STRING (SIZE (32)),
     expandedKey OCTET STRING (SIZE (4032)),
     both SEQUENCE {
         seed OCTET STRING (SIZE (32)),
         expandedKey OCTET STRING (SIZE (4032))
         }
     }

   ML-DSA-87-PrivateKey ::= CHOICE {
     seed [0] OCTET STRING (SIZE (32)),
     expandedKey OCTET STRING (SIZE (4896)),
     both SEQUENCE {
         seed OCTET STRING (SIZE (32)),
         expandedKey OCTET STRING (SIZE (4896))
         }
     }

      |  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 CHOICE allows three representations of the private key:

   1.  The seed format (tag [0]) contains just the 32-byte seed value
       (xi) from which both the expanded private key and public key can
       be derived using ML-DSA.KeyGen_internal(xi).

   2.  The expandedKey format contains the expanded private key that was
       derived from the seed.

   3.  The both format contains both the seed and expanded private key,
       allowing for for interoperability; some may want to use and
       retain the seed and others may only support expanded private
       keys.

   When encoding an ML-DSA private key in a OneAsymmetricKey object, any
   of these three formats may be used, though the seed format is
   RECOMMENDED for storage efficiency.

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   The privateKeyAlgorithm field uses the AlgorithmIdentifier structure
   with the appropriate OID as defined in Section 2.  If present, the
   publicKey field will hold the encoded public key as defined in
   Section 4.

   NOTE: While the private key can be stored in multiple formats, the
   seed-only format is RECOMMENDED as it is the most compact
   representation.  Both the expanded private key and the public key can
   be deterministically derived from the seed using ML-
   DSA.KeyGen_internal(xi).  Alternatively, the public key can be
   generated from the private key.  While the publicKey field and
   expandedKey format are technically redundant when using the seed-only
   format, they MAY be included to enable keypair consistency checks
   during import operations.

   When parsing the private key, the ASN.1 tag explicitly indicates
   which variant of CHOICE is present.  Implementations should use the
   context-specific tag IMPLICIT [0] (raw value 0x80) for seed, OCTET
   STRING (0x04) for expandedKey, and SEQUENCE (0x30) for both to parse
   the private key, rather than any other heuristic like length of the
   enclosing OCTET STRING.

   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-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).

8.  Operational Considerations

8.1.  Private Key Format

   An ML-DSA.KeyGen seed (xi) represents the RECOMMENDED format for
   storing and transmitting ML-DSA private keys.  This format is
   explicitly permitted by [FIPS204] as an acceptable representation of
   a keypair.  In particular, generating the seed in one cryptographic
   module and then importing or exporting it into another cryptographic
   module is allowed.  The internal key generation function ML-
   DSA.KeyGen_internal(xi) can be accessed for this purpose.

   Note also that unlike other private key compression methods in other
   algorithms, expanding a private key from a seed is a one-way
   function, meaning that once a full key is expanded from seed and the

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   seed discarded, the seed cannot be re-created even if the full
   expanded private key is available.  For this reason it is RECOMMENDED
   that implementations retain and export the seed, even when also
   exporting the expanded private key.  ML-DSA seed extraction can be
   implemented by including the seed xi randomly generated at line 1 of
   Algorithm 1 ML-DSA.KeyGen in the returned output.

   When encoding an ML-DSA private key in a OneAsymmetricKey object, any
   of these three formats may be used, though the seed format is
   RECOMMENDED for storage efficiency.

8.2.  Private Key Consistency Testing

   When receiving a private key that contains both the seed and the
   expandedKey, the recipient SHOULD perform a seed consistency check to
   ensure that the sender properly generated the private key.
   Recipients that do not perform this seed consistency check avoid
   keygen and compare operations, but are unable to ensure that the seed
   and expandedKey match.

   If the check is done and the seed and the expandedKey are not
   consistent, the recipient MUST reject the private key as malformed.

   The seed consistency check consists of regenerating the expanded form
   from the seed via ML-DSA.KeyGen_internal and ensuring it is bytewise
   equal to the value presented in the private key.

   Appendix C.4 includes some examples of inconsistent seeds and
   expanded private keys.

8.3.  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.  This restriction is
   primarily to increase interoperability.

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   ML-DSA and HashML-DSA are incompatible algorithms that require
   different Verify() routines.  This introduces the complexity of
   informing the verifier whether to use ML-DSA.Verify() or HashML-
   DSA.Verify().  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 whether the key will need to produce pure or
   pre-hashed signatures at key generation time.  The External Mu mode
   described in Appendix D avoids all of these operational concerns.

   A minor security reason for disallowing HashML-DSA is that the design
   of the ML-DSA algorithm provides enhanced resistance against
   collision attacks, compared with HashML-DSA or conventional RSA or
   ECDSA signature algorithms.  Specifically, ML-DSA prepends the
   SHAKE256 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].
   This means that in the unlikely discovery of a collision attack
   against the SHA-3 family, 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 this enhanced security
   property.  In spite of its lack of targeted collision protection, the
   practical security risk of using HashML-DSA in X.509 signatures would
   be immaterial.  That is because a hash of the issuing CA's public key
   is already included in the Authority Key Identifier (AKI) extension
   which is signed as part of the tbsCertificate structure.  Even when
   it is a SHA-1 hash, general second pre-images against the AKI hash of
   existing issuing CAs would be impractical.

9.  Security Considerations

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

   The ML-DSA signature scheme is strongly unforgeable under chosen
   message attacks (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 depends on high quality random numbers that are suitable for
   use in cryptography.  The use of inadequate pseudo-random number
   generators (PRNGs) to generate such values can significantly
   undermine various security properties.  For instance, using an
   inadequate PRNG for key generation, might allow an attacker to
   efficiently recover the private key by trying a small set of
   possibilities, rather than brute force search the whole keyspace.

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   The generation of random numbers of a sufficient level of quality for
   use in cryptography is difficult; see Section 3.6.1 of [FIPS204] for
   some additional information.

   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.

   ML-DSA offers both deterministic and randomized signing.  Signatures
   generated with either mode are compatible and a verifyer can't tell
   them apart.  In the deterministic case, a signature only depends on
   the private key and the message to be signed.  This makes the
   implementation easier to test and does not require a randomness
   source during signing.  In the randomized case, signing mixes in a
   256-bit random string from an approved random bit generator (RBG).
   When randomized, ML-DSA is easier to harden against fault and
   hardware side-channel attacks.

   A 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, unless its private key was compromised.  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).  A full discussion of these properties in ML-DSA can be found
   at [CDFFJ21].

10.  References

10.1.  Normative References

   [CSOR]     NIST, "Computer Security Objects Register", 20 August
              2024, <https://csrc.nist.gov/projects/computer-security-
              objects-register/algorithm-registration>.

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   [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>.

   [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>.

   [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>.

10.2.  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>.

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   [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>.

   [FIPS204-ExternalMuFAQ]
              National Institute of Standards and Technology (NIST),
              "FIPS 204 Section 6 FAQ", 2025,
              <https://csrc.nist.gov/csrc/media/Projects/post-quantum-
              cryptography/documents/faq/fips204-sec6-03192025.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>.

   [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>.

   [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].

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   <CODE BEGINS>
   X509-ML-DSA-2025
   { iso(1) identified-organization(3) dod(6)
     internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
     id-mod-x509-ml-dsa-2025(TBD1) }

   DEFINITIONS IMPLICIT TAGS ::= BEGIN

   EXPORTS ALL;

   IMPORTS

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

   --
   -- ML-DSA Identifiers
   --

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

   sigAlgs OBJECT IDENTIFIER ::= { nistAlgorithms 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 }

   --
   -- Public Key Algorithms
   --

   PublicKeys PUBLIC-KEY ::= {
     -- This expands PublicKeys from [RFC 5912]
     pk-ml-dsa-44 |
     pk-ml-dsa-65 |
     pk-ml-dsa-87,
     ...
   }

   --
   -- ML-DSA Public Keys

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   --

   pk-ml-dsa-44 PUBLIC-KEY ::= {
     IDENTIFIER id-ml-dsa-44
     -- KEY no ASN.1 wrapping; 1312 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { digitalSignature, nonRepudiation,
                      keyCertSign, cRLSign }
     PRIVATE-KEY ML-DSA-44-PrivateKey
     }

   ML-DSA-44-PrivateKey ::= CHOICE {
     seed [0] OCTET STRING (SIZE (32)),
     expandedKey OCTET STRING (SIZE (2560)),
     both SEQUENCE {
         seed OCTET STRING (SIZE (32)),
         expandedKey OCTET STRING (SIZE (2560))
         }
     }

   pk-ml-dsa-65 PUBLIC-KEY ::= {
     IDENTIFIER id-ml-dsa-65
     -- KEY no ASN.1 wrapping; 1952 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { digitalSignature, nonRepudiation,
                      keyCertSign, cRLSign }
     PRIVATE-KEY ML-DSA-65-PrivateKey
     }

   ML-DSA-65-PrivateKey ::= CHOICE {
     seed [0] OCTET STRING (SIZE (32)),
     expandedKey OCTET STRING (SIZE (4032)),
     both SEQUENCE {
         seed OCTET STRING (SIZE (32)),
         expandedKey OCTET STRING (SIZE (4032))
         }
     }

   pk-ml-dsa-87 PUBLIC-KEY ::= {
     IDENTIFIER id-ml-dsa-87
     -- KEY no ASN.1 wrapping; 2592 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { digitalSignature, nonRepudiation,
                       keyCertSign, cRLSign }
     PRIVATE-KEY ML-DSA-87-PrivateKey
     }

   ML-DSA-87-PrivateKey ::= CHOICE {

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     seed [0] OCTET STRING (SIZE (32)),
     expandedKey OCTET STRING (SIZE (4896)),
     both SEQUENCE {
         seed OCTET STRING (SIZE (32)),
         expandedKey OCTET STRING (SIZE (4896))
         }
     }

   ML-DSA-44-PublicKey ::= OCTET STRING (SIZE (1312))

   ML-DSA-65-PublicKey ::= OCTET STRING (SIZE (1952))

   ML-DSA-87-PublicKey ::= OCTET STRING (SIZE (2602))

   --
   -- Signature Algorithms
   --

   SignatureAlgorithms SIGNATURE-ALGORITHM ::= {
     -- This expands SignatureAlgorithms from [RFC 5912]
     sa-ml-dsa-44 |
     sa-ml-dsa-65 |
     sa-ml-dsa-87,
     ... }

   --
   -- ML-DSA Signature Algorithm Identifiers
   --

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

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     }

   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 raw keys, not including ASN.1 encoding overhead from
   OneAsymmetricKey and SubjectPublicKeyInfo wrappers.  Private key
   sizes are shown for both the seed format and expanded format.

   |=======+=======+=====+========+========+==========+==========|
   | Level | (k,l) | eta |  Sig.  | Public | Private  | Private  |
   |       |       |     |  (B)   | Key(B) | Seed(B)  | Expand(B)|
   |=======+=======+=====+========+========+==========+==========|
   |   2   | (4,4) |  2  |  2420  |  1312  |    32    |   2560   |
   |   3   | (6,5) |  4  |  3309  |  1952  |    32    |   4032   |
   |   5   | (8,7) |  2  |  4627  |  2592  |    32    |   4896   |
   |=======+=======+=====+========+========+==========+==========|

                        Figure 1: ML-DSA Parameters

Appendix C.  Examples

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

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C.1.  Example Private Keys

   The following examples show ML-DSA private keys in different formats,
   all derived from the same seed 000102...1e1f.  For each security
   level, we show the seed-only format (using a context-specific [0]
   primitive tag with an implicit encoding of OCTET STRING), the
   expanded format, and both formats together.

   NOTE: All examples use the same seed value, showing how the same seed
   produces different expanded private keys for each security level.

C.1.1.  ML-DSA-44 Private Key Examples

   Each of the examples includes the textual encoding [RFC7468] followed
   by the so-called "pretty print"; the private keys are the same.

C.1.1.1.  Seed Format

   -----BEGIN PRIVATE KEY-----
   MDQCAQAwCwYJYIZIAWUDBAMRBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
   GhscHR4f
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
     }
     OCTET_STRING {
       [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
   5161718191a1b1c1d1e1f` }
     }
   }

C.1.1.2.  Expanded Format

   -----BEGIN PRIVATE KEY-----
   MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX
   0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex
   +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA
   SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII
   wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG
   IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk
   ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu
   EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi
   wCRBCUNxCiEgYaIBUiJSG4CAmjQAE5NN0zIpIhcKmJJpGhRRICchnMAgYqKBSBhp
   GoVNg0RpWyBBAxJCyxhGAakNDAIxg7AhWiJKyJIF2ZBpBDBqSwZK0rIBHEBAgUIy
   UjJyVKZAWhgQDDISksKAUhJiXIIoC7RsA0KNUxAMFAEO4TZSiIQkkQIKY0YmIAYp

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   EcIo0CBIArNsojYJWoZIy7Rhi0ZixECCGokJEAJNJLJFIBIlJMkFiCiMycBNWUgi
   CiduwTRkTJBgW0RQgoZJQ4gEQ7KMYDCAoogthKRtjKYp0MaEQgZGiYhRAKmNAUmN
   5DgNpAaN05RxQrJsGoRhG6MoQrQoCKBxGsUx4KBMATdlJChiFCiQCRBh2UAiGzNg
   CQKS0CSBIAQISRhEoyItXIhEFJgIpEZhAZVkCzkKDJRQykBq0rIgwDgBgjCOE7kI
   kYCEFIgpwBiREjUNoCQi4gQG2cKFBCgSHMmJGAJy0kApwggS2AYqmZRxm7hoI4Qp
   GiKJFEUR3IJEUJZFDESEwLIEmqYFQ4YsRDJuiEQhIKhMmjBw47gtYyaIAyVJA0OM
   SKgJyhRyUzROEkMIG6cEWTAi2ZSA4jQigUISnDAqlDQmYQRFJCYoE0YJSjJtESgJ
   GLglYigRE0ENQbIRkIRMixISosaIycAwIgYG0hiOhIYwkERSEogx2SBxE8UoQwYO
   AzBgzKaEWCZSTIgBHvclYshf+kOs+kkhfysXLXu8FGIObZgKcaq73wxF6aIG7LFC
   P+4V3swXYBMAFJ2SI81ubG4fqOQfx8ZJOKtokF/T3NpQ2HCC59DXHRvJsrhMhVI8
   qP5srSlK34O+FbEI/3IdDMh7w906dZAYSw6EVmOpH8nhw8U6YdhnQgsE8JI1V1O8
   ZaBjaP1BKV/QmSQTLG+R9nlkwUJnSnJcNDkUxM7PWMB0vK9FWMl795EeB6ptCTjy
   7iuzwajFldY16ENC/eoB3CSyEa0vwoHPd+WREMerxUvwyG1IC5vidkcdydYDzumM
   /as+n8+3A3k1YFSepEUPp7M/uRacRLTSX7nEV/SXkc09oD6slglYE8EFEyzNpOY+
   SSKM0j2KHzeFbxQtk7kNsJ+Cr4kljGOquAR6gMA2yTV+ogRvjcY1TwxSlfNCu0F9
   PP6wsf0zYiwp4Uy72S4TY8ZevUUEt1EjKblnDjLhssZ6VOfxpV+Ln56gToyjpwXm
   KjxeY3N0r7eutt3qYSzeKPAaIC16pONHItJ90/m4mJTQGf1dTXEZ7+NyO7oQTLi7
   CYHgdN46/iANqq6tgmzEXyRNv0Ma+rNO+994JHTS/VcRj2RiFJNO2Zy6OwA+jWej
   g29vGfxBkQzlFj7jrpnrhNUU63YeY2hOpW+XkdLdSqxuYWi5SMgX91oiKssOjNwD
   zEr+j2cVfho2O3+u/58XK5iRNnfFod0IXp7kwiBSwa9YGTEWZz3NO/xfNLhV3MbH
   eIVknp5x9D1K6g9Lcsp+2gV4uhPTGmWNLQYKmmb/ae0b55l6L7HScj04+b+r4Y+O
   ezzakG5Om16ULI6uspYHDr/TZJR6lAzJeL7Wazd0nm1dzXvoxJREDiuEzs/vuYwL
   7fs8QeM1nSzXGX++cgxIqmxrZGXB7mPjVpwq3HREkTcLf3gm/gt3odGdZBAdAyuR
   gQa0LS73N0flYB/kulDyPt5SHwMagX0VKUpDci6DeHhLbbDPG6norpEdkgG5zpzD
   AZxvXCfLmNomFEtkIlp8kysw92Hnii1Zodi4PsY0Si9t1H52VwbQC/SnmmqSbDup
   HYEsjyx5erF5Zwnl0WhWd4KTUp8ChtAVw7U5lhlkKjM+nlk9bj9TU5lCCOnmozKF
   HX9lJSKpKLkX4n4tbUITff4uv6b7HGeybAJUUoaF9+vb4xWmjqotp2noqfQtPmAA
   fHEzCSaywAEtg+rU5P0e2HLM0ZciAdKwJ/NUWsLTDNeLwddA/sy8b8KgRGxuMOrF
   H1ppCYqi1EfyCFtOTkuSzMJpIdLeR4UYzQkM4meuotJ62lf9iLSXbYn7hDzcz0mn
   bKJnnmgBv6f7AxiW+1BilwS5kjk2u13ThTERIcrfsRmV5ZtzA0z2ftA6uBOGdkjQ
   JYKAh+lJqa/Ra5XXLZmx7coleqwTL/t6Bwmu1anA/wX7Dyu/KECe7XtfWAG+lkzt
   AZ4ct4UdOFHxApBnThn/sAizAcSs9kGiuxQhbh1pyr9Ste8idJaw8weZqFXRF/rT
   dEpvozUD6nmLUt3X7lQmYJ2/zT8ME7Fk1sBR9+1KEZcZpxLjiNMoQCCB/xNUtVTS
   wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr
   3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC
   M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ
   gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J
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   vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k
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   EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg=
   -----END PRIVATE KEY-----

Massimo, et al.         Expires 29 December 2025               [Page 22]
Internet-Draft           ML-DSA in Certificates                June 2025

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
     }
     OCTET_STRING {
       OCTET_STRING { `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d178
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   fd5d4d7119efe3723bba104cb8bb0981e074de3afe200daaaead826cc45f244d

Massimo, et al.         Expires 29 December 2025               [Page 23]
Internet-Draft           ML-DSA in Certificates                June 2025

   bf431afab34efbdf782474d2fd57118f646214934ed99cba3b003e8d67a3836f
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   b0689e21d8eb0ff69668` }
     }
   }

C.1.1.3.  Both Format

Massimo, et al.         Expires 29 December 2025               [Page 24]
Internet-Draft           ML-DSA in Certificates                June 2025

   -----BEGIN PRIVATE KEY-----
   MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR
   EhMUFRYXGBkaGxwdHh8EggoA17K0clSq4NtF55MNSpjSyX2PE5fReJ2voXAksxbp
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   6tTk/R7YcszRlyIB0rAn81RawtMM14vB10D+zLxvwqBEbG4w6sUfWmkJiqLUR/II
   W05OS5LMwmkh0t5HhRjNCQziZ66i0nraV/2ItJdtifuEPNzPSadsomeeaAG/p/sD
   GJb7UGKXBLmSOTa7XdOFMREhyt+xGZXlm3MDTPZ+0Dq4E4Z2SNAlgoCH6Umpr9Fr
   ldctmbHtyiV6rBMv+3oHCa7VqcD/BfsPK78oQJ7te19YAb6WTO0Bnhy3hR04UfEC
   kGdOGf+wCLMBxKz2QaK7FCFuHWnKv1K17yJ0lrDzB5moVdEX+tN0Sm+jNQPqeYtS
   3dfuVCZgnb/NPwwTsWTWwFH37UoRlxmnEuOI0yhAIIH/E1S1VNLCN6/tOxUcS6jp
   9L3rhJmjBm4mu8aeivCJ3scXMdHcUp6rF+9zdHNMD+R1SUyDg2vdNKA7m8iZFHFg
   Yb+5jsbmHD7UQ47cryUkPGRwhrnqcBiw2aigsAzssAq94kmNacIzYQGncsvk9XFS

Massimo, et al.         Expires 29 December 2025               [Page 25]
Internet-Draft           ML-DSA in Certificates                June 2025

