



Internet Engineering Task Force (IETF)                         S. Turner
Request for Comments: 9935                                         sn3rd
Category: Standards Track                                  P. Kampanakis
ISSN: 2070-1721                                               J. Massimo
                                                                     AWS
                                                        B. E. Westerbaan
                                                              Cloudflare
                                                              March 2026


Internet X.509 Public Key Infrastructure - Algorithm Identifiers for the
       Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM)

Abstract

   The Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) is a
   quantum-resistant Key Encapsulation Mechanism.  This document
   specifies the conventions for using the ML-KEM in X.509 Public Key
   Infrastructure.  The conventions for the subject public keys and
   private keys are also specified.

Status of This Memo

   This is an Internet Standards Track document.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It represents the consensus of the IETF community.  It has
   received public review and has been approved for publication by the
   Internet Engineering Steering Group (IESG).  Further information on
   Internet Standards is available in Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   https://www.rfc-editor.org/info/rfc9935.

Copyright Notice

   Copyright (c) 2026 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
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   Trust Legal Provisions and are provided without warranty as described
   in the Revised BSD License.

Table of Contents

   1.  Introduction
     1.1.  Applicability Statement
   2.  Conventions and Definitions
   3.  Algorithm Identifiers
   4.  Subject Public Key Fields
   5.  Key Usage Bits
   6.  Private Key Format
   7.  Implementation Considerations
   8.  Private Key Consistency Testing
   9.  Security Considerations
   10. IANA Considerations
   11. References
     11.1.  Normative References
     11.2.  Informative References
   Appendix A.  ASN.1 Module
   Appendix B.  Parameter Set Security and Sizes
   Appendix C.  Examples
     C.1.  Example Private Keys
       C.1.1.  ML-KEM-512 Private Key Examples
       C.1.2.  ML-KEM-768 Private Key Examples
       C.1.3.  ML-KEM-1024 Private Key Examples
     C.2.  Example Public Keys
     C.3.  Example Certificates
     C.4.  Examples of Bad Private Keys
       C.4.1.  ML-KEM Inconsistent Seed and Expanded Private Keys
   Acknowledgments
   Authors' Addresses

1.  Introduction

   The Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM)
   standardized in [FIPS203] is a quantum-resistant Key Encapsulation
   Mechanism (KEM) standardized by the US National Institute of
   Standards and Technology (NIST) Post-Quantum Cryptography (PQC)
   Project [NIST-PQC].  Prior to standardization, versions of the
   mechanism were known as Kyber.  ML-KEM and Kyber are not compatible.
   This document specifies the use of ML-KEM in Public Key
   Infrastructure using X.509 (PKIX) certificates [RFC5280] at three
   security levels: ML-KEM-512, ML-KEM-768, and ML-KEM-1024, using
   object identifiers (OIDs) assigned by NIST.  The private key format
   is also specified.

1.1.  Applicability Statement

   ML-KEM certificates are used in protocols where the public key is
   used to generate and encapsulate a shared secret used to derive a
   symmetric key used to encrypt a payload; see [RFC9936].  To be used
   in TLS, ML-KEM certificates could only be used as end-entity identity
   certificates and would require significant updates to the protocol;
   for example, see [KEM-TLS].

2.  Conventions and Definitions

   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.

3.  Algorithm Identifiers

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

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

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

   The fields in AlgorithmIdentifier have the following meanings:

   *  algorithm identifies the cryptographic algorithm with an OID.

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

   The AlgorithmIdentifier for an ML-KEM public key MUST use one of the
   id-alg-ml-kem OIDs from NIST [CSOR] listed below, based on the
   security level.  The parameters field of the AlgorithmIdentifier for
   the ML-KEM public key MUST be absent.

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

     kems OBJECT IDENTIFIER ::= { nistAlgorithms 4 }

     id-alg-ml-kem-512 OBJECT IDENTIFIER ::= { kems 1 }

     id-alg-ml-kem-768 OBJECT IDENTIFIER ::= { kems 2 }

     id-alg-ml-kem-1024 OBJECT IDENTIFIER ::= { kems 3 }

4.  Subject Public Key Fields

   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
     }

   The fields in SubjectPublicKeyInfo have the following meaning:

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

   *  subjectPublicKey contains the byte stream of the public key.

   For each ML-KEM parameter set (see Table 1), we define a PUBLIC-KEY
   ASN.1 type as follows:

     pk-ml-kem-512 PUBLIC-KEY ::= {
       IDENTIFIER id-alg-ml-kem-512
       -- KEY no ASN.1 wrapping; 800 octets --
       PARAMS ARE absent
       CERT-KEY-USAGE { keyEncipherment }
       PRIVATE-KEY ML-KEM-512-PrivateKey -- defined in Section 6
       }

     pk-ml-kem-768 PUBLIC-KEY ::= {
       IDENTIFIER id-alg-ml-kem-768
       -- KEY no ASN.1 wrapping; 1184 octets --
       PARAMS ARE absent
       CERT-KEY-USAGE { keyEncipherment }
       PRIVATE-KEY ML-KEM-768-PrivateKey -- defined in Section 6
       }

     pk-ml-kem-1024 PUBLIC-KEY ::= {
       IDENTIFIER id-alg-ml-kem-1024
       -- KEY no ASN.1 wrapping; 1568 octets --
       PARAMS ARE absent
       CERT-KEY-USAGE { keyEncipherment }
       PRIVATE-KEY ML-KEM-1024-PrivateKey -- defined in Section 6
       }

     ML-KEM-512-PublicKey ::= OCTET STRING (SIZE (800))

     ML-KEM-768-PublicKey ::= OCTET STRING (SIZE (1184))

     ML-KEM-1024-PublicKey ::= OCTET STRING (SIZE (1568))

   When an ML-KEM public key appears outside of a SubjectPublicKeyInfo
   type in an environment that uses ASN.1 encoding, it can be encoded as
   an OCTET STRING by using the ML-KEM-512-PublicKey, ML-KEM-
   768-PublicKey, and ML-KEM-1024-PublicKey types corresponding to the
   correct key size.

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

   When the ML-KEM 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 ML-KEM-PrivateKey CHOICE formats defined in
   Section 6.  The seed format is RECOMMENDED, as it efficiently stores
   both the private and public key.

   Appendix C.2 contains examples for ML-KEM 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 certificates, then keyEncipherement
   MUST be the only key usage set for certificates that indicate id-alg-
   ml-kem-* in SubjectPublicKeyInfo, (with * being one of 512, 768, or
   1024.)

6.  Private Key Format

   [FIPS203] specifies two formats for an ML-KEM private key: a 64-octet
   seed and an (expanded) private key, which is referred to as the
   decapsulation key.  The expanded private key (and public key) is
   computed from the seed using ML-KEM.KeyGen_internal(d,z) (algorithm
   16) using the first 32 octets as _d_ and the remaining 32 octets as
   _z_. If the expanded private key is generated without exporting the
   seed, ML-KEM.KeyGen() (algorithm 19) is used; it combines seed
   generation with ML-KEM.KeyGen_internal(d,z).

   A key pair is generated by sampling 64 octets uniformly at random for
   the seed (private key) from a cryptographically secure pseudorandom
   number generator (CSPRNG).  The public key can then be computed using
   ML-KEM.KeyGen_internal(d,z) as described earlier.

   "Asymmetric Key Packages" [RFC5958] describes how to encode a private
   key in a structure that both identifies which 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 ]],
       ...
     }

   For ML-KEM private keys, the privateKey field in OneAsymmetricKey
   contains one of the following DER-encoded CHOICE structures.  The
   seed format is a fixed 64-byte OCTET STRING (66 bytes total with the
   0x8040 tag and length) for all security levels, while the expandedKey
   and both formats vary in size by security level:

     ML-KEM-512-PrivateKey ::= CHOICE {
       seed [0] OCTET STRING (SIZE (64)),
       expandedKey OCTET STRING (SIZE (1632)),
       both SEQUENCE {
         seed OCTET STRING (SIZE (64)),
         expandedKey OCTET STRING (SIZE (1632))
         }
       }

     ML-KEM-768-PrivateKey ::= CHOICE {
       seed [0] OCTET STRING (SIZE (64)),
       expandedKey OCTET STRING (SIZE (2400)),
       both SEQUENCE {
         seed OCTET STRING (SIZE (64)),
         expandedKey OCTET STRING (SIZE (2400))
         }
       }

     ML-KEM-1024-PrivateKey ::= CHOICE {
       seed [0] OCTET STRING (SIZE (64)),
       expandedKey OCTET STRING (SIZE (3168)),
       both SEQUENCE {
         seed OCTET STRING (SIZE (64)),
         expandedKey OCTET STRING (SIZE (3168))
         }
       }

   The CHOICE allows three representations of the private key:

   *  The seed format (tag [0]) contains just the 64-byte seed value
      from which both the expanded private key and public key can be
      derived using ML-KEM.KeyGen_internal(d,z) (algorithm 16) using the
      first 32 octets as _d_ and the remaining 32 octets as _z_.

   *  The expandedKey format contains the expanded private key that was
      derived from the seed.  If the seed is not exported, both the
      expanded private key and public key can be derived using ML-
      KEM.KeyGen() (algorithm 16).

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

   The privateKeyAlgorithm field uses the AlgorithmIdentifier structure
   with the appropriate OID as defined in Section 3.

   The publicKey field contains the byte stream of the public key.  If
   present, the publicKey field will hold the encoded public key as
   defined in Section 4.

   Note that 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-
   KEM.KeyGen_internal(d,z) (algorithm 16) using the first 32 octets as
   _d_ and the remaining 32 octets as _z_.  Alternatively, the public
   key can be extracted from the expanded private key.  While the
   publicKey field and expandedKey format are technically redundant when
   using the seed-only format, they MAY be included to enable key pair
   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.1 contains examples for ML-KEM private keys encoded using
   the textual encoding defined in [RFC7468].

7.  Implementation Considerations

   Though Section 7.1 of [FIPS203] mentions the potential to save seed
   values for future expansion, Algorithm 19 does not make the seed
   values available to a caller for serialization.  Similarly, the
   algorithm that expands seed values is not listed as one of the "main
   algorithms" and features "internal" in the name even though it is
   clear that it is allowed to be exposed externally for the purposes of
   expanding a key from a seed.  Below are possible ways to extend the
   APIs defined in [FIPS203] to support serialization of seed values as
   private keys.

   To support serialization of seed values as private keys, let
   Algorithm 19b denote the same procedure as Algorithm 19 in [FIPS203],
   except it returns (ek, dk, d, z) on line 7.  Additionally, Algorithm
   16 should be promoted to be a "main algorithm" for external use in
   expanding seed values.

   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 a seed and
   the seed discarded, the seed cannot be recreated 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.

8.  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 they 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.

   When receiving a private key that contains an expandedKey, [FIPS203]
   stipulates in Section 7.3 that before use, a "hash check" MUST be
   performed.  That section stipulates two other checks on the type and
   length of the expandedKey, which are ensured by this standard.

   The seed consistency check consists of regenerating the expanded form
   from the seed via ML-KEM.KeyGen_internal(d,z) (algorithm 16) using
   the first 32 octets as _d_ and the remaining 32 octets as _z_ 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.

9.  Security Considerations

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

   Protection of the private key information, i.e., the seed, is vital
   to public key cryptography.  Disclosure of the private key material
   to another entity can lead to masquerades.

   The generation of private keys relies on random numbers.  The use of
   inadequate pseudorandom number generators (PRNGs) to generate these
   values can result in little or no security.  An attacker may find it
   much easier to reproduce the PRNG environment that produced the keys,
   searching the resulting small set of possibilities, rather than brute
   force searching the whole key space.  The generation of quality
   random numbers is difficult.  ML-KEM key generation has specific
   requirements around randomness generation as described in Section 3.3
   of [FIPS203].

   Many protocols only rely on the IND-CCA security of a KEM.  Some
   (implicitly) require further binding properties, formalized in
   [CDM23].  The private key format influences these binding properties.
   Per [KEMMY24], ML-KEM is LEAK-BIND-K-PK-secure and LEAK-BIND-K-CT-
   secure when using the expanded private key format, but not MAL-BIND-
   K-CT nor MAL-BIND-K-PK secure.  Using the 64-byte seed format
   provides a step up in binding security, and additionally provides
   MAL-BIND-K-CT security (but still does not provide security for MAL-
   BIND-K-PK).

   For more detailed ML-KEM specific security considerations regarding
   this, randomness, misbinding properties, decapsulation failures, key
   reuse, and key checks, refer to [ML-KEM-SEC-CONS].

10.  IANA Considerations

   For the ASN.1 module in Appendix A, IANA has assigned an OID for the
   module identifier (121) with a description of "id-mod-x509-ml-kem-
   2025" in the "SMI Security for PKIX Module Identifier" registry
   (1.3.6.1.5.5.7.0).

11.  References

11.1.  Normative References

   [CSOR]     NIST, "Computer Security Objects Register (CSOR)", 13 June
              2025, <https://csrc.nist.gov/projects/computer-security-
              objects-register/algorithm-registration>.

   [FIPS203]  NIST, "Module-Lattice-Based Key-Encapsulation Mechanism
              Standard", NIST FIPS 203, DOI 10.6028/NIST.FIPS.203,
              August 2024, <https://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.203.pdf>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC5280]  Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
              Housley, R., and W. Polk, "Internet X.509 Public Key
              Infrastructure Certificate and Certificate Revocation List
              (CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, May 2008,
              <https://www.rfc-editor.org/info/rfc5280>.

   [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/info/rfc5912>.

   [RFC5958]  Turner, S., "Asymmetric Key Packages", RFC 5958,
              DOI 10.17487/RFC5958, August 2010,
              <https://www.rfc-editor.org/info/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/info/rfc8174>.

   [RFC9629]  Housley, R., Gray, J., and T. Okubo, "Using Key
              Encapsulation Mechanism (KEM) Algorithms in the
              Cryptographic Message Syntax (CMS)", RFC 9629,
              DOI 10.17487/RFC9629, August 2024,
              <https://www.rfc-editor.org/info/rfc9629>.

   [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 - 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>.

11.2.  Informative References

   [CDM23]    Cremers, C., Dax, A., and N. Medinger, "Keeping Up with
              the KEMs: Stronger Security Notions for KEMs and automated
              analysis of KEM-based protocols", Cryptology ePrint
              Archive, Paper 2023/1933, 2023,
              <https://eprint.iacr.org/2023/1933.pdf>.

   [KEM-TLS]  Wiggers, T., Celi, S., Schwabe, P., Stebila, D., and N.
              Sullivan, "KEM-based Authentication for TLS 1.3", Work in
              Progress, Internet-Draft, draft-celi-wiggers-tls-authkem-
              06, 4 November 2025,
              <https://datatracker.ietf.org/doc/html/draft-celi-wiggers-
              tls-authkem-06>.

   [KEMMY24]  Schmieg, S., "Unbindable Kemmy Schmidt: ML-KEM is neither
              MAL-BIND-K-CT nor MAL-BIND-K-PK", Cryptology ePrint
              Archive, Paper 2024/523, 2024,
              <https://eprint.iacr.org/2024/523.pdf>.

   [ML-KEM-SEC-CONS]
              Fluhrer, S., Dang, Q., Mattsson, J. P., Milner, K., and D.
              Shiu, "ML-KEM Security Considerations", Work in Progress,
              Internet-Draft, draft-sfluhrer-cfrg-ml-kem-security-
              considerations-04, 17 November 2025,
              <https://datatracker.ietf.org/doc/html/draft-sfluhrer-
              cfrg-ml-kem-security-considerations-04>.

   [NIST-PQC] NIST, "Post-Quantum Cryptography (PQC)", 28 July 2025,
              <https://csrc.nist.gov/projects/post-quantum-
              cryptography>.

   [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/info/rfc7468>.

   [RFC9881]  Massimo, J., Kampanakis, P., Turner, S., and B. E.
              Westerbaan, "Internet X.509 Public Key Infrastructure --
              Algorithm Identifiers for the Module-Lattice-Based Digital
              Signature Algorithm (ML-DSA)", RFC 9881,
              DOI 10.17487/RFC9881, October 2025,
              <https://www.rfc-editor.org/info/rfc9881>.

