LAMPS S. Turner
Internet-Draft sn3rd
Intended status: Standards Track P. Kampanakis
Expires: 8 May 2025 J. Massimo
AWS
B. Westerbaan
Cloudflare
4 November 2024
Internet X.509 Public Key Infrastructure - Algorithm Identifiers for the
Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM)
draft-ietf-lamps-kyber-certificates-06
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 draft-ietf-lamps-kyber-">https://lamps-
draft-ietf-lamps-kyber-">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
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provisions of BCP 78 and BCP 79.
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Table of Contents
1. Introduction
1.1. Applicability Statement
2. Conventions and Definitions
3. Algorithm Identifiers
4. Subject Public Key Fields
5. Private Key Format
6. Security Considerations
7. IANA Considerations
8. References
8.1. Normative References
8.2. Informative References
Appendix A. ASN.1 Module
Appendix B. Security Strengths
Appendix C. Examples
C.1. Example Private Key
C.2. Example Public Key
C.3. Example Certificate
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) 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, which is included herein for
convenience, is defined 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 object
identifier.
* parameters, which are optional, are the associated parameters for
the algorithm identifier in the algorithm field.
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
}
| NOTE: The above syntax is from [RFC5912] and is compatible with
| the 2021 ASN.1 syntax [X680]. See [RFC5280] for the 1988 ASN.1
| syntax.
The fields in SubjectPublicKeyInfo have the following meaning:
* algorithm is the algorithm identifier and parameters for the
public key (see above).
* subjectPublicKey contains the byte stream of the public key.
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_.
"Asymmetric Key Packages" [RFC5958] describes how to encode a private
key in a structure that both identifies what algorithm the private
key is for and allows for the public key and additional attributes
about the key to be included as well. For illustration, the ASN.1
structure OneAsymmetricKey is replicated below.
OneAsymmetricKey ::= SEQUENCE {
version Version,
privateKeyAlgorithm SEQUENCE {
algorithm PUBLIC-KEY.&id({PublicKeySet}),
parameters PUBLIC-KEY.&Params({PublicKeySet}
{@privateKeyAlgorithm.algorithm})
OPTIONAL}
privateKey OCTET STRING (CONTAINING
PUBLIC-KEY.&PrivateKey({PublicKeySet}
{@privateKeyAlgorithm.algorithm})),
attributes [0] Attributes OPTIONAL,
...,
[[2: publicKey [1] BIT STRING (CONTAINING
PUBLIC-KEY.&Params({PublicKeySet}
{@privateKeyAlgorithm.algorithm})
OPTIONAL,
...
}
| NOTE: The above syntax is from [RFC5958] and is compatible with
| the 2021 ASN.1 syntax [X680].
When used in a OneAsymmetricKey type, the privateKey OCTET STRING
contains the raw octet string encoding of the 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,
DOI 10.6028/nist.fips.203, August 2024,
<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, March 1997,
<https://www.rfc-editor.org/rfc/rfc2119>.
[RFC5280] Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
Housley, R., and W. Polk, "Internet X.509 Public Key
Infrastructure Certificate and Certificate Revocation List
(CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, May 2008,
<https://www.rfc-editor.org/rfc/rfc5280>.
[RFC5912] Hoffman, P. and J. Schaad, "New ASN.1 Modules for the
Public Key Infrastructure Using X.509 (PKIX)", RFC 5912,
DOI 10.17487/RFC5912, June 2010,
<https://www.rfc-editor.org/rfc/rfc5912>.
[RFC5958] Turner, S., "Asymmetric Key Packages", RFC 5958,
DOI 10.17487/RFC5958, August 2010,
<https://www.rfc-editor.org/rfc/rfc5958>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/rfc/rfc8174>.
[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/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, February 2021,
<https://www.itu.int/rec/T-REC-X.680>.
[X690] ITU-T, "Information technology - Abstract Syntax Notation
One (ASN.1): ASN.1 encoding rules: Specification of Basic
Encoding Rules (BER), Canonical Encoding Rules (CER) and
Distinguished Encoding Rules (DER)", ITU-T
Recommendation X.690, ISO/IEC 8825-1:2021, February 2021,
<https://www.itu.int/rec/T-REC-X.690>.
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", 2023,
<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, 17 October 2024,
<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-05,
15 October 2024, <https://datatracker.ietf.org/doc/html/
draft-ietf-lamps-cms-kyber-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-01, 11 October 2024,
<https://datatracker.ietf.org/doc/html/draft-sfluhrer-
cfrg-ml-kem-security-considerations-01>.