   P1G9BYgs3zWLhJzBQKofryJCOhKFHODjP9SJdaSVn6XF/kGMk5CBkatudBt3v+As
   vWmO55XEZtYVYZ5kQTgsbqwBg07pq3POqAu+I1x42pG9ebb4L4mXhdaHANOT5nXC
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   rCSwqRq8SlZGYBRCuhC+z9MJk4gAUdB/VqBak3nnqOa+/uPyL6oQY5j3cGAG5C6b
   4e+J0lwnLxGpUJXFh9cTcyKE3p29PHIXsGieIdjrD/aWaA==
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
     }
     OCTET_STRING {
       SEQUENCE {
         OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
   15161718191a1b1c1d1e1f` }
         OCTET_STRING { `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d1
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   20122524c90588288cc9c04d5948220a276ec134644c90605b44508286494388
   0443b28c603080a2882d84a46d8ca629d0c68442064689885100a98d01498de4
   380da4068dd3947142b26c1a84611ba32842b42808a0711ac531e0a04c013765
   242862142890091061d940221b3360090292d02481200408491844a3222d5c88
   44149808a446610195640b390a0c9450ca406ad2b220c0380182308e13b90891
   8084148829c0189112350da02422e20406d9c2850428121cc989180272d24029
   c20812d8062a9994719bb8682384291a2289144511dc82445096450c4484c0b2
   049aa60543862c44326e88442120a84c9a3070e3b82d63268803254903438c48
   a809ca147253344e1243081ba704593022d99480e234228142129c302a943426
   6104452426281346094a326d11280918b82562281113410d41b21190844c8b12
   12a2c688c9c030220606d2188e848630904452128831d9207113c52843060e03
   3060cca6845826524c88011ef72562c85ffa43acfa49217f2b172d7bbc14620e

Massimo, et al.         Expires 29 December 2025               [Page 26]
Internet-Draft           ML-DSA in Certificates                June 2025

   6d980a71aabbdf0c45e9a206ecb1423fee15decc17601300149d9223cd6e6c6e
   1fa8e41fc7c64938ab68905fd3dcda50d87082e7d0d71d1bc9b2b84c85523ca8
   fe6cad294adf83be15b108ff721d0cc87bc3dd3a7590184b0e845663a91fc9e1
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   2bb3c1a8c595d635e84342fdea01dc24b211ad2fc281cf77e59110c7abc54bf0
   c86d480b9be276471dc9d603cee98cfdab3e9fcfb703793560549ea4450fa7b3
   3fb9169c44b4d25fb9c457f49791cd3da03eac96095813c105132ccda4e63e49
   228cd23d8a1f37856f142d93b90db09f82af89258c63aab8047a80c036c9357e
   a2046f8dc6354f0c5295f342bb417d3cfeb0b1fd33622c29e14cbbd92e1363c6
   5ebd4504b7512329b9670e32e1b2c67a54e7f1a55f8b9f9ea04e8ca3a705e62a
   3c5e637374afb7aeb6ddea612cde28f01a202d7aa4e34722d27dd3f9b89894d0
   19fd5d4d7119efe3723bba104cb8bb0981e074de3afe200daaaead826cc45f24
   4dbf431afab34efbdf782474d2fd57118f646214934ed99cba3b003e8d67a383
   6f6f19fc41910ce5163ee3ae99eb84d514eb761e63684ea56f9791d2dd4aac6e
   6168b948c817f75a222acb0e8cdc03cc4afe8f67157e1a363b7faeff9f172b98
   913677c5a1dd085e9ee4c22052c1af58193116673dcd3bfc5f34b855dcc6c778
   85649e9e71f43d4aea0f4b72ca7eda0578ba13d31a658d2d060a9a66ff69ed1b
   e7997a2fb1d2723d38f9bfabe18f8e7b3cda906e4e9b5e942c8eaeb296070ebf
   d364947a940cc978bed66b37749e6d5dcd7be8c494440e2b84cecfefb98c0bed
   fb3c41e3359d2cd7197fbe720c48aa6c6b6465c1ee63e3569c2adc744491370b
   7f7826fe0b77a1d19d64101d032b918106b42d2ef73747e5601fe4ba50f23ede
   521f031a817d15294a43722e8378784b6db0cf1ba9e8ae911d9201b9ce9cc301
   9c6f5c27cb98da26144b64225a7c932b30f761e78a2d59a1d8b83ec6344a2f6d
   d47e765706d00bf4a79a6a926c3ba91d812c8f2c797ab1796709e5d168567782
   93529f0286d015c3b5399619642a333e9e593d6e3f5353994208e9e6a332851d
   7f652522a928b917e27e2d6d42137dfe2ebfa6fb1c67b26c0254528685f7ebdb
   e315a68eaa2da769e8a9f42d3e60007c71330926b2c0012d83ead4e4fd1ed872
   ccd1972201d2b027f3545ac2d30cd78bc1d740feccbc6fc2a0446c6e30eac51f
   5a69098aa2d447f2085b4e4e4b92ccc26921d2de478518cd090ce267aea2d27a
   da57fd88b4976d89fb843cdccf49a76ca2679e6801bfa7fb031896fb50629704
   b9923936bb5dd385311121cadfb11995e59b73034cf67ed03ab813867648d025
   828087e949a9afd16b95d72d99b1edca257aac132ffb7a0709aed5a9c0ff05fb
   0f2bbf28409eed7b5f5801be964ced019e1cb7851d3851f10290674e19ffb008
   b301c4acf641a2bb14216e1d69cabf52b5ef227496b0f30799a855d117fad374
   4a6fa33503ea798b52ddd7ee5426609dbfcd3f0c13b164d6c051f7ed4a119719
   a712e388d328402081ff1354b554d2c237afed3b151c4ba8e9f4bdeb8499a306
   6e26bbc69e8af089dec71731d1dc529eab17ef7374734c0fe475494c83836bdd
   34a03b9bc89914716061bfb98ec6e61c3ed4438edcaf25243c647086b9ea7018
   b0d9a8a0b00cecb00abde2498d69c2336101a772cbe4f571523f51bd05882cdf
   358b849cc140aa1faf22423a12851ce0e33fd48975a4959fa5c5fe418c939081
   91ab6e741b77bfe02cbd698ee795c466d615619e6441382c6eac01834ee9ab73
   cea80bbe235c78da91bd79b6f82f899785d68700d393e675c2224d6b7a1ad213
   20495679adaed70167b50866713a53109db7b6f7d81304ecdfd83b319b1ef248
   306b45ad29e7ddcc863dac56048b5d69ea175011f7614c00a86a863cde1872a8
   932878b9ac7e1ac5bda4997b72064f0cd75f4c814e034de11acb9013cf7ea926
   b4e7eaace070c7ba2188efad2e431e1223d45dd05c4d8403c2e45cee6413ecbe
   7527e873e455c4e610a61839aacc0bd56d2483e78f298b66a478eb2f558cbafc

Massimo, et al.         Expires 29 December 2025               [Page 27]
Internet-Draft           ML-DSA in Certificates                June 2025

   a86be847baeb02c5b216c8cd88fea4df249b09e670a20703abac24b0a91abc4a
   5646601442ba10becfd30993880051d07f56a05a9379e7a8e6befee3f22faa10
   6398f7706006e42e9be1ef89d25c272f11a95095c587d713732284de9dbd3c72
   17b0689e21d8eb0ff69668` }
       }
     }
   }

C.1.2.  ML-DSA-65 Private Key Examples

   Each of the examples includes the textual encoding [RFC7468] followed
   by the so-called "pretty print"; the private keys are the same.

C.1.2.1.  Seed Format

   -----BEGIN PRIVATE KEY-----
   MDQCAQAwCwYJYIZIAWUDBAMSBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
   GhscHR4f
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
     }
     OCTET_STRING {
       [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
   5161718191a1b1c1d1e1f` }
     }
   }

C.1.2.2.  Expanded Format

   -----BEGIN PRIVATE KEY-----
   MIIP2AIBADALBglghkgBZQMEAxIEgg/EBIIPwEhoPZGXjjHrPd24sEc0gtK4il9i
   WUn9j1ilYeaWvUwn2FP6abgZkCPozWeN2fq/kEdkb/0Ms8x/eVgFpx5w0jcbBWPj
   zTNGFJyMnrzyOwpOWpAO6pxlYnkKfGPjhmPaot3bbkgNxAWh5wGUi3SEHvXMHD8r
   8yeXLpUQUQzVN17MCFVxdxGHIiGGI4EABCR3gGFHUAdQFxcDVQRRUSVHGDgEYXVy
   IkQQiGhghkYBJ0dWcYCHBmaGQzJEQSIENjhmdQKCNjQkQyIFc2QQZFVUdyJ1VoFD
   NhRiVQggZDdoVGh1Q1N1EGhxgzOAVHUFJYB1KBiEOBEIcmAgIAhYgwGDYROCghIG
   FxFXh2h4iHhkN1RgFlcVUIRxiGYHJzKIBmR0GFZ2IYAxgnZkFXgkUCVkZkMRNQQ2
   R4ASZnMUMBFmBlWGRxg2iGNQOEeGEQEgI1YRYTeGB4UyEkAHVHiCMENmYRZgQlVB
   goVgU2d4VjhDRDBjJhB3BzF4QnIUERZTA4UnaGdGAVCCNzUyB2YQdQRoEkgGZgMD
   JlIxJEVAiAAxgIh2chcwcYJHIVEngBFlRHSGYXIjM4CGYGRGg1IVhCA2gBGAIRgY
   MxdzVFNIgQBEhlNnQ3BXcliDNGA4QjKFaBAGBCYEJYRWAjVoIFGDhjhDJCEiQkVk
   WFhncUVyhQR4hxcYBhiDYIaGQVZQgRZQJkZwBggmYic4MXJAclcwBycohiBmdYho
   JgcGQCAzA0NmMVVGQkU0VmcYc0Vlg3AiUIRoViiAcDZwhGI3FxAGVxdYR3hwhlVT
   eCI1FEZ3KFZzAyKHABQzIGFxWEVSZjJQJlEzR3c4A1UWQxNHNRBmJ1F1dAJGiIFw

Massimo, et al.         Expires 29 December 2025               [Page 28]
Internet-Draft           ML-DSA in Certificates                June 2025

   Z0NGgYYBdlJFMzCHIQQ0NAEDIodjUVUmUIEwd0VEQWgVQYNjZBEgQCaHMENndxKA
   iEY1VFMAYkWBBFg2USSEJ4A0UWZjWEN4VgFGURV0IyFDZoUiR3cxNFAXg2JCBVAA
   ZIRHEjRAiABgRzVAV4MzYwghBhUiUgckiFE0hjcGdiJYhXEmVnNHaBZGRoQlhwgS
   JwVQCDgyACMggGY0UzYAM0aFckcGNVQANXcSJ1IwcUJTaHQ3RXAFZkMiRIKFIHIY
   MzAgUzczQHcngFUlMGNSUEBnM0YTGAcoBxckg3djRXMYWFFgIzNENiUWQzgWCFh3
   NGJCiDAHA2WFN1UAdVIxUDcCEyRjBDcIaAY2FQMDAENYY1cIAhEGZHNGNSJiAzBD
   gCEIUodXgyEHiGdICFY0dDZzQoQFhGaEFDcAVRCHNCZEdyESc4RzZSZHJXcURwQX
   hkQmAkcRh0CBIhZgWEcXgTcGdoCBcFgYVYVHE2NCEHVYAWNYNYUYRAOEcRAzh0Ji
   gkd0E2VUQnBzRjV3dQBmJWJoQgISRoOGRhZkYDEiU4iEVACEVzRGR1RHJWBUYWaE
   ZjCIBjgnFWMocYOEBlIkdoEWBmITAzAYaAKAE4RjBQVlcjh1g2VyMjBogEYSJgZl
   FnVXBTJBMidnNRcIAVMAFihGATSIdwERiBVXExVGQxFwRzKIKFY2gjRVUEGGJ2Vj
   ERFodQUQQlRBRCeFIhEXF4gVNoUVdEcWYlU2VYNjAlAoVXaHUycTcQNyNwVxR2Fx
   NlGEEkI2ZERmQUNSBSEIUVcDM2OGAlhCZigUgRBUYmgXMDh1ZDMhZYhWhmNjKBNA
   YlQBIECIZUeIYXFldiNyYjSGcDARURVjIFB1NQISIQhCZTFDVWcRFSVyAQaFNjAV
   BVdYYFh4QxQxMnh4gIc4R4hjeIGBOHNCYXg4hSRmdzNQYCEVFGQjgjJoATVEB4NH
   U4VTV1KDIzUYdgEVITQyV3MzNlUYhhWBYWgkGEIhIjCEFEgVEgEQMCR3ckJUQ2YG
   dxdwdgMBRSVANQAYOHMjdzUmUIY1cRNzRIFgUndFZVNzAIWDd4UDUSERVIBiiFAY
   AmgThlIFNGgBMgckGAMhMAVyOGQHZCcRQQGDhSVRBjJgcQSGUXaDOChXJ2I1RRhz
   UIMTKIY3ZmFCYxFnUDMRJVN2QXYDFDMXchIjRBioLk9cnqD6+Z6wTXinMycREXwz
   8Y7KIfh0M3atpSGYBKftmlVX/NZ6NVCzpLjFiGKcAhR1+j1W1dbPuxoJvajRTeYi
   3f8W2LyZsUJ4qK8ddr7RV2ct2cMjFvl+jare+NnaaVhnJVZ/uWtZmQ1L8LycGVuQ
   t0KV9WdbJCV8JxDBdbAVPykRMowut6u5rUbnCotTw56mQs7ks8tCYg6GPOi2UM6K
   3NkjchoWhwI8ZzqMu2sD1RzRl+jDRuutzpOVD4jO4gHbnjIIQ+KfMA2aGVANcKTK
   8nLGnk7vafu4pV79fKK+2ZDS07WChI+cRcKrxUz8R9NPBsD/pW/Ndiq5y6kUbXcl
   IYljskDXK20iyTFx+9R3iLducgQt7wh40j32MaGh5aYCdobeW0oQ6RBpyPK6Almw
   TWQJ2pZWfKUtpJcCblg6Ds78HwHmuYjiH5dnorfhZy3rmh4qP8yGOqkVF8M0YgYB
   tP55cw6TSTX0tvvE4yaVFFwrX2oSf+zAondFHrw/1SNET57nycNFNPNW21RPwxwb
   /eX2XHfqL3wurkxV668QQnHFZv1OusccemLHSVKBeuZ1UE2VmbG3YrasoWioMkjJ
   2a2wzrFVbldZSQu8DHkAeVrXISMDi2YvZPEGqZk2gaJdWa97yXojW+koTFvEWmyQ
   yxwpmcZj2WtHjiMH+FVIlX1ldA4mc+nr0TUoKQOPRiuP07VoHaVcAlJSOFNSXqCt
   ZH5xrCxaiJPmA6yX5WwEzrLyb1xbS22Uq4ETgP0A8iCP6GU1CGrr/TXCkSBiTAT7
   thE5KdnFVjUCU3ZsIJ/bqDyV/M00KigJk1XQC8hj9O71lusLQuvMfHlJHM6uIF6g
   uAWfu4pXJsWUnSsV5+KcUfybAu4aT8NXtfG++cSt1GoqkgwvvwijfrFRS/oVEQpD
   kqdMbxPFDFz/2XUxCY180jtg6zXEpCi0bFU4bhAQxLp/cOTH7LdXXzBjpx6E39zw
   mliyzbD5nyftN4YQ0ly617+mug1ZGJz+iOq5tG1+bbAwfqvkGY6ZvXH3eatmWB4J
   Evx7HSWFJF6aEmh6l1zV6OHcwEXV+JHExoXbB8+B53OJs2Pra9/jmyf/hMl+7+4W
   LjtFH+aRRxnLZDbYVZYP+RXXzqat6v38HAV4bEn5I6R0/9/DFToG5u0LCtIg1yUk
   Q01Sc8Cqtt3k6RR21YGiaVpg3m2fRNd6oIJm6TjutKlZfJtkmGBZ5JJipOqyRU4U
   AVrQU2xCczpdd9eZXCogRGAJ6/5WMsgMCO0rl681BmSJ9ZfrGx8R8E9g4MkEAVnE
   SrPmDgoVIp0ZEii+0Xu8Osk5s8Z87hNfNSwnIWycMfcqPocEDF9hkwbrC2zKKpzn
   sioWlNAMqcBeMVEmRX8mzoT5YXJBhgeC+GS0c9hAF0kZArG9yM3FgA3UYSf7gKcc
   CVtHOlYlKbOx5+Q34Vil9mZumXTQBbBiwjCebc6Y+bZYxuP5ohbVjIyRQr0cjIWp
   2ocuu/rT/qnZq6K2jA6PGcb/XwBYTUXa+dbJ1p7QS42o1ocli3eAeSdhLFMERv6n
   aXrj+SZpiSm8alqM8+ICTA8MXuV7WGm/mBiByvnjZl/H9+/GeJKfh6VuqkLqTR/2
   aRgi3XmkcJa3dtHY8BRW5Yc7BzhAbDgsVzrpzeLZ5/IxtsxcZ2589DljNzATpYB1
   OB/wlJvghFRtcuT4o+X+SqUJGt0jTir+ADCxtmOunS0yQQmGuUAqqvJGW3Sl4tC8
   OOOpK73dih/te5SMI8zm+MCP41aDW6ZbD5hAaGFu9IE479ib81elTS6783bL3Mac
   Xx9hxk0nlLwGzLmr32biUIXYyDDirjsP4PB6evi5MgvzQpcJl9Z9fBJZOo+/reY1

Massimo, et al.         Expires 29 December 2025               [Page 29]
Internet-Draft           ML-DSA in Certificates                June 2025

   qsUwg6cCLEfV93pStXtZjak5KubYavxG/AZFUYG5x1pkbcIfgeS/ITdT3nN/0qFA
   AnkgrdNaIj+fX0RlzrYMA+0EVaMzpcyDrb9D8fQsLMuDKMIcerf67Sshz63i2lUi
   Oqqyr5tBxzMjQXRjQbOaovQ4FWUPVIBRFCTPppAXecTRi2OMwCh6qvMWgDONILF8
   dEn9xqJ4qNlqgu5MTspAEl4tZSkAcceu8b5qmRWY+51ZUSUjvNSzjFZrjoCnOuMz
   4TRBQyfvHYPEfEnf55Nt8TOKXiR3h4aPyE/cuVrInBhcS7X9V7IzisQrQcEKgj3z
   liTzaxWi8GdYTgbKLgjMr/Fhj+Ad0G3zUS4Lck3shQbaJCFayswsUbgq2NMCAC+0
   EGix2k+LsUeYezUWutXb3fATGP0/qbxDcCrEmMcZ2V8uhBtiKl5ISKPFwmKVmZLq
   en1yyoo2gCj0l9+tkzVcuxu5eG0U/yz1kDF4SPlYVkJxEN2jb1GSqBbOnIgWzHu/
   yATvxACFo4ULifHn/lZW26QQ+QapfDIzbBrn6Bc3qD4Ic1TkKNqFONlI2/XfrLWd
   0rX9O8gD9LpDLJpznfLPqe2UhDIPl+3/GkjGuGswAs+3ct1eVivEw9aD7ZZLYZn6
   BRSweQ2VgJW3uFxr6HX7tVnhkwFGzOpjo4ihlP4Jw96gO+Ut4n6QEBev6AmvYwpz
   gr9cTNTRuPQVeftDSO3kygX0zT8TmjGyVE5Rbb5Ahrm7SyvtR+LSMJgt1RkkKdN3
   t8B0XMBo4vWkqgTH/4cgntElmXag/Jsl6ehR1ONQLALIXW3/Ap4hHQHr8OnnGI1W
   j4Q32BOw8SLy+xdgO2k+2cOPF8/VC4FebZ38DtLM8Z9jmSdKFCDyNaWdi/ckNF4U
   5F2eS+iTTfw/qSZ422HXEYv1PLiiIlszX36uUOP5QSN2KNt22Oo493pyrzomyB/k
   NSOzNVNaXR23w480EIK7VzTQieiuMJz9o6C8tc1bCXETyO35YWqk9uZjG5ElJ2+z
   9oCjQ0HD22aNxsrUX8k7JwjKKvdczOc0/RkcUAidrVOYL92uAlMf+T4fIf85X8Ch
   KHTt8GtvlkfpWnMkWGxx39kdkB1iGFgZD+zQDM0RC7rFn5bLiEw8k5lHSKVvQSg7
   /EH7iQUhU6iUWIw8uQF/PWYybJhWN+V1rLgSNGNCZUAl1gLeO6lAwZrBpjPf/al3
   tSm4AT4ZwdbQaA9NrmLJJEUK5mqrgvIUcwYdqz1iskf5B+NVGTmtP1Rl6dCKgr/q
   F+6htrK5I3V0d/mTAAsvQ7cPKKqrH+miatH9M2FhbAsOJC/nZgS3AzofMOl+KPUm
   yjyID+K42dGwyf8YizHLnZdCWsq5shbZimrjVeWD2nHohk7j0WsHWXlhkO9UXB5i
   v++Sr2yhR7EyRNbIkvyO8iOrP0P5JML0Zgl+6A==
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
     }
     OCTET_STRING {
       OCTET_STRING { `48683d91978e31eb3dddb8b0473482d2b88a5f625949
   fd8f58a561e696bd4c27d853fa69b8199023e8cd678dd9fabf9047646ffd0cb3
   cc7f795805a71e70d2371b0563e3cd3346149c8c9ebcf23b0a4e5a900eea9c65
   62790a7c63e38663daa2dddb6e480dc405a1e701948b74841ef5cc1c3f2bf327
   972e9510510cd5375ecc08557177118722218623810004247780614750075017
   1703550451512547183804617572224410886860864601274756718087066686
   4332444122043638667502823634244322057364106455547722755681433614
   6255082064376854687543537510687183338054750525807528188438110872
   6020200858830183611382821206171157876878887864375460165715508471
   8866072732880664741856762180318276641578245025646643113504364780
   1266731430116606558647183688635038478611012023561161378607853212
   4007547882304366611660425541828560536778563843443063261077073178
   4272141116530385276867460150823735320766107504681248066603032652
   3124454088003180887672173071824721512780116544748661722333808660
   6446835215842036801180211818331773545348810044865367437057725883
   3460384232856810060426042584560235682051838638432421224245645858
   6771457285047887171806188360868641565081165026467006082662273831