   [RFC9936]  Prat, J., Ounsworth, M., and D. Van Geest, "Use of ML-KEM
              in the Cryptographic Message Syntax (CMS)", RFC 9936,
              DOI 10.17487/RFC9936, March 2026,
              <https://www.rfc-editor.org/info/rfc9936>.

Appendix A.  ASN.1 Module

   This appendix includes the ASN.1 module [X680] for the ML-KEM.  Note
   that as per [RFC5280], certificates use the Distinguished Encoding
   Rules; see [X690].  This module imports objects from [RFC5912] and
   [RFC9629].

   <CODE BEGINS>
   X509-ML-KEM-2025
   { iso(1) identified-organization(3) dod(6)
     internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
     id-mod-x509-ml-kem-2025(121) }

   DEFINITIONS IMPLICIT TAGS ::= BEGIN

   EXPORTS ALL;

   IMPORTS

    PUBLIC-KEY
      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) }

    KEM-ALGORITHM
      FROM KEMAlgorithmInformation-2023  -- [RFC 9629]
        { iso(1) identified-organization(3) dod(6) internet(1)
          security(5) mechanisms(5) pkix(7) id-mod(0)
          id-mod-kemAlgorithmInformation-2023(109) };

   --
   -- ML-KEM Identifiers
   --

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

   kems OBJECT IDENTIFIER ::= { nistAlgorithms 4 }

   id-alg-ml-kem-512 OBJECT IDENTIFIER ::= { kems 1 }

   id-alg-ml-kem-768 OBJECT IDENTIFIER ::= { kems 2 }

   id-alg-ml-kem-1024 OBJECT IDENTIFIER ::= { kems 3 }

   --
   -- Public Key Algorithms
   --

   PublicKeys PUBLIC-KEY ::= {
     -- This expands PublicKeys from [RFC 5912]
     pk-ml-kem-512 |
     pk-ml-kem-768 |
     pk-ml-kem-1024,
     ...
     }

   --
   -- ML-KEM Public Keys
   --

   pk-ml-kem-512 PUBLIC-KEY ::= {
     IDENTIFIER id-alg-ml-kem-512
     -- KEY no ASN.1 wrapping; 800 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY ML-KEM-512-PrivateKey
     }

   ML-KEM-512-PrivateKey ::= CHOICE {
     seed [0] OCTET STRING (SIZE (64)),
     expandedKey OCTET STRING (SIZE (1632)),
     both SEQUENCE {
         seed OCTET STRING (SIZE (64)),
         expandedKey OCTET STRING (SIZE (1632))
         }
     }

   pk-ml-kem-768 PUBLIC-KEY ::= {
     IDENTIFIER id-alg-ml-kem-768
     -- KEY no ASN.1 wrapping; 1184 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY ML-KEM-768-PrivateKey
     }

   ML-KEM-768-PrivateKey ::= CHOICE {
     seed [0] OCTET STRING (SIZE (64)),
     expandedKey OCTET STRING (SIZE (2400)),
     both SEQUENCE {
         seed OCTET STRING (SIZE (64)),
         expandedKey OCTET STRING (SIZE (2400))
         }
     }

   pk-ml-kem-1024 PUBLIC-KEY ::= {
     IDENTIFIER id-alg-ml-kem-1024
     -- KEY no ASN.1 wrapping; 1568 octets --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyEncipherment }
     PRIVATE-KEY ML-KEM-1024-PrivateKey
     }

   ML-KEM-1024-PrivateKey ::= CHOICE {
     seed [0] OCTET STRING (SIZE (64)),
     expandedKey OCTET STRING (SIZE (3168)),
     both SEQUENCE {
         seed OCTET STRING (SIZE (64)),
         expandedKey OCTET STRING (SIZE (3168))
         }
     }

   ML-KEM-512-PublicKey ::= OCTET STRING (SIZE (800))

   ML-KEM-768-PublicKey ::= OCTET STRING (SIZE (1184))

   ML-KEM-1024-PublicKey ::= OCTET STRING (SIZE (1568))

   END
   <CODE ENDS>

Appendix B.  Parameter Set Security and Sizes

   Instead of defining the strength of a quantum algorithm in a typical
   manner using the imprecise notion of bits of security, NIST has
   defined security levels by picking a reference scheme, which is
   expected to offer notable levels of resistance to both quantum and
   classical attacks.  To wit, a KEM algorithm that achieves NIST PQC
   security must require computational resources to break IND-CCA
   security comparable or greater than that required for key search on
   AES-128, AES-192, and AES-256 for Levels 1, 3, and 5, respectively.
   Levels 2 and 4 use collision search for SHA-256 and SHA-384 as
   reference.

     +=======+===============+========+========+============+========+
     | Level | Parameter Set | Encap. | Decap. | Ciphertext | Secret |
     |       |               | Key    | Key    |            |        |
     +=======+===============+========+========+============+========+
     | 1     | ML-KEM-512    | 800    | 1632   | 768        | 32     |
     +-------+---------------+--------+--------+------------+--------+
     | 3     | ML-KEM-768    | 1184   | 2400   | 1088       | 32     |
     +-------+---------------+--------+--------+------------+--------+
     | 5     | ML-KEM-1024   | 1568   | 3168   | 1568       | 32     |
     +-------+---------------+--------+--------+------------+--------+

            Table 1: Mapping Between NIST Security Level, ML-KEM
                     Parameter Sets, and Sizes in Bytes

Appendix C.  Examples

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

C.1.  Example Private Keys

   The following examples show ML-KEM 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-KEM-512 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-----
   MFQCAQAwCwYJYIZIAWUDBAQBBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
   GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8=
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 }
     }
     OCTET_STRING {
       [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
   5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343
   5363738393a3b3c3d3e3f` }
     }
   }

C.1.1.2.  Expanded Format

   -----BEGIN PRIVATE KEY-----
   MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHBVT9Q2NE8nhbGzsbrBhLZnkAMz
   bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px
   uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy
   KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX
   mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC
   hmtccTxqjX0Wz3i4GdbxLp5adCM5CPCxXjxLqDKcXN2lXISSjjqoBj5aqWdkA/kX
   NbEQEMf1kwkTZNyGRFvIBIQKmiFyQhJGn4p7DOCsaY64bK05p/SCTZpRY6rCHuaA
   iwU8ij+ssLZ0S1Jiu8smpD9mTIcytkz8es8JlgX0HHlgYJdqxDODP+ADQ/sYKDAK
   QkdBEW5LRbsnbqgRKaDbTG5gvOYREB6MYlR0kl4CImeTCKPncI0Zcqe0I+sjKFHD
   bS7VPT7Tu3UAY3BhpdwikvocRmwHNUaDMovsLB7Sy1yZt47KCWkDjPfDTdEYck4x
   yuCGIGs0MCtSD10Xet7Vs8zgKszoCOomvMByYl/bk/F0WKX8HU2jlDgKH1fpzGYQ
   lDigdfDSgT/MShmcx22zgj8nCwBhWUGSlAQRo3/7r64sFQFlzsXGv3PFlfuSzRUx
   JgfaBwd4ZSvZlEvEi8fRpTQzi60LrWZWxdUCznhQqxWHJE7rWPQ5q14IV0pxjIqs
   PXfHmLuhVCczvnNEjyP7cMDlNTonyIMixSGEk6+7OAhkNNbWCla6iH3UmMOrJqCH
   CZOBWqakCXXyGK3KFYLWT/yGUvuzqab7wwT5GUX6Sq7yh4/XFd9wET0jefRIhvgS
   yD/ytxmmnh7HSuSxWszTrtWlPOdqewmCRxYzuXPLQKGgAV0KQk+hGkecAjAXQ20q
   KQDpk+taCgZ0AMf0qt8gH8T6MSZKY7rpXMjWXDmVgV5ZfRBDVc8pqlMzyTJRhp1b
   zb5IcST2Ari2pmwWxHYWSK12XPXYAGtRXpBafwrAdrDGLvoygVPnylcBaZ8TBfHm
   vG+QsOSbaTUSts6ZKouAFt38GmYsfj+WGcvYad13GvMIlszVkYrGy3dGbF53mZbW
   f/mqvJdQPyx7fi0ADYZFD7GAfKTKvaRlgloxx4mht6SRqzhydl0yDQtxkg+iE8lA
   k0Frg7gSTmn2XmLLUADcw3qpoP/3OXDEdy81fSQYnKb1MFVowOI3ajdipoxgXlY8
   XSCVcuD8dTLKKUcpU1VntfxBPF6HktJGRTbMgI+YrddGZPFBVm+QFqkKVBgpqYoE
   ZM5BqLtEwtT6PCwglGByjvFKGnxMm5jRIgO0zDUpFgqasteDj3/2tTrgWqMafWRr
   evpsRZMlJqPDdVYZvplMIRwqMcBbNEeDbLIVC+GCna5rBMVTXP9Ubjkrp5dBFyD5
   JPSQpaxUlfITVtVQt4KmTBaItrZVvMeEIZekNML2Vjtbfwmni8xIgjJ4NWHRb0y6
   tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z
   gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek
   b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX
   thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM
   FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm
   gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h
   uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2
   NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g
   uBw7xZoGWhttY7JsgvEB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj
   JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw==
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 }
     }
     OCTET_STRING {
       OCTET_STRING { `70554fd436344f2785b1b3b1bac184b6679003336c26
   f15a7de878c4825c6be03f3c4a480f75b7486aad31d3a00518623fd207ab528d
   d62721495835ae0062c367b74a71baf10aad0e8a2902076be31348beb15ccc09
   57cdebb4aff226756bbc601b6568ab784acbaeb34702f0f86a26202118b22b23
   f83558776c79c14dba983379c803e0dcc3160a11757030e69c6919798d81eb69
   8a9a4483a99e5a5cb2c31c9a661799f3cc89c790706ea041629045d42a83aed8
   8860e394c69187e2105d28cc14ec393592d67dd00aa43fe8b4eae4414002866b
   5c713c6a8d7d16cf78b819d6f12e9e5a74233908f0b15e3c4ba8329c5cdda55c
   84928e3aa8063e5aa9676403f91735b11010c7f593091364dc86445bc804840a
   9a21724212469f8a7b0ce0ac698eb86cad39a7f4824d9a5163aac21ee6808b05
   3c8a3facb0b6744b5262bbcb26a43f664c8732b64cfc7acf099605f41c796060
   976ac433833fe00343fb1828300a424741116e4b45bb276ea81129a0db4c6e60
   bce611101e8c625474925e0222679308a3e7708d1972a7b423eb232851c36d2e
   d53d3ed3bb7500637061a5dc2292fa1c466c07354683328bec2c1ed2cb5c99b7
   8eca0969038cf7c34dd118724e31cae086206b34302b520f5d177aded5b3cce0
   2acce808ea26bcc072625fdb93f17458a5fc1d4da394380a1f57e9cc66109438
   a075f0d2813fcc4a199cc76db3823f270b0061594192940411a37ffbafae2c15
   0165cec5c6bf73c595fb92cd15312607da070778652bd9944bc48bc7d1a53433
   8bad0bad6656c5d502ce7850ab1587244eeb58f439ab5e08574a718c8aac3d77
   c798bba1542733be73448f23fb70c0e5353a27c88322c5218493afbb38086434
   d6d60a56ba887dd498c3ab26a0870993815aa6a40975f218adca1582d64ffc86
   52fbb3a9a6fbc304f91945fa4aaef2878fd715df70113d2379f44886f812c83f
   f2b719a69e1ec74ae4b15accd3aed5a53ce76a7b0982471633b973cb40a1a001
   5d0a424fa11a479c023017436d2a2900e993eb5a0a067400c7f4aadf201fc4fa
   31264a63bae95cc8d65c3995815e597d104355cf29aa5333c93251869d5bcdbe
   487124f602b8b6a66c16c4761648ad765cf5d8006b515e905a7f0ac076b0c62e
   fa328153e7ca5701699f1305f1e6bc6f90b0e49b693512b6ce992a8b8016ddfc
   1a662c7e3f9619cbd869dd771af30896ccd5918ac6cb77466c5e779996d67ff9
   aabc97503f2c7b7e2d000d86450fb1807ca4cabda465825a31c789a1b7a491ab
   3872765d320d0b71920fa213c94093416b83b8124e69f65e62cb5000dcc37aa9
   a0fff73970c4772f357d24189ca6f5305568c0e2376a3762a68c605e563c5d20
   9572e0fc7532ca294729535567b5fc413c5e8792d2464536cc808f98add74664
   f141566f9016a90a541829a98a0464ce41a8bb44c2d4fa3c2c209460728ef14a
   1a7c4c9b98d12203b4cc3529160a9ab2d7838f7ff6b53ae05aa31a7d646b7afa
   6c45932526a3c3755619be994c211c2a31c05b3447836cb2150be1829dae6b04
   c5535cff546e392ba797411720f924f490a5ac5495f21356d550b782a64c1688
   b6b655bcc7842197a434c2f6563b5b7f09a78bcc488232783561d16f4cbab675
   5400050781570c66604b817ad1252294736e8b01861a4b5a74519b8b6fe51489
   a5072392e587626c713776575d33806a1c8e2732af97c2680f51666331c4eb8b
   bc0431c4f96832daf1b3c45528fba153f6c78b1c198702947ccd337727a46fb5
   3ba11de5cb4191346859516cb6ad72400f3cf209b236aef35a580ac87eb3e30f
   afd66973ca8a7dd2675af41f7a17b61433cd1af80f7708869f665488497980b1
   ac10a0cdcb636a00ed8681b35e429124ca80350725b85f83a5eac3a4a3cc1600
   903e65293560b9b336e5af0d529dac1a048119302cb7a9bcc110b94851bf0211
   7f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26cdb
   33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61baab
   71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec372
   25c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b32
   4334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b81c
   3bc59a065a1b6d63b26c82f101ff648063b376e2bb6c5b7455f655a50c2feada
   de150efa0e0e6f365aea202122232425262728292a2b2c2d2e2f303132333435
   363738393a3b3c3d3e3f` }
     }
   }

