Internet-Draft ML-KEM in Certificates December 2024
Turner, et al. Expires 15 June 2025 [Page]
Workgroup:
LAMPS
Internet-Draft:
draft-ietf-lamps-kyber-certificates-latest
Published:
Intended Status:
Standards Track
Expires:
Authors:
S. Turner
sn3rd
P. Kampanakis
AWS
J. Massimo
AWS
B. Westerbaan
Cloudflare

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 (KEM). This document describes 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 described.

About This Document

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

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

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

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

Status of This Memo

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

Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.

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This Internet-Draft will expire on 15 June 2025.

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Table of Contents

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) PQC Project [NIST-PQC]. Prior to standardization, the earlier 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 X.509 (PKIX) certificates [RFC5280] at three security levels: ML-KEM-512, ML-KEM-768, and ML-KEM-1024, using object identifiers 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 [I-D.ietf-lamps-cms-kyber]. 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; see [I-D.celi-wiggers-tls-authkem].

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
    }

The fields in AlgorithmIdentifier have the following meanings:

The AlgorithmIdentifier for a ML-KEM public key MUST use one of the id-alg-ml-kem object identifiers listed below, based on the security level. The parameters field of the AlgorithmIdentifier for the ML-KEM public key MUST be absent.

When any of the ML-KEM AlgorithmIdentifier appears in the SubjectPublicKeyInfo field of an X.509 certificate, the key usage certificate extension MUST only contain keyEncipherment Section 4.2.1.3 of [RFC5280].

  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 }

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

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

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

    ML-KEM-PublicKey ::= OCTET STRING

    ML-KEM-PrivateKey ::= OCTET STRING

No additional encoding of the ML-KEM public key value is applied in the SubjectPublicKeyInfo field of an X.509 certificate [RFC5280]. However, whenever the ML-KEM public key value appears outside of a certificate, it MAY be encoded as an OCTET STRING.

No additional encoding of the ML-KEM private key value is applied in the PrivateKeyInfo field of an Asymmetric Key Package [RFC5958]. However, whenever the ML-KEM private key value appears outside of a Asymmetric Key Package, it MAY be encoded as an OCTET STRING.

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:

Appendix C.2 contains examples for ML-KEM public keys encoded using the textual encoding defined in [RFC7468].

5. Private Key Format

In short, an ML-KEM private key is encoded by storing its 64-octet seed in the privateKey field as follows.

[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.

A keypair is generated by sampling 64 octets uniformly at random for the seed (private key) from a cryptographically secure pseudorandom number generator (CSPRNGs). 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 what algorithm the private key is for and allows for the public key and additional attributes about the key to be included as well. For illustration, the ASN.1 structure OneAsymmetricKey is replicated below.

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

When used in a OneAsymmetricKey type, the privateKey OCTET STRING contains the raw octet string encoding of the 64-octet seed. The publicKey field SHOULD be omitted because the public key can be computed as noted earlier in this section.

Appendix C.1 contains examples for ML-KEM private keys encoded using the textual encoding defined in [RFC7468].

6. 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.

For ML-KEM specific security considerations refer to [I-D.sfluhrer-cfrg-ml-kem-security-considerations].

The generation of private keys relies on random numbers. The use of inadequate pseudo-random 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, and [RFC4086] offers important guidance in this area.

ML-KEM key generation as standardized in [FIPS203] has specific requirements around randomness generation, described in section 3.3, 'Randomness generation'.

Key formats have implications on KEM binding properties, initially formalized in [CDM23]. Per the analysis of the final [FIPS203] in [KEMMY24], a compliant instantiation of ML-KEM is LEAK-BIND-K-PK-secure and LEAK-BIND-K-CT-secure when using the expanded key format, but not MAL-BIND-K-PK-secure nor MAL-BIND-K-CT-secure. This means that the computed shared secret binds to the encapsulation key used to compute it against a malicious adversary that has access to leaked, honestly-generated key material but is not capable of manufacturing maliciously generated keypairs. This binding to the encapsulation key broadly protects against re-encapsulation attacks but not completely.

Using the 64-byte seed format provides a step up in binding security by mitigating an attack enabled by the hash of the public encapsulation key stored in the expanded private decapsulation key format, providing MAL-BIND-K-CT security and LEAK-BIND-K-PK security.

7. IANA Considerations

For the ASN.1 Module in Appendix A, IANA is requested to assign an object identifier (OID) for the module identifier (TBD) with a Description of "id-mod-x509-ml-kem-2024". The OID for the module should be allocated in the "SMI Security for PKIX Module Identifier" registry (1.3.6.1.5.5.7.0).