Massimo, et al.         Expires 29 December 2025               [Page 30]
Internet-Draft           ML-DSA in Certificates                June 2025

   7240725730072728862066758868260706402033034366315546424534566718
   7345658370225084685628807036708462371710065717584778708655537822
   3514467728567303228700143320617158455266325026513347773803551643
   1347351066275175740246888170674346818601765245333087210434340103
   2287635155265081307745444168154183636411204026873043677712808846
   3554530062458104583651248427803451666358437856014651157423214366
   8522477731345017836242055000648447123440880060473540578333630821
   0615225207248851348637067622588571265673476816464684258708122705
   5008383200232080663453360033468572470635540035771227523071425368
   7437457005664322448285207218333020533733407727805525306352504067
   3346131807280717248377634573185851602333443625164338160858773462
   4288300703658537550075523150370213246304370868063615030300435863
   5708021106647346352262033043802108528757832107886748085634743673
   4284058466841437005510873426447721127384736526472577144704178644
   2602471187408122166058471781370676808170581855854713634210755801
   6358358518440384711033874262824774136554427073463577750066256268
   4202124683864616646031225388845400845734464754472560546166846630
   8806382715632871838406522476811606621303301868028013846305056572
   3875836572323068804612260665167557053241322767351708015300162846
   0134887701118815571315464311704732882856368234555041862765631111
   6875051042544144278522111717881536851574471662553655836302502855
   7687532713710372370571476171365184124236644466414352052108515703
   3363860258426628148110546268173038756433216588568663632813406254
   0120408865478861716576237262348670301151156320507535021221084265
   3143556711152572010685363015055758605878431431327878808738478863
   7881813873426178388524667733506021151464238232680135440783475385
   5357528323351876011521343257733336551886158161682418422122308414
   4815120110302477724254436606771770760301452540350018387323773526
   5086357113734481605277456553730085837785035121115480628850180268
   1386520534680132072418032130057238640764271141018385255106326071
   0486517683382857276235451873508313288637666142631167503311255376
   4176031433177212234418a82e4f5c9ea0faf99eb04d78a7332711117c33f18e
   ca21f8743376ada5219804a7ed9a5557fcd67a3550b3a4b8c588629c021475fa
   3d56d5d6cfbb1a09bda8d14de622ddff16d8bc99b14278a8af1d76bed157672d
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   97e8c346ebadce93950f88cee201db9e320843e29f300d9a19500d70a4caf272
   c69e4eef69fbb8a55efd7ca2bed990d2d3b582848f9c45c2abc54cfc47d34f06
   c0ffa56fcd762ab9cba9146d7725218963b240d72b6d22c93171fbd47788b76e
   72042def0878d23df631a1a1e5a6027686de5b4a10e91069c8f2ba0259b04d64
   09da96567ca52da497026e583a0ecefc1f01e6b988e21f9767a2b7e1672deb9a
   1e2a3fcc863aa91517c334620601b4fe79730e934935f4b6fbc4e32695145c2b
   5f6a127fecc0a277451ebc3fd523444f9ee7c9c34534f356db544fc31c1bfde5
   f65c77ea2f7c2eae4c55ebaf104271c566fd4ebac71c7a62c74952817ae67550
   4d9599b1b762b6aca168a83248c9d9adb0ceb1556e5759490bbc0c7900795ad7
   2123038b662f64f106a9993681a25d59af7bc97a235be9284c5bc45a6c90cb1c
   2999c663d96b478e2307f85548957d65740e2673e9ebd1352829038f462b8fd3

Massimo, et al.         Expires 29 December 2025               [Page 31]
Internet-Draft           ML-DSA in Certificates                June 2025

   b5681da55c0252523853525ea0ad647e71ac2c5a8893e603ac97e56c04ceb2f2
   6f5c5b4b6d94ab811380fd00f2208fe86535086aebfd35c29120624c04fbb611
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   eb0b42ebcc7c79491cceae205ea0b8059fbb8a5726c5949d2b15e7e29c51fc9b
   02ee1a4fc357b5f1bef9c4add46a2a920c2fbf08a37eb1514bfa15110a4392a7
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   e4c7ecb7575f3063a71e84dfdcf09a58b2cdb0f99f27ed378610d25cbad7bfa6
   ba0d59189cfe88eab9b46d7e6db0307eabe4198e99bd71f779ab66581e0912fc
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   2ae6d86afc46fc06455181b9c75a646dc21f81e4bf213753de737fd2a1400279
   20add35a223f9f5f4465ceb60c03ed0455a333a5cc83adbf43f1f42c2ccb8328
   c21c7ab7faed2b21cfade2da55223aaab2af9b41c7332341746341b39aa2f438
   15650f5480511424cfa6901779c4d18b638cc0287aaaf31680338d20b17c7449
   fdc6a278a8d96a82ee4c4eca40125e2d65290071c7aef1be6a991598fb9d5951
   2523bcd4b38c566b8e80a73ae333e134414327ef1d83c47c49dfe7936df1338a
   5e247787868fc84fdcb95ac89c185c4bb5fd57b2338ac42b41c10a823df39624
   f36b15a2f067584e06ca2e08ccaff1618fe01dd06df3512e0b724dec8506da24
   215acacc2c51b82ad8d302002fb41068b1da4f8bb147987b3516bad5dbddf013
   18fd3fa9bc43702ac498c719d95f2e841b622a5e4848a3c5c262959992ea7a7d
   72ca8a368028f497dfad93355cbb1bb9786d14ff2cf590317848f95856427110
   dda36f5192a816ce9c8816cc7bbfc804efc40085a3850b89f1e7fe5656dba410
   f906a97c32336c1ae7e81737a83e087354e428da8538d948dbf5dfacb59dd2b5
   fd3bc803f4ba432c9a739df2cfa9ed9484320f97edff1a48c6b86b3002cfb772
   dd5e562bc4c3d683ed964b6199fa0514b0790d958095b7b85c6be875fbb559e1
   930146ccea63a388a194fe09c3dea03be52de27e901017afe809af630a7382bf
   5c4cd4d1b8f41579fb4348ede4ca05f4cd3f139a31b2544e516dbe4086b9bb4b
   2bed47e2d230982dd5192429d377b7c0745cc068e2f5a4aa04c7ff87209ed125
   9976a0fc9b25e9e851d4e3502c02c85d6dff029e211d01ebf0e9e7188d568f84
   37d813b0f122f2fb17603b693ed9c38f17cfd50b815e6d9dfc0ed2ccf19f6399

Massimo, et al.         Expires 29 December 2025               [Page 32]
Internet-Draft           ML-DSA in Certificates                June 2025

   274a1420f235a59d8bf724345e14e45d9e4be8934dfc3fa92678db61d7118bf5
   3cb8a2225b335f7eae50e3f941237628db76d8ea38f77a72af3a26c81fe43523
   b335535a5d1db7c38f341082bb5734d089e8ae309cfda3a0bcb5cd5b097113c8
   edf9616aa4f6e6631b9125276fb3f680a34341c3db668dc6cad45fc93b2708ca
   2af75ccce734fd191c50089dad53982fddae02531ff93e1f21ff395fc0a12874
   edf06b6f9647e95a7324586c71dfd91d901d621858190fecd00ccd110bbac59f
   96cb884c3c93994748a56f41283bfc41fb89052153a894588c3cb9017f3d6632
   6c985637e575acb812346342654025d602de3ba940c19ac1a633dffda977b529
   b8013e19c1d6d0680f4dae62c924450ae66aab82f21473061dab3d62b247f907
   e3551939ad3f5465e9d08a82bfea17eea1b6b2b923757477f993000b2f43b70f
   28aaab1fe9a26ad1fd3361616c0b0e242fe76604b7033a1f30e97e28f526ca3c
   880fe2b8d9d1b0c9ff188b31cb9d97425acab9b216d98a6ae355e583da71e886
   4ee3d16b0759796190ef545c1e62bfef92af6ca147b13244d6c892fc8ef223ab
   3f43f924c2f466097ee8` }
     }
   }

C.1.2.3.  Both Format

   -----BEGIN PRIVATE KEY-----
   MIIP/gIBADALBglghkgBZQMEAxIEgg/qMIIP5gQgAAECAwQFBgcICQoLDA0ODxAR
   EhMUFRYXGBkaGxwdHh8Egg/ASGg9kZeOMes93biwRzSC0riKX2JZSf2PWKVh5pa9
   TCfYU/ppuBmQI+jNZ43Z+r+QR2Rv/QyzzH95WAWnHnDSNxsFY+PNM0YUnIyevPI7
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   XswIVXF3EYciIYYjgQAEJHeAYUdQB1AXFwNVBFFRJUcYOARhdXIiRBCIaGCGRgEn
   R1ZxgIcGZoZDMkRBIgQ2OGZ1AoI2NCRDIgVzZBBkVVR3InVWgUM2FGJVCCBkN2hU
   aHVDU3UQaHGDM4BUdQUlgHUoGIQ4EQhyYCAgCFiDAYNhE4KCEgYXEVeHaHiIeGQ3
   VGAWVxVQhHGIZgcnMogGZHQYVnYhgDGCdmQVeCRQJWRmQxE1BDZHgBJmcxQwEWYG
   VYZHGDaIY1A4R4YRASAjVhFhN4YHhTISQAdUeIIwQ2ZhFmBCVUGChWBTZ3hWOENE
   MGMmEHcHMXhCchQRFlMDhSdoZ0YBUII3NTIHZhB1BGgSSAZmAwMmUjEkRUCIADGA
   iHZyFzBxgkchUSeAEWVEdIZhciMzgIZgZEaDUhWEIDaAEYAhGBgzF3NUU0iBAESG
   U2dDcFdyWIM0YDhCMoVoEAYEJgQlhFYCNWggUYOGOEMkISJCRWRYWGdxRXKFBHiH
   FxgGGINghoZBVlCBFlAmRnAGCCZiJzgxckByVzAHJyiGIGZ1iGgmBwZAIDMDQ2Yx
   VUZCRTRWZxhzRWWDcCJQhGhWKIBwNnCEYjcXEAZXF1hHeHCGVVN4IjUURncoVnMD
   IocAFDMgYXFYRVJmMlAmUTNHdzgDVRZDE0c1EGYnUXV0AkaIgXBnQ0aBhgF2UkUz
   MIchBDQ0AQMih2NRVSZQgTB3RURBaBVBg2NkESBAJocwQ2d3EoCIRjVUUwBiRYEE
   WDZRJIQngDRRZmNYQ3hWAUZRFXQjIUNmhSJHdzE0UBeDYkIFUABkhEcSNECIAGBH
   NUBXgzNjCCEGFSJSBySIUTSGNwZ2IliFcSZWc0doFkZGhCWHCBInBVAIODIAIyCA
   ZjRTNgAzRoVyRwY1VAA1dxInUjBxQlNodDdFcAVmQyJEgoUgchgzMCBTNzNAdyeA
   VSUwY1JQQGczRhMYBygHFySDd2NFcxhYUWAjM0Q2JRZDOBYIWHc0YkKIMAcDZYU3
   VQB1UjFQNwITJGMENwhoBjYVAwMAQ1hjVwgCEQZkc0Y1ImIDMEOAIQhSh1eDIQeI
   Z0gIVjR0NnNChAWEZoQUNwBVEIc0JkR3IRJzhHNlJkcldxRHBBeGRCYCRxGHQIEi
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   NXd1AGYlYmhCAhJGg4ZGFmRgMSJTiIRUAIRXNEZHVEclYFRhZoRmMIgGOCcVYyhx
   g4QGUiR2gRYGYhMDMBhoAoAThGMFBWVyOHWDZXIyMGiARhImBmUWdVcFMkEyJ2c1
   FwgBUwAWKEYBNIh3ARGIFVcTFUZDEXBHMogoVjaCNFVQQYYnZWMREWh1BRBCVEFE
   J4UiERcXiBU2hRV0RxZiVTZVg2MCUChVdodTJxNxA3I3BXFHYXE2UYQSQjZkRGZB
   Q1IFIQhRVwMzY4YCWEJmKBSBEFRiaBcwOHVkMyFliFaGY2MoE0BiVAEgQIhlR4hh

Massimo, et al.         Expires 29 December 2025               [Page 33]
Internet-Draft           ML-DSA in Certificates                June 2025

   cWV2I3JiNIZwMBFRFWMgUHU1AhIhCEJlMUNVZxEVJXIBBoU2MBUFV1hgWHhDFDEy
   eHiAhzhHiGN4gYE4c0JheDiFJGZ3M1BgIRUUZCOCMmgBNUQHg0dThVNXUoMjNRh2
   ARUhNDJXczM2VRiGFYFhaCQYQiEiMIQUSBUSARAwJHdyQlRDZgZ3F3B2AwFFJUA1
   ABg4cyN3NSZQhjVxE3NEgWBSd0VlU3MAhYN3hQNRIRFUgGKIUBgCaBOGUgU0aAEy
   ByQYAyEwBXI4ZAdkJxFBAYOFJVEGMmBxBIZRdoM4KFcnYjVFGHNQgxMohjdmYUJj
   EWdQMxElU3ZBdgMUMxdyEiNEGKguT1yeoPr5nrBNeKczJxERfDPxjsoh+HQzdq2l
   IZgEp+2aVVf81no1ULOkuMWIYpwCFHX6PVbV1s+7Ggm9qNFN5iLd/xbYvJmxQnio
   rx12vtFXZy3ZwyMW+X6Nqt742dppWGclVn+5a1mZDUvwvJwZW5C3QpX1Z1skJXwn
   EMF1sBU/KREyjC63q7mtRucKi1PDnqZCzuSzy0JiDoY86LZQzorc2SNyGhaHAjxn
   Ooy7awPVHNGX6MNG663Ok5UPiM7iAdueMghD4p8wDZoZUA1wpMrycsaeTu9p+7il
   Xv18or7ZkNLTtYKEj5xFwqvFTPxH008GwP+lb812KrnLqRRtdyUhiWOyQNcrbSLJ
   MXH71HeIt25yBC3vCHjSPfYxoaHlpgJ2ht5bShDpEGnI8roCWbBNZAnallZ8pS2k
   lwJuWDoOzvwfAea5iOIfl2eit+FnLeuaHio/zIY6qRUXwzRiBgG0/nlzDpNJNfS2
   +8TjJpUUXCtfahJ/7MCid0UevD/VI0RPnufJw0U081bbVE/DHBv95fZcd+ovfC6u
   TFXrrxBCccVm/U66xxx6YsdJUoF65nVQTZWZsbditqyhaKgySMnZrbDOsVVuV1lJ
   C7wMeQB5WtchIwOLZi9k8QapmTaBol1Zr3vJeiNb6ShMW8RabJDLHCmZxmPZa0eO
   Iwf4VUiVfWV0DiZz6evRNSgpA49GK4/TtWgdpVwCUlI4U1JeoK1kfnGsLFqIk+YD
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   KxXn4pxR/JsC7hpPw1e18b75xK3UaiqSDC+/CKN+sVFL+hURCkOSp0xvE8UMXP/Z
   dTEJjXzSO2DrNcSkKLRsVThuEBDEun9w5Mfst1dfMGOnHoTf3PCaWLLNsPmfJ+03
   hhDSXLrXv6a6DVkYnP6I6rm0bX5tsDB+q+QZjpm9cfd5q2ZYHgkS/HsdJYUkXpoS
   aHqXXNXo4dzARdX4kcTGhdsHz4Hnc4mzY+tr3+ObJ/+EyX7v7hYuO0Uf5pFHGctk
   NthVlg/5FdfOpq3q/fwcBXhsSfkjpHT/38MVOgbm7QsK0iDXJSRDTVJzwKq23eTp
   FHbVgaJpWmDebZ9E13qggmbpOO60qVl8m2SYYFnkkmKk6rJFThQBWtBTbEJzOl13
   15lcKiBEYAnr/lYyyAwI7SuXrzUGZIn1l+sbHxHwT2DgyQQBWcRKs+YOChUinRkS
   KL7Re7w6yTmzxnzuE181LCchbJwx9yo+hwQMX2GTBusLbMoqnOeyKhaU0AypwF4x
   USZFfybOhPlhckGGB4L4ZLRz2EAXSRkCsb3IzcWADdRhJ/uApxwJW0c6ViUps7Hn
   5DfhWKX2Zm6ZdNAFsGLCMJ5tzpj5tljG4/miFtWMjJFCvRyMhanahy67+tP+qdmr
   oraMDo8Zxv9fAFhNRdr51snWntBLjajWhyWLd4B5J2EsUwRG/qdpeuP5JmmJKbxq
   Wozz4gJMDwxe5XtYab+YGIHK+eNmX8f378Z4kp+HpW6qQupNH/ZpGCLdeaRwlrd2
   0djwFFblhzsHOEBsOCxXOunN4tnn8jG2zFxnbnz0OWM3MBOlgHU4H/CUm+CEVG1y
   5Pij5f5KpQka3SNOKv4AMLG2Y66dLTJBCYa5QCqq8kZbdKXi0Lw446krvd2KH+17
   lIwjzOb4wI/jVoNbplsPmEBoYW70gTjv2JvzV6VNLrvzdsvcxpxfH2HGTSeUvAbM
   uavfZuJQhdjIMOKuOw/g8Hp6+LkyC/NClwmX1n18Elk6j7+t5jWqxTCDpwIsR9X3
   elK1e1mNqTkq5thq/Eb8BkVRgbnHWmRtwh+B5L8hN1Pec3/SoUACeSCt01oiP59f
   RGXOtgwD7QRVozOlzIOtv0Px9Cwsy4Mowhx6t/rtKyHPreLaVSI6qrKvm0HHMyNB
   dGNBs5qi9DgVZQ9UgFEUJM+mkBd5xNGLY4zAKHqq8xaAM40gsXx0Sf3Gonio2WqC
   7kxOykASXi1lKQBxx67xvmqZFZj7nVlRJSO81LOMVmuOgKc64zPhNEFDJ+8dg8R8
   Sd/nk23xM4peJHeHho/IT9y5WsicGFxLtf1XsjOKxCtBwQqCPfOWJPNrFaLwZ1hO
   BsouCMyv8WGP4B3QbfNRLgtyTeyFBtokIVrKzCxRuCrY0wIAL7QQaLHaT4uxR5h7
   NRa61dvd8BMY/T+pvENwKsSYxxnZXy6EG2IqXkhIo8XCYpWZkup6fXLKijaAKPSX
   362TNVy7G7l4bRT/LPWQMXhI+VhWQnEQ3aNvUZKoFs6ciBbMe7/IBO/EAIWjhQuJ
   8ef+VlbbpBD5Bql8MjNsGufoFzeoPghzVOQo2oU42Ujb9d+stZ3Stf07yAP0ukMs
   mnOd8s+p7ZSEMg+X7f8aSMa4azACz7dy3V5WK8TD1oPtlkthmfoFFLB5DZWAlbe4
   XGvodfu1WeGTAUbM6mOjiKGU/gnD3qA75S3ifpAQF6/oCa9jCnOCv1xM1NG49BV5
   +0NI7eTKBfTNPxOaMbJUTlFtvkCGubtLK+1H4tIwmC3VGSQp03e3wHRcwGji9aSq
   BMf/hyCe0SWZdqD8myXp6FHU41AsAshdbf8CniEdAevw6ecYjVaPhDfYE7DxIvL7

Massimo, et al.         Expires 29 December 2025               [Page 34]
Internet-Draft           ML-DSA in Certificates                June 2025