C.1.1.3.  Both Format

   -----BEGIN PRIVATE KEY-----
   MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR
   EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC
   BmBwVU/UNjRPJ4Wxs7G6wYS2Z5ADM2wm8Vp96HjEglxr4D88SkgPdbdIaq0x06AF
   GGI/0gerUo3WJyFJWDWuAGLDZ7dKcbrxCq0OiikCB2vjE0i+sVzMCVfN67Sv8iZ1
   a7xgG2Voq3hKy66zRwLw+GomICEYsisj+DVYd2x5wU26mDN5yAPg3MMWChF1cDDm
   nGkZeY2B62mKmkSDqZ5aXLLDHJpmF5nzzInHkHBuoEFikEXUKoOu2Ihg45TGkYfi
   EF0ozBTsOTWS1n3QCqQ/6LTq5EFAAoZrXHE8ao19Fs94uBnW8S6eWnQjOQjwsV48
   S6gynFzdpVyEko46qAY+WqlnZAP5FzWxEBDH9ZMJE2TchkRbyASECpohckISRp+K
   ewzgrGmOuGytOaf0gk2aUWOqwh7mgIsFPIo/rLC2dEtSYrvLJqQ/ZkyHMrZM/HrP
   CZYF9Bx5YGCXasQzgz/gA0P7GCgwCkJHQRFuS0W7J26oESmg20xuYLzmERAejGJU
   dJJeAiJnkwij53CNGXKntCPrIyhRw20u1T0+07t1AGNwYaXcIpL6HEZsBzVGgzKL
   7Cwe0stcmbeOyglpA4z3w03RGHJOMcrghiBrNDArUg9dF3re1bPM4CrM6AjqJrzA
   cmJf25PxdFil/B1No5Q4Ch9X6cxmEJQ4oHXw0oE/zEoZnMdts4I/JwsAYVlBkpQE
   EaN/+6+uLBUBZc7Fxr9zxZX7ks0VMSYH2gcHeGUr2ZRLxIvH0aU0M4utC61mVsXV
   As54UKsVhyRO61j0OateCFdKcYyKrD13x5i7oVQnM75zRI8j+3DA5TU6J8iDIsUh
   hJOvuzgIZDTW1gpWuoh91JjDqyaghwmTgVqmpAl18hityhWC1k/8hlL7s6mm+8ME
   +RlF+kqu8oeP1xXfcBE9I3n0SIb4Esg/8rcZpp4ex0rksVrM067VpTznansJgkcW
   M7lzy0ChoAFdCkJPoRpHnAIwF0NtKikA6ZPrWgoGdADH9KrfIB/E+jEmSmO66VzI
   1lw5lYFeWX0QQ1XPKapTM8kyUYadW82+SHEk9gK4tqZsFsR2Fkitdlz12ABrUV6Q
   Wn8KwHawxi76MoFT58pXAWmfEwXx5rxvkLDkm2k1ErbOmSqLgBbd/BpmLH4/lhnL
   2GnddxrzCJbM1ZGKxst3Rmxed5mW1n/5qryXUD8se34tAA2GRQ+xgHykyr2kZYJa
   MceJobekkas4cnZdMg0LcZIPohPJQJNBa4O4Ek5p9l5iy1AA3MN6qaD/9zlwxHcv
   NX0kGJym9TBVaMDiN2o3YqaMYF5WPF0glXLg/HUyyilHKVNVZ7X8QTxeh5LSRkU2
   zICPmK3XRmTxQVZvkBapClQYKamKBGTOQai7RMLU+jwsIJRgco7xShp8TJuY0SID
   tMw1KRYKmrLXg49/9rU64FqjGn1ka3r6bEWTJSajw3VWGb6ZTCEcKjHAWzRHg2yy
   FQvhgp2uawTFU1z/VG45K6eXQRcg+ST0kKWsVJXyE1bVULeCpkwWiLa2VbzHhCGX
   pDTC9lY7W38Jp4vMSIIyeDVh0W9MurZ1VAAFB4FXDGZgS4F60SUilHNuiwGGGkta
   dFGbi2/lFImlByOS5YdibHE3dlddM4BqHI4nMq+XwmgPUWZjMcTri7wEMcT5aDLa
   8bPEVSj7oVP2x4scGYcClHzNM3cnpG+1O6Ed5ctBkTRoWVFstq1yQA888gmyNq7z
   WlgKyH6z4w+v1mlzyop90mda9B96F7YUM80a+A93CIafZlSISXmAsawQoM3LY2oA
   7YaBs15CkSTKgDUHJbhfg6Xqw6SjzBYAkD5lKTVgubM25a8NUp2sGgSBGTAst6m8
   wRC5SFG/AhF/GZ3EhahSt0c/CbgxpoMdW1TAt5DSJc9ruS2UYqJs2zPdpRI8eq8O
   JqC4NlXuoovzqAdHJQGP1rrktgHPYbqrcaej01GXo0PnS0onLBJdVAiWQm2Ft5WN
   Ozimuph+w3Ilx7RM2xLd5FObSrCCNjaD8Ev3oJzFxB3+gwobFi4LMkM0Ni8IShRG
   dyM0S63QAPjYxTfEj5mPBTB869Ht4LgcO8WaBlobbWOybILxAf9kgGOzduK7bFt0
   VfZVpQwv6treFQ76Dg5vNlrqICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9
   Pj8=
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 }
     }
     OCTET_STRING {
       SEQUENCE {
         OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
   15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334
   35363738393a3b3c3d3e3f` }
         OCTET_STRING { `70554fd436344f2785b1b3b1bac184b6679003336c
   26f15a7de878c4825c6be03f3c4a480f75b7486aad31d3a00518623fd207ab52
   8dd62721495835ae0062c367b74a71baf10aad0e8a2902076be31348beb15ccc
   0957cdebb4aff226756bbc601b6568ab784acbaeb34702f0f86a26202118b22b
   23f83558776c79c14dba983379c803e0dcc3160a11757030e69c6919798d81eb
   698a9a4483a99e5a5cb2c31c9a661799f3cc89c790706ea041629045d42a83ae
   d88860e394c69187e2105d28cc14ec393592d67dd00aa43fe8b4eae441400286
   6b5c713c6a8d7d16cf78b819d6f12e9e5a74233908f0b15e3c4ba8329c5cdda5
   5c84928e3aa8063e5aa9676403f91735b11010c7f593091364dc86445bc80484
   0a9a21724212469f8a7b0ce0ac698eb86cad39a7f4824d9a5163aac21ee6808b
   053c8a3facb0b6744b5262bbcb26a43f664c8732b64cfc7acf099605f41c7960
   60976ac433833fe00343fb1828300a424741116e4b45bb276ea81129a0db4c6e
   60bce611101e8c625474925e0222679308a3e7708d1972a7b423eb232851c36d
   2ed53d3ed3bb7500637061a5dc2292fa1c466c07354683328bec2c1ed2cb5c99
   b78eca0969038cf7c34dd118724e31cae086206b34302b520f5d177aded5b3cc
   e02acce808ea26bcc072625fdb93f17458a5fc1d4da394380a1f57e9cc661094
   38a075f0d2813fcc4a199cc76db3823f270b0061594192940411a37ffbafae2c
   150165cec5c6bf73c595fb92cd15312607da070778652bd9944bc48bc7d1a534
   338bad0bad6656c5d502ce7850ab1587244eeb58f439ab5e08574a718c8aac3d
   77c798bba1542733be73448f23fb70c0e5353a27c88322c5218493afbb380864
   34d6d60a56ba887dd498c3ab26a0870993815aa6a40975f218adca1582d64ffc
   8652fbb3a9a6fbc304f91945fa4aaef2878fd715df70113d2379f44886f812c8
   3ff2b719a69e1ec74ae4b15accd3aed5a53ce76a7b0982471633b973cb40a1a0
   015d0a424fa11a479c023017436d2a2900e993eb5a0a067400c7f4aadf201fc4
   fa31264a63bae95cc8d65c3995815e597d104355cf29aa5333c93251869d5bcd
   be487124f602b8b6a66c16c4761648ad765cf5d8006b515e905a7f0ac076b0c6
   2efa328153e7ca5701699f1305f1e6bc6f90b0e49b693512b6ce992a8b8016dd
   fc1a662c7e3f9619cbd869dd771af30896ccd5918ac6cb77466c5e779996d67f
   f9aabc97503f2c7b7e2d000d86450fb1807ca4cabda465825a31c789a1b7a491
   ab3872765d320d0b71920fa213c94093416b83b8124e69f65e62cb5000dcc37a
   a9a0fff73970c4772f357d24189ca6f5305568c0e2376a3762a68c605e563c5d
   209572e0fc7532ca294729535567b5fc413c5e8792d2464536cc808f98add746
   64f141566f9016a90a541829a98a0464ce41a8bb44c2d4fa3c2c209460728ef1
   4a1a7c4c9b98d12203b4cc3529160a9ab2d7838f7ff6b53ae05aa31a7d646b7a
   fa6c45932526a3c3755619be994c211c2a31c05b3447836cb2150be1829dae6b
   04c5535cff546e392ba797411720f924f490a5ac5495f21356d550b782a64c16
   88b6b655bcc7842197a434c2f6563b5b7f09a78bcc488232783561d16f4cbab6
   755400050781570c66604b817ad1252294736e8b01861a4b5a74519b8b6fe514
   89a5072392e587626c713776575d33806a1c8e2732af97c2680f51666331c4eb
   8bbc0431c4f96832daf1b3c45528fba153f6c78b1c198702947ccd337727a46f
   b53ba11de5cb4191346859516cb6ad72400f3cf209b236aef35a580ac87eb3e3
   0fafd66973ca8a7dd2675af41f7a17b61433cd1af80f7708869f665488497980
   b1ac10a0cdcb636a00ed8681b35e429124ca80350725b85f83a5eac3a4a3cc16
   00903e65293560b9b336e5af0d529dac1a048119302cb7a9bcc110b94851bf02
   117f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26c
   db33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61ba
   ab71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec3
   7225c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b
   324334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b8
   1c3bc59a065a1b6d63b26c82f101ff648063b376e2bb6c5b7455f655a50c2fea
   dade150efa0e0e6f365aea202122232425262728292a2b2c2d2e2f3031323334
   35363738393a3b3c3d3e3f` }
       }
     }
   }

C.1.2.  ML-KEM-768 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-----
   MFQCAQAwCwYJYIZIAWUDBAQCBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
   GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8=
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 }
     }
     OCTET_STRING {
       [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
   5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343
   5363738393a3b3c3d3e3f` }
     }
   }