8. References

8.1. Normative References

[FIPS203]
"Module-lattice-based key-encapsulation mechanism standard", National Institute of Standards and Technology (U.S.), DOI 10.6028/nist.fips.203, , <https://doi.org/10.6028/nist.fips.203>.
[RFC2119]
Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <https://www.rfc-editor.org/rfc/rfc2119>.
[RFC5280]
Cooper, D., Santesson, S., Farrell, S., Boeyen, S., Housley, R., and W. Polk, "Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, , <https://www.rfc-editor.org/rfc/rfc5280>.
[RFC5912]
Hoffman, P. and J. Schaad, "New ASN.1 Modules for the Public Key Infrastructure Using X.509 (PKIX)", RFC 5912, DOI 10.17487/RFC5912, , <https://www.rfc-editor.org/rfc/rfc5912>.
[RFC5958]
Turner, S., "Asymmetric Key Packages", RFC 5958, DOI 10.17487/RFC5958, , <https://www.rfc-editor.org/rfc/rfc5958>.
[RFC8174]
Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, , <https://www.rfc-editor.org/rfc/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, , <https://www.rfc-editor.org/rfc/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, , <https://www.itu.int/rec/T-REC-X.680>.
[X690]
ITU-T, "Information technology - Abstract Syntax Notation One (ASN.1): ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)", ITU-T Recommendation X.690, ISO/IEC 8825-1:2021, , <https://www.itu.int/rec/T-REC-X.690>.

8.2. 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", , <https://eprint.iacr.org/2023/1933.pdf>.
[I-D.celi-wiggers-tls-authkem]
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-04, , <https://datatracker.ietf.org/doc/html/draft-celi-wiggers-tls-authkem-04>.
[I-D.ietf-lamps-cms-kyber]
Prat, J., Ounsworth, M., and D. Van Geest, "Use of ML-KEM in the Cryptographic Message Syntax (CMS)", Work in Progress, Internet-Draft, draft-ietf-lamps-cms-kyber-06, , <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-cms-kyber-06>.
[I-D.ietf-lamps-dilithium-certificates]
Massimo, J., Kampanakis, P., Turner, S., and B. Westerbaan, "Internet X.509 Public Key Infrastructure: Algorithm Identifiers for ML-DSA", Work in Progress, Internet-Draft, draft-ietf-lamps-dilithium-certificates-05, , <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-dilithium-certificates-05>.
[I-D.sfluhrer-cfrg-ml-kem-security-considerations]
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-02, , <https://datatracker.ietf.org/doc/html/draft-sfluhrer-cfrg-ml-kem-security-considerations-02>.
[KEMMY24]
Schmieg, S., "Unbindable Kemmy Schmidt: ML-KEM is neither MAL-BIND-K-CT nor MAL-BIND-K-PK", , <https://eprint.iacr.org/2024/523.pdf>.
[NIST-PQC]
National Institute of Standards and Technology (NIST), "Post-Quantum Cryptography Project", , <https://csrc.nist.gov/projects/post-quantum-cryptography>.
[RFC4086]
Eastlake 3rd, D., Schiller, J., and S. Crocker, "Randomness Requirements for Security", BCP 106, RFC 4086, DOI 10.17487/RFC4086, , <https://www.rfc-editor.org/rfc/rfc4086>.
[RFC7468]
Josefsson, S. and S. Leonard, "Textual Encodings of PKIX, PKCS, and CMS Structures", RFC 7468, DOI 10.17487/RFC7468, , <https://www.rfc-editor.org/rfc/rfc7468>.

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-2024
{ iso(1) identified-organization(3) dod(6)
  internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
  id-mod-x509-ml-kem-2024(TBD) }

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
  --
  -- To use the following with the PKIX1Explicit-2009 [RFC5912], replace
  -- the PublicKeyAlgorithms therein with the following:
  --
  -- PublicKeyAlgorithms PUBLIC-KEY ::= {
  --   PKIXAlgs-2009.PublicKeys,
  --   ...,
  --   PKIX1-PSS-OAEP-Algorithms-2009.PublicKeys,
  --   X509-ML-KEM-2024.PublicKeys }

  --
  -- Public Key (pk-) 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 --
  PARAMS ARE absent
  CERT-KEY-USAGE { keyEncipherment }
  --- PRIVATE-KEY no ASN.1 wrapping --
  }

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

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

END

<CODE ENDS>

Appendix B. Security Strengths

Instead of defining the strength of a quantum algorithm in a traditional manner using the imprecise notion of bits of security, NIST has defined security levels by picking a reference scheme, which NIST expects to offer notable levels of resistance to both quantum and classical attack. To wit, a KEM algorithm that achieves NIST PQC security must require computational resources to break IND-CCA2 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.