   F2A7aT7Zw48Xz9ULgV5tnfwO0szxn2OZJ0oUIPI1pZ2L9yQ0XhTkXZ5L6JNN/D+p
   JnjbYdcRi/U8uKIiWzNffq5Q4/lBI3Yo23bY6jj3enKvOibIH+Q1I7M1U1pdHbfD
   jzQQgrtXNNCJ6K4wnP2joLy1zVsJcRPI7flhaqT25mMbkSUnb7P2gKNDQcPbZo3G
   ytRfyTsnCMoq91zM5zT9GRxQCJ2tU5gv3a4CUx/5Ph8h/zlfwKEodO3wa2+WR+la
   cyRYbHHf2R2QHWIYWBkP7NAMzRELusWflsuITDyTmUdIpW9BKDv8QfuJBSFTqJRY
   jDy5AX89ZjJsmFY35XWsuBI0Y0JlQCXWAt47qUDBmsGmM9/9qXe1KbgBPhnB1tBo
   D02uYskkRQrmaquC8hRzBh2rPWKyR/kH41UZOa0/VGXp0IqCv+oX7qG2srkjdXR3
   +ZMACy9Dtw8oqqsf6aJq0f0zYWFsCw4kL+dmBLcDOh8w6X4o9SbKPIgP4rjZ0bDJ
   /xiLMcudl0JayrmyFtmKauNV5YPaceiGTuPRawdZeWGQ71RcHmK/75KvbKFHsTJE
   1siS/I7yI6s/Q/kkwvRmCX7o
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
     }
     OCTET_STRING {
       SEQUENCE {
         OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
   15161718191a1b1c1d1e1f` }
         OCTET_STRING { `48683d91978e31eb3dddb8b0473482d2b88a5f6259
   49fd8f58a561e696bd4c27d853fa69b8199023e8cd678dd9fabf9047646ffd0c
   b3cc7f795805a71e70d2371b0563e3cd3346149c8c9ebcf23b0a4e5a900eea9c
   6562790a7c63e38663daa2dddb6e480dc405a1e701948b74841ef5cc1c3f2bf3
   27972e9510510cd5375ecc085571771187222186238100042477806147500750
   1717035504515125471838046175722244108868608646012747567180870666
   8643324441220436386675028236342443220573641064555477227556814336
   1462550820643768546875435375106871833380547505258075281884381108
   7260202008588301836113828212061711578768788878643754601657155084
   7188660727328806647418567621803182766415782450256466431135043647
   8012667314301166065586471836886350384786110120235611613786078532
   1240075478823043666116604255418285605367785638434430632610770731
   7842721411165303852768674601508237353207661075046812480666030326
   5231244540880031808876721730718247215127801165447486617223338086
   6064468352158420368011802118183317735453488100448653674370577258
   8334603842328568100604260425845602356820518386384324212242456458
   5867714572850478871718061883608686415650811650264670060826622738
   3172407257300727288620667588682607064020330343663155464245345667
   1873456583702250846856288070367084623717100657175847787086555378
   2235144677285673032287001433206171584552663250265133477738035516
   4313473510662751757402468881706743468186017652453330872104343401
   0322876351552650813077454441681541836364112040268730436777128088
   4635545300624581045836512484278034516663584378560146511574232143
   6685224777313450178362420550006484471234408800604735405783336308
   2106152252072488513486370676225885712656734768164646842587081227
   0550083832002320806634533600334685724706355400357712275230714253
   6874374570056643224482852072183330205337334077278055253063525040

Massimo, et al.         Expires 29 December 2025               [Page 35]
Internet-Draft           ML-DSA in Certificates                June 2025

   6733461318072807172483776345731858516023334436251643381608587734
   6242883007036585375500755231503702132463043708680636150303004358
   6357080211066473463522620330438021085287578321078867480856347436
   7342840584668414370055108734264477211273847365264725771447041786
   4426024711874081221660584717813706768081705818558547136342107558
   0163583585184403847110338742628247741365544270734635777500662562
   6842021246838646166460312253888454008457344647544725605461668466
   3088063827156328718384065224768116066213033018680280138463050565
   7238758365723230688046122606651675570532413227673517080153001628
   4601348877011188155713154643117047328828563682345550418627656311
   1168750510425441442785221117178815368515744716625536558363025028
   5576875327137103723705714761713651841242366444664143520521085157
   0333638602584266281481105462681730387564332165885686636328134062
   5401204088654788617165762372623486703011511563205075350212210842
   6531435567111525720106853630150557586058784314313278788087384788
   6378818138734261783885246677335060211514642382326801354407834753
   8553575283233518760115213432577333365518861581616824184221223084
   1448151201103024777242544366067717707603014525403500183873237735
   2650863571137344816052774565537300858377850351211154806288501802
   6813865205346801320724180321300572386407642711410183852551063260
   7104865176833828572762354518735083132886376661426311675033112553
   764176031433177212234418a82e4f5c9ea0faf99eb04d78a7332711117c33f1
   8eca21f8743376ada5219804a7ed9a5557fcd67a3550b3a4b8c588629c021475
   fa3d56d5d6cfbb1a09bda8d14de622ddff16d8bc99b14278a8af1d76bed15767
   2dd9c32316f97e8daadef8d9da69586725567fb96b59990d4bf0bc9c195b90b7
   4295f5675b24257c2710c175b0153f2911328c2eb7abb9ad46e70a8b53c39ea6
   42cee4b3cb42620e863ce8b650ce8adcd923721a1687023c673a8cbb6b03d51c
   d197e8c346ebadce93950f88cee201db9e320843e29f300d9a19500d70a4caf2
   72c69e4eef69fbb8a55efd7ca2bed990d2d3b582848f9c45c2abc54cfc47d34f
   06c0ffa56fcd762ab9cba9146d7725218963b240d72b6d22c93171fbd47788b7
   6e72042def0878d23df631a1a1e5a6027686de5b4a10e91069c8f2ba0259b04d
   6409da96567ca52da497026e583a0ecefc1f01e6b988e21f9767a2b7e1672deb
   9a1e2a3fcc863aa91517c334620601b4fe79730e934935f4b6fbc4e32695145c
   2b5f6a127fecc0a277451ebc3fd523444f9ee7c9c34534f356db544fc31c1bfd
   e5f65c77ea2f7c2eae4c55ebaf104271c566fd4ebac71c7a62c74952817ae675
   504d9599b1b762b6aca168a83248c9d9adb0ceb1556e5759490bbc0c7900795a
   d72123038b662f64f106a9993681a25d59af7bc97a235be9284c5bc45a6c90cb
   1c2999c663d96b478e2307f85548957d65740e2673e9ebd1352829038f462b8f
   d3b5681da55c0252523853525ea0ad647e71ac2c5a8893e603ac97e56c04ceb2
   f26f5c5b4b6d94ab811380fd00f2208fe86535086aebfd35c29120624c04fbb6
   113929d9c556350253766c209fdba83c95fccd342a28099355d00bc863f4eef5
   96eb0b42ebcc7c79491cceae205ea0b8059fbb8a5726c5949d2b15e7e29c51fc
   9b02ee1a4fc357b5f1bef9c4add46a2a920c2fbf08a37eb1514bfa15110a4392
   a74c6f13c50c5cffd97531098d7cd23b60eb35c4a428b46c55386e1010c4ba7f
   70e4c7ecb7575f3063a71e84dfdcf09a58b2cdb0f99f27ed378610d25cbad7bf
   a6ba0d59189cfe88eab9b46d7e6db0307eabe4198e99bd71f779ab66581e0912
   fc7b1d2585245e9a12687a975cd5e8e1dcc045d5f891c4c685db07cf81e77389
   b363eb6bdfe39b27ff84c97eefee162e3b451fe6914719cb6436d855960ff915

Massimo, et al.         Expires 29 December 2025               [Page 36]
Internet-Draft           ML-DSA in Certificates                June 2025

   d7cea6adeafdfc1c05786c49f923a474ffdfc3153a06e6ed0b0ad220d7252443
   4d5273c0aab6dde4e91476d581a2695a60de6d9f44d77aa08266e938eeb4a959
   7c9b64986059e49262a4eab2454e14015ad0536c42733a5d77d7995c2a204460
   09ebfe5632c80c08ed2b97af35066489f597eb1b1f11f04f60e0c9040159c44a
   b3e60e0a15229d191228bed17bbc3ac939b3c67cee135f352c27216c9c31f72a
   3e87040c5f619306eb0b6cca2a9ce7b22a1694d00ca9c05e315126457f26ce84
   f9617241860782f864b473d84017491902b1bdc8cdc5800dd46127fb80a71c09
   5b473a562529b3b1e7e437e158a5f6666e9974d005b062c2309e6dce98f9b658
   c6e3f9a216d58c8c9142bd1c8c85a9da872ebbfad3fea9d9aba2b68c0e8f19c6
   ff5f00584d45daf9d6c9d69ed04b8da8d687258b77807927612c530446fea769
   7ae3f926698929bc6a5a8cf3e2024c0f0c5ee57b5869bf981881caf9e3665fc7
   f7efc678929f87a56eaa42ea4d1ff6691822dd79a47096b776d1d8f01456e587
   3b0738406c382c573ae9cde2d9e7f231b6cc5c676e7cf43963373013a5807538
   1ff0949be084546d72e4f8a3e5fe4aa5091add234e2afe0030b1b663ae9d2d32
   410986b9402aaaf2465b74a5e2d0bc38e3a92bbddd8a1fed7b948c23cce6f8c0
   8fe356835ba65b0f984068616ef48138efd89bf357a54d2ebbf376cbdcc69c5f
   1f61c64d2794bc06ccb9abdf66e25085d8c830e2ae3b0fe0f07a7af8b9320bf3
   42970997d67d7c12593a8fbfade635aac53083a7022c47d5f77a52b57b598da9
   392ae6d86afc46fc06455181b9c75a646dc21f81e4bf213753de737fd2a14002
   7920add35a223f9f5f4465ceb60c03ed0455a333a5cc83adbf43f1f42c2ccb83
   28c21c7ab7faed2b21cfade2da55223aaab2af9b41c7332341746341b39aa2f4
   3815650f5480511424cfa6901779c4d18b638cc0287aaaf31680338d20b17c74
   49fdc6a278a8d96a82ee4c4eca40125e2d65290071c7aef1be6a991598fb9d59
   512523bcd4b38c566b8e80a73ae333e134414327ef1d83c47c49dfe7936df133
   8a5e247787868fc84fdcb95ac89c185c4bb5fd57b2338ac42b41c10a823df396
   24f36b15a2f067584e06ca2e08ccaff1618fe01dd06df3512e0b724dec8506da
   24215acacc2c51b82ad8d302002fb41068b1da4f8bb147987b3516bad5dbddf0
   1318fd3fa9bc43702ac498c719d95f2e841b622a5e4848a3c5c262959992ea7a
   7d72ca8a368028f497dfad93355cbb1bb9786d14ff2cf590317848f958564271
   10dda36f5192a816ce9c8816cc7bbfc804efc40085a3850b89f1e7fe5656dba4
   10f906a97c32336c1ae7e81737a83e087354e428da8538d948dbf5dfacb59dd2
   b5fd3bc803f4ba432c9a739df2cfa9ed9484320f97edff1a48c6b86b3002cfb7
   72dd5e562bc4c3d683ed964b6199fa0514b0790d958095b7b85c6be875fbb559
   e1930146ccea63a388a194fe09c3dea03be52de27e901017afe809af630a7382
   bf5c4cd4d1b8f41579fb4348ede4ca05f4cd3f139a31b2544e516dbe4086b9bb
   4b2bed47e2d230982dd5192429d377b7c0745cc068e2f5a4aa04c7ff87209ed1
   259976a0fc9b25e9e851d4e3502c02c85d6dff029e211d01ebf0e9e7188d568f
   8437d813b0f122f2fb17603b693ed9c38f17cfd50b815e6d9dfc0ed2ccf19f63
   99274a1420f235a59d8bf724345e14e45d9e4be8934dfc3fa92678db61d7118b
   f53cb8a2225b335f7eae50e3f941237628db76d8ea38f77a72af3a26c81fe435
   23b335535a5d1db7c38f341082bb5734d089e8ae309cfda3a0bcb5cd5b097113
   c8edf9616aa4f6e6631b9125276fb3f680a34341c3db668dc6cad45fc93b2708
   ca2af75ccce734fd191c50089dad53982fddae02531ff93e1f21ff395fc0a128
   74edf06b6f9647e95a7324586c71dfd91d901d621858190fecd00ccd110bbac5
   9f96cb884c3c93994748a56f41283bfc41fb89052153a894588c3cb9017f3d66
   326c985637e575acb812346342654025d602de3ba940c19ac1a633dffda977b5
   29b8013e19c1d6d0680f4dae62c924450ae66aab82f21473061dab3d62b247f9
   07e3551939ad3f5465e9d08a82bfea17eea1b6b2b923757477f993000b2f43b7

Massimo, et al.         Expires 29 December 2025               [Page 37]
Internet-Draft           ML-DSA in Certificates                June 2025

   0f28aaab1fe9a26ad1fd3361616c0b0e242fe76604b7033a1f30e97e28f526ca
   3c880fe2b8d9d1b0c9ff188b31cb9d97425acab9b216d98a6ae355e583da71e8
   864ee3d16b0759796190ef545c1e62bfef92af6ca147b13244d6c892fc8ef223
   ab3f43f924c2f466097ee8` }
       }
     }
   }

C.1.3.  ML-DSA-87 Private Key Examples

   Each of the examples includes the textual encoding [RFC7468] followed
   by the so-called "pretty print"; the private keys are the same.

C.1.3.1.  Seed Format

   -----BEGIN PRIVATE KEY-----
   MDQCAQAwCwYJYIZIAWUDBAMTBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
   GhscHR4f
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
     }
     OCTET_STRING {
       [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
   5161718191a1b1c1d1e1f` }
     }
   }

C.1.3.2.  Expanded Format

   -----BEGIN PRIVATE KEY-----
   MIITOAIBADALBglghkgBZQMEAxMEghMkBIITIJeSvOwvJDBoaoL8zzwvX/Zl53HX
   q0G5AljPp+kOyXEk2OnuTpChbGAvXsm8OFF9ww4ynVqydnO9hfTJsDAPd2OJiGdQ
   tXwk2z/AEuYe3ll1Mzc3T6cSSZFUmvJDSW0GN8s74FpZSCNb95h1+JbY/gyrMMhJ
   SNtNYxWqrxYKxiQ2ZCIBSBYRCREslAKJIkUsYrhFAEUqCJZwkBJuFJNw1EYQhERR
   WJaRDKkpgrJByQhxxChoBJaJSECFmyJtHChkWRJBnLiRhASJRJAFyzRioIaQQCaS
   IJkpEwVpXDRopDKOGSaSWUYQCaRJI0JNEjZhWBBlASiQGjNMmYYx06JJCYIlQxQo
   wDiBAxVNWyiGCIdIIzFSlCIlw8BNpJghmEAg0UKGy0BwW7BxnJYswRIGU0YJDEUC
   FEZukbQhVLCM5EZCmiCMASElE0EFWkAiE8kMoBhAUsIwyzQsS8hoG6RgSYSEYzAp
   SqBpW4AE0jgKFCZM4rJEi6IRJEZJxBRSC0JxA7IQkiiAASSI4wgRCgUoGcSBACAi
   3ERoQhIiRAAqySZqDIcx4MBEmRSEGDYNETdCIhiMY7KRDJgIoaABCJJEBBMkXJhx
   goRxhDJSUbAxnEIuGqgoAgiRAcCJC8cFiiRlIsJkTIiRXIJoE6VkUCCGIQQCkZRE
   SCIwIjlKApiECaKIGRkpREiMIpUMoQRyBIdwEiEQQgaEG0mFiQZK0zYI28BAWLZR
   DKcJjCRhmZBkjMKQWySQEKNJAyVhQzKKEZhEyLIgBDhBEEcsGcZEHCUsBIgw2UZp
   myAAG0aCWqSAW6BJGJAlACaAC8IxWkByVMYgwbAxJLFNEJUoFAAKoMhNVKKII5iB

Massimo, et al.         Expires 29 December 2025               [Page 38]
Internet-Draft           ML-DSA in Certificates                June 2025

   YJAEAhYsEyFAkYaNCMKRkRQm0LQMCcZgUUQuBBEmACkRk8IIY6QxIgAowRQIDEAs
   QRQGnCByVCIGiwhNoUhpEDBBHChJRBiOzJZI2UJQGwZJDEWIIwQNIDAuI4UsFAcw
   QLaFTMAgRIYgGQBsVAJIzIhsWQYySRSEBMdQE0ko5AYJ08YQyChMIzlEUqRkzKhJ
   RDgyComEADQsIoWNEDEJCTJlHImMQEApIYUACaFthMBk4gItSARAEgmO4EIuk0QI
   EhBqAYQFkjCKyzSOoiYuXIYRCzUIGBAAAjQmJCOJ0YQAJEZgE7JJJChGGAJxoDiQ
   iRRE05YtoxhAIychwBhQQ8gEQUKNXCZBRKJtSBIOQDIlCxSCCkguy4KIA6NgGyUm
   jLggJLCFmAQhCKcsgzhkVDKJAQQBI0mEApVp0aRNE6QMkUYNYZSAkDhFXMZQARcg
   U8YomxgQQRJokBIhwBCEQhaSU4IpgSZJ2KQFmiYkJAMp4EAm0gJIESRoEZmJmBSF
   ySANUBKMHAgQAhAAAJUowSiQWbSF0xRlCkBuESllGMJMITRl2DBpEDBSGTFmjBiK
   yMAITJgwo6YgQRYiGAUuIiUqZLglCrMBYyCECYAJGSgOAhEBo5QR45hsWCAhCUEQ
   YDYiCAZxEsKFWqCFwMaEXDgGy7ZpFISEUyKCoaZAzIYAxCYioKgImDRy1CBBQ8SQ
   SBZoGxZSGjcCUCBCSEiKIBFB4gBswMIMFAZJETFNGQYKiUYJG4FlRMgAggZwABZy
   zCRQikKJnJaQZChwkrJomCZiYZRAwRaJ2EJkGiFOYpBkIcgkiyhtXEKSoMZNDIWA
   zIhN1EKNQjSKCwRRwyaGJCWBEjUGoEQEyJSBW7QxHAgGXCQIAydqIMIl4YCQGbRt
   o0YMSxhgUMYsG5ItERUEogAEIUgu2BYG0hCKg6IlCDENCThR2UhJCxZMIzIlGRkC
   SkQJ0bIhC4MsIyWFkxaFRKBEG4NQAiJySwSAmxRlIZNgGBMK2UYNIkVhyLRAoUIt
   ArgJABREm7YRC5eMQBBKghRq2pAFHAKODBlyo7SNJDBQEYcJZMYo5BiSmLRsYRZR
   QEYOHDJI2iBRiDaKI7EhgpAoGhUy4hhhkgSOE7aQExNoyYRoTEBtCzMAgUZN0jgM
   BJaBpIhQApCFIrAE06Rx0oAQypZAUaZBpIQo4AhSCzCM0jgKDClRw4IJyiCR2DaS
   o6YokkIiohYBGjSGN9mmWRaYgewhz0gRhp0dfxOfBTfpbxGEWFQF/ReAivHgYjnT
   s05ayovxNpZ3tEescYrEfYUMTXewvjHcn1COOXjyQnSrAYX3J6vf9Z9EkDcb8EYQ
   42TmTsh1750g3JQHfh4WYyeoebirUWFgsqP3dDe5s8x9F66t3ITbYnRqNawJb3gv
   YqfwGqbWaT3uyQsjxmmFoCMH4KHK5ZimcyTboPUvIkMidekyVwZcO35eHP4d/U0N
   8IbfISQ0FKLSfiAjCoKb5OtMgsFtNfeLDl4ZgzLgAHS7ZGEvqxfUyJccto5e2rA2
   nxFXs0aavYOE4tlVPxt454bh7p0LmNOfg8zs830evTqdY67HZhZKEBcaT9jGPa8Y
   LEISWMX1KapVy3664uFlIxXh9x6KdBMUENAyR+3hHTTbkfbwiqJHj9eJZ5wElJ9x
   vAFx4H46i7V1PbvapBGmNQq0bu+/hvxVHCnv5M3XZh1c9sPbItDO3eWZhURZ2X8g
   33RVvfNWoZjQ9+ttNBEfyUCyXAVDt4jt2p0mgQ6sPWzJxRMnws+D6IfUCJ4ZaV4R
   rdg39vRAzDYPk/Mv7oqWY3Esa704yEq3tUgj7DY+t+QutZ/B/OYPvVUwez7IX9na
   8yBte0s5F/HIt6kuPGfYmID98uR/WgyZRZXbFwr0G6v1oltNwcQt1qnbJx52TeL7
   AVpJqFDHkZvkcAajNuLjJf3lOsWZVU0KfeTvRexAw51rr/MRvu512J4CrTH0vkvS
   CukZT17d2qZlB3YRbp8nD3dxSteo6JrO90t/99jb7Cf4AgqYUkfizazvSJSk1ouj
   fKkS1r5zUByZUYHlt3cjNQs2Mdo3AOE/02bhMb8Gs262sDRQkyCfCnvv+uH92HWw
   BofBFjw1PX0qyQk3s06XjpL4Ia3JZiIC7OiaF+e7Za4X2DuQ275qUBpOE0W+5OWl
   tTry5bo9HvP04FrfCzpM8uUwNg/uZJKZArVx9v0uMFZSpMsBD3n4FeGPK7uMyJ+m
   /Hb3fInik88XWgsZWAD+ctLM3X115b2QvGrENdakQO+FLpocjFPeA78ZM2XXNary
   nFFiphfjZOf5RBaND7SP70BVj0VCl8w91QhmLPI/uI4ZVKpF0cXhFbzDbwWz4JjV
   VSIPQL4mKbNFB7hGTFTCe13seNqPImUFFHl6+GolEry34pIzee9tc8E3AGwbOPUe
   N/k1heKQQaPk469GAHzhO4tfexfV1l19VmjkJ7y+fsHXxAjAVKSMGueXv5msvI0m
   B1IpNf1mXqeCLZMPI+q/94O7I2l1aeIEuUMUHgDAiBCVa+BSU2Xbq1TtSMt2lkzN
   9cvTrucoLUoAANJ4TXuPqxay9/DVIlcyse+8TrHP7etD/eebaezA++qh5rQHKGc7
   1LLpig1KjwL4U5UHMPKNNesS/MeXaLjhjkvaDlijMaL3HXzMLUUbMrHGXDEqz0fu
   UTshlUxBwAyHOHLulM8U9GA3QlNh9L21SCH3EUYM666MB1CKkhn4j6a+2qZ47tUB
   lEoWrm97W7ei4eNX5w17mEYaLHHLD6di1q2YJAgdN/KS/UvouEw2EQ3HRDYCAb7r
   4L1snQXoaSVtL/P5lRe379KjN3QFbLVnFnWotJLp9fJiDrjvk4HT0d8Zk4t7X/qs
   WbyBEPqHuo16PQFl+OQd0PgE8Rud7Q81Kll4NdBjB6jgxu9NIZBDOeHPRYkjo+ie
   Al2UU0c2bALz3WNo1OR+hdPSqXBb1XlhhS5aV5+TscUUxTn0nqEWOipJOw78tH9H
   SPapnhC/cHgoLkrOGBNuKos+4KOA3NOz7z5l4bgVconWJGetSIugOSsukKHt7cvc