C.1.2.2.  Expanded Format

   -----BEGIN PRIVATE KEY-----
   MIIJeAIBADALBglghkgBZQMEBAIEgglkBIIJYCfSp38zdW9hII7xE6voJZWHPUq8
   cw5bXWeVKb9qTOtjg0JyMahhL0FVBRWsulLkjq2LlCgzu+aGXRPRSnnSxcPgfwoF
   bY3nqt/KugWMSTyAs3yrjFYnU7s7prbsgpf4heqnVA1TABWoRAblWxNmtXfiNs5Y
   om2KHrWkTVQjI8IWfZv0pH+YVpnKBbrkO43sYX8COAo4kK/UuMfsft4mVToCXzzl
   vF16YhMDBCNcsa1INrVmtbhjvZvbRaKESnBHtsjTg+RIUl4EC03IorSMbDfJbWLU
   Pz/YjiiBxAogXJ4kj2UrWSeBp3n4aIDyoUe2eGPzkcwaWpCMAJXgchIpHi74o265
   qcDGBzIls0cDpK8Ek4LEdXPaaP3pJFrUROMbH721IfH2Hze8DO8pIGfmcNKKH/2Q
   T28RkKmWkYoTA3psq/PDc7+Cls03qzO6d0aAnMP4reGzY5vVe/zGllCqrx3hmPxM
   BGMpnlLEYXgMxCj8XQSlxRhQy6bCpSdDQGdXk92gm+RMKeY5XGX4XSoKfG30EeaR
   Gx8stsNRzS6HX1G2OL53YJfpPi8rL4PaC+70qoW6nnY6tkUCoMpSIunqtbO3CI7V
   IGDoyCablDpxqwrhxbG2h9LgGc+ANrz5v257rDqqNuQWYPqkVA8mSM2ToYnsXC3q
   cLrKqk/8kG+QgQ6htnvyTyx4z2uogarqYcBlK/+VsbrkQm0Xc7nMLKgsIeOMY247
   HFIyRJhrC+ioP13Vzy1Udi+zxev1m46IUwKxzkcDPt92D04Cm+QLbVZrGd11is1c
   dBKHgTEkT5AXLFPyZmPCHZBTAdSLr5HJF8x3eenYgCzBDYmjcFCZoq06OoiWdDwR
   RGmAk74lfay2bceFIouRLI2WXRSqKDQsOsSpP++lMrIJRd3BAgE5wU1ji5CMTd3p
   oGRblbLkQU1Au3nwRBODDxWoc8KLtwWcJ0EAIBXyBAjwWOcVsL+ZW1OAt90yWgVq
   uX5lmivgzfbDNzHGg6Y0t3HoySoTmu5LsOSccHcyHUL8GZ98HymMpiXSI6XCY6A8
   xIFZt4EmZbeGN+ThhyCywpprmfQnZqTLxNxQi6lLqDuJw6XHj4uya72beb64yBgk
   kPV5PuW5YBO3S34WninRYvExVGTqfXJDbYm3VRYRksgcwt0ci4u6eV70Ju4cwBw3
   qqN7LP+LCjeLR8vQtNSTmM/CcSlZaZ+gvYzYRmasxh9UG4T6lrnIVOTnXpFErdtE
   uFZqV9+7VFzkI8AzRvKywakXgNFSqN4aTUycrN5zksmWiIzCOZwCw4szU634rKso
   OSTaAKBbduc4xyyTDWy6Ca4WiZD6of7yIm54CGHUFu/0AvT3WfxkirH5cQAQkIf5
   bksUjSyzHkgFMU6gzZX7Aj6sDZiUdLpCAde0HSb1OUshfupbNLcaizeTHA5ZQnHg
   t8czJXJAIz57pzVgPkJah97ncHnjfLKKIXZFlM5TUNjaK2KgcXSUMDLsicmICcc7
   ZCPTDB0oOnZqZNiXA8PWKbSXgo1IMgw0YhB5eimKoQ1CPI3aBp0CvFnmzfA6CWuL
   PaTKubgMpKFJB2cszvHsT68jSgvFt+nUc/KzEzs7JqHRdctnp4BZGWmcAvdlMbmc
   X4kYBwS7TKRTXFuJcmecZgoHxeUUuHAJyGLrj1FXaV77P8QKne9rgcHMAqJJrk8J
   StDZvTSFwcHGgIBSCnyMYyAyzuc4FU5cUXbAfaVgJHdqQw/nbqz2ZaP3uDIQIhW8
   gvEJOcg1VwQzao+sHYHkuwSFql18dNa1m75cXpcqDYusQRtVtdVVfNaAoaj3G064
   a8SMmgUJcxpUvZ1ykLJ5Y+Q3Lcmxmc/crAsBrNKKYjlREuTENkjWIsSMgjTQFEDo
   zDdskn8jpa/JrAR0xmInTkJFJchVLs47P+JlFt6QG8fVFb3olVjmJslcgLkzQvgB
   AATznmxslIccXjRMqzlmyDX5qWpZr9McQChrOLHBp4RwurlHUYk0RTzoZzapGfH1
   ptUQqG9UVPw5gMtcdlvSvV97NrFBDWY1yM60fE3aDXaijqyTnHHDAkgEhmxxYmZY
   RCFjwsIhF+UKzvzmN4qYVlIwKk7wws4Mxxa3eW4ray43d9+hrD2iWaMbWptTD4y2
   OKgaYqwwGEmrr5WnMBvaMAaJCb/bfmfbzLs4pVUaJbGjoPaFdIrVdT2IgPABbGJ0
   hhZjhMVXH+I2WQA2TQODEeLYdds2ZoaTK17GAkMKNp6Hpu9cM4eGZXglvUwFes65
   I+sJNeaQXmO0ztf4CFenc91ksVDSZhLqmsEgUtsgF78YQ8y0sygbaQ3HKK36hcAC
   gbjjwJKHM1+Fa0/CiS9povV5Ia2gGRTECYhmLVd2lmKnhjUbm2ZJPat5WU2YbeIQ
   DWW6D/TqWLgVONJKRDWiWPrCVASqf0H2WLE4UGXhWNy2ARVzJyD0BFmqrBXkBpU6
   kKxSmX0czQcAYO/GXbnmUzVEZ/rVbscTyG51QMQjrPJmn1L6b0rGiI2HHvPoR8Ap
   qKr7uS4XskqgebH0GbphdbRCr7EZCdSla3CgM1soc5IYqnyTSOLDwvPrPRWkHmQX
   wN2Uv+shQZsxGnuxOhgLvoMyGKmmsXRHzIXyJYWVh6cwdwSay8/UTQ8CVDjhXRU4
   Jw1Ybhv4MZKpRZz2PA6XL4UpdnmDHs8SFQmFHLg0D28Qew+hoO/Rs2qBibwIXE9c
   t4TlU/QbkY+AOXzhlW94W+43fKmqi+aZitowwmt8PYxrVSVMyWIDsgxCruCsTh67
   QI5JqeP4edCrB4XrcCVCXRMFoimcAV4SDRY7DhlJTOVyU9AkbRgnRcuBl6t0OLPB
   u3lyvsWjBuujVnhVwBRpn+9lrlTHcKDYXBhADPZCrtxmB3e6SxOFAr1aeBL2IfhK
   SClrmN1DIrbxWCi4qPDgCoukSlPDqLFDVxsHQKvVZ9rxzenHnCBLbV4lnRdmoxu7
   y05qBc9FAhdrMBwcL0Ekd1AVe87IXoCbMKTWDXdHzdD1uZqoyCaYdRd5OqqAgKCx
   JKhVjfcrvje3X07btr6CFtbGM/srIoDiURPYaV5DSBw+6zl+sZJQUim2eiAeqJPD
   4ssy2ovDQvpN6gV4ok4W2Pj5ODqVt3BQ9Nn9L1cz7sHWPvPCPr+ZGBc2aacgISIj
   JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw==
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 }
     }
     OCTET_STRING {
       OCTET_STRING { `27d2a77f33756f61208ef113abe82595873d4abc730e
   5b5d679529bf6a4ceb6383427231a8612f41550515acba52e48ead8b942833bb
   e6865d13d14a79d2c5c3e07f0a056d8de7aadfcaba058c493c80b37cab8c5627
   53bb3ba6b6ec8297f885eaa7540d530015a84406e55b1366b577e236ce58a26d
   8a1eb5a44d542323c2167d9bf4a47f985699ca05bae43b8dec617f02380a3890
   afd4b8c7ec7ede26553a025f3ce5bc5d7a62130304235cb1ad4836b566b5b863
   bd9bdb45a2844a7047b6c8d383e448525e040b4dc8a2b48c6c37c96d62d43f3f
   d88e2881c40a205c9e248f652b592781a779f86880f2a147b67863f391cc1a5a
   908c0095e07212291e2ef8a36eb9a9c0c6073225b34703a4af049382c47573da
   68fde9245ad444e31b1fbdb521f1f61f37bc0cef292067e670d28a1ffd904f6f
   1190a996918a13037a6cabf3c373bf8296cd37ab33ba7746809cc3f8ade1b363
   9bd57bfcc69650aaaf1de198fc4c0463299e52c461780cc428fc5d04a5c51850
   cba6c2a5274340675793dda09be44c29e6395c65f85d2a0a7c6df411e6911b1f
   2cb6c351cd2e875f51b638be776097e93e2f2b2f83da0beef4aa85ba9e763ab6
   4502a0ca5222e9eab5b3b7088ed52060e8c8269b943a71ab0ae1c5b1b687d2e0
   19cf8036bcf9bf6e7bac3aaa36e41660faa4540f2648cd93a189ec5c2dea70ba
   caaa4ffc906f90810ea1b67bf24f2c78cf6ba881aaea61c0652bff95b1bae442
   6d1773b9cc2ca82c21e38c636e3b1c523244986b0be8a83f5dd5cf2d54762fb3
   c5ebf59b8e885302b1ce47033edf760f4e029be40b6d566b19dd758acd5c7412
   878131244f90172c53f26663c21d905301d48baf91c917cc7779e9d8802cc10d
   89a3705099a2ad3a3a8896743c1144698093be257dacb66dc785228b912c8d96
   5d14aa28342c3ac4a93fefa532b20945ddc1020139c14d638b908c4ddde9a064
   5b95b2e4414d40bb79f04413830f15a873c28bb7059c2741002015f20408f058
   e715b0bf995b5380b7dd325a056ab97e659a2be0cdf6c33731c683a634b771e8
   c92a139aee4bb0e49c7077321d42fc199f7c1f298ca625d223a5c263a03cc481
   59b7812665b78637e4e18720b2c29a6b99f42766a4cbc4dc508ba94ba83b89c3
   a5c78f8bb26bbd9b79beb8c8182490f5793ee5b96013b74b7e169e29d162f131
   5464ea7d72436d89b755161192c81cc2dd1c8b8bba795ef426ee1cc01c37aaa3
   7b2cff8b0a378b47cbd0b4d49398cfc2712959699fa0bd8cd84666acc61f541b
   84fa96b9c854e4e75e9144addb44b8566a57dfbb545ce423c03346f2b2c1a917
   80d152a8de1a4d4c9cacde7392c996888cc2399c02c38b3353adf8acab283924
   da00a05b76e738c72c930d6cba09ae168990faa1fef2226e780861d416eff402
   f4f759fc648ab1f97100109087f96e4b148d2cb31e4805314ea0cd95fb023eac
   0d989474ba4201d7b41d26f5394b217eea5b34b71a8b37931c0e594271e0b7c7
   33257240233e7ba735603e425a87dee77079e37cb28a21764594ce5350d8da2b
   62a07174943032ec89c98809c73b6423d30c1d283a766a64d89703c3d629b497
   828d48320c346210797a298aa10d423c8dda069d02bc59e6cdf03a096b8b3da4
   cab9b80ca4a14907672ccef1ec4faf234a0bc5b7e9d473f2b3133b3b26a1d175
   cb67a7805919699c02f76531b99c5f89180704bb4ca4535c5b8972679c660a07
   c5e514b87009c862eb8f5157695efb3fc40a9def6b81c1cc02a249ae4f094ad0
   d9bd3485c1c1c68080520a7c8c632032cee738154e5c5176c07da56024776a43
   0fe76eacf665a3f7b832102215bc82f10939c8355704336a8fac1d81e4bb0485
   aa5d7c74d6b59bbe5c5e972a0d8bac411b55b5d5557cd680a1a8f71b4eb86bc4
   8c9a0509731a54bd9d7290b27963e4372dc9b199cfdcac0b01acd28a62395112
   e4c43648d622c48c8234d01440e8cc376c927f23a5afc9ac0474c662274e4245
   25c8552ece3b3fe26516de901bc7d515bde89558e626c95c80b93342f8010004
   f39e6c6c94871c5e344cab3966c835f9a96a59afd31c40286b38b1c1a78470ba
   b947518934453ce86736a919f1f5a6d510a86f5454fc3980cb5c765bd2bd5f7b
   36b1410d6635c8ceb47c4dda0d76a28eac939c71c3024804866c716266584421
   63c2c22117e50acefce6378a985652302a4ef0c2ce0cc716b7796e2b6b2e3777
   dfa1ac3da259a31b5a9b530f8cb638a81a62ac301849abaf95a7301bda300689
   09bfdb7e67dbccbb38a5551a25b1a3a0f685748ad5753d8880f0016c62748616
   6384c5571fe2365900364d038311e2d875db366686932b5ec602430a369e87a6
   ef5c338786657825bd4c057aceb923eb0935e6905e63b4ced7f80857a773dd64
   b150d26612ea9ac12052db2017bf1843ccb4b3281b690dc728adfa85c00281b8
   e3c09287335f856b4fc2892f69a2f57921ada01914c40988662d57769662a786
   351b9b66493dab79594d986de2100d65ba0ff4ea58b81538d24a4435a258fac2
   5404aa7f41f658b1385065e158dcb60115732720f40459aaac15e406953a90ac
   52997d1ccd070060efc65db9e653354467fad56ec713c86e7540c423acf2669f
   52fa6f4ac6888d871ef3e847c029a8aafbb92e17b24aa079b1f419ba6175b442
   afb11909d4a56b70a0335b28739218aa7c9348e2c3c2f3eb3d15a41e6417c0dd
   94bfeb21419b311a7bb13a180bbe833218a9a6b17447cc85f225859587a73077
   049acbcfd44d0f025438e15d1538270d586e1bf83192a9459cf63c0e972f8529
   7679831ecf121509851cb8340f6f107b0fa1a0efd1b36a8189bc085c4f5cb784
   e553f41b918f80397ce1956f785bee377ca9aa8be6998ada30c26b7c3d8c6b55
   254cc96203b20c42aee0ac4e1ebb408e49a9e3f879d0ab0785eb7025425d1305
   a2299c015e120d163b0e19494ce57253d0246d182745cb8197ab7438b3c1bb79
   72bec5a306eba3567855c014699fef65ae54c770a0d85c18400cf642aedc6607
   77ba4b138502bd5a7812f621f84a48296b98dd4322b6f15828b8a8f0e00a8ba4
   4a53c3a8b143571b0740abd567daf1cde9c79c204b6d5e259d1766a31bbbcb4e
   6a05cf4502176b301c1c2f41247750157bcec85e809b30a4d60d7747cdd0f5b9
   9aa8c826987517793aaa8080a0b124a8558df72bbe37b75f4edbb6be8216d6c6
   33fb2b2280e25113d8695e43481c3eeb397eb192505229b67a201ea893c3e2cb
   32da8bc342fa4dea0578a24e16d8f8f9383a95b77050f4d9fd2f5733eec1d63e
   f3c23ebf9918173669a7202122232425262728292a2b2c2d2e2f303132333435
   363738393a3b3c3d3e3f` }
     }
   }

C.1.2.3.  Both Format

   -----BEGIN PRIVATE KEY-----
   MIIJvgIBADALBglghkgBZQMEBAIEggmqMIIJpgRAAAECAwQFBgcICQoLDA0ODxAR
   EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC
   CWAn0qd/M3VvYSCO8ROr6CWVhz1KvHMOW11nlSm/akzrY4NCcjGoYS9BVQUVrLpS
   5I6ti5QoM7vmhl0T0Up50sXD4H8KBW2N56rfyroFjEk8gLN8q4xWJ1O7O6a27IKX
   +IXqp1QNUwAVqEQG5VsTZrV34jbOWKJtih61pE1UIyPCFn2b9KR/mFaZygW65DuN
   7GF/AjgKOJCv1LjH7H7eJlU6Al885bxdemITAwQjXLGtSDa1ZrW4Y72b20WihEpw
   R7bI04PkSFJeBAtNyKK0jGw3yW1i1D8/2I4ogcQKIFyeJI9lK1kngad5+GiA8qFH
   tnhj85HMGlqQjACV4HISKR4u+KNuuanAxgcyJbNHA6SvBJOCxHVz2mj96SRa1ETj
   Gx+9tSHx9h83vAzvKSBn5nDSih/9kE9vEZCplpGKEwN6bKvzw3O/gpbNN6szundG
   gJzD+K3hs2Ob1Xv8xpZQqq8d4Zj8TARjKZ5SxGF4DMQo/F0EpcUYUMumwqUnQ0Bn
   V5PdoJvkTCnmOVxl+F0qCnxt9BHmkRsfLLbDUc0uh19Rtji+d2CX6T4vKy+D2gvu
   9KqFup52OrZFAqDKUiLp6rWztwiO1SBg6Mgmm5Q6casK4cWxtofS4BnPgDa8+b9u
   e6w6qjbkFmD6pFQPJkjNk6GJ7Fwt6nC6yqpP/JBvkIEOobZ78k8seM9rqIGq6mHA
   ZSv/lbG65EJtF3O5zCyoLCHjjGNuOxxSMkSYawvoqD9d1c8tVHYvs8Xr9ZuOiFMC
   sc5HAz7fdg9OApvkC21WaxnddYrNXHQSh4ExJE+QFyxT8mZjwh2QUwHUi6+RyRfM
   d3np2IAswQ2Jo3BQmaKtOjqIlnQ8EURpgJO+JX2stm3HhSKLkSyNll0Uqig0LDrE
   qT/vpTKyCUXdwQIBOcFNY4uQjE3d6aBkW5Wy5EFNQLt58EQTgw8VqHPCi7cFnCdB
   ACAV8gQI8FjnFbC/mVtTgLfdMloFarl+ZZor4M32wzcxxoOmNLdx6MkqE5ruS7Dk
   nHB3Mh1C/BmffB8pjKYl0iOlwmOgPMSBWbeBJmW3hjfk4YcgssKaa5n0J2aky8Tc
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   Pj8=
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 }
     }
     OCTET_STRING {
       SEQUENCE {
         OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
   15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334
   35363738393a3b3c3d3e3f` }
         OCTET_STRING { `27d2a77f33756f61208ef113abe82595873d4abc73
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   35363738393a3b3c3d3e3f` }
       }
     }
   }

C.1.3.  ML-KEM-1024 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-----
   MFQCAQAwCwYJYIZIAWUDBAQDBEKAQAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
   GhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj8=
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 }
     }
     OCTET_STRING {
       [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
   5161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343
   5363738393a3b3c3d3e3f` }
     }
   }

C.1.3.2.  Expanded Format

   -----BEGIN PRIVATE KEY-----
   MIIMeAIBADALBglghkgBZQMEBAMEggxkBIIMYPd7f2sVxz/izFRrZ/t3TKGbQs1G
   Pqn7uYTKR3p3tscQh8vwUavkc2qQcsbocMgxHFWWP1AKPHsbjypYVY9JxiUntsWU
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   mSfqY3MWJquybsTkMbjrazsLweglc+5zsaAhGDGDUoEIri6srduVtGSguYRpwxnM
   J7+gG8MQVKaMBVArFmK4ef6YoXEcNCb2Q2ywIUzqN5rDp+X7YBhKN8HaHtphxsOc
   HdToR4RYEfKjWKQ3MVKFNtSjKRsEFYwsPcZBYkiCZ4vHgF9YqdlMcQRWeEaiBE5l
   rs4qIlNytgJHmaVHfWAjdQSqXArFe8cKNVjAjE3mh+8TArT8tVlEE9IsuVm8Mb5C
   NFBAPGvFfcQRs/76wQUqxLsWLERUWkyoCJJlf6E6CyxILO1inMSZnZacWT1KrfBz
   zD46RY54qKoDlAjmUr6TsgyLQuxbDlAjnaxyYFKFGm0VMS7DntIItyIJpXfGsncB
   EolXSdUmDn3URsCwEYwQAL5oAdJhH88AeSqcxPS0mSL5otS5yPpaXQ1gUGYxp+lx
   zuhAsI+mPBNynX6lqscDUqmEzbZpMxy6dY/ofsOTGz4xYfzHR6p0lCRon+rhS/fJ
   ov+6EwKyErgDctjpBJ22mjoSYdCihZqbTVeJngukFgehtnp8DhKSNon4xjlTd9lw
   x0kKQSlhGh0Fw7eBO+2UVCByP3+VJah3k/r7v8qYLma7gGgcgySKidoITBmIL0jz
   Hn/AkJOknp/QlpGwIe30Y6/FGbYoU4FhGDRhFfsLiCzGSC88XLzBwYlGl+EjlZiz
   Syqaes0VJE0GkMiBlAl6m+2lheh8Q3EkYkwhB2jmIV03ZIJlPriZR4d8EY03DGlq
   b/zBAYrkE6CKjQ/6qBmUXaehZ8IpkTKQytHICjaSWHYmEOolPmLcJCJqMMiSwSE2
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   wrEgoodphuIXtyvXzuRKcmWxHO4asiYXYrMaNzg4aWnAgl+3lFLmUuEUL8c8nfb7
   pBF5W0cXkispui1Tq+WowNzBYBsJbJbXk4/VpoqHl8e5R3qGpHLrXaJQyy/sMY2D
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   ytzRwdN4EZ5pRCnbGZrIkeTFNDdXCFuzrng2ZzUMRFjZdnLoYegLHSZ5UQ6jpvI2
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   isWHXvKbVv0UHm7xX3AKC2bzlZXFiBdzc8RmmyG8Bx5MOqXwtKMbYljzXaJKw80p
   x/IJJBDFB4NVsTj7U6a5rm4LnAgkPnuqRcRzduuMfxPUz1Gqc2+jFUDJJB83DaVE
   v5+cKNmlfi8qfKlaTktGbmQas7zHat8ROdVnpvErUvOmXn7AquJryqjFWDOwTlmZ
   jryaGTD7ttIjPFPSwfi5UY48Lec6Gd7ms4Clsylxz2ThKf1sH6bnXUojRQHpZt06
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   acdzdo/LTQecCQWXA6DDqU3kuZ6jovFlg9D5Fwo5UNsHtPC8MIApJ/n3lhtiWYkm
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   7VjcYod2uYOILhF1YTSeXBMafhFqBGOGHX0YZjxWJ8OMcUfdqt/Uis16RTUgISIj
   JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw==
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 }
     }
     OCTET_STRING {
       OCTET_STRING { `f77b7f6b15c73fe2cc546b67fb774ca19b42cd463ea9
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     }
   }