Table 1: ML-KEM security strengths
Level Parameter Set Encap. Key Decap. Key Ciphertext SS
1 ML-KEM-512 800 1632 768 32
3 ML-KEM-768 1184 2400 1952 32
5 ML-KEM-1024 1568 3168 2592 32

Appendix C. Examples

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

C.1. Example Private Key

The following is an example of a ML-KEM-512 private key with hex seed 0001…3f:

-----BEGIN PRIVATE KEY-----
MFICAQAwCwYJYIZIAWUDBAQBBEAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
HB0eHyAhIiMkJSYnKCkqKywtLi8wMTIzNDU2Nzg5Ojs8PT4/
-----END PRIVATE KEY-----

SEQUENCE {
  INTEGER { 0 }
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.1 }
  }
  OCTET_STRING { `000102030405060708090a0b0c0d0e0f10111213141516
1718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343536
3738393a3b3c3d3e3f` }
}

The following is an example of a ML-KEM-768 private key from the same seed.

-----BEGIN PRIVATE KEY-----
MFICAQAwCwYJYIZIAWUDBAQCBEAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
HB0eHyAhIiMkJSYnKCkqKywtLi8wMTIzNDU2Nzg5Ojs8PT4/
-----END PRIVATE KEY-----

SEQUENCE {
  INTEGER { 0 }
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 }
  }
  OCTET_STRING { `000102030405060708090a0b0c0d0e0f10111213141516
1718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343536
3738393a3b3c3d3e3f` }
}

The following is an example of a ML-KEM-1024 private key from the same seed.

-----BEGIN PRIVATE KEY-----
MFICAQAwCwYJYIZIAWUDBAQDBEAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
HB0eHyAhIiMkJSYnKCkqKywtLi8wMTIzNDU2Nzg5Ojs8PT4/
-----END PRIVATE KEY-----

SEQUENCE {
  INTEGER { 0 }
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.3 }
  }
  OCTET_STRING { `000102030405060708090a0b0c0d0e0f10111213141516
1718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343536
3738393a3b3c3d3e3f` }
}

C.2. Example Public Key

The following is the ML-KEM-512 public key corresponding to the private key in the previous section.

-----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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` }
}

The following is the ML-KEM-768 public key corresponding to the private key in the previous section.

-----BEGIN PUBLIC KEY-----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-----END PUBLIC KEY-----

SEQUENCE {
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.4.2 }
  }
  BIT_STRING { `00` `298aa10d423c8dda069d02bc59e6cdf03a096b8b3da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` }
}

The following is the ML-KEM-1024 public key corresponding to the private key in the previous section.

-----BEGIN PUBLIC KEY-----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-----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` }
}

The following example, in addition to encoding the ML-KEM-768 private key, has an attribute included as well as the public key:

  -----BEGIN PRIVATE KEY-----
  TODO insert example private key with attribute
  -----END PRIVATE KEY-------

C.3. Example Certificates

The following is the ML-KEM-512 certificate that corresponding to the public key in the previous section signed with the ML-DSA-44 private key from [I-D.ietf-lamps-dilithium-certificates].

-----BEGIN CERTIFICATE-----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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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e0b324334362f084a14467723344badd000f8d8c537c48f998f05307cebd1ede
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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41462687daacad9ebf0f70000000000000000000000000000000015233640` }
}

The following is the ML-KEM-768 certificate that corresponding to the public key in the previous section signed with the ML-DSA-65 private key from [I-D.ietf-lamps-dilithium-certificates].

-----BEGIN CERTIFICATE-----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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
f787` }
          }
        }
        SEQUENCE {
          # authorityKeyIdentifier
          OBJECT_IDENTIFIER { 2.5.29.35 }
          OCTET_STRING {
            SEQUENCE {
              [0 PRIMITIVE] { `1b0563e3cd3346149c8c9ebcf23b0a4e5
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            }
          }
        }
      }
    }
  }
  SEQUENCE {
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  }
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5223e6db2ebf60a343c6d929ea3cce114216b8b363a83afb4d9102364a6beed0
00000000000000000000000000000000000050c15191f25` }
}

The following is the ML-KEM-1024 certificate that corresponding to the public key in the previous section signed with the ML-DSA-87 private key from [I-D.ietf-lamps-dilithium-certificates].

-----BEGIN CERTIFICATE-----
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-----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 {
            OCTET_STRING { `da82182c39ebdb350d904ee4bc507b72043f
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          }
        }
        SEQUENCE {
          # authorityKeyIdentifier
          OBJECT_IDENTIFIER { 2.5.29.35 }
          OCTET_STRING {
            SEQUENCE {
              [0 PRIMITIVE] { `89886750b57c24db3fc012e61ede59753
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            }
          }
        }
      }
    }
  }
  SEQUENCE {
    OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
  }
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000000000000000000000000000000000000000000004080f171d292e31` }
}

Acknowledgments

TODO acknowledge.

Authors' Addresses

Sean Turner
sn3rd
Panos Kampanakis
AWS
Jake Massimo
AWS
Bas Westerbaan
Cloudflare