Massimo, et al.         Expires 29 December 2025               [Page 39]
Internet-Draft           ML-DSA in Certificates                June 2025

   kx3BcpjM73ZkXH0zCgXCzkD4m4VGjzV6IXdR4VRjEwTsTgS7RbNniQnHSvUc43A2
   TY9PfrHmHgAodCnJlh3oMiypomKbEwnYAOkrwdxQVdzHl/M4ZusM/Y1JAlDUj/yo
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   -----END PRIVATE KEY-----

Massimo, et al.         Expires 29 December 2025               [Page 40]
Internet-Draft           ML-DSA in Certificates                June 2025

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
     }
     OCTET_STRING {
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Massimo, et al.         Expires 29 December 2025               [Page 41]
Internet-Draft           ML-DSA in Certificates                June 2025

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Massimo, et al.         Expires 29 December 2025               [Page 42]
Internet-Draft           ML-DSA in Certificates                June 2025

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Massimo, et al.         Expires 29 December 2025               [Page 43]
Internet-Draft           ML-DSA in Certificates                June 2025

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   ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257e8
   ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2c1
   4db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287be
   b8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b015414
   9f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a69131c
   cce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364dfaa
   6d9d5a6eb99ae4ddf424` }
     }
   }

C.1.3.3.  Both Format

   -----BEGIN PRIVATE KEY-----
   MIITXgIBADALBglghkgBZQMEAxMEghNKMIITRgQgAAECAwQFBgcICQoLDA0ODxAR
   EhMUFRYXGBkaGxwdHh8EghMgl5K87C8kMGhqgvzPPC9f9mXncderQbkCWM+n6Q7J
   cSTY6e5OkKFsYC9eybw4UX3DDjKdWrJ2c72F9MmwMA93Y4mIZ1C1fCTbP8AS5h7e
   WXUzNzdPpxJJkVSa8kNJbQY3yzvgWllII1v3mHX4ltj+DKswyElI201jFaqvFgrG
   JDZkIgFIFhEJESyUAokiRSxiuEUARSoIlnCQEm4Uk3DURhCERFFYlpEMqSmCskHJ
   CHHEKGgElolIQIWbIm0cKGRZEkGcuJGEBIlEkAXLNGKghpBAJpIgmSkTBWlcNGik
   Mo4ZJpJZRhAJpEkjQk0SNmFYEGUBKJAaM0yZhjHTokkJgiVDFCjAOIEDFU1bKIYI
   h0gjMVKUIiXDwE2kmCGYQCDRQobLQHBbsHGclizBEgZTRgkMRQIURm6RtCFUsIzk
   RkKaIIwBISUTQQVaQCITyQygGEBSwjDLNCxLyGgbpGBJhIRjMClKoGlbgATSOAoU
   JkziskSLohEkRknEFFILQnEDshCSKIABJIjjCBEKBSgZxIEAICLcRGhCEiJEACrJ
   JmoMhzHgwESZFIQYNg0RN0IiGIxjspEMmAihoAEIkkQEEyRcmHGChHGEMlJRsDGc
   Qi4aqCgCCJEBwIkLxwWKJGUiwmRMiJFcgmgTpWRQIIYhBAKRlERIIjAiOUoCmIQJ
   oogZGSlESIwilQyhBHIEh3ASIRBCBoQbSYWJBkrTNgjbwEBYtlEMpwmMJGGZkGSM
   wpBbJJAQo0kDJWFDMooRmETIsiAEOEEQRywZxkQcJSwEiDDZRmmbIAAbRoJapIBb
   oEkYkCUAJoALwjFaQHJUxiDBsDEksU0QlSgUAAqgyE1UoogjmIFgkAQCFiwTIUCR
   ho0IwpGRFCbQtAwJxmBRRC4EESYAKRGTwghjpDEiACjBFAgMQCxBFAacIHJUIgaL
   CE2hSGkQMEEcKElEGI7MlkjZQlAbBkkMRYgjBA0gMC4jhSwUBzBAtoVMwCBEhiAZ
   AGxUAkjMiGxZBjJJFIQEx1ATSSjkBgnTxhDIKEwjOURSpGTMqElEODIKiYQANCwi
   hY0QMQkJMmUciYxAQCkhhQAJoW2EwGTiAi1IBEASCY7gQi6TRAgSEGoBhAWSMIrL
   NI6iJi5chhELNQgYEAACNCYkI4nRhAAkRmATskkkKEYYAnGgOJCJFETTli2jGEAj
   JyHAGFBDyARBQo1cJkFEom1IEg5AMiULFIIKSC7LgogDo2AbJSaMuCAksIWYBCEI
   pyyDOGRUMokBBAEjSYQClWnRpE0TpAyRRg1hlICQOEVcxlABFyBTxiibGBBBEmiQ
   EiHAEIRCFpJTgimBJknYpAWaJiQkAyngQCbSAkgRJGgRmYmYFIXJIA1QEowcCBAC
   EAAAlSjBKJBZtIXTFGUKQG4RKWUYwkwhNGXYMGkQMFIZMWaMGIrIwAhMmDCjpiBB
   FiIYBS4iJSpkuCUKswFjIIQJgAkZKA4CEQGjlBHjmGxYICEJQRBgNiIIBnESwoVa
   oIXAxoRcOAbLtmkUhIRTIoKhpkDMhgDEJiKgqAiYNHLUIEFDxJBIFmgbFlIaNwJQ

Massimo, et al.         Expires 29 December 2025               [Page 44]
Internet-Draft           ML-DSA in Certificates                June 2025

   IEJISIogEUHiAGzAwgwUBkkRMU0ZBgqJRgkbgWVEyACCBnAAFnLMJFCKQomclpBk
   KHCSsmiYJmJhlEDBFonYQmQaIU5ikGQhyCSLKG1cQpKgxk0MhYDMiE3UQo1CNIoL
   BFHDJoYkJYESNQagRATIlIFbtDEcCAZcJAgDJ2ogwiXhgJAZtG2jRgxLGGBQxiwb
   ki0RFQSiAAQhSC7YFgbSEIqDoiUIMQ0JOFHZSEkLFkwjMiUZGQJKRAnRsiELgywj
   JYWTFoVEoEQbg1ACInJLBICbFGUhk2AYEwrZRg0iRWHItEChQi0CuAkAFESbthEL
   l4xAEEqCFGrakAUcAo4MGXKjtI0kMFARhwlkxijkGJKYtGxhFlFARg4cMkjaIFGI
   NoojsSGCkCgaFTLiGGGSBI4TtpATE2jJhGhMQG0LMwCBRk3SOAwEloGkiFACkIUi
   sATTpHHSgBDKlkBRpkGkhCjgCFILMIzSOAoMKVHDggnKIJHYNpKjpiiSQiKiFgEa
   NIY32aZZFpiB7CHPSBGGnR1/E58FN+lvEYRYVAX9F4CK8eBiOdOzTlrKi/E2lne0
   R6xxisR9hQxNd7C+MdyfUI45ePJCdKsBhfcnq9/1n0SQNxvwRhDjZOZOyHXvnSDc
   lAd+HhZjJ6h5uKtRYWCyo/d0N7mzzH0Xrq3chNtidGo1rAlveC9ip/AaptZpPe7J
   CyPGaYWgIwfgocrlmKZzJNug9S8iQyJ16TJXBlw7fl4c/h39TQ3wht8hJDQUotJ+
   ICMKgpvk60yCwW0194sOXhmDMuAAdLtkYS+rF9TIlxy2jl7asDafEVezRpq9g4Ti
   2VU/G3jnhuHunQuY05+DzOzzfR69Op1jrsdmFkoQFxpP2MY9rxgsQhJYxfUpqlXL
   frri4WUjFeH3Hop0ExQQ0DJH7eEdNNuR9vCKokeP14lnnASUn3G8AXHgfjqLtXU9
   u9qkEaY1CrRu77+G/FUcKe/kzddmHVz2w9si0M7d5ZmFRFnZfyDfdFW981ahmND3
   6200ER/JQLJcBUO3iO3anSaBDqw9bMnFEyfCz4Poh9QInhlpXhGt2Df29EDMNg+T
   8y/uipZjcSxrvTjISre1SCPsNj635C61n8H85g+9VTB7Pshf2drzIG17SzkX8ci3
   qS48Z9iYgP3y5H9aDJlFldsXCvQbq/WiW03BxC3WqdsnHnZN4vsBWkmoUMeRm+Rw
   BqM24uMl/eU6xZlVTQp95O9F7EDDnWuv8xG+7nXYngKtMfS+S9IK6RlPXt3apmUH
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   geW3dyM1CzYx2jcA4T/TZuExvwazbrawNFCTIJ8Ke+/64f3YdbAGh8EWPDU9fSrJ
   CTezTpeOkvghrclmIgLs6JoX57tlrhfYO5DbvmpQGk4TRb7k5aW1OvLluj0e8/Tg
   Wt8LOkzy5TA2D+5kkpkCtXH2/S4wVlKkywEPefgV4Y8ru4zIn6b8dvd8ieKTzxda
   CxlYAP5y0szdfXXlvZC8asQ11qRA74UumhyMU94DvxkzZdc1qvKcUWKmF+Nk5/lE
   Fo0PtI/vQFWPRUKXzD3VCGYs8j+4jhlUqkXRxeEVvMNvBbPgmNVVIg9AviYps0UH
   uEZMVMJ7Xex42o8iZQUUeXr4aiUSvLfikjN5721zwTcAbBs49R43+TWF4pBBo+Tj
   r0YAfOE7i197F9XWXX1WaOQnvL5+wdfECMBUpIwa55e/may8jSYHUik1/WZep4It
   kw8j6r/3g7sjaXVp4gS5QxQeAMCIEJVr4FJTZdurVO1Iy3aWTM31y9Ou5ygtSgAA
   0nhNe4+rFrL38NUiVzKx77xOsc/t60P955tp7MD76qHmtAcoZzvUsumKDUqPAvhT
   lQcw8o016xL8x5douOGOS9oOWKMxovcdfMwtRRsyscZcMSrPR+5ROyGVTEHADIc4
   cu6UzxT0YDdCU2H0vbVIIfcRRgzrrowHUIqSGfiPpr7apnju1QGUShaub3tbt6Lh
   41fnDXuYRhosccsPp2LWrZgkCB038pL9S+i4TDYRDcdENgIBvuvgvWydBehpJW0v
   8/mVF7fv0qM3dAVstWcWdai0kun18mIOuO+TgdPR3xmTi3tf+qxZvIEQ+oe6jXo9
   AWX45B3Q+ATxG53tDzUqWXg10GMHqODG700hkEM54c9FiSOj6J4CXZRTRzZsAvPd
   Y2jU5H6F09KpcFvVeWGFLlpXn5OxxRTFOfSeoRY6Kkk7Dvy0f0dI9qmeEL9weCgu
   Ss4YE24qiz7go4Dc07PvPmXhuBVyidYkZ61Ii6A5Ky6Qoe3ty9yTHcFymMzvdmRc
   fTMKBcLOQPibhUaPNXohd1HhVGMTBOxOBLtFs2eJCcdK9RzjcDZNj09+seYeACh0
   KcmWHegyLKmiYpsTCdgA6SvB3FBV3MeX8zhm6wz9jUkCUNSP/KgCL0kpDi1TdhYv
   uqmC0WRTyCWzX2UVY16pK+pyNnuqVN4/nq6mlUKoGkEn9xy6olfzJP7+8U8I+9Za
   BJzS+zYllKjiP/GiYX21sVj28Bz1CrDtlcbnCYQRZBCLBuG0CrCrEcQIMB09nY6m
   npaKlgCz0X84ARzigHTiwuEL9hl8YC2NDOfTo+8tiWI7yfEuozh5HpJmu4zgKxJM
   bHkpuuppMkQJhFSggOt1I+E7sbfFtndfq6urvpB1/laHqkUTl7uc/M0FEkPpv1rv
   JAYtM13l/OJOndveEZEFLYDDbfn4Q0hy8nftT1oc6OvTuWCCSk5PEAGwTLaF+b7k
   0N2wxXFZisICGmYG/SM0XG+7hPDOBf5Sc0Uht7B8Y4jTo7mTGL8BMVBKqd+69Uj5
   0yqc1MaJNSSxEzCi06rT7SpYlm67ATRGXVQ/13l69Un1aOrr6Vf2T+yFRnSQK5dV
   h1aYaUbqOreiUcu+oRpoe9Q/XQvYnNLKumHVIYN0mQ7ouSIZ7SXcoBHGipdXwBO9
   g3st1zTjdR9k/LSyPc1rxX6lZ/Vxbhc2ckR1HiMDsiqVPncnVpVs3MAT/9LDJJB1

Massimo, et al.         Expires 29 December 2025               [Page 45]
Internet-Draft           ML-DSA in Certificates                June 2025

   RCKlclKdTJLx67GfHa1NA28v3zHKkQG9+BrqlIrtzyF6qPzNegdxqidT4agjv0HJ
   U3ei/6YbImUTgVPOhtLIfdB6SzLSf18ocmQUMc6aGKUCqu/Zr8Ww0TzUbDV+OOae
   HulFrdGZKTKlseXFYpyfSPdmGFPaAHh8nXj7klVTvwelDdW52TWFNCDk0aca5i/5
   DKGTzdbC9L7SY0Far5o1CUvCoi4qZjx2RQAc0ZC3vBfHX+rfjofOXCS3Y7ZYTtMu
   cbAmgULqPtaJgVe/kjvr8BktG/XuMKfTUWNKYLUE3eOKLhFPeum/F21KGLoolae7
   S0dESpuo27TBJM1Bu7MvS8sd5IxKu1EGB6ABtaAAu6Q2GLbBnkNRe0W0JAWSi2fH
   E4gYWLrTpCURwnFv+c0zIDS2crUv8WYQgFzb51RKioS2bhx0WnPBtrzaW3e5UfNs
   D3pTct6eXR+bvN6IQ8aQkALdpIdeZ1ca8L7FgYVsMsCcJA5mTnYeV80NjcinHLkY
   pXYtERKFzYtWE929DKCKwDQrK97jj5b6dUuysIcXnBE8k5hqgQNW65RUC5PLnexK
   qSkP8S7Bqi5lbJvj1ZB1PDZsYBQGwGG8IgM6H9H04REdA5uIE7mDy1BsPqf/MFeY
   PovwFoL7sA9DAFMTyCwTkpGKYWWhMzj/4RqZLB+z0QMqpnmkGMi6T4oLwZnhDPa9
   d6FP3WoGCTUUNI46iXRDSuijZ2Npxr4s+Q5nKzQ/zgSsayLgz0dWi8RdcKaOaMZJ
   pIMK4hhZDBpDfnojpU7+RPZwhutpe5+leDXwuPcPCpKSJu+zNsDiGDOgKCGM1jcy
   yAqkd+YtFB26gYVPcNpo2v9KhMtt53klToqX5zVlN0r0CSrwXL1mVK/D/XLwriMm
   lctmaOr+zEBpvZC7UouD76L7zb2TsomSliHtdNgIc4/BA+6xBVEIUfyTGfFx6gzt
   C5e1ufte+YUYa8UgmPnrR29nt8x2ZdR1h5dctFpQ/GQQBxm/djRfD98eCe/p+4AN
   wRTka+CHmhlcwGhw4j0mMdrnHDmUSByHYcQNB8W/ypXnGLeyJYWvA+00F1pG1Xrz
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   LszWFZ1a6o5VTXoJZSsGv3ymmacZnnFtBd1VMEGo8rMD0japurqvufpSjyiiyiqn
   gLlAODwJmqZaAHS4P9HwvFt7XkbCXlSDizy8/JX4fx1HGzuolENPpYlS/ct38WE3
   JpMwbbpOjyFtHI5cr/D+g2ClHGB2NkQWn9xqgmfy4/kJphsqZ4vOaukEA6g2sae3
   6M2LVMNwh6nhREbZXmkI0u7b/MZT4C/fdx9wGnm55aJu0KlHhCBw87VwF0IhEhnn
   YXYsN/DQodG5dQ/uV34SCBFcZqwH7Akeaj/EqmolO8uoaO3TFU3K9RYvYV6FSQps
   o0LzTEOsYaPqa/7v2FDhkOsdjaTSi17O6xZ4wCQz7NXUiyU2QEJX6Mp771hV8rgT
   7S9MQJRFozF8m+GjWuL7TSuHkhuQS/LBTbUUzuBFJRz8J2N02xXJneoVrN4ZfG61
   JJiOObYyh764Z2hlqqO60bQ7jKsVy/J6SYdZ4yA6vzaelyQvCwFUFJ8UrCM823Oi
   K3+48JMlvyrOg7trXbihIaK2ghSaaRMczOUiKYQLET/HsLzFhAW/6H8flf/C6W/F
   WWVn6UNk36ptnVpuuZrk3fQk
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
     }
     OCTET_STRING {
       SEQUENCE {
         OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
   15161718191a1b1c1d1e1f` }
         OCTET_STRING { `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab
   41b90258cfa7e90ec97124d8e9ee4e90a16c602f5ec9bc38517dc30e329d5ab2
   7673bd85f4c9b0300f776389886750b57c24db3fc012e61ede59753337374fa7
   124991549af243496d0637cb3be05a5948235bf79875f896d8fe0cab30c84948
   db4d6315aaaf160ac6243664220148161109112c94028922452c62b84500452a
   08967090126e149370d446108444515896910ca92982b241c90871c428680496
   894840859b226d1c28645912419cb891840489449005cb3462a0869040269220

Massimo, et al.         Expires 29 December 2025               [Page 46]
Internet-Draft           ML-DSA in Certificates                June 2025

   99291305695c3468a4328e19269259461009a44923424d123661581065012890
   1a334c998631d3a249098225431428c0388103154d5b28860887482331529422
   25c3c04da49821984020d14286cb40705bb0719c962cc112065346090c450214
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   446842122244002ac9266a0c8731e0c04499148418360d11374222188c63b291
   0c9808a1a0010892440413245c987182847184325251b0319c422e1aa8280208
   9101c0890bc7058a246522c2644c88915c826813a56450208621040291944448
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   1b498589064ad33608dbc04058b6510ca7098c24619990648cc2905b249010a3
   4903256143328a119844c8b22004384110472c19c6441c252c048830d946699b
   20001b46825aa4805ba0491890250026800bc2315a407254c620c1b03124b14d
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   26d0b40c09c66051442e04112600291193c20863a431220028c114080c402c41
   14069c20725422068b084da148691030411c284944188ecc9648d942501b0649
   0c458823040d20302e23852c14073040b6854cc02044862019006c540248cc88
   6c59063249148404c750134928e40609d3c610c8284c23394452a464cca84944
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   1444d3962da31840232721c0185043c80441428d5c264144a26d48120e403225
   0b14820a482ecb828803a3601b25268cb82024b08598042108a72c8338645432
   89010401234984029569d1a44d13a40c91460d6194809038455cc65001172053
   c6289b1810411268901221c01084421692538229812649d8a4059a2624240329
   e04026d20248112468119989981485c9200d50128c1c0810021000009528c128
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   06cbb669148484532282a1a640cc8600c42622a0a808983472d4204143c49048
   16681b16521a370250204248488a201141e2006cc0c20c14064911314d19060a
   8946091b816544c800820670001672cc24508a42899c969064287092b2689826
   62619440c11689d842641a214e62906421c8248b286d5c4292a0c64d0c8580cc
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   5c240803276a20c225e1809019b46da3460c4b186050c62c1b922d111504a200
   0421482ed81606d2108a83a22508310d093851d948490b164c2332251919024a
   4409d1b2210b832c23258593168544a0441b83500222724b04809b1465219360
   18130ad9460d224561c8b440a1422d02b8090014449bb6110b978c40104a8214
   6ada90051c028e0c1972a3b48d24305011870964c628e4189298b46c61165140
   460e1c3248da205188368a23b1218290281a1532e2186192048e13b690131368
   c984684c406d0b330081464dd2380c049681a4885002908522b004d3a471d280
   10ca964051a641a48428e008520b308cd2380a0c2951c38209ca2091d83692a3
   a628924222a216011a348637d9a659169881ec21cf4811869d1d7f139f0537e9
   6f1184585405fd17808af1e06239d3b34e5aca8bf1369677b447ac718ac47d85
   0c4d77b0be31dc9f508e3978f24274ab0185f727abdff59f4490371bf04610e3
   64e64ec875ef9d20dc94077e1e166327a879b8ab516160b2a3f77437b9b3cc7d
   17aeaddc84db62746a35ac096f782f62a7f01aa6d6693deec90b23c66985a023
   07e0a1cae598a67324dba0f52f22432275e93257065c3b7e5e1cfe1dfd4d0df0