C.1.3.3.  Both Format

   -----BEGIN PRIVATE KEY-----
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   VhBuiVIWO4ulklMMxaoK60OtOY/p6XuqUj16RDFnfD068HGeR124XKla9Qib6r6w
   Wy+qtIlrpg+ByIRypXtGqCiCagzftEb4GJGC0r9erE7BzF3q9ZnIoT5II1QG0X/9
   3INEtsZphKhoqpL6AiJ6CGlQ6wyHAe1Y3GKHdrmDiC4RdWE0nlwTGn4RagRjhh19
   GGY8VifDjHFH3arf1IrNekU1ICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9
   Pj8=
   -----END PRIVATE KEY-----

   SEQUENCE {
     INTEGER { 0 }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 }
     }
     OCTET_STRING {
       SEQUENCE {
         OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
   15161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f3031323334
   35363738393a3b3c3d3e3f` }
         OCTET_STRING { `f77b7f6b15c73fe2cc546b67fb774ca19b42cd463e
   a9fbb984ca477a77b6c71087cbf051abe4736a9072c6e870c8311c55963f500a
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   fbb4c30c1266b918e52925dfe17b37f95d22bca54f475919ac859098c0f0d08a
   c5875ef29b56fd141e6ef15f700a0b66f39595c588177373c4669b21bc071e4c
   3aa5f0b4a31b6258f35da24ac3cd29c7f2092410c5078355b138fb53a6b9ae6e
   0b9c08243e7baa45c47376eb8c7f13d4cf51aa736fa31540c9241f370da544bf
   9f9c28d9a57e2f2a7ca95a4e4b466e641ab3bcc76adf1139d567a6f12b52f3a6
   5e7ec0aae26bcaa8c55833b04e59998ebc9a1930fbb6d2233c53d2c1f8b9518e
   3c2de73a19dee6b380a5b32971cf64e129fd6c1fa6e75d4a234501e966dd3a54
   0af5c8f4f34a6b4a253ee28492566d5e67c6f55855fcb0506fb06c156744d9a0
   3a31a26fa94cad14f157b7f303d07a69c773768fcb4d079c09059703a0c3a94d
   e4b99ea3a2f16583d0f9170a3950db07b4f0bc30802927f9f7961b6259892636
   a9502a2705303637799dd344da451c1cf7bf67840ceb3079ab8c6b8c1927f640
   53c612450c45c9e603bc16666e596b3471e103b6f15447424d17022048111ffb
   d37e1c670f64f14b8a7b32b94c1a49b45dd2fc38cd5289d910ad63602cf5e130
   42c64ac6797b89fb551ad08e05a92d200cccb7e712ef23c9312cb350f029ab53
   7e287347fd3075ac10906a783f1c6c07ccb88f41228c4be1c640f790b5c3a5d5
   d3ca792495d74bc461562658c07ac600276b924ab5bc9be1f0494cb76f82f460
   a7480972663381e169996061d799859ec54d4f5ca5c411c01db1597b16597766
   9de13a928a34afbac258fea8c4764239c9421dc3119bf5b47699206978327b1c
   5345ef746a7983841f056e2534100ab24d4e9abbd0b17c6a95bd4c3c0e40f69e
   1612aceeb28b99086c95116e7204273893390bf46b899b36286b0ebf1947bb98
   84f732ca27da82b19b5dc0cc7f8885714910888b2310c4f9319d410b34e6433b
   9003e2176bb995257456106e8952163b8ba592530cc5aa0aeb43ad398fe9e97b
   aa523d7a4431677c3d3af0719e475db85ca95af5089beabeb05b2faab4896ba6
   0f81c88472a57b46a828826a0cdfb446f8189182d2bf5eac4ec1cc5deaf599c8
   a13e48235406d17ffddc8344b6c66984a868aa92fa02227a086950eb0c8701ed
   58dc628776b983882e117561349e5c131a7e116a0463861d7d18663c5627c38c
   7147ddaadfd48acd7a4535202122232425262728292a2b2c2d2e2f3031323334
   35363738393a3b3c3d3e3f` }
       }
     }
   }

C.2.  Example Public Keys

   The following is the ML-KEM-512 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-----
   MIIDMjALBglghkgBZQMEBAEDggMhADmVgV5ZfRBDVc8pqlMzyTJRhp1bzb5IcST2
   Ari2pmwWxHYWSK12XPXYAGtRXpBafwrAdrDGLvoygVPnylcBaZ8TBfHmvG+QsOSb
   aTUSts6ZKouAFt38GmYsfj+WGcvYad13GvMIlszVkYrGy3dGbF53mZbWf/mqvJdQ
   Pyx7fi0ADYZFD7GAfKTKvaRlgloxx4mht6SRqzhydl0yDQtxkg+iE8lAk0Frg7gS
   Tmn2XmLLUADcw3qpoP/3OXDEdy81fSQYnKb1MFVowOI3ajdipoxgXlY8XSCVcuD8
   dTLKKUcpU1VntfxBPF6HktJGRTbMgI+YrddGZPFBVm+QFqkKVBgpqYoEZM5BqLtE
   wtT6PCwglGByjvFKGnxMm5jRIgO0zDUpFgqasteDj3/2tTrgWqMafWRrevpsRZMl
   JqPDdVYZvplMIRwqMcBbNEeDbLIVC+GCna5rBMVTXP9Ubjkrp5dBFyD5JPSQpaxU
   lfITVtVQt4KmTBaItrZVvMeEIZekNML2Vjtbfwmni8xIgjJ4NWHRb0y6tnVUAAUH
   gVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10zgGocjicy
   r5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyekb7U7oR3l
   y0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oXthQzzRr4
   D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPMFgCQPmUp
   NWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGmgx1bVMC3
   kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9huqtxp6PT
   UZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2NoPwS/eg
   nMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3guBw7xZoG
   WhttY7Js
   -----END PUBLIC KEY-----

   SEQUENCE {
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 }
     }
     BIT_STRING { `00` `3995815e597d104355cf29aa5333c93251869d5bcdb
   e487124f602b8b6a66c16c4761648ad765cf5d8006b515e905a7f0ac076b0c62
   efa328153e7ca5701699f1305f1e6bc6f90b0e49b693512b6ce992a8b8016ddf
   c1a662c7e3f9619cbd869dd771af30896ccd5918ac6cb77466c5e779996d67ff
   9aabc97503f2c7b7e2d000d86450fb1807ca4cabda465825a31c789a1b7a491a
   b3872765d320d0b71920fa213c94093416b83b8124e69f65e62cb5000dcc37aa
   9a0fff73970c4772f357d24189ca6f5305568c0e2376a3762a68c605e563c5d2
   09572e0fc7532ca294729535567b5fc413c5e8792d2464536cc808f98add7466
   4f141566f9016a90a541829a98a0464ce41a8bb44c2d4fa3c2c209460728ef14
   a1a7c4c9b98d12203b4cc3529160a9ab2d7838f7ff6b53ae05aa31a7d646b7af
   a6c45932526a3c3755619be994c211c2a31c05b3447836cb2150be1829dae6b0
   4c5535cff546e392ba797411720f924f490a5ac5495f21356d550b782a64c168
   8b6b655bcc7842197a434c2f6563b5b7f09a78bcc488232783561d16f4cbab67
   55400050781570c66604b817ad1252294736e8b01861a4b5a74519b8b6fe5148
   9a5072392e587626c713776575d33806a1c8e2732af97c2680f51666331c4eb8
   bbc0431c4f96832daf1b3c45528fba153f6c78b1c198702947ccd337727a46fb
   53ba11de5cb4191346859516cb6ad72400f3cf209b236aef35a580ac87eb3e30
   fafd66973ca8a7dd2675af41f7a17b61433cd1af80f7708869f665488497980b
   1ac10a0cdcb636a00ed8681b35e429124ca80350725b85f83a5eac3a4a3cc160
   0903e65293560b9b336e5af0d529dac1a048119302cb7a9bcc110b94851bf021
   17f199dc485a852b7473f09b831a6831d5b54c0b790d225cf6bb92d9462a26cd
   b33dda5123c7aaf0e26a0b83655eea28bf3a8074725018fd6bae4b601cf61baa
   b71a7a3d35197a343e74b4a272c125d540896426d85b7958d3b38a6ba987ec37
   225c7b44cdb12dde4539b4ab082363683f04bf7a09cc5c41dfe830a1b162e0b3
   24334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede0b81
   c3bc59a065a1b6d63b26c` }
   }

   The following is the ML-KEM-768 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-----
   MIIEsjALBglghkgBZQMEBAIDggShACmKoQ1CPI3aBp0CvFnmzfA6CWuLPaTKubgM
   pKFJB2cszvHsT68jSgvFt+nUc/KzEzs7JqHRdctnp4BZGWmcAvdlMbmcX4kYBwS7
   TKRTXFuJcmecZgoHxeUUuHAJyGLrj1FXaV77P8QKne9rgcHMAqJJrk8JStDZvTSF
   wcHGgIBSCnyMYyAyzuc4FU5cUXbAfaVgJHdqQw/nbqz2ZaP3uDIQIhW8gvEJOcg1
   VwQzao+sHYHkuwSFql18dNa1m75cXpcqDYusQRtVtdVVfNaAoaj3G064a8SMmgUJ
   cxpUvZ1ykLJ5Y+Q3Lcmxmc/crAsBrNKKYjlREuTENkjWIsSMgjTQFEDozDdskn8j
   pa/JrAR0xmInTkJFJchVLs47P+JlFt6QG8fVFb3olVjmJslcgLkzQvgBAATznmxs
   lIccXjRMqzlmyDX5qWpZr9McQChrOLHBp4RwurlHUYk0RTzoZzapGfH1ptUQqG9U
   VPw5gMtcdlvSvV97NrFBDWY1yM60fE3aDXaijqyTnHHDAkgEhmxxYmZYRCFjwsIh
   F+UKzvzmN4qYVlIwKk7wws4Mxxa3eW4ray43d9+hrD2iWaMbWptTD4y2OKgaYqww
   GEmrr5WnMBvaMAaJCb/bfmfbzLs4pVUaJbGjoPaFdIrVdT2IgPABbGJ0hhZjhMVX
   H+I2WQA2TQODEeLYdds2ZoaTK17GAkMKNp6Hpu9cM4eGZXglvUwFes65I+sJNeaQ
   XmO0ztf4CFenc91ksVDSZhLqmsEgUtsgF78YQ8y0sygbaQ3HKK36hcACgbjjwJKH
   M1+Fa0/CiS9povV5Ia2gGRTECYhmLVd2lmKnhjUbm2ZJPat5WU2YbeIQDWW6D/Tq
   WLgVONJKRDWiWPrCVASqf0H2WLE4UGXhWNy2ARVzJyD0BFmqrBXkBpU6kKxSmX0c
   zQcAYO/GXbnmUzVEZ/rVbscTyG51QMQjrPJmn1L6b0rGiI2HHvPoR8ApqKr7uS4X
   skqgebH0GbphdbRCr7EZCdSla3CgM1soc5IYqnyTSOLDwvPrPRWkHmQXwN2Uv+sh
   QZsxGnuxOhgLvoMyGKmmsXRHzIXyJYWVh6cwdwSay8/UTQ8CVDjhXRU4Jw1Ybhv4
   MZKpRZz2PA6XL4UpdnmDHs8SFQmFHLg0D28Qew+hoO/Rs2qBibwIXE9ct4TlU/Qb
   kY+AOXzhlW94W+43fKmqi+aZitowwmt8PYxrVSVMyWIDsgxCruCsTh67QI5JqeP4
   edCrB4XrcCVCXRMFoimcAV4SDRY7DhlJTOVyU9AkbRgnRcuBl6t0OLPBu3lyvsWj
   BuujVnhVwBRpn+9lrlTHcKDYXBhADPZCrtxmB3e6SxOFAr1aeBL2IfhKSClrmN1D
   IrbxWCi4qPDgCoukSlPDqLFDVxsHQKvVZ9rxzenHnCBLbV4lnRdmoxu7y05qBc9F
   AhdrMBwcL0Ekd1AVe87IXoCbMKTWDXdHzdD1uZqoyCaYdRd5OqqAgKCxJKhVjfcr
   vje3X07btr6CFtbGM/srIoDiURPYaV5DSBw+6zl+sZJQUim2eiAeqJPD4ssy2ovD
   QvpN6gV4
   -----END PUBLIC KEY-----

   SEQUENCE {
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 }
     }
     BIT_STRING { `00` `298aa10d423c8dda069d02bc59e6cdf03a096b8b3da
   4cab9b80ca4a14907672ccef1ec4faf234a0bc5b7e9d473f2b3133b3b26a1d17
   5cb67a7805919699c02f76531b99c5f89180704bb4ca4535c5b8972679c660a0
   7c5e514b87009c862eb8f5157695efb3fc40a9def6b81c1cc02a249ae4f094ad
   0d9bd3485c1c1c68080520a7c8c632032cee738154e5c5176c07da56024776a4
   30fe76eacf665a3f7b832102215bc82f10939c8355704336a8fac1d81e4bb048
   5aa5d7c74d6b59bbe5c5e972a0d8bac411b55b5d5557cd680a1a8f71b4eb86bc
   48c9a0509731a54bd9d7290b27963e4372dc9b199cfdcac0b01acd28a6239511
   2e4c43648d622c48c8234d01440e8cc376c927f23a5afc9ac0474c662274e424
   525c8552ece3b3fe26516de901bc7d515bde89558e626c95c80b93342f801000
   4f39e6c6c94871c5e344cab3966c835f9a96a59afd31c40286b38b1c1a78470b
   ab947518934453ce86736a919f1f5a6d510a86f5454fc3980cb5c765bd2bd5f7
   b36b1410d6635c8ceb47c4dda0d76a28eac939c71c3024804866c71626658442
   163c2c22117e50acefce6378a985652302a4ef0c2ce0cc716b7796e2b6b2e377
   7dfa1ac3da259a31b5a9b530f8cb638a81a62ac301849abaf95a7301bda30068
   909bfdb7e67dbccbb38a5551a25b1a3a0f685748ad5753d8880f0016c6274861
   66384c5571fe2365900364d038311e2d875db366686932b5ec602430a369e87a
   6ef5c338786657825bd4c057aceb923eb0935e6905e63b4ced7f80857a773dd6
   4b150d26612ea9ac12052db2017bf1843ccb4b3281b690dc728adfa85c00281b
   8e3c09287335f856b4fc2892f69a2f57921ada01914c40988662d57769662a78
   6351b9b66493dab79594d986de2100d65ba0ff4ea58b81538d24a4435a258fac
   25404aa7f41f658b1385065e158dcb60115732720f40459aaac15e406953a90a
   c52997d1ccd070060efc65db9e653354467fad56ec713c86e7540c423acf2669
   f52fa6f4ac6888d871ef3e847c029a8aafbb92e17b24aa079b1f419ba6175b44
   2afb11909d4a56b70a0335b28739218aa7c9348e2c3c2f3eb3d15a41e6417c0d
   d94bfeb21419b311a7bb13a180bbe833218a9a6b17447cc85f225859587a7307
   7049acbcfd44d0f025438e15d1538270d586e1bf83192a9459cf63c0e972f852
   97679831ecf121509851cb8340f6f107b0fa1a0efd1b36a8189bc085c4f5cb78
   4e553f41b918f80397ce1956f785bee377ca9aa8be6998ada30c26b7c3d8c6b5
   5254cc96203b20c42aee0ac4e1ebb408e49a9e3f879d0ab0785eb7025425d130
   5a2299c015e120d163b0e19494ce57253d0246d182745cb8197ab7438b3c1bb7
   972bec5a306eba3567855c014699fef65ae54c770a0d85c18400cf642aedc660
   777ba4b138502bd5a7812f621f84a48296b98dd4322b6f15828b8a8f0e00a8ba
   44a53c3a8b143571b0740abd567daf1cde9c79c204b6d5e259d1766a31bbbcb4
   e6a05cf4502176b301c1c2f41247750157bcec85e809b30a4d60d7747cdd0f5b
   99aa8c826987517793aaa8080a0b124a8558df72bbe37b75f4edbb6be8216d6c
   633fb2b2280e25113d8695e43481c3eeb397eb192505229b67a201ea893c3e2c
   b32da8bc342fa4dea0578` }
   }

   The following is the ML-KEM-1024 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-----
   MIIGMjALBglghkgBZQMEBAMDggYhAEuUwpRQERGRgjs1FMmsHqPZglzLhjk6LfsE
   ZU+iGS03v60cSXxlAu7lyoCnO/zguvWlSohYWkATl6PSMvQmp6+wgrwhpEMXCQ6q
   x1ksLqiKZTxEkeoZOTEzX1LpiaPEzFbZxVNzLVfEcPtBq3WbZdLQREU4L82cTjRK
   ESj6nhHgQ1jhku0BSyMjKn7isi4jcX9EER7jNXU5nDdkbamBPsmyEq/pTl3FwjMK
   cpTMH0I0ptP7tPFoWriJLASssXzRwXDXsGEbanF2x5TMjGf1X8kjwq0gMQDzZZkY
   gsMCQ9d4E4Q7XsfJZAMiY3BgkuzwDHUWvmTkWYykImwGm7XmfkF1zyKGyN1cSIps
   WGHzG6oL0CaUcOi1Ud07zTjIbBL5zbF2x33ItsAqcB9HiQLIVT9pTA2CcntMSlws
   EEEhKqEnSAi4IRGzd+x1IU6bGXj3YATUE52YYT9LjpjSCve1NAc6UJqVm3p1ZPm0
   DKIYv2GCkyCoUCAXlU0yjXrGx2nsKXAHVuewaFs0DV4RgFlQSkmppQoQGY6xCleE
   Z460J9e0uruVUpM7BiiXlz4TGOrwoOrDdYSmVAGxcD4EKszYN1MUg/JBytzRwdN4
   EZ5pRCnbGZrIkeTFNDdXCFuzrng2ZzUMRFjZdnLoYegLHSZ5UQ6jpvI2DHekaULH
   oGpVTSKAgMhLR67xTbF2IMsWwGqzChvkzacIK+n4fpwhHEaRY0mluo6qUgHHKUo8
   CIW1O2V0UhCIJexkbJCgRhIyTufQMa/lNDEyy+9ntu+xpewoCbdzU4znez2LBOsL
   PCJWAR5McWwZqLoHUr9xSSEXZJ8GFcMpD8KaRv3kvVLbkobWAziCRCWcFaesK2QK
   YMwDN2pYQaP7ikc1aPqbGiZyFfNMAWl7Dw5icXXXIQW3cHwpueYUvcM6b2yBipU3
   C0J4gte0dnlqnsbrmTJ0zZsjkagrpF4zk9Lprpchyp1sG5iLWCdxP5CmWF3pQzUo
   wCsDzhC7X3IBOND7tMMMEma5GOUpJd/hezf5XSK8pU9HWRmshZCYwPDQisWHXvKb
   Vv0UHm7xX3AKC2bzlZXFiBdzc8RmmyG8Bx5MOqXwtKMbYljzXaJKw80px/IJJBDF
   B4NVsTj7U6a5rm4LnAgkPnuqRcRzduuMfxPUz1Gqc2+jFUDJJB83DaVEv5+cKNml
   fi8qfKlaTktGbmQas7zHat8ROdVnpvErUvOmXn7AquJryqjFWDOwTlmZjryaGTD7
   ttIjPFPSwfi5UY48Lec6Gd7ms4Clsylxz2ThKf1sH6bnXUojRQHpZt06VAr1yPTz
   SmtKJT7ihJJWbV5nxvVYVfywUG+wbBVnRNmgOjGib6lMrRTxV7fzA9B6acdzdo/L
   TQecCQWXA6DDqU3kuZ6jovFlg9D5Fwo5UNsHtPC8MIApJ/n3lhtiWYkmNqlQKicF
   MDY3eZ3TRNpFHBz3v2eEDOsweauMa4wZJ/ZAU8YSRQxFyeYDvBZmbllrNHHhA7bx
   VEdCTRcCIEgRH/vTfhxnD2TxS4p7MrlMGkm0XdL8OM1SidkQrWNgLPXhMELGSsZ5
   e4n7VRrQjgWpLSAMzLfnEu8jyTEss1DwKatTfihzR/0wdawQkGp4PxxsB8y4j0Ei
   jEvhxkD3kLXDpdXTynkklddLxGFWJljAesYAJ2uSSrW8m+HwSUy3b4L0YKdICXJm
   M4HhaZlgYdeZhZ7FTU9cpcQRwB2xWXsWWXdmneE6koo0r7rCWP6oxHZCOclCHcMR
   m/W0dpkgaXgyexxTRe90anmDhB8FbiU0EAqyTU6au9CxfGqVvUw8DkD2nhYSrO6y
   i5kIbJURbnIEJziTOQv0a4mbNihrDr8ZR7uYhPcyyifagrGbXcDMf4iFcUkQiIsj
   EMT5MZ1BCzTmQzuQA+IXa7mVJXRWEG6JUhY7i6WSUwzFqgrrQ605j+npe6pSPXpE
   MWd8PTrwcZ5HXbhcqVr1CJvqvrBbL6q0iWumD4HIhHKle0aoKIJqDN+0RvgYkYLS
   v16sTsHMXer1mcihPkgjVAbRf/3cg0S2xmmEqGiqkvoCInoIaVDrDIcB7VjcYod2
   uYOILhF1
   -----END PUBLIC KEY-----

   SEQUENCE {
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 }
     }
     BIT_STRING { `00` `4b94c29450111191823b3514c9ac1ea3d9825ccb863
   93a2dfb04654fa2192d37bfad1c497c6502eee5ca80a73bfce0baf5a54a88585
   a401397a3d232f426a7afb082bc21a44317090eaac7592c2ea88a653c4491ea1
   93931335f52e989a3c4cc56d9c553732d57c470fb41ab759b65d2d04445382fc
   d9c4e344a1128fa9e11e04358e192ed014b23232a7ee2b22e23717f44111ee33
   575399c37646da9813ec9b212afe94e5dc5c2330a7294cc1f4234a6d3fbb4f16
   85ab8892c04acb17cd1c170d7b0611b6a7176c794cc8c67f55fc923c2ad20310
   0f365991882c30243d77813843b5ec7c964032263706092ecf00c7516be64e45
   98ca4226c069bb5e67e4175cf2286c8dd5c488a6c5861f31baa0bd0269470e8b
   551dd3bcd38c86c12f9cdb176c77dc8b6c02a701f478902c8553f694c0d82727
   b4c4a5c2c1041212aa1274808b82111b377ec75214e9b1978f76004d4139d986
   13f4b8e98d20af7b534073a509a959b7a7564f9b40ca218bf61829320a850201
   7954d328d7ac6c769ec29700756e7b0685b340d5e118059504a49a9a50a10198
   eb10a5784678eb427d7b4babb9552933b062897973e1318eaf0a0eac37584a65
   401b1703e042accd837531483f241cadcd1c1d378119e694429db199ac891e4c
   5343757085bb3ae783667350c4458d97672e861e80b1d2679510ea3a6f2360c7
   7a46942c7a06a554d228080c84b47aef14db17620cb16c06ab30a1be4cda7082
   be9f87e9c211c46916349a5ba8eaa5201c7294a3c0885b53b657452108825ec6
   46c90a04612324ee7d031afe5343132cbef67b6efb1a5ec2809b773538ce77b3
   d8b04eb0b3c2256011e4c716c19a8ba0752bf71492117649f0615c3290fc29a4
   6fde4bd52db9286d603388244259c15a7ac2b640a60cc03376a5841a3fb8a473
   568fa9b1a267215f34c01697b0f0e627175d72105b7707c29b9e614bdc33a6f6
   c818a95370b427882d7b476796a9ec6eb993274cd9b2391a82ba45e3393d2e9a
   e9721ca9d6c1b988b5827713f90a6585de9433528c02b03ce10bb5f720138d0f
   bb4c30c1266b918e52925dfe17b37f95d22bca54f475919ac859098c0f0d08ac
   5875ef29b56fd141e6ef15f700a0b66f39595c588177373c4669b21bc071e4c3
   aa5f0b4a31b6258f35da24ac3cd29c7f2092410c5078355b138fb53a6b9ae6e0
   b9c08243e7baa45c47376eb8c7f13d4cf51aa736fa31540c9241f370da544bf9
   f9c28d9a57e2f2a7ca95a4e4b466e641ab3bcc76adf1139d567a6f12b52f3a65
   e7ec0aae26bcaa8c55833b04e59998ebc9a1930fbb6d2233c53d2c1f8b9518e3
   c2de73a19dee6b380a5b32971cf64e129fd6c1fa6e75d4a234501e966dd3a540
   af5c8f4f34a6b4a253ee28492566d5e67c6f55855fcb0506fb06c156744d9a03
   a31a26fa94cad14f157b7f303d07a69c773768fcb4d079c09059703a0c3a94de
   4b99ea3a2f16583d0f9170a3950db07b4f0bc30802927f9f7961b6259892636a
   9502a2705303637799dd344da451c1cf7bf67840ceb3079ab8c6b8c1927f6405
   3c612450c45c9e603bc16666e596b3471e103b6f15447424d17022048111ffbd
   37e1c670f64f14b8a7b32b94c1a49b45dd2fc38cd5289d910ad63602cf5e1304
   2c64ac6797b89fb551ad08e05a92d200cccb7e712ef23c9312cb350f029ab537
   e287347fd3075ac10906a783f1c6c07ccb88f41228c4be1c640f790b5c3a5d5d
   3ca792495d74bc461562658c07ac600276b924ab5bc9be1f0494cb76f82f460a
   7480972663381e169996061d799859ec54d4f5ca5c411c01db1597b165977669
   de13a928a34afbac258fea8c4764239c9421dc3119bf5b47699206978327b1c5
   345ef746a7983841f056e2534100ab24d4e9abbd0b17c6a95bd4c3c0e40f69e1
   612aceeb28b99086c95116e7204273893390bf46b899b36286b0ebf1947bb988
   4f732ca27da82b19b5dc0cc7f8885714910888b2310c4f9319d410b34e6433b9
   003e2176bb995257456106e8952163b8ba592530cc5aa0aeb43ad398fe9e97ba
   a523d7a4431677c3d3af0719e475db85ca95af5089beabeb05b2faab4896ba60
   f81c88472a57b46a828826a0cdfb446f8189182d2bf5eac4ec1cc5deaf599c8a
   13e48235406d17ffddc8344b6c66984a868aa92fa02227a086950eb0c8701ed5
   8dc628776b983882e1175` }
   }

C.3.  Example Certificates

   The following is the ML-KEM-512 certificate corresponding to the
   public key in the previous section signed with the ML-DSA-44 private
   key from [RFC9881].  The textual encoding [RFC7468] is followed by
   the so-called "pretty print"; the certificates are the same.

   -----BEGIN CERTIFICATE-----
   MIINpDCCBBqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44808wCwYJYIZIAWUDBAMR
   MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
   MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
   TEFNUFMgV0cwggMyMAsGCWCGSAFlAwQEAQOCAyEAOZWBXll9EENVzymqUzPJMlGG
   nVvNvkhxJPYCuLambBbEdhZIrXZc9dgAa1FekFp/CsB2sMYu+jKBU+fKVwFpnxMF
   8ea8b5Cw5JtpNRK2zpkqi4AW3fwaZix+P5YZy9hp3Xca8wiWzNWRisbLd0ZsXneZ
   ltZ/+aq8l1A/LHt+LQANhkUPsYB8pMq9pGWCWjHHiaG3pJGrOHJ2XTINC3GSD6IT
   yUCTQWuDuBJOafZeYstQANzDeqmg//c5cMR3LzV9JBicpvUwVWjA4jdqN2KmjGBe
   VjxdIJVy4Px1MsopRylTVWe1/EE8XoeS0kZFNsyAj5it10Zk8UFWb5AWqQpUGCmp
   igRkzkGou0TC1Po8LCCUYHKO8UoafEybmNEiA7TMNSkWCpqy14OPf/a1OuBaoxp9
   ZGt6+mxFkyUmo8N1Vhm+mUwhHCoxwFs0R4NsshUL4YKdrmsExVNc/1RuOSunl0EX
   IPkk9JClrFSV8hNW1VC3gqZMFoi2tlW8x4Qhl6Q0wvZWO1t/CaeLzEiCMng1YdFv
   TLq2dVQABQeBVwxmYEuBetElIpRzbosBhhpLWnRRm4tv5RSJpQcjkuWHYmxxN3ZX
   XTOAahyOJzKvl8JoD1FmYzHE64u8BDHE+Wgy2vGzxFUo+6FT9seLHBmHApR8zTN3
   J6RvtTuhHeXLQZE0aFlRbLatckAPPPIJsjau81pYCsh+s+MPr9Zpc8qKfdJnWvQf
   ehe2FDPNGvgPdwiGn2ZUiEl5gLGsEKDNy2NqAO2GgbNeQpEkyoA1ByW4X4Ol6sOk
   o8wWAJA+ZSk1YLmzNuWvDVKdrBoEgRkwLLepvMEQuUhRvwIRfxmdxIWoUrdHPwm4
   MaaDHVtUwLeQ0iXPa7ktlGKibNsz3aUSPHqvDiaguDZV7qKL86gHRyUBj9a65LYB
   z2G6q3Gno9NRl6ND50tKJywSXVQIlkJthbeVjTs4prqYfsNyJce0TNsS3eRTm0qw
   gjY2g/BL96CcxcQd/oMKGxYuCzJDNDYvCEoURncjNEut0AD42MU3xI+ZjwUwfOvR
   7eC4HDvFmgZaG21jsmyjUjBQMA4GA1UdDwEB/wQEAwIFIDAdBgNVHQ4EFgQUDsWS
   pZcefo2geKhuRnTy+xH26NcwHwYDVR0jBBgwFoAUMpoHsfq7SPUqMJ8RoYmPhI4j
   Iv8wCwYJYIZIAWUDBAMRA4IJdQDcV8LA/De8Ss6UL3tMcHXKc0iTXaBPPLyoCimW
   KG/BhZ299qdyg6Qv/hWMxXfuQLvBIJUiE9boIUvDJH1Bv5q+wBXDM4Pcb585a972
   fB7Lj7rTYwGezp4QRGsn4bMOUHtOS/9MaD9LAw8XlEDSl69KgN+jN+Cak+PS1Q3O
   u+TpeM2fo304+3vTfHlNiePSNOqkd1pzs2nwVIbQGIWctpF1rIHC7NJ/XOO3ZsN3
   Cr758OLyAotCdGCRnj16Fhxh1rJ976b6y+Yo96CDMgl22lYPJoihlBekuKc4ugkE
   g4vJEwAtPlMoaogn7XJcWkKIhGKp1M7nG9KvgQxCRvIfRURuDyHaiOAkOayK+Hp6
   4AV02pbYX/w1X9bW1KOeId42EUQpF2iFu3ilOJi1JmMFyMP8lZZYq/8fPv3KGZPF
   YJpd6yaA7ReIQaNiFgCMqx7nw/Zti7sa2a5dor3YqYRjZ8UlJUuYUKxNDde/u46W
   mIEGSYcynpOiEYbyeWmXW4ye7qhT1Q7bmFPV8Mjzn3rXytzUzUZfrK8j9cHxAozY
   sF7RDuBmauliYfV1jaroCcHrohVTnSSiSMQKV4q6HjKPIpf4qENs4SVh9xkWXdbB
   OaiGgFhsI+sxlDGPRwbKrj6gVcbyFuJIPRL1LylJ2qFXzpzHyfAS3fHFvgv+S0AJ
   DnfNk3OcT7G9jQhESQOkTXA4LqxPI+0c6asvauXlICnN8RdOjraY4+DQL8cYidEi
   SAnXsOKNSzj+b225zdPvfBB/4eJTtV7VdnQOhETJErofxEWbpA8zobl/+bu2smdY
   Pg1a83hwVo+HxfkSz1iHW9WT9+iwhnm28RqzLdmmzZGJSfgEFkADriwXUEr+LIkX
   0xeMGvyXxdxv9S6Y6y+n0Al0ql0tzGviVoDqA0xNLU+Mupou5ftDTJj7U1oxIUHj
   HlFeE06+JRoTPbDcl+cBil31SlxuZ1u7cOE33nbPOw0jWDXeA8M5uE3aMQah5VRf
   tZXmdijH4zEN1/++Q5oJAF1SCTsnTkZ0lk3ZlIfpO0H1sJpINzLlBO04dLlQx2Nc
   NFIExuPsVO7kW1rDLqkh8srBKrdUa/8ngD3kppXW7iaBhSnUE0N6lrwi5g/fJbNU
   H0W7r0b31u0KDQ8cNKlK8PZL5pu/ulJTGZ5Dz4HORwVt2aXQojZfGQ0rashKxes8
   F+Ewgse7NUAt3HqX94+0SWpfpNCVlZknK5XfhZJV08XVZ2TkTDoJ6aBLqua/a5Xg
   jWTwroAJuB84jx2B1eCeYxjt+3cEaB274XU++H6m5kP/1QtJ3L1r545NaRQAylZF
   MwCtCTVyAavhrTcrQwhl8rVGAKOlXaCfHSln8y9u26qMHeL9BIP7JeMeZxCYQQ5b
   QxN0WvGmK11W6XG2CTc0qQ0RdUOvfrXTfl5A+I6DS4T2Z26APgkoq2JSQihO3JEg
   S7zknl2NoAummhweGU/qSPzX+4/KlxwcCCs8mD8ZkkwhdB5poU4uTES/eCO+rrm3
   wxLmiIcv2RwNdN8bRkxm35SQCCfc6riit4AxkaRKz5b27FWedfkH9bOgQaQGxm/v
   5IwGHsFGeQFJyV1pNvo0aB9vvMTL3VZOsoXooxrdlc0kv7jJ9Q6eF8ZAFYXvxnaS
   D+/OsH1b1+6WCVZIDRzRsMauvaifYUZNMQQ/CKSkDkFPjBDY5Xca9yZkGl+S+Pzz
   7ODu6y3lvvUk+V6sPKEAS4ejZOocriV75SPfz0WlRZoljJXOm3tKCo6L2e56ntVs
   hRiIBaLG5stQf2EihTSZUf21zNjb15E7KcdbTtr8TE0iJAuVYxBtNRWsVhExOMO/
   QqXWnHL015pv8Dubwt6iDr8ObCDNOItPtszlNjCz4yN51aGTrHGZ0CJcbcUWqxOm
   W1wrQmnYWUaz1eDahmbnowXshqI8RcGqvzUlZ0/g6nEbAJZgbk7jozC1VlwOKMM4
   erhkw5mrrpicX3cvP3wl3JyhB6vbAfK4XQH3CfrnK12BhpgG0+9V5DKxTL02f+5m
   ckJI9cZqSYx8rhlDlNbR33kSOY0Ba2RwvmMxhdypd38l5S8oSwTRu5eJ4VrrSeeM
   wiW3gIxLA+o+SD2iFKyafsWLeu+Axx5/HlIVB+g82dGKkZrrESEvO9LpdlaS+AMW
   9BccbDD2SGE2UZKlK4zx2QwYvnFG/ZDRjmvQV0dQOxiy0j2l7WHmbedlTTUUd5FU
   0cfSG+cJHnToa/VRU4mDHvFpnV+AF0dA1s0oemhN5vOqhDzHnKasFFpUDH88mS7K
   gbXELYiHTQEB/s/Hr0crjwVQQCbJFe4bBJzhcnwuOcdNUKLmF7MidvoyKYYu20oE
   P6F0/RoDwS2FW3RyrKeSzlLWnuarfTq84iMaPgKrOl8XNfaSgGRsG3kxGe0s3rVs
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   /nl7vXBVLb9Nojt9AkIO637bT+1wszCvOH8nelnzNDsCBi9B8+mdgzizEN08UKSk
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   s7TAwcrR1drv9BRiaH2qytnr8PcAAAAAAAAAAAAAAAAAAAAAFSM2QA==
   -----END CERTIFICATE-----