Massimo, et al.         Expires 29 December 2025               [Page 47]
Internet-Draft           ML-DSA in Certificates                June 2025

   86df21243414a2d27e20230a829be4eb4c82c16d35f78b0e5e198332e00074bb
   64612fab17d4c8971cb68e5edab0369f1157b3469abd8384e2d9553f1b78e786
   e1ee9d0b98d39f83ccecf37d1ebd3a9d63aec766164a10171a4fd8c63daf182c
   421258c5f529aa55cb7ebae2e1652315e1f71e8a74131410d03247ede11d34db
   91f6f08aa2478fd789679c04949f71bc0171e07e3a8bb5753dbbdaa411a6350a
   b46eefbf86fc551c29efe4cdd7661d5cf6c3db22d0cedde599854459d97f20df
   7455bdf356a198d0f7eb6d34111fc940b25c0543b788edda9d26810eac3d6cc9
   c51327c2cf83e887d4089e19695e11add837f6f440cc360f93f32fee8a966371
   2c6bbd38c84ab7b54823ec363eb7e42eb59fc1fce60fbd55307b3ec85fd9daf3
   206d7b4b3917f1c8b7a92e3c67d89880fdf2e47f5a0c994595db170af41babf5
   a25b4dc1c42dd6a9db271e764de2fb015a49a850c7919be47006a336e2e325fd
   e53ac599554d0a7de4ef45ec40c39d6baff311beee75d89e02ad31f4be4bd20a
   e9194f5edddaa6650776116e9f270f77714ad7a8e89acef74b7ff7d8dbec27f8
   020a985247e2cdacef4894a4d68ba37ca912d6be73501c995181e5b77723350b
   3631da3700e13fd366e131bf06b36eb6b0345093209f0a7beffae1fdd875b006
   87c1163c353d7d2ac90937b34e978e92f821adc9662202ece89a17e7bb65ae17
   d83b90dbbe6a501a4e1345bee4e5a5b53af2e5ba3d1ef3f4e05adf0b3a4cf2e5
   30360fee64929902b571f6fd2e305652a4cb010f79f815e18f2bbb8cc89fa6fc
   76f77c89e293cf175a0b195800fe72d2ccdd7d75e5bd90bc6ac435d6a440ef85
   2e9a1c8c53de03bf193365d735aaf29c5162a617e364e7f944168d0fb48fef40
   558f454297cc3dd508662cf23fb88e1954aa45d1c5e115bcc36f05b3e098d555
   220f40be2629b34507b8464c54c27b5dec78da8f22650514797af86a2512bcb7
   e2923379ef6d73c137006c1b38f51e37f93585e29041a3e4e3af46007ce13b8b
   5f7b17d5d65d7d5668e427bcbe7ec1d7c408c054a48c1ae797bf99acbc8d2607
   522935fd665ea7822d930f23eabff783bb23697569e204b943141e00c0881095
   6be0525365dbab54ed48cb76964ccdf5cbd3aee7282d4a0000d2784d7b8fab16
   b2f7f0d5225732b1efbc4eb1cfedeb43fde79b69ecc0fbeaa1e6b40728673bd4
   b2e98a0d4a8f02f853950730f28d35eb12fcc79768b8e18e4bda0e58a331a2f7
   1d7ccc2d451b32b1c65c312acf47ee513b21954c41c00c873872ee94cf14f460
   37425361f4bdb54821f711460cebae8c07508a9219f88fa6bedaa678eed50194
   4a16ae6f7b5bb7a2e1e357e70d7b98461a2c71cb0fa762d6ad9824081d37f292
   fd4be8b84c36110dc744360201beebe0bd6c9d05e869256d2ff3f99517b7efd2
   a33774056cb5671675a8b492e9f5f2620eb8ef9381d3d1df19938b7b5ffaac59
   bc8110fa87ba8d7a3d0165f8e41dd0f804f11b9ded0f352a597835d06307a8e0
   c6ef4d21904339e1cf458923a3e89e025d945347366c02f3dd6368d4e47e85d3
   d2a9705bd57961852e5a579f93b1c514c539f49ea1163a2a493b0efcb47f4748
   f6a99e10bf7078282e4ace18136e2a8b3ee0a380dcd3b3ef3e65e1b8157289d6
   2467ad488ba0392b2e90a1ededcbdc931dc17298ccef76645c7d330a05c2ce40
   f89b85468f357a217751e154631304ec4e04bb45b3678909c74af51ce370364d
   8f4f7eb1e61e00287429c9961de8322ca9a2629b1309d800e92bc1dc5055dcc7
   97f33866eb0cfd8d490250d48ffca8022f49290e2d5376162fbaa982d16453c8
   25b35f6515635ea92bea72367baa54de3f9eaea69542a81a4127f71cbaa257f3
   24fefef14f08fbd65a049cd2fb362594a8e23ff1a2617db5b158f6f01cf50ab0
   ed95c6e709841164108b06e1b40ab0ab11c408301d3d9d8ea69e968a9600b3d1
   7f38011ce28074e2c2e10bf6197c602d8d0ce7d3a3ef2d89623bc9f12ea33879
   1e9266bb8ce02b124c6c7929baea693244098454a080eb7523e13bb1b7c5b677
   5fabababbe9075fe5687aa451397bb9cfccd051243e9bf5aef24062d335de5fc
   e24e9ddbde1191052d80c36df9f8434872f277ed4f5a1ce8ebd3b960824a4e4f

Massimo, et al.         Expires 29 December 2025               [Page 48]
Internet-Draft           ML-DSA in Certificates                June 2025

   1001b04cb685f9bee4d0ddb0c571598ac2021a6606fd23345c6fbb84f0ce05fe
   52734521b7b07c6388d3a3b99318bf0131504aa9dfbaf548f9d32a9cd4c68935
   24b11330a2d3aad3ed2a58966ebb0134465d543fd7797af549f568eaebe957f6
   4fec854674902b97558756986946ea3ab7a251cbbea11a687bd43f5d0bd89cd2
   caba61d5218374990ee8b92219ed25dca011c68a9757c013bd837b2dd734e375
   1f64fcb4b23dcd6bc57ea567f5716e17367244751e2303b22a953e772756956c
   dcc013ffd2c32490754422a572529d4c92f1ebb19f1dad4d036f2fdf31ca9101
   bdf81aea948aedcf217aa8fccd7a0771aa2753e1a823bf41c95377a2ffa61b22
   65138153ce86d2c87dd07a4b32d27f5f2872641431ce9a18a502aaefd9afc5b0
   d13cd46c357e38e69e1ee945add1992932a5b1e5c5629c9f48f7661853da0078
   7c9d78fb925553bf07a50dd5b9d935853420e4d1a71ae62ff90ca193cdd6c2f4
   bed263415aaf9a35094bc2a22e2a663c7645001cd190b7bc17c75feadf8e87ce
   5c24b763b6584ed32e71b0268142ea3ed6898157bf923bebf0192d1bf5ee30a7
   d351634a60b504dde38a2e114f7ae9bf176d4a18ba2895a7bb4b47444a9ba8db
   b4c124cd41bbb32f4bcb1de48c4abb510607a001b5a000bba43618b6c19e4351
   7b45b42405928b67c713881858bad3a42511c2716ff9cd332034b672b52ff166
   10805cdbe7544a8a84b66e1c745a73c1b6bcda5b77b951f36c0f7a5372de9e5d
   1f9bbcde8843c6909002dda4875e67571af0bec581856c32c09c240e664e761e
   57cd0d8dc8a71cb918a5762d111285cd8b5613ddbd0ca08ac0342b2bdee38f96
   fa754bb2b087179c113c93986a810356eb94540b93cb9dec4aa9290ff12ec1aa
   2e656c9be3d590753c366c601406c061bc22033a1fd1f4e1111d039b8813b983
   cb506c3ea7ff3057983e8bf01682fbb00f43005313c82c1392918a6165a13338
   ffe11a992c1fb3d1032aa679a418c8ba4f8a0bc199e10cf6bd77a14fdd6a0609
   3514348e3a8974434ae8a3676369c6be2cf90e672b343fce04ac6b22e0cf4756
   8bc45d70a68e68c649a4830ae218590c1a437e7a23a54efe44f67086eb697b9f
   a57835f0b8f70f0a929226efb336c0e21833a028218cd63732c80aa477e62d14
   1dba81854f70da68daff4a84cb6de779254e8a97e73565374af4092af05cbd66
   54afc3fd72f0ae232695cb6668eafecc4069bd90bb528b83efa2fbcdbd93b289
   929621ed74d808738fc103eeb105510851fc9319f171ea0ced0b97b5b9fb5ef9
   85186bc52098f9eb476f67b7cc7665d47587975cb45a50fc64100719bf76345f
   0fdf1e09efe9fb800dc114e46be0879a195cc06870e23d2631dae71c3994481c
   8761c40d07c5bfca95e718b7b22585af03ed34175a46d57af3518e32a7fc1aa4
   482732a81a87f724f8d2e780b3a39d451a380f75c2d680cc7213eab1d4a59d39
   4ae3810a1c90818d52f93fb203e2d8b1b5fa8f60b2d585d9135d648846f138b8
   6953242d2bb1f2ecdf389b4de7651817b8e4e64b333f1aac523a93f2748a9c38
   ffbc29ced457b6f9781b08a67a1975d031ccd71545c0037434056c2434d13e6c
   4beebf46fc12222c0b2eccd6159d5aea8e554d7a09652b06bf7ca699a7199e71
   6d05dd553041a8f2b303d236a9babaafb9fa528f28a2ca2aa780b940383c099a
   a65a0074b83fd1f0bc5b7b5e46c25e54838b3cbcfc95f87f1d471b3ba894434f
   a58952fdcb77f161372693306dba4e8f216d1c8e5caff0fe8360a51c60763644
   169fdc6a8267f2e3f909a61b2a678bce6ae90403a836b1a7b7e8cd8b54c37087
   a9e14446d95e6908d2eedbfcc653e02fdf771f701a79b9e5a26ed0a947842070
   f3b5701742211219e761762c37f0d0a1d1b9750fee577e1208115c66ac07ec09
   1e6a3fc4aa6a253bcba868edd3154dcaf5162f615e85490a6ca342f34c43ac61
   a3ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257
   e8ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2
   c14db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287
   beb8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b0154

Massimo, et al.         Expires 29 December 2025               [Page 49]
Internet-Draft           ML-DSA in Certificates                June 2025

   149f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a6913
   1ccce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364df
   aa6d9d5a6eb99ae4ddf424` }
       }
     }
   }

C.2.  Example Public Keys

   The following is the ML-DSA-44 public key corresponding to the
   private key in the previous section.  The textual encoding [RFC7468]
   is followed by the so-called "pretty print"; the public keys are the
   same.

   -----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-----

Massimo, et al.         Expires 29 December 2025               [Page 50]
Internet-Draft           ML-DSA in Certificates                June 2025

   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` }
   }

Massimo, et al.         Expires 29 December 2025               [Page 51]
Internet-Draft           ML-DSA in Certificates                June 2025

   The following is the ML-DSA-65 public key corresponding to the
   private key in the previous section.  The textual encoding [RFC7468]
   is followed by the so-called "pretty print"; the public keys are the
   same.

Massimo, et al.         Expires 29 December 2025               [Page 52]
Internet-Draft           ML-DSA in Certificates                June 2025

   -----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 29 December 2025               [Page 53]
Internet-Draft           ML-DSA in Certificates                June 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 29 December 2025               [Page 54]
Internet-Draft           ML-DSA in Certificates                June 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.  The textual encoding [RFC7468]
   is followed by the so-called "pretty print"; the public keys are the
   same.

   -----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

Massimo, et al.         Expires 29 December 2025               [Page 55]
Internet-Draft           ML-DSA in Certificates                June 2025

   KbhcLeBaZfphXu4WSVvZBzdnIRW1PpHF2QAozz8ak5U6FT3lO0QITpzP9rc2aTkm
   2u/rstd6pa1om5LzFoZmnfFtFxXMWPeiz7ct0aUekvglmTp0Aivn6etgVGVEVwlN
   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

Massimo, et al.         Expires 29 December 2025               [Page 56]
Internet-Draft           ML-DSA in Certificates                June 2025

   a85a4bab17e7f943d1b8a333aa3ae7ce16b440d6018f9e04daf5725c7f1a93fa
   d1a5a27b67895bd249aa91685de20af32c8b7e268c7f96877d0c85001135a4f0
   a8f1b8264fa6ebe5a349d8aecad1a16299ccf2fd9c7b85bace2ced3aa1276ba6
   1ee78ed7e5ca5b67cdd458a9354030e6abbbabf56a0a2316fec9dba83b51d42f
   d3167f1e0f90855d5c66509b210265dc1e54ec44b43ba7cf9aef118b44d80912
   ce75166a6651e116cebe49229a7062c09931f71abd2293f76f7efc3215ba9780
   0037e58e470bdbbb43c1b0439eaf79c54d93b44aac9efe9fbe151874cfb2a64c
   bee28cc4c0fe7775e5d870f1c02e5b2e3c5004c995f24c9b779cb753a277d0e7
   1fd425eb6bc2ca56ce129db51f70740f31e63976b50c7312e9797d78c5b1ac24
   a5fa347cc916e0a83f5c3b675cd30b81e3fa10b93444e07397571cce98b28da5
   1db9056bc728c5b0b1181e2fbd387b4c79ab1a5fefece37167af772ddad14eb4
   c3982da5a59d0e9eb173ec6315091170027a3ab5ef6aa129cb8585727b9358a2
   8501d713a72f3f1db31714286f9b6408013af06045d75592fc0b7dd47c73ed9c
   75b11e9d7c69f7cadfc3280a9062c5273c43be1c34f87448864cea7b5c97d6d3
   2f59bd5f25384653bb5c4faa45bea8b89402843e645b6b9269e2bd988ddacb03
   3328ffb060450f7df080053e6969b251e875ecec32cfc592840d69ab69a75e06
   b379c535d95266b082f4f09c93162b33b0d9f7307a4eaaa52104437fed66f8ee
   3eabbd45d67b25a8133f496468b52baffdbfad93eef1a9818b5e42ec722788a3
   d8d3529fc777d2ba570801dfae01ec88302837c1fb9e0355727645ee1046c3f9
   15f6ae82dad4fb6b0356a46518ffc834155c3b4fe6dafa6cc8a5ccf53c73a084
   9d8d44f7dcf72754e70e1b7dfb447bb4ef49d1a718f6171bbce200950e0ce926
   106b151a3e871d5ce49731bd6650a9b0ca972da1c5f136d44820ea6383c08f3b
   384cf2338e789c513f618cc5694a6f0cee104511e1ed7c5f23a1ebfd8a0db842
   4553240156dbf622831b0c643d1c551b6f3f7a98d29b85c2de05a65fa615eee1
   6495bd90737672115b53e91c5d90028cf3f1a93953a153de53b44084e9ccff6b
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   3a4f3633fd434d787c170977b417df598e1d0dde506bb71d6f0bc17ec70e3b03
   cdc1965cb36993f633b0472e50d0923ac6c66fdf1d3e6459cc121f0f5f94d09e
   9dbcf5d690e23233838a0bacb7c638d1b2650a4308cd171b6855126d1da672a6
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   dd2f00298e7141a226b3d7cee414f604d1e0ba54d11d5fe58bccea6ad77ad2e8

Massimo, et al.         Expires 29 December 2025               [Page 57]
Internet-Draft           ML-DSA in Certificates                June 2025

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   c21e821d7b6acb47a5a995e40caced5c223b8fe6de5e18e9d2e5893aefebb7aa
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   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.  The textual encoding [RFC7468] is
   followed by the so-called "pretty print"; the certificates are the
   same.

   -----BEGIN CERTIFICATE-----
   MIIPlDCCBgqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMR
   MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
   MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
   TEFNUFMgV0cwggUyMAsGCWCGSAFlAwQDEQOCBSEA17K0clSq4NtF55MNSpjSyX2P
   E5fReJ2voXAksxbpvslPyZRtQvGbeadBO7qjPnFJy0LtURVpOsBB+suYit61/g4d
   hjEYSZW1ksOX0ilOLhT5CqQUujgmiZrEP0zMrLwm6agyuVEY1ctDPL75ZgsAE44I
   F/YediyidMNq1VTrIqrBFi5KsBrLoeOMTv2PgLZbMz0PcuVd/nHOnB67mInnxWEG

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   wP1zgDoq7P6v3teqPLLO2lTRK9jNNqeM+XWUO0er0l6ICsRS5XQu0ejRqCr6huWQ
   x1jBWuTShA2SvKGlCQ9ASWWX/KfYuVE/GhvabpUKqpjeRnUH1KT1pPBZkhZYLDVy
   9i7aiQWrNYFnDEoCd3oz4Mpylf2PT/bRoKOnaD1l9fX3/GDaAj6CbF+SFEwC99G6
   EHWYdVPqk2f8122ZC3+pnNRa/biDbUPkWfUYffBYR5cJoB6mg1k1+nBGCZDNPcG6
   QBupS6sd3kGsZ6szGdysoGBI1MTu8n7hOpwX0FOPQw8tZC3CQVZg3niHfY2KvHJS
   OXjAQuQoX0MZhGxEEmJCl2hEwQ5Va6IVtacZ5Z0MayqW05hZBx/cws3nUkp77a5U
   6FsxjoVOj+Ky8+36yXGRKCcKr9HlBEw6T9r9n/MfkHhLjo5FlhRKDa9YZRHT2ZYr
   nqla8Ze05fxg8rHtFd46W+9fib3HnZEFHZsoFudPpUUx79wcvnTUSIV/R2vNWPIc
   C2U7O3ak4HamVZowJxhVXMY/dIWaq6uSXwI4YcqM0Pe62yhx9n1VMm10URNa1F9K
   G6aRGPuyyKMO7JOS7z+XcGbJrdXHEMxkexUU0hfZWMcBfD6Q/SDATmdLkEhuk3Cj
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   KWQ+WG5bBVoMIRlG1PNuZ1vtWGD6BCoxXZgmFk1qkjfDWl+/SVSQpb1N8ki5XEqu
   d4S2BWcxZqxCRbW0sIKgnpMj5i8geMW3Z4NEbe/XNq06NwLUmwiYRJAKYYMzl7xE
   GbMNepegs4fBkRR0xNQbU+Mql3rLbw6nXbZbs55Z5wHnaVfe9vLURVnDGncSK1IE
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   kLMui9R/wf0TCehilMDDtRznfm37b2ci5o9MP/LrTDRpMVBudDuwIZmLgPQ/bj08
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   JmzoLE0KNsUR6o/3xAlUmjqCZMqYPYxtXgNfJEJDp3V1iqyZK1iES3EQ0/h8m7oZ
   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

Massimo, et al.         Expires 29 December 2025               [Page 59]
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   REmwvPrzJatZZ7cwfsKTezSSQlv2O4q70+2X2h0VtUg/pkz3GknE07S3ggDR9Qkg
   bywQS/42luPIADbbAKXhHaBaX/TaD/uZVn+BOZ5sqWmxEbbHtvzlSea02J1Fk4Hq
   kWbpuzByCJ25SuDRr+Xyn84ZDnetumQ0lBkc2ro+rZKXw8YGMyt0aX8ZwJxL4qNB
   /WFFEproVsOru8G7iwXgt4QP8WRBSp2kTlQUbNTF3gxOTsslkUErTnvcRQ0GpK06
   DRQG8wbjgewpHyw7O8Sfi34EjAzic0gwtIp501/MWmKpRUgAow9LPreiaLq2TBIQ
   DXEhUb9fEhY77QKeir8cpue3sShqcz9TLa5REJGqsP/8/URk7lZjiI+YWbRLp2U2
   D//0NPEq8fxrzNtacZRxSdx2id/yTWumtj5swjFA4yk0tunadltDMgEYuKgR+Jw9
   G3/yFTDnepHK41V6x8eE/4JjUAvIJWADDWxudO7oF/wsY0AnUuWe9DkW09g8IWhk
   NukDTdpsl08hCLF06qH3MSHJrdUAzs2GGLMCvtrXK2L3k70PcLqMXhbPSr7d1RGW
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   KzsIRyW0ZbsaIsy0tgzzyhQvdoOoJn+2sKjcCzpfY6tgRD9sfucOm1sGet/cM5YP
   iJYei2qKMeYcvACWiI8GNGY37OzhlikbleO4xXnfJwEOYx66NjTHZqkz1/TiCBGU
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   yYEQWvdtYlHMFM2z9DDta59RRATOemm7AA1fYsfodrV/QPJi5qPmvpHtCvfItbdL
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   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" }
           }
         }

Massimo, et al.         Expires 29 December 2025               [Page 60]
Internet-Draft           ML-DSA in Certificates                June 2025

         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 { 2.16.840.1.101.3.4.3.17 }
         }
         BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f139
   7d1789dafa17024b316e9bec94fc9946d42f19b79a7413bbaa33e7149cb42ed5
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   39859071fdcc2cde7524a7bedae54e85b318e854e8fe2b2f3edfac9719128270
   aafd1e5044c3a4fdafd9ff31f90784b8e8e4596144a0daf586511d3d9962b9ea

Massimo, et al.         Expires 29 December 2025               [Page 61]
Internet-Draft           ML-DSA in Certificates                June 2025

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   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 {

Massimo, et al.         Expires 29 December 2025               [Page 62]
Internet-Draft           ML-DSA in Certificates                June 2025

             # subjectKeyIdentifier
             OBJECT_IDENTIFIER { 2.5.29.14 }
             OCTET_STRING {
               OCTET_STRING { `329a07b1fabb48f52a309f11a1898f848e23
   22ff` }
             }
           }
         }
       }
     }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
     }
     BIT_STRING { `00` `67a8951fc308e12f6867611fdc254bf4bcb514f7f5f
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   624b4741c5710362de9d4f8de4b10f6db1e9f8098f4024593ea073893cb1fe7b
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   7b7307ec2937b3492425bf63b8abbd3ed97da1d15b5483fa64cf71a49c4d3b4b

Massimo, et al.         Expires 29 December 2025               [Page 63]
Internet-Draft           ML-DSA in Certificates                June 2025

   78200d1f509206f2c104bfe3696e3c80036db00a5e11da05a5ff4da0ffb99567
   f81399e6ca969b111b6c7b6fce549e6b4d89d459381ea9166e9bb3072089db94
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   beeef101f232d6e97c2c4dff3f40000000000000000000000000017263843` }
   }

   The following is a self-signed certificate for the ML-DSA-65 public
   key in the previous section.  The textual encoding [RFC7468] is
   followed by the so-called "pretty print"; the certificates are the
   same.