   SEQUENCE {
     SEQUENCE {
       [0] {
         INTEGER { 2 }
       }
       INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34f` }
       SEQUENCE {
         OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
       }
       SEQUENCE {
         SET {
           SEQUENCE {
             # organizationName
             OBJECT_IDENTIFIER { 2.5.4.10 }
             PrintableString { "IETF" }
           }
         }
         SET {
           SEQUENCE {
             # commonName
             OBJECT_IDENTIFIER { 2.5.4.3 }
             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 { 2.16.840.1.101.3.4.4.1 }
         }
         BIT_STRING { `00` `3995815e597d104355cf29aa5333c93251869d5
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   0b81c3bc59a065a1b6d63b26c` }
       }
       [3] {
         SEQUENCE {
           SEQUENCE {
             # keyUsage
             OBJECT_IDENTIFIER { 2.5.29.15 }
             BOOLEAN { TRUE }
             OCTET_STRING {
               BIT_STRING { b`001` }
             }
           }
           SEQUENCE {
             # subjectKeyIdentifier
             OBJECT_IDENTIFIER { 2.5.29.14 }
             OCTET_STRING {
               OCTET_STRING { `0ec592a5971e7e8da078a86e4674f2fb11f6
   e8d7` }
             }
           }
           SEQUENCE {
             # authorityKeyIdentifier
             OBJECT_IDENTIFIER { 2.5.29.35 }
             OCTET_STRING {
               SEQUENCE {
                 [0 PRIMITIVE] { `329a07b1fabb48f52a309f11a1898f848
   e2322ff` }
               }
             }
           }
         }
       }
     }
     SEQUENCE {
       OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
     }
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   }

   The following is the ML-KEM-768 certificate corresponding to the
   public key in the previous section signed with the ML-DSA-65 private
   key from [RFC9881].  The textual encoding [RFC7468] is followed by
   the so-called "pretty print"; the certificates are the same.

   -----BEGIN CERTIFICATE-----
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   MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
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   -----END CERTIFICATE-----

   SEQUENCE {
     SEQUENCE {
       [0] {
         INTEGER { 2 }
       }
       INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34f` }
       SEQUENCE {
         OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
       }
       SEQUENCE {
         SET {
           SEQUENCE {
             # organizationName
             OBJECT_IDENTIFIER { 2.5.4.10 }
             PrintableString { "IETF" }
           }
         }
         SET {
           SEQUENCE {
             # commonName
             OBJECT_IDENTIFIER { 2.5.4.3 }
             PrintableString { "LAMPS WG" }
           }
         }
       }
       SEQUENCE {
         UTCTime { "200203043210Z" }
         UTCTime { "400129043210Z" }
       }
       SEQUENCE {
         SET {
           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 { 2.16.840.1.101.3.4.4.2 }
         }
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       }
       [3] {
         SEQUENCE {
           SEQUENCE {
             # keyUsage
             OBJECT_IDENTIFIER { 2.5.29.15 }
             BOOLEAN { TRUE }
             OCTET_STRING {
               BIT_STRING { b`001` }
             }
           }
           SEQUENCE {
             # subjectKeyIdentifier
             OBJECT_IDENTIFIER { 2.5.29.14 }
             OCTET_STRING {
               OCTET_STRING { `42bcb5a167fa330449612dbd8187056a7518
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             }
           }
           SEQUENCE {
             # authorityKeyIdentifier
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             OCTET_STRING {
               SEQUENCE {
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         }
       }
     }
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     }
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   5223e6db2ebf60a343c6d929ea3cce114216b8b363a83afb4d9102364a6beed0
   00000000000000000000000000000000000050c15191f25` }
   }

   The following is the ML-KEM-1024 certificate corresponding to the
   public key in the previous section signed with the ML-DSA-87 private
   key from [RFC9881].  The textual encoding [RFC7468] is followed by
   the so-called "pretty print"; the certificates are the same.

   -----BEGIN CERTIFICATE-----
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   kNggIp4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQIDxcdKS4x
   -----END CERTIFICATE-----

   SEQUENCE {
     SEQUENCE {
       [0] {
         INTEGER { 2 }
       }
       INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34f` }
       SEQUENCE {
         OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
       }
       SEQUENCE {
         SET {
           SEQUENCE {
             # organizationName
             OBJECT_IDENTIFIER { 2.5.4.10 }
             PrintableString { "IETF" }
           }
         }
         SET {
           SEQUENCE {
             # commonName
             OBJECT_IDENTIFIER { 2.5.4.3 }
             PrintableString { "LAMPS WG" }
           }
         }
       }
       SEQUENCE {
         UTCTime { "200203043210Z" }
         UTCTime { "400129043210Z" }
       }
       SEQUENCE {
         SET {
           SEQUENCE {
             # organizationName
             OBJECT_IDENTIFIER { 2.5.4.10 }
             PrintableString { "IETF" }
           }
         }
         SET {
           SEQUENCE {
             # commonName
             OBJECT_IDENTIFIER { 2.5.4.3 }
             PrintableString { "LAMPS WG" }
           }
         }
       }
       SEQUENCE {
         SEQUENCE {
           OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 }
         }
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       }
       [3] {
         SEQUENCE {
           SEQUENCE {
             # keyUsage
             OBJECT_IDENTIFIER { 2.5.29.15 }
             BOOLEAN { TRUE }
             OCTET_STRING {
               BIT_STRING { b`001` }
             }
           }
           SEQUENCE {
             # subjectKeyIdentifier
             OBJECT_IDENTIFIER { 2.5.29.14 }
             OCTET_STRING {
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           }
           SEQUENCE {
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               SEQUENCE {
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   e24f2bfb5847bea3f02898772d2f28a0185951db3b37c8b5d2c0d9c327a60036
   980c944b29c12dd3a0cecf6dc542f6f0df8ca84674086f7554f596bec85347d8
   78c569a44e87928292ead6eca246fdaad6efb6f5827f323adf8daa9bb056ebf4
   a2644c7f4a5fc3cc5f2a03778b1ccd31151da4bc7b27fb9001e6e732d9938917
   65bd5eec1849404fa11ae674858a4180bcfcc0f93ed64ca94a041af1e5ea3169
   7db3baf913fa35a92903eab84e5e31b8337278aa8e743f7e5dd13769c591febf
   89b1e8ab7066810c39298c1125718819b8b7ea2abc75f86e62eadea05a8a5c36
   d2e655cb805af1d54fce7838890d214a2a7e7112383adccdbdc2e648c9db7d1d
   7f8575e7aa8c6c9070c1c245b737f939bc8edf272777f90d820229e000000000
   000000000000000000000000000000000000000000004080f171d292e31` }
   }

C.4.  Examples of Bad 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.

C.4.1.  ML-KEM Inconsistent Seed and Expanded Private Keys

   Four ML-KEM-512-PrivateKey examples of inconsistent seed and expanded
   private keys are shown as follows:

   1.  The first ML-KEM-512-PrivateKey example includes the both CHOICE,
       i.e., both seed and expandedKey are included.  The seed and
       expanded values can be checked for inconsistencies.

   2.  The second ML-KEM-512-PrivateKey example includes only
       expandedKey.  The expanded private key has a mutated s_0 and a
       valid public key hash, but a pairwise consistency check would
       find that the public key fails to match private.

   3.  The third ML-KEM-512-PrivateKey example includes only
       expandedKey.  The expanded private key has a mutated H(ek); both
       a public key digest check and a pairwise consistency check should
       fail.

   4.  The fourth ML-KEM-512-PrivateKey example includes the both
       CHOICE, i.e., both seed and expandedKey are included.  There is
       mismatch of the seed and expanded private key in only the z
       implicit rejection secret; here, the private and public vectors
       match and the pairwise consistency check passes, but z is
       different.

   The following is the first example:

   -----BEGIN PRIVATE KEY-----
   MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR
   EhMUFRYXGBkaGxwdHh8hIiMkJSYnKCkqKywtLi8wMTIzNDU2Nzg5Ojs8PT4/QASC
   BmDvsn6JOEO1+bZhFYaTegU33BzhWY5u8TDVVBiwaUFnGLk3E4KY1lkkOQvUIErq
   c6VzJCCGVwzLkAdwiCoTOZIeHEYlqwgwpJUosrxyCyFgSFL9d57oFT3+QyRXG5tG
   Z6yFlUbOoVEPV5ltPMMKMY3QBrartJ/LOwD2QT6F4hF5wXkl2bU8dgwLDAJYxZhd
   eQNgMTo6rLojsTCL939wAcA1ks/zfCXBJD+J8FAzBikeocuHoaM49HaPzIzm95fE
   co8AWycN0JG8djQHiqjfaMYpNg0ldjW82ZycuxOtenMbZsc+GLFUmWiqZjxgupeV
   G4+lQZpRmsKU0ptIymHRcsMUCMHicS+19miPXIOPEQvORmEOqa0e12RZkkLj6y27
   Uk4kZ5TB82bpqjccBB1Oq4lQ88ns0V2fYMVt5UFCoM153A8tBBNbfAPnIWrpRQHa
   +TdRbDHeyhTHg2/GExQ8lhhfB4DP/C+v+XBY4F5xMh4euYjsWXsPC5MPyX1n6aDe
   eYnB9q61wWkTK6indGy1clrZwQX70Ta7I8brALnFQDuUlzhqE8f51osDoBUHqCEm
   eh0Za60KkLtpppJFWElopV7adFlUSzNG8IIV8p2hk5PxN6gYGBcLtsrp1ruBYkLg
   GaZp1MWYIEiMc4nv4jOYO7yTZCRkwJN8e4wBlyr6ysU17FdsuxI7wJRHYa26pyxh
   6h0kg1utBI8xSTZXA4/Ep0JZmMOdAxP97IsoF2IpPE8AlTqsKkZSSH99ZCyg2aLT
   5JsFAVw5wQbHuYwaUgFWM2Z4xk81IJKVbKZD4SCboXaeYRSjdkCCp0oItlz8t8cF
   WVw9G29Otkqcu8Y5jJzMYwSUARi5VmuIdKK4JLGshait+hvQ2xCzEEPQqbn7rIZ3
   ecO4uKllgS/og7cVtb6tSFdSElRfxBLw024tYiKszHLKB0hbVzR2Gy0xKVef8Xsi
   CJg8GxdrunLDlrfe237IW7VX4UvBdp3V4YGG+scfw1tMV0o7FWK8+sEMd1VVhBZX
   q0aRqxBRo8uY5m1IG2pIYDqSZmlIRr/zGygxEYYCeK+p2x5YyDpt2IEIoVWu8cCm
   loiUsRuop7njMsrudKX/hipV3DfkmwHUtKe6BaAb2MKLprTD1T+QCyWMgpBoImQW
   I2F6qEbx4pGmwhssh0iF9ikVUnA7GQSpNyPpV4LuksVV28LwDBdfLJuwuIo4R5Xg
   1Ju86oha8Qz7xHKpQ7MKRS7l7I+D4V2Uopy/MrLU/Hxeg5Go663FkA+2QJ76km8y
   +qE8o28vM25KSgdLAnsUeIPgnIkXfGWc0Sc5ZytrscTGIcXAQsiQhxWLcz2IFylr
   ODGwJXVnN2Dt+a2QV46nFX8kF2LUo0OEy0j/XEMJ8MqgmQTaNhgtLCUpCIYwS3S7
   Fz/HRj/+AzbZISXgNV5dQF700VAsjEfftEN3AcGIgWzZ5D0+waOM98MejCU5vLyF
   lbe4gXyv9jmgw1cI6wsGsFtIHBzwwIc8Oy+PWqNswRPIGHJWNn+ZKTaetmrspooj
   wme20LlsCg2asSt6gTs/C7BWVbAZcwTuR2hadCelkhKC0zz4Jmyqhim4GMQTnEGG
   wYcd92UvxsLZZMaOBGUG4y1oUnmy1hoKORa2y8xCVs7saBUDaanfGivRaoTByGal
   EG4ugDqhfI6RG7A2CCKkfLsdNDGBuRLqYg6RZXN0ai679nnZYsJTV0m/YV8iioKU
   mFhvgx4sK44rMAIKgmC+7LxHvHGra45wtjgwpg8NYH/vcbxvYwk/IyaOmQKGiGIA
   zLqF+4OEVlMQlUOxeh3spjJtm4rV2kUshji24i9h4ROPZ8DVZq4lqTfxJcsaVnJQ
   4HhdomaWKnJ6lEpgMreOQlyYxp2GOAJf52GdIyKsAV9y2bfWMmuHhAniYarDxz0N
   +6JY0Q67VTT7AVHVx1aeVh3Vg6qVi7XX447eQoMy230pwnAMSI4fARfjZwA/5mev
   42xo+n6QWhj1BC8iEafPhBz/F5BtGVQwjMSii111xw/9+lygBlJOSR+8Gbu45oQ/
   uRoNz67mpuEldXK2fWtiQmYsoAnY0qhOArxWajY+/0pEdTMpOV105HVzD50LQ05m
   hHpZnF6s80FNh4KdUx3AVX9XISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+
   P0A=
   -----END PRIVATE KEY-----

   The following is the second example:

   -----BEGIN PRIVATE KEY-----
   MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHFVT9Q2NE8nhbGzsbrBhLZnkAMz
   bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px
   uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy
   KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX
   mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC
   hmtccTxqjX0Wz3i4GdbxLp5adCM5CPCxXjxLqDKcXN2lXISSjjqoBj5aqWdkA/kX
   NbEQEMf1kwkTZNyGRFvIBIQKmiFyQhJGn4p7DOCsaY64bK05p/SCTZpRY6rCHuaA
   iwU8ij+ssLZ0S1Jiu8smpD9mTIcytkz8es8JlgX0HHlgYJdqxDODP+ADQ/sYKDAK
   QkdBEW5LRbsnbqgRKaDbTG5gvOYREB6MYlR0kl4CImeTCKPncI0Zcqe0I+sjKFHD
   bS7VPT7Tu3UAY3BhpdwikvocRmwHNUaDMovsLB7Sy1yZt47KCWkDjPfDTdEYck4x
   yuCGIGs0MCtSD10Xet7Vs8zgKszoCOomvMByYl/bk/F0WKX8HU2jlDgKH1fpzGYQ
   lDigdfDSgT/MShmcx22zgj8nCwBhWUGSlAQRo3/7r64sFQFlzsXGv3PFlfuSzRUx
   JgfaBwd4ZSvZlEvEi8fRpTQzi60LrWZWxdUCznhQqxWHJE7rWPQ5q14IV0pxjIqs
   PXfHmLuhVCczvnNEjyP7cMDlNTonyIMixSGEk6+7OAhkNNbWCla6iH3UmMOrJqCH
   CZOBWqakCXXyGK3KFYLWT/yGUvuzqab7wwT5GUX6Sq7yh4/XFd9wET0jefRIhvgS
   yD/ytxmmnh7HSuSxWszTrtWlPOdqewmCRxYzuXPLQKGgAV0KQk+hGkecAjAXQ20q
   KQDpk+taCgZ0AMf0qt8gH8T6MSZKY7rpXMjWXDmVgV5ZfRBDVc8pqlMzyTJRhp1b
   zb5IcST2Ari2pmwWxHYWSK12XPXYAGtRXpBafwrAdrDGLvoygVPnylcBaZ8TBfHm
   vG+QsOSbaTUSts6ZKouAFt38GmYsfj+WGcvYad13GvMIlszVkYrGy3dGbF53mZbW
   f/mqvJdQPyx7fi0ADYZFD7GAfKTKvaRlgloxx4mht6SRqzhydl0yDQtxkg+iE8lA
   k0Frg7gSTmn2XmLLUADcw3qpoP/3OXDEdy81fSQYnKb1MFVowOI3ajdipoxgXlY8
   XSCVcuD8dTLKKUcpU1VntfxBPF6HktJGRTbMgI+YrddGZPFBVm+QFqkKVBgpqYoE
   ZM5BqLtEwtT6PCwglGByjvFKGnxMm5jRIgO0zDUpFgqasteDj3/2tTrgWqMafWRr
   evpsRZMlJqPDdVYZvplMIRwqMcBbNEeDbLIVC+GCna5rBMVTXP9Ubjkrp5dBFyD5
   JPSQpaxUlfITVtVQt4KmTBaItrZVvMeEIZekNML2Vjtbfwmni8xIgjJ4NWHRb0y6
   tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z
   gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek
   b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX
   thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM
   FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm
   gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h
   uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2
   NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g
   uBw7xZoGWhttY7JsgvEB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj
   JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw==
   -----END PRIVATE KEY-----

   The following is the third example:

   -----BEGIN PRIVATE KEY-----
   MIIGeAIBADALBglghkgBZQMEBAEEggZkBIIGYHBVT9Q2NE8nhbGzsbrBhLZnkAMz
   bCbxWn3oeMSCXGvgPzxKSA91t0hqrTHToAUYYj/SB6tSjdYnIUlYNa4AYsNnt0px
   uvEKrQ6KKQIHa+MTSL6xXMwJV83rtK/yJnVrvGAbZWireErLrrNHAvD4aiYgIRiy
   KyP4NVh3bHnBTbqYM3nIA+DcwxYKEXVwMOacaRl5jYHraYqaRIOpnlpcssMcmmYX
   mfPMiceQcG6gQWKQRdQqg67YiGDjlMaRh+IQXSjMFOw5NZLWfdAKpD/otOrkQUAC
   hmtccTxqjX0Wz3i4GdbxLp5adCM5CPCxXjxLqDKcXN2lXISSjjqoBj5aqWdkA/kX
   NbEQEMf1kwkTZNyGRFvIBIQKmiFyQhJGn4p7DOCsaY64bK05p/SCTZpRY6rCHuaA
   iwU8ij+ssLZ0S1Jiu8smpD9mTIcytkz8es8JlgX0HHlgYJdqxDODP+ADQ/sYKDAK
   QkdBEW5LRbsnbqgRKaDbTG5gvOYREB6MYlR0kl4CImeTCKPncI0Zcqe0I+sjKFHD
   bS7VPT7Tu3UAY3BhpdwikvocRmwHNUaDMovsLB7Sy1yZt47KCWkDjPfDTdEYck4x
   yuCGIGs0MCtSD10Xet7Vs8zgKszoCOomvMByYl/bk/F0WKX8HU2jlDgKH1fpzGYQ
   lDigdfDSgT/MShmcx22zgj8nCwBhWUGSlAQRo3/7r64sFQFlzsXGv3PFlfuSzRUx
   JgfaBwd4ZSvZlEvEi8fRpTQzi60LrWZWxdUCznhQqxWHJE7rWPQ5q14IV0pxjIqs
   PXfHmLuhVCczvnNEjyP7cMDlNTonyIMixSGEk6+7OAhkNNbWCla6iH3UmMOrJqCH
   CZOBWqakCXXyGK3KFYLWT/yGUvuzqab7wwT5GUX6Sq7yh4/XFd9wET0jefRIhvgS
   yD/ytxmmnh7HSuSxWszTrtWlPOdqewmCRxYzuXPLQKGgAV0KQk+hGkecAjAXQ20q
   KQDpk+taCgZ0AMf0qt8gH8T6MSZKY7rpXMjWXDmVgV5ZfRBDVc8pqlMzyTJRhp1b
   zb5IcST2Ari2pmwWxHYWSK12XPXYAGtRXpBafwrAdrDGLvoygVPnylcBaZ8TBfHm
   vG+QsOSbaTUSts6ZKouAFt38GmYsfj+WGcvYad13GvMIlszVkYrGy3dGbF53mZbW
   f/mqvJdQPyx7fi0ADYZFD7GAfKTKvaRlgloxx4mht6SRqzhydl0yDQtxkg+iE8lA
   k0Frg7gSTmn2XmLLUADcw3qpoP/3OXDEdy81fSQYnKb1MFVowOI3ajdipoxgXlY8
   XSCVcuD8dTLKKUcpU1VntfxBPF6HktJGRTbMgI+YrddGZPFBVm+QFqkKVBgpqYoE
   ZM5BqLtEwtT6PCwglGByjvFKGnxMm5jRIgO0zDUpFgqasteDj3/2tTrgWqMafWRr
   evpsRZMlJqPDdVYZvplMIRwqMcBbNEeDbLIVC+GCna5rBMVTXP9Ubjkrp5dBFyD5
   JPSQpaxUlfITVtVQt4KmTBaItrZVvMeEIZekNML2Vjtbfwmni8xIgjJ4NWHRb0y6
   tnVUAAUHgVcMZmBLgXrRJSKUc26LAYYaS1p0UZuLb+UUiaUHI5Llh2JscTd2V10z
   gGocjicyr5fCaA9RZmMxxOuLvAQxxPloMtrxs8RVKPuhU/bHixwZhwKUfM0zdyek
   b7U7oR3ly0GRNGhZUWy2rXJADzzyCbI2rvNaWArIfrPjD6/WaXPKin3SZ1r0H3oX
   thQzzRr4D3cIhp9mVIhJeYCxrBCgzctjagDthoGzXkKRJMqANQcluF+DperDpKPM
   FgCQPmUpNWC5szblrw1SnawaBIEZMCy3qbzBELlIUb8CEX8ZncSFqFK3Rz8JuDGm
   gx1bVMC3kNIlz2u5LZRiomzbM92lEjx6rw4moLg2Ve6ii/OoB0clAY/WuuS2Ac9h
   uqtxp6PTUZejQ+dLSicsEl1UCJZCbYW3lY07OKa6mH7DciXHtEzbEt3kU5tKsII2
   NoPwS/egnMXEHf6DChsWLgsyQzQ2LwhKFEZ3IzRLrdAA+NjFN8SPmY8FMHzr0e3g
   uBw7xZoGWhttY7Jsg/EB/2SAY7N24rtsW3RV9lWlDC/q2t4VDvoODm82WuogISIj
   JCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+Pw==
   -----END PRIVATE KEY-----

   The following is the fourth example:

   -----BEGIN PRIVATE KEY-----
   MIIGvgIBADALBglghkgBZQMEBAEEggaqMIIGpgRAAAECAwQFBgcICQoLDA0ODxAR
   EhMUFRYXGBkaGxwdHh8gISIjJCUmJygpKissLS4vMDEyMzQ1Njc4OTo7PD0+PwSC
   BmBwVU/UNjRPJ4Wxs7G6wYS2Z5ADM2wm8Vp96HjEglxr4D88SkgPdbdIaq0x06AF
   GGI/0gerUo3WJyFJWDWuAGLDZ7dKcbrxCq0OiikCB2vjE0i+sVzMCVfN67Sv8iZ1
   a7xgG2Voq3hKy66zRwLw+GomICEYsisj+DVYd2x5wU26mDN5yAPg3MMWChF1cDDm
   nGkZeY2B62mKmkSDqZ5aXLLDHJpmF5nzzInHkHBuoEFikEXUKoOu2Ihg45TGkYfi
   EF0ozBTsOTWS1n3QCqQ/6LTq5EFAAoZrXHE8ao19Fs94uBnW8S6eWnQjOQjwsV48
   S6gynFzdpVyEko46qAY+WqlnZAP5FzWxEBDH9ZMJE2TchkRbyASECpohckISRp+K
   ewzgrGmOuGytOaf0gk2aUWOqwh7mgIsFPIo/rLC2dEtSYrvLJqQ/ZkyHMrZM/HrP
   CZYF9Bx5YGCXasQzgz/gA0P7GCgwCkJHQRFuS0W7J26oESmg20xuYLzmERAejGJU
   dJJeAiJnkwij53CNGXKntCPrIyhRw20u1T0+07t1AGNwYaXcIpL6HEZsBzVGgzKL
   7Cwe0stcmbeOyglpA4z3w03RGHJOMcrghiBrNDArUg9dF3re1bPM4CrM6AjqJrzA
   cmJf25PxdFil/B1No5Q4Ch9X6cxmEJQ4oHXw0oE/zEoZnMdts4I/JwsAYVlBkpQE
   EaN/+6+uLBUBZc7Fxr9zxZX7ks0VMSYH2gcHeGUr2ZRLxIvH0aU0M4utC61mVsXV
   As54UKsVhyRO61j0OateCFdKcYyKrD13x5i7oVQnM75zRI8j+3DA5TU6J8iDIsUh
   hJOvuzgIZDTW1gpWuoh91JjDqyaghwmTgVqmpAl18hityhWC1k/8hlL7s6mm+8ME
   +RlF+kqu8oeP1xXfcBE9I3n0SIb4Esg/8rcZpp4ex0rksVrM067VpTznansJgkcW
   M7lzy0ChoAFdCkJPoRpHnAIwF0NtKikA6ZPrWgoGdADH9KrfIB/E+jEmSmO66VzI
   1lw5lYFeWX0QQ1XPKapTM8kyUYadW82+SHEk9gK4tqZsFsR2Fkitdlz12ABrUV6Q
   Wn8KwHawxi76MoFT58pXAWmfEwXx5rxvkLDkm2k1ErbOmSqLgBbd/BpmLH4/lhnL
   2GnddxrzCJbM1ZGKxst3Rmxed5mW1n/5qryXUD8se34tAA2GRQ+xgHykyr2kZYJa
   MceJobekkas4cnZdMg0LcZIPohPJQJNBa4O4Ek5p9l5iy1AA3MN6qaD/9zlwxHcv
   NX0kGJym9TBVaMDiN2o3YqaMYF5WPF0glXLg/HUyyilHKVNVZ7X8QTxeh5LSRkU2
   zICPmK3XRmTxQVZvkBapClQYKamKBGTOQai7RMLU+jwsIJRgco7xShp8TJuY0SID
   tMw1KRYKmrLXg49/9rU64FqjGn1ka3r6bEWTJSajw3VWGb6ZTCEcKjHAWzRHg2yy
   FQvhgp2uawTFU1z/VG45K6eXQRcg+ST0kKWsVJXyE1bVULeCpkwWiLa2VbzHhCGX
   pDTC9lY7W38Jp4vMSIIyeDVh0W9MurZ1VAAFB4FXDGZgS4F60SUilHNuiwGGGkta
   dFGbi2/lFImlByOS5YdibHE3dlddM4BqHI4nMq+XwmgPUWZjMcTri7wEMcT5aDLa
   8bPEVSj7oVP2x4scGYcClHzNM3cnpG+1O6Ed5ctBkTRoWVFstq1yQA888gmyNq7z
   WlgKyH6z4w+v1mlzyop90mda9B96F7YUM80a+A93CIafZlSISXmAsawQoM3LY2oA
   7YaBs15CkSTKgDUHJbhfg6Xqw6SjzBYAkD5lKTVgubM25a8NUp2sGgSBGTAst6m8
   wRC5SFG/AhF/GZ3EhahSt0c/CbgxpoMdW1TAt5DSJc9ruS2UYqJs2zPdpRI8eq8O
   JqC4NlXuoovzqAdHJQGP1rrktgHPYbqrcaej01GXo0PnS0onLBJdVAiWQm2Ft5WN
   Ozimuph+w3Ilx7RM2xLd5FObSrCCNjaD8Ev3oJzFxB3+gwobFi4LMkM0Ni8IShRG
   dyM0S63QAPjYxTfEj5mPBTB869Ht4LgcO8WaBlobbWOybILxAf9kgGOzduK7bFt0
   VfZVpQwv6treFQ76Dg5vNlrqICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9
   Pj4=
   -----END PRIVATE KEY-----

Acknowledgments

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

   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, and Wei-Jun Wang.

Authors' Addresses

   Sean Turner
   sn3rd
   Email: sean@sn3rd.com


   Panos Kampanakis
   AWS
   Email: kpanos@amazon.com


   Jake Massimo
   AWS
   Email: jakemas@amazon.com


   Bas Westerbaan
   Cloudflare
   Email: bas@westerbaan.name