Massimo, et al.         Expires 29 December 2025               [Page 64]
Internet-Draft           ML-DSA in Certificates                June 2025

   -----BEGIN CERTIFICATE-----
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   MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
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   xMNQwr5XK68O4uL7Fsz+oIAo2ZrEmuu3WTfdzhEc2rYv/zzqi6IjPR5W+8XFoecm
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   KqRRVdbIrhU2fk6wA7j994UQcZSXOfn/8JAj6vRRBNKoSkWQbu1GcaRNwo0nmHu1
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Massimo, et al.         Expires 29 December 2025               [Page 65]
Internet-Draft           ML-DSA in Certificates                June 2025

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   VDPOA6g/D99DIB6D9ghUFSgai/1Rvo5eaVs7B9X7c0+qK8H0zusYGDFd5fr9b+7W

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   9j0Zo54bGu4uAW+7vh7pq8jqOG+L3bMkth8b/7ZsLfkkYCtlqP2VfOL8qwWGzOFL
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   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" }
           }
         }
       }

Massimo, et al.         Expires 29 December 2025               [Page 67]
Internet-Draft           ML-DSA in Certificates                June 2025

       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 { 2.16.840.1.101.3.4.3.18 }
         }
         BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f6
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Massimo, et al.         Expires 29 December 2025               [Page 68]
Internet-Draft           ML-DSA in Certificates                June 2025

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

Massimo, et al.         Expires 29 December 2025               [Page 69]
Internet-Draft           ML-DSA in Certificates                June 2025

           }
           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 { `1b0563e3cd3346149c8c9ebcf23b0a4e5a90
   0eea` }
             }
           }
         }
       }
     }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
     }
     BIT_STRING { `00` `11816868a90c66934bdbb1d19c53a6a5dc30535ff6d
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Massimo, et al.         Expires 29 December 2025               [Page 70]
Internet-Draft           ML-DSA in Certificates                June 2025

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   1519b7a1727d35aa7ed5080833abaa1d5481c11dbbacfee987988ff7713d2f89
   6befcc545cf95b12af2c076bbfe65baf4be8c8bb4d518e4d54fa12012cc2fab8
   e98d4c75fc454023c906acf9b390deb86f8a4d9b3dac9b2f3584858b83a416a2
   3b29fb696b591dde6146666ba1ba3759c5419e75affa96e39f76ca96e32112d9
   d72383ad38fe5354019428fd24d9e69be4f4611d1bddce0ed99f80d972d037ef
   0fa9c70aff4c285701ad9ec949f186bc6ff07bbd16b17ca26091cb25bcb381e6
   73e595835e955d09756c4d1628ad42b5150a41a88d0811dae946117334441881

Massimo, et al.         Expires 29 December 2025               [Page 71]
Internet-Draft           ML-DSA in Certificates                June 2025

   58c2463544c028430c12baa7891b7c9a3d3edecd8483a84641015afa8f747380
   db1fd0c324fea5433ce03a83f0fdf43201e83f6085415281a8bfd51be8e5e695
   b3b07d5fb734faa2bc1f4ceeb1818315de5fafd6feed6f63d19a39e1b1aee2e0
   16fbbbe1ee9abc8ea386f8bddb324b61f1bffb66c2df924602b65a8fd957ce2f
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   a7d26893f568fd1eb38412745e4210185aee88b1cb4d1e8ea1b1e73dc7a06ea6
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   eb8d17320ceffd4e733c1b5023dd3d1f894f61da15c94270f7bee4702391fc4e
   44432b8f34e02326cca1ffa6701697d5263a5ff4eba3f3e20d17117fe383cc0f
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   6887a80367396c60725dd0247564bf1aa28c322b4a16254b66dc9fcc582fa7b5
   3cdc5f242ab111f0c91e6910c180e2a9166992e309d99e7eb983c2b57ebee9ba
   48ae62c141917147f62014b945e6de6bb4769d2f70c28ce5b2bd3d2d3a1bd07d
   aa1e3a88e049aad8ae6e46cef0a5134485d4f3ec9ffaac158d2cf1fa63a553b0
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   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.  The textual encoding [RFC7468] is
   followed by the so-called "pretty print"; the certificates are the
   same.

   -----BEGIN CERTIFICATE-----
   MIIdMzCCCwqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMT
   MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
   MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
   TEFNUFMgV0cwggoyMAsGCWCGSAFlAwQDEwOCCiEAl5K87C8kMGhqgvzPPC9f9mXn
   cderQbkCWM+n6Q7JcSSnOzI7m6Iatk12fEM/WlIe/+GPhuRqGIlSxEZ+BItynn/E
   0RXn5I2hiW1f4RmxDc3e9iyzB5VAdLQjNuUoNt5h2pQfjTfqaKyBBvq+GQcGea9g
   CFNxIPcHk7jqnMDm57e0yaXHQhxg8kRRuh6TPbGi7hbHlVnyGz0bgwWFCqQq+7E/

Massimo, et al.         Expires 29 December 2025               [Page 72]
Internet-Draft           ML-DSA in Certificates                June 2025

   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
   9wdA8x5jl2tQxzEul5fXjFsawkpfo0fMkW4Kg/XDtnXNMLgeP6ELk0ROBzl1cczp
   iyjaUduQVrxyjFsLEYHi+9OHtMeasaX+/s43Fnr3ct2tFOtMOYLaWlnQ6esXPsYx
   UJEXACejq172qhKcuFhXJ7k1iihQHXE6cvPx2zFxQob5tkCAE68GBF11WS/At91H
   xz7Zx1sR6dfGn3yt/DKAqQYsUnPEO+HDT4dEiGTOp7XJfW0y9ZvV8lOEZTu1xPqk
   W+qLiUAoQ+ZFtrkmnivZiN2ssDMyj/sGBFD33wgAU+aWmyUeh17Owyz8WShA1pq2
   mnXgazecU12VJmsIL08JyTFiszsNn3MHpOqqUhBEN/7Wb47j6rvUXWeyWoEz9JZG
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   iKLGDCHoIde2rLR6WpleQMrO1cIjuP5t5eGOnS5Yk67+u3quf/GhRiYOLxEOk5Uo
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   AaJcvx3LZOfN7gksMUH7VVD+PQ3YLocOV4srRlAIGBE7j2Vpdzxnc4W2mkK3fcun
   rP/ZX9RFLiOqodN+HaIVHqZY1Ao1lrJ6yfgSncbPBkN3JiS1n09GEjDfRxyiYIfD
   lC1cZoffYIKDWTWj+Hy3YrDDsdDdpKZTOWW+8be4KS4lTAFNCQ/thXxEwYOcaUwK
   ZOP62QoR9TRyK27hV08uFJ1V10TeSIcCTghRFDHAYnUOFsdKufMkLy2z/7EqjWEH
   +qIp1vY3OwfzbTkys72wTBndZOrdf5PDxWTDWKHIHc8cnDHlsGVo+XVEwX3BVpjF
   yziYOpr8Qng/qnc6UsnYJgaQvp4xVqpbwVCd6j9pWHaVzW/xcrqD5qbYp9a767vN
   o2cnMZg/ibxYMdw3w/PFxW+sxpfzyyC9Xbrb1wLlSESsL2JpAf4Vnbk9/Udz2P5z
   ViuEbB/IVtGAJ2KEDrxy15iL3nXLynDTGdMs4MwCU7sq1FVyPuDH9HNs5uZmXFrK
   MqSBxTg5vCWRZ7AT0EIzle65qq7jIGFJp9VQ1n/F/f5Kilw10lELZkN5q49yhVoq
   9Hq84qYyBI6vieXLSojevFOllRA6zOTxz/GKz/B6/h61cWqh5AtjE0w6OulXn6h/

Massimo, et al.         Expires 29 December 2025               [Page 73]
Internet-Draft           ML-DSA in Certificates                June 2025

   UVvgk8LSnbbWtlyTZh4AY2tZJwTQk8xnFsI0LrGFPUjIXGOsiihURix7d+fjvR6s
   W8oo/6oAtdNJ+KVHrYdblqjCspEMkwEwmj+ROKVpMRH1WzwAnKlHw538gtmOscqk
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   AYYwDwYDVR0TAQH/BAUwAwEB/zAdBgNVHQ4EFgQUiYhnULV8JNs/wBLmHt5ZdTM3
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   3J98fPMtFHVbMPEwhJjZizrOPmedfxNYjxX4PYY9TruXu4HDyatYvtuR87PSAHVt
   kxXs9T6wDRgeBJDsBw5lsxDAo6W+F6dv2kxmx2hs4ik0JF93wSeygXg0uUgSF8SA
   w6B7hE/ZvPUteNt674Mc2zqOyOAYWM6dWjDJMtKmfdLk2vA1ph0BubRHI9MHGzil
   qUj7SkA31jdMX2a/ARe5b/fbWiFtjIjk/AGEqnJqZLR23DBqDolg0vS75lYUGBpR
   /33bwU5HCHr3hIO7LwVhJOzxki+2hBOApsR61lh/81UPnGFNIopvVtNa7n8Za6ri
   vIHEVcf48CsSJSN4mdVPkRx3CbtvPC2BXUhu83TE2iBwmdwfz/P1WefFL1rGCkQw
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   KisjM3U9YKiZKrtiAiCSruWJ+bB4HArinzITmfqwNpX4TzgpwoF5B3nxfRzVonee
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Massimo, et al.         Expires 29 December 2025               [Page 74]
Internet-Draft           ML-DSA in Certificates                June 2025

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Massimo, et al.         Expires 29 December 2025               [Page 75]
Internet-Draft           ML-DSA in Certificates                June 2025

   ZTIl7tStk6k0AtZ77tHmw2iu5730yoXlTrKxe72lAdDQlvXLTkdXXw+oxg+O078n
   Zt5jdDQgFMXYxyqanZgc5scGn3X4Q/uXgZ0QSlhPErGjtIC5/XdAUraYJZNo6lu3
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   rnVLSDqKkbgKCwwRPEiw8SU8WZu5zwG9ygURLGN4obLeSQU8UHyCteEbbpGrstXp
   AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQMEhUdHiUs
   -----END CERTIFICATE-----

   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 }

Massimo, et al.         Expires 29 December 2025               [Page 76]
Internet-Draft           ML-DSA in Certificates                June 2025

             PrintableString { "LAMPS WG" }
           }
         }
       }
       SEQUENCE {
         SEQUENCE {
           OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
         }
         BIT_STRING { `00` `9792bcec2f2430686a82fccf3c2f5ff665e771d
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Massimo, et al.         Expires 29 December 2025               [Page 77]
Internet-Draft           ML-DSA in Certificates                June 2025

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   74073326b31212aece0a34a60` }
       }
       [3] {
         SEQUENCE {
           SEQUENCE {
             # keyUsage
             OBJECT_IDENTIFIER { 2.5.29.15 }

Massimo, et al.         Expires 29 December 2025               [Page 78]
Internet-Draft           ML-DSA in Certificates                June 2025

             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 { `89886750b57c24db3fc012e61ede59753337
   374f` }
             }
           }
         }
       }
     }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
     }
     BIT_STRING { `00` `08783d565efc7b97440f8bd9818b466be538dbccedb
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Massimo, et al.         Expires 29 December 2025               [Page 79]
Internet-Draft           ML-DSA in Certificates                June 2025

   ba948d2ee630dc89054ab5344ad3ea90c481615f87c143531999e92c36b234ad
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   fc5bf5c450e7de8b721c7ad632adbebb02c5864bba9f3a685842c206879bbcb8
   4d00dcb7fe9bbf2069792d38d12ff7180c013406d381d7c51fd06c9be308c50b
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   43a87d8787c09d59c59f4cddf45c7ab1942fc738c0fe9ced0fc5b5597e328157
   288d305ee13a054558e91184cc688226e3aba1d47459211fc6ddea1a2823d11f
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   74b8e1160ba4a2f5b992de20ac9153d65b0fd6df5b8c5dfa5e62c5dc174a97dc
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   4e01f2c6719724fd87dba13cb6820c54645b2b8ad8ce2d14ecf38385380fd77e
   d1cf987af0ab39b0ab4806d55890cc99d9e1528351a33edd1a438113d2af1c6a

Massimo, et al.         Expires 29 December 2025               [Page 80]
Internet-Draft           ML-DSA in Certificates                June 2025

   4ae0c19a87d2cd38136cf32df268b4e2e71da897fe2fe1c3bcdbe87b4d4d2cf9
   122aec6dea01b6c6ece4a45e5d63fa0e5beb9612d3289ed1d5515eff83f51216
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   090541d3bdb8e99cb029a135e2ed1f6c490572e625ebce83c7fa02df21d16b0f
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   bdc31172568deaec20964d5bc529612d580ba0a7bbcb425bffe1bf3ef1a40eb7
   504d046ba213e00a0714d11950e94b0e249e3ee6e0b6cdb4ea32b4024011a68e
   51160a133b25f99034273255916a92ea3a94fb2bcfafcc0a2e9e9dc2f8c3195d
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   73e6347149a1cf4b5332289d635d5d23c2730b30368a5ce3cceba6155347f0df

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Internet-Draft           ML-DSA in Certificates                June 2025

   21f611044505bce3806bd8edba86324637c6a9210830b636602a83527b41eee6
   0f2d2df4c7c6a571ee8514848a47beb0a7203f8e4b91e4fa67ea3022fe9d9f94
   14884016e66fe48536167e12f0dc550e801004c11a86c5b798e26ca9b1f25841
   624ad2327137908dd23ba5f65eeb107b8bf1e4f45218e44f15e75dae8df9e78b
   edf5e65cb12278f1524d4597c037d40aa1222ad514046393d5f7e29759e61087
   bf1f1d3907d2d2b6f21bb8a1a7098c533a897cbcb8891b56a1bc65ab8625bab6
   6f36e2afc6eb084cdb2159be5437e5c437a738ef80ada9eb1d08b173d22a3a6e
   4eae6b29b329a93c2dc6b47993606e7ecff40431831e83aa7c64a09e7eb291b1
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   79b9eed31e2b9b3095ab64ab961c57f6a6660cb172aedeb3d85bc9bf3b9fa8fc
   4673de2813d138ef85e0d456e501e59dbade75add36acf197baf472f6351f23e
   780214dbc6947aabb673e033d61aa61f9a87285f8afbc5bf879c91bea9692fa9
   33f7010116f028b32de397100350f5808e1761a61f08361a2dc8c3cf0faaf111
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   5112c6378a1b2de49053c507c82b5e11b6e91abb2d5e90000000000000000000
   0000000000000000000000000000000000000000000040c12151d1e252c` }
   }

C.4.  Example Inconsistent Seed and Expanded Private Keys

      |  WARNING: These private keys are purposely bad do not use them
      |  in production systems.

   The following examples demonstrate inconsistent seed and expanded
   private keys.

   Three ML-DSA-44-PrivateKey examples of inconsistent seed and expanded
   private keys follow:

   1.  The first ML-DSA-PrivateKey example includes the both CHOICE ,
       i.e., both seed and expandedKey are included.  The seed and
       expanded values can be checked for inconsistencies.

Massimo, et al.         Expires 29 December 2025               [Page 82]
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   2.  The second ML-DSA-PrivateKey example includes only expandedKey.
       The public key fails to match the tr hash value in the private
       key.

   3.  The third ML-DSA-PrivateKey example also includes only
       expandedKey.  The private s_1 and s_2 vectors imply a t vector
       whose private low bits do not match the t_0 vector portion of the
       private key (its high bits t_1 are the primary content of the
       public key).

   The second and third examples would not be detected by
   implementations that do not regenerate the public key from the
   private key, or neglect to then check consistency of tr or t_0.

   The following is the first example:

   -----BEGIN PRIVATE KEY-----
   MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR
   EhMUFRYXGBkaGxwdHh8EggoAUQyb/R3XN09Oiucd1YKBEGqTQS7Y+jV/dLu0Zh7L
   GSHTp1/JO4jvDmqbhRvs7BmZm+gQaMhZ1t8RXGCMFQEXDrbAVcIvYlWSSXbYlaX1
   TSw4WWxAPM72+XPiKl+MfCuoNjNEcJCniyK7Qc/e2vvLLt7PkHDM5hLkKrCh8T65
   3DwUkDGJwoHgsDHalISCEgijtDDSKEoEByDDRELgQC5EoHEBqSwDJmQSQSQYMiQA
   Ii5KlmALGZAiMyBShkUbCEyTGIQZAG1TgAwQpChQBgogBgwjETLSxEDSEgIENIYj
   lQygtkxbSJGMEoQgGQKRGIEKJRAcoGlgkCgDxjCTBJARuJAERTLBIEzawpDZiCwY
   RiTKsAUjsWyKEIwEgXDLpDDYRmLBxhDIyEXBlgwEEgrkKGYcJXCcsohigGxiOEWE
   gEyjoA0jBw7IRiAklSkkRgVICHATIUxghCGQsg3QNoAZgE0blmEUEIUaJkCcwIij
   GBADAiGSMlGYCDIiOYpAEm4MJkEYGU4iAmTCMBFCFhJjFiwRo4TigCXSRmKakgAR
   uA2LhgBRlnHIRiQIiUEDFUChIm4kNWmAJC7CiIUEMYxawIlCRI1YxgCZMpIbISDL
   Am4YGXDYxiRBNnIZkGVYOG4IIAwCFCpjFoUBtCVQwmgJGVAisk3DGCokGCKbRmgQ
   NUIgNmLbNAWLsmxIEIoByI0hMA6MFCZCJAQLN4xDBilCSIbYGIXIpAQUtjHRNgwi
   gykAok1cuA1kiEXIAEgUOExiomjUBi7ZAg3MthFhOGTIMpJRyElSgAHgwDEAIgrB
   RGaAtIRQCDASxiikCGBKsGHKxkESyGhSsHGbAAwIR2ZhGGxRFImBRoYJOUSDAjEK
   kWnhIlFZRkGiBjLaBnCZMCzIJi3akpDBACDasGWCJDKDRIVcxGwAQyKJxhCjBABh
   hCSjQBJRIA0YMoBBNirIsCkgRwgaEkTDtpEiKYzYMmbDlhBiJnIbRWXDpmXZwGAU
   EAjQxG1JMoXQBg0RJEzjtAABqUUAM4BCMGBKgEmCNCBDGAgSBiaSRILKMAHhNo5b
   IiIkBwZUEIlLoEGYRgpMFEoKNIQgI07AFgUDRiyAtkEUkzHLJgARmG0KEg7YEGKQ
   NgwUAXGJBirIJmZSBFHkBkDckiHIEHFkGC7kuABSkGiLqChLJEkRJoGZiJFUNg0K
   mIG8aRx5dr9/gBkPfhwZrwn4DSmTPr/Vn01JddemyttdtkeLCZ4DW7+GKb7Z8S4f
   HY7JlsvtetEEMyRAS8/INLBzTBrGWIRQqWxf3YcrxGG51NDOlvdrYH7wnySOku6m
   N12BMMwLEfKkmOSU747o81iHE+wiM2bPH+rG7eP6rIrB7NRY67odfeBGboLHeSdf
   79U3GOWczZiFB5wtZGzNoVpiExABNAydQC4OJIPvpxR0ULrErVz9y33/zj9KIZJy
   +saqdCSssuX3kbavVhZQz7eytus2Aji7uSWgPb4M7FqBoFcpobHX/jVvHD8oaBt2
   TOjtuObFujQUnDcztr62etukrM+IwyyLR4WCpFev9qGM+ZP9TCsLbEDu/rVMVS81
   dnKlkkYhy/pUgsGU2jg1bTD83Wib8laAlKZgXSqLBsyP2hpmU66+mX/2gQR9rCzh
   gJSFDfiIGPo1nU2yelQMJ8YOniHNv8I5ZRKylmRFpDZo+QPVoXMnwTg0eF/c3UCO
   PTc59SFlUpxMSPttjYLHEnPlqJnHLb/PZMWlqfd+FE+i4GfHfKDH6RF3NUjPY0Jx
   I1EJ5l/HxG+zK4c1abd6LU4fMGnnKrNKlNSF5yoq8b68GIspz/Mnni3Z8++arXx/
   hzMVayoTe6vtL0ZtyByyV26jjrxOEMpf0ZLzjkWB+Q9a+Z6QxEcTtpVlsOhnxB9w

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   cWFz1hzdOz1ZaMv89k3iYgajdmNIHeUQdz8wwc1621onspo5YlzuruFSorrzz/Ru
   yyg3iHNFmRv2SCNuWcziAFTSd8HBtInzNWmeqBeF7HW1hsCpRoR02ZV4iM+REFrj
   qPVHh3zqURGGSdu1y29uK6M2vjUp0w8NfyuvzbHIy2hJz3Py9kiZotfF4kOgU25D
   11b+/IcaVavqBxCUAz9N4c29aBGZO8reC+X9kPWuNE8NY7e3j4YmPcWppZGfXnY9
   PNV0pLyhLeifev2Wk1ahcLVYLE6l/cFE6qxmThkD8uTrZ7h75JmUqDmKNVjtJW5N
   YS5XSZQz4bFhsdXvpED5F5jwr2NUPpZZDkjuEKXu81ll14F4wx98g776d6LI/zTY
   a06arDBhDhmeyDQZFhMtlu575XeFZGdP11IVo4UPSCQKzc/AMxlrjNrQw2wNZJ+t
   6JDEJq75MS7q5C7gvPpBd3qdmbNQwLFvyCj8ohXcpqc1Lgw12BFNtm5L2JXXle/7
   QmhVrMEkSwJznkd+bOqky9uPbI1Nr1fw0+NJBeqCJtxVvjngV3rE97E1RqzHFxaH
   QQvju+iK/j03mKXQes6be6UWIrYz8+RhZ4jwlK2nPDklHM0+0p2sNlha3BYl+Fob
   uXxZug5ze+Lor7aiIiy18xn64MxZ4QBP3pFpKeW3YJKoLcJSexuJlKJ8Ky5WjnJ+
   skZeuWRgmW/OYyRcKyyylrgnWv0A2oyBqe8ujjv5MD2Oi1Oq/mxtA+a8IAQ0oqOL
   F00uc91QcXXoUdXnQ+ZCCeNIUg1shMyx+2v6smyMLuSFEQ3R17Br1Sgw6lu2gD0S
   XMYOX6h8w0Ww9ml1Huth5xm21mYiPLiejT3vPOyWrJNQ7pg4l/0VGBTG+1zaN5fo
   paZzqkJijn+EH7d+G8RVLGhU0gkbplrNqDAIHAiCnO76b3CuBam2ngtjQzBPUlSU
   AqXPtG17rJg2B+fzgPKAgh8vuZLEaXP7/XeNMwNe6QsNuU9gfln7Tt+pqYpwm1gH
   Wkqor1xYXy+1md2Ct3tLbznupLFIfQ3NVBkeDW+NVvpPvC+CF/NefkSuzOaBPlTa
   itxMHENeGFxR5cf0Sp43j59iGKdWBtJBCV8uWf4qRgRG8fdbfQ+l1qAJEx4v8r4H
   2Hsm6eS/CeZlEpe9fnobwS1BBNoczKSL+noqpxcmgAjbcEtZtsBXSJVBsj4OCdt3
   fA/6IfpWRsNBIVR1aD2p/a0U/RH3FCZKDhwF2ZhBLeHEWWQOCr1v0W68/rllFuIW
   YcyqOojDEup7oFhc0k4aUwdv50HJAWk3ehaPvbP+zlz84DmyVMQjXYJl9gZShi+9
   tFV4KJ8aZz/kCdufmWwtLJKHIBuVkX/hqbYO8Xg4XyWv2pZpZIGeW779l8wQE1MI
   2Yt6grThI3sytb+dM3JvqUW79clvJ288BqRZMJSNO2vUIo4vPqyM/Wcuy465qS0V
   ns+zr0zC2uo3z3LqK57arYABNRm8CV2VxaOqH61GvYyUrA==
   -----END PRIVATE KEY-----

   The following is the second example:

   -----BEGIN PRIVATE KEY-----
   MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX
   0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQzmgex
   +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA
   SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII
   wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG
   IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk
   ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu
   EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi
   wCRBCUNxCiEgYaIBUiJSG4CAmjQAE5NN0zIpIhcKmJJpGhRRICchnMAgYqKBSBhp
   GoVNg0RpWyBBAxJCyxhGAakNDAIxg7AhWiJKyJIF2ZBpBDBqSwZK0rIBHEBAgUIy
   UjJyVKZAWhgQDDISksKAUhJiXIIoC7RsA0KNUxAMFAEO4TZSiIQkkQIKY0YmIAYp
   EcIo0CBIArNsojYJWoZIy7Rhi0ZixECCGokJEAJNJLJFIBIlJMkFiCiMycBNWUgi
   CiduwTRkTJBgW0RQgoZJQ4gEQ7KMYDCAoogthKRtjKYp0MaEQgZGiYhRAKmNAUmN
   5DgNpAaN05RxQrJsGoRhG6MoQrQoCKBxGsUx4KBMATdlJChiFCiQCRBh2UAiGzNg
   CQKS0CSBIAQISRhEoyItXIhEFJgIpEZhAZVkCzkKDJRQykBq0rIgwDgBgjCOE7kI
   kYCEFIgpwBiREjUNoCQi4gQG2cKFBCgSHMmJGAJy0kApwggS2AYqmZRxm7hoI4Qp
   GiKJFEUR3IJEUJZFDESEwLIEmqYFQ4YsRDJuiEQhIKhMmjBw47gtYyaIAyVJA0OM
   SKgJyhRyUzROEkMIG6cEWTAi2ZSA4jQigUISnDAqlDQmYQRFJCYoE0YJSjJtESgJ
   GLglYigRE0ENQbIRkIRMixISosaIycAwIgYG0hiOhIYwkERSEogx2SBxE8UoQwYO

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Internet-Draft           ML-DSA in Certificates                June 2025

   AzBgzKaEWCZSTIgBHvclYshf+kOs+kkhfysXLXu8FGIObZgKcaq73wxF6aIG7LFC
   P+4V3swXYBMAFJ2SI81ubG4fqOQfx8ZJOKtokF/T3NpQ2HCC59DXHRvJsrhMhVI8
   qP5srSlK34O+FbEI/3IdDMh7w906dZAYSw6EVmOpH8nhw8U6YdhnQgsE8JI1V1O8
   ZaBjaP1BKV/QmSQTLG+R9nlkwUJnSnJcNDkUxM7PWMB0vK9FWMl795EeB6ptCTjy
   7iuzwajFldY16ENC/eoB3CSyEa0vwoHPd+WREMerxUvwyG1IC5vidkcdydYDzumM
   /as+n8+3A3k1YFSepEUPp7M/uRacRLTSX7nEV/SXkc09oD6slglYE8EFEyzNpOY+
   SSKM0j2KHzeFbxQtk7kNsJ+Cr4kljGOquAR6gMA2yTV+ogRvjcY1TwxSlfNCu0F9
   PP6wsf0zYiwp4Uy72S4TY8ZevUUEt1EjKblnDjLhssZ6VOfxpV+Ln56gToyjpwXm
   KjxeY3N0r7eutt3qYSzeKPAaIC16pONHItJ90/m4mJTQGf1dTXEZ7+NyO7oQTLi7
   CYHgdN46/iANqq6tgmzEXyRNv0Ma+rNO+994JHTS/VcRj2RiFJNO2Zy6OwA+jWej
   g29vGfxBkQzlFj7jrpnrhNUU63YeY2hOpW+XkdLdSqxuYWi5SMgX91oiKssOjNwD
   zEr+j2cVfho2O3+u/58XK5iRNnfFod0IXp7kwiBSwa9YGTEWZz3NO/xfNLhV3MbH
   eIVknp5x9D1K6g9Lcsp+2gV4uhPTGmWNLQYKmmb/ae0b55l6L7HScj04+b+r4Y+O
   ezzakG5Om16ULI6uspYHDr/TZJR6lAzJeL7Wazd0nm1dzXvoxJREDiuEzs/vuYwL
   7fs8QeM1nSzXGX++cgxIqmxrZGXB7mPjVpwq3HREkTcLf3gm/gt3odGdZBAdAyuR
   gQa0LS73N0flYB/kulDyPt5SHwMagX0VKUpDci6DeHhLbbDPG6norpEdkgG5zpzD
   AZxvXCfLmNomFEtkIlp8kysw92Hnii1Zodi4PsY0Si9t1H52VwbQC/SnmmqSbDup
   HYEsjyx5erF5Zwnl0WhWd4KTUp8ChtAVw7U5lhlkKjM+nlk9bj9TU5lCCOnmozKF
   HX9lJSKpKLkX4n4tbUITff4uv6b7HGeybAJUUoaF9+vb4xWmjqotp2noqfQtPmAA
   fHEzCSaywAEtg+rU5P0e2HLM0ZciAdKwJ/NUWsLTDNeLwddA/sy8b8KgRGxuMOrF
   H1ppCYqi1EfyCFtOTkuSzMJpIdLeR4UYzQkM4meuotJ62lf9iLSXbYn7hDzcz0mn
   bKJnnmgBv6f7AxiW+1BilwS5kjk2u13ThTERIcrfsRmV5ZtzA0z2ftA6uBOGdkjQ
   JYKAh+lJqa/Ra5XXLZmx7coleqwTL/t6Bwmu1anA/wX7Dyu/KECe7XtfWAG+lkzt
   AZ4ct4UdOFHxApBnThn/sAizAcSs9kGiuxQhbh1pyr9Ste8idJaw8weZqFXRF/rT
   dEpvozUD6nmLUt3X7lQmYJ2/zT8ME7Fk1sBR9+1KEZcZpxLjiNMoQCCB/xNUtVTS
   wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr
   3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC
   M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ
   gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J
   l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y
   SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP
   DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs
   vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k
   3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q
   EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg=
   -----END PRIVATE KEY-----

   The following is the third example:

   -----BEGIN PRIVATE KEY-----
   MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX
   0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex
   +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA
   SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII
   wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG
   IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk
   ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu
   EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi

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   wCRBCUNxCiEgYaIBUiJSG4CAmjQAE5NN0zIpIhcKmJJpGhRRICchnMAgYqKBSBhp
   GoVNg0RpWyBBAxJCyxhGAakNDAIxg7AhWiJKyJIF2ZBpBDBqSwZK0rIBHEBAgUIy
   UjJyVKZAWhgQDDISksKAUhJiXIIoC7RsA0KNUxAMFAEO4TZSiIQkkQIKY0YmIAYp
   EcIo0CBIArNsojYJWoZIy7Rhi0ZixECCGokJEAJNJLJFIBIlJMkFiCiMycBNWUgi
   CiduwTRkTJBgW0RQgoZJQ4gEQ7KMYDCAoogthKRtjKYp0MaEQgZGiYhRAKmNAUmN
   5DgNpAaN05RxQrJsGoRhG6MoQrQoCKBxGsUx4KBMATdlJChiFCiQCRBh2UAiGzNg
   CQKS0CSBIAQISRhEoyItXIhEFJgIpEZhAZVkCzkKDJRQykBq0rIgwDgBgjCOE7kI
   kYCEFIgpwBiREjUNoCQi4gQG2cKFBCgSHMmJGAJy0kApwggS2AYqmZRxm7hoI4Qp
   GiKJFEUR3IJEUJZFDESEwLIEmqYFQ4YsRDJuiEQhIKhMmjBw47gtYyaIAyVJA0OM
   SKgJyhRyUzROEkMIG6cEWTAi2ZSA4jQigUISnDAqlDQmYQRFJCYoE0YJSjJtESgJ
   GLglYigRE0ENQbIRkIRMixISosaIycAwIgYG0hiOhIYwkERSEogx2SBxE8UoQwYO
   AzBgzKaEWCZSTIgBH/clYshf+kOs+kkhfysXLXu8FGIObZgKcaq73wxF6aIG7LFC
   P+4V3swXYBMAFJ2SI81ubG4fqOQfx8ZJOKtokF/T3NpQ2HCC59DXHRvJsrhMhVI8
   qP5srSlK34O+FbEI/3IdDMh7w906dZAYSw6EVmOpH8nhw8U6YdhnQgsE8JI1V1O8
   ZaBjaP1BKV/QmSQTLG+R9nlkwUJnSnJcNDkUxM7PWMB0vK9FWMl795EeB6ptCTjy
   7iuzwajFldY16ENC/eoB3CSyEa0vwoHPd+WREMerxUvwyG1IC5vidkcdydYDzumM
   /as+n8+3A3k1YFSepEUPp7M/uRacRLTSX7nEV/SXkc09oD6slglYE8EFEyzNpOY+
   SSKM0j2KHzeFbxQtk7kNsJ+Cr4kljGOquAR6gMA2yTV+ogRvjcY1TwxSlfNCu0F9
   PP6wsf0zYiwp4Uy72S4TY8ZevUUEt1EjKblnDjLhssZ6VOfxpV+Ln56gToyjpwXm
   KjxeY3N0r7eutt3qYSzeKPAaIC16pONHItJ90/m4mJTQGf1dTXEZ7+NyO7oQTLi7
   CYHgdN46/iANqq6tgmzEXyRNv0Ma+rNO+994JHTS/VcRj2RiFJNO2Zy6OwA+jWej
   g29vGfxBkQzlFj7jrpnrhNUU63YeY2hOpW+XkdLdSqxuYWi5SMgX91oiKssOjNwD
   zEr+j2cVfho2O3+u/58XK5iRNnfFod0IXp7kwiBSwa9YGTEWZz3NO/xfNLhV3MbH
   eIVknp5x9D1K6g9Lcsp+2gV4uhPTGmWNLQYKmmb/ae0b55l6L7HScj04+b+r4Y+O
   ezzakG5Om16ULI6uspYHDr/TZJR6lAzJeL7Wazd0nm1dzXvoxJREDiuEzs/vuYwL
   7fs8QeM1nSzXGX++cgxIqmxrZGXB7mPjVpwq3HREkTcLf3gm/gt3odGdZBAdAyuR
   gQa0LS73N0flYB/kulDyPt5SHwMagX0VKUpDci6DeHhLbbDPG6norpEdkgG5zpzD
   AZxvXCfLmNomFEtkIlp8kysw92Hnii1Zodi4PsY0Si9t1H52VwbQC/SnmmqSbDup
   HYEsjyx5erF5Zwnl0WhWd4KTUp8ChtAVw7U5lhlkKjM+nlk9bj9TU5lCCOnmozKF
   HX9lJSKpKLkX4n4tbUITff4uv6b7HGeybAJUUoaF9+vb4xWmjqotp2noqfQtPmAA
   fHEzCSaywAEtg+rU5P0e2HLM0ZciAdKwJ/NUWsLTDNeLwddA/sy8b8KgRGxuMOrF
   H1ppCYqi1EfyCFtOTkuSzMJpIdLeR4UYzQkM4meuotJ62lf9iLSXbYn7hDzcz0mn
   bKJnnmgBv6f7AxiW+1BilwS5kjk2u13ThTERIcrfsRmV5ZtzA0z2ftA6uBOGdkjQ
   JYKAh+lJqa/Ra5XXLZmx7coleqwTL/t6Bwmu1anA/wX7Dyu/KECe7XtfWAG+lkzt
   AZ4ct4UdOFHxApBnThn/sAizAcSs9kGiuxQhbh1pyr9Ste8idJaw8weZqFXRF/rT
   dEpvozUD6nmLUt3X7lQmYJ2/zT8ME7Fk1sBR9+1KEZcZpxLjiNMoQCCB/xNUtVTS
   wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr
   3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC
   M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ
   gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J
   l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y
   SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP
   DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs
   vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k
   3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q
   EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg=
   -----END PRIVATE KEY-----

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

   Some applications require pre-hashing that ease operational
   requirements around large or inconsistently-sized payloads.  When
   signing with pre-hashing, the signature generation process can be
   separated into a pre-hash step requiring only the message and other
   public information, and a core signature step which uses the public
   key.

   In the context of ML-DSA, pre-hashing can be performed with the
   HashML-DSA algorithm defined in Section 5.4 of [FIPS204].  ML-DSA
   itself supports a External Mu pre-hashing mode which externalizes the
   message pre-hashing originally performed inside the signing
   operation.  This mode is also laid out in [FIPS204-ExternalMuFAQ].
   This document specifies only the use of ML-DSA's External Mu mode,
   and not HashML-DSA, in PKIX for reasons laid out in Section 8.3.

   Implementations of ML-DSA using the External Mu pre-hashing mode
   requires the following algorithms, which are modified versions of the
   algorithms presented in [FIPS204].  The nomenclature used here has
   been modified from the NIST FAQ [FIPS204-ExternalMuFAQ] for clarity.

   Pre-hash operation:

ComputeMu(pk, M, ctx):

  # Referred to as 'ExternalMu-ML-DSA.Prehash(pk, M, ctx)'
  # in the FIPS 204 FAQ.
  # M is the message, a bit-string
  # mu and ctx are byte-strings.
  # ctx is the context string, which defaults to the empy string.

  mu = H(BytesToBits(H(pk, 64) || IntegerToBytes(0, 1) ||
                IntegerToBytes(|ctx|, 1) || ctx) || M, 64)
  # The functions `BytesToBits` and `IntegerToBytes` are defined in FIPS 204.
  return mu

                Figure 2: ComputeMu prehash operation

   Sign operations:

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SignMu(sk, mu):

  # Referred to as 'ExternalMu-ML-DSA.Sign(sk, mu)'
  # in the FIPS 204 FAQ.

  if |mu| != 64 then
    return error  # return an error indication if the input mu is not
                  # 64 bytes.
  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 = SignMu_internal(sk, mu, rnd, isExternalMu=true)
  return sigma

ML-DSA.SignMu_internal(sk, M', rnd, isExternalMu=false):
    # mu can be passed as an argument instead of M'
    # defaulting is ExternalMu to false means that
    # this modified version of Sign_internal can be used
    # in place of the original without interfering with
    # functioning of pure ML-DSA mode.
    # ... identical to FIPS 204 Algorithm 7, but with Line 6 replaced with
  6: if (isExternalMu):
       mu = M'
     else:
       mu = H(BytesToBits(tr) || M', 64)

               Figure 3: The operations for signing mu

   There is no need to specify an External Mu Verify() routine because
   this is identical to the original ML-DSA.Verify().  This makes
   External Mu mode simply an internal optimization of the signer, and
   allows an ML-DSA key to sometimes be used with the "one-shot" Sign()
   API and sometimes the External Mu API without any interoperability
   concens.

   The External Mu mode requires the ComputeMu routine to have access to
   the hash of the signer's public key which may not be available in
   some architectures, or require fetching it.  That may allow for
   mismatches between tr and sk.  At worst, 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.  That is not believed to be a security concern since

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   mu is never used as-is within ML-DSA.Sign_internal() (Algorithm 7 in
   [FIPS204]).  Rather, it is hashed with values unknown to an attacker
   on lines 7 and 15.  Thus, a signing oracle exposing SignMu() does not
   leak any bits of the secret key.  The External Mu mode also requires
   SHAKE256 to be available to the ComputeMu routine.

Acknowledgments

   The authors wish to thank the following people for their
   contributions to this document: Corey Bonnell, Dierdre Connolly,
   Viktor Dukhovni, Russ Housley, Alicja Kario, Mike Ounsworth, and
   Daniel Van Geest.

   In addition, we would like to thank those who contributed to the
   private key format discussion: Tony Arcieri, Bob Beck, Dmitry
   Belyavskiy, David Benjamin, Daniel Bernstein, Uri Blumenthal, Theo
   Buehler, Stephen Farrell, Jean-Pierre Fiset, Scott Fluhrer, Alex
   Gaynor, John Gray, Peter Gutmann, David Hook, Tim Hudson, Paul
   Kehrer, John Kemp, Watson Ladd, Adam Langley, John Mattsson, Damien
   Miller, Robert Relyea, Michael Richardson, Markku-Juhani O.
   Saarinen, Rich Salz, Roland Shoemaker, Sophie Schmieg, Simo Sorce,
   Michael St. Johns, Falko Strenzke, Filippo Valsorda, Loganaden
   Velvindron, Carl Wallace, and Wei-Jun Wang.

Authors' Addresses

   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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