[KEMMY24] Schmieg, S., "Unbindable Kemmy Schmidt: ML-KEM is neither
MAL-BIND-K-CT nor MAL-BIND-K-PK", 2024,
<https://eprint.iacr.org/2024/523.pdf>.
[NIST-PQC] National Institute of Standards and Technology (NIST),
"Post-Quantum Cryptography Project", 20 December 2016,
<https://csrc.nist.gov/projects/post-quantum-
cryptography>.
[RFC4086] Eastlake 3rd, D., Schiller, J., and S. Crocker,
"Randomness Requirements for Security", BCP 106, RFC 4086,
DOI 10.17487/RFC4086, June 2005,
<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,
April 2015, <https://www.rfc-editor.org/rfc/rfc7468>.
Appendix A. ASN.1 Module
This appendix includes the ASN.1 module [X680] for the ML-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.
| TODO: what should go in this table?
+=======+===============+=============+========+============+====+
| Level | Parameter Set | Encap. Key | Decap. | Ciphertext | SS |
| | | | Key | | |
+=======+===============+=============+========+============+====+
| 1 | ML-KEM-512 | 800 | 1632 | 768 | 32 |
+-------+---------------+-------------+--------+------------+----+
| 3 | ML-KEM-768 | 1184 | 2400 | 1952 | 32 |
+-------+---------------+-------------+--------+------------+----+
| 5 | ML-KEM-1024 | 1568 | 3168 | 2592 | 32 |
+-------+---------------+-------------+--------+------------+----+
Table 1: ML-KEM security strengths
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-----
0 82: SEQUENCE
2 2: INTEGER 0
5 11: SEQUENCE {
7 9: OBJECT IDENTIFIER '2.16.840.1.101.3.4.4.1'
: }
18 64: OCTET STRING
: 00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
: 10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f
: 20 21 22 23 24 25 26 27 28 29 2a 2b 2c 2d 2e 2f
: 30 31 32 33 34 35 36 37 38 39 3a 3b 3c 3d 3e 3f
: }
The following is an example of a ML-KEM-768 private key from the same
seed.
-----BEGIN PRIVATE KEY-----
MFICAQAwCwYJYIZIAWUDBAQCBEAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
HB0eHyAhIiMkJSYnKCkqKywtLi8wMTIzNDU2Nzg5Ojs8PT4/
-----END PRIVATE KEY-----
0 82: SEQUENCE
2 2: INTEGER 0
5 11: SEQUENCE {
7 9: OBJECT IDENTIFIER '2.16.840.1.101.3.4.4.2'
: }
18 64: OCTET STRING
: 00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
: 10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f
: 20 21 22 23 24 25 26 27 28 29 2a 2b 2c 2d 2e 2f
: 30 31 32 33 34 35 36 37 38 39 3a 3b 3c 3d 3e 3f
: }
The following is an example of a ML-KEM-1024 private key from the
same seed.
-----BEGIN PRIVATE KEY-----
MFICAQAwCwYJYIZIAWUDBAQDBEAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob
HB0eHyAhIiMkJSYnKCkqKywtLi8wMTIzNDU2Nzg5Ojs8PT4/
-----END PRIVATE KEY-----
0 82: SEQUENCE
2 2: INTEGER 0
5 11: SEQUENCE {
7 9: OBJECT IDENTIFIER '2.16.840.1.101.3.4.4.3'
: }
18 64: OCTET STRING
: 00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
: 10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f
: 20 21 22 23 24 25 26 27 28 29 2a 2b 2c 2d 2e 2f
: 30 31 32 33 34 35 36 37 38 39 3a 3b 3c 3d 3e 3f
: }
| NOTE: The private key is the seed and all three examples keys
| use the same seed; therefore, the private above are the same
| except for the OID used to represent the ML-KEM algorithm's
| security strength.
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-----
0 818: SEQUENCE {
4 11: SEQUENCE {
6 9: OBJECT IDENTIFIER '2.16.840.1.101.3.4.4.1'
: }
17 801: BIT STRING
: 00 39 95 81 5e 59 7d 10 43 55 cf 29 aa 53 33 c9
: 32 51 86 9d 5b cd be 48 71 24 f6 02 b8 b6 a6 6c
: 7f 0a c0 76 b0 c6 2e fa 32 81 53 e7 ca 57 01 69
: 9f 13 05 f1 e6 bc 6f 90 b0 e4 9b 69 35 12 b6 ce
: 99 2a 8b 80 16 dd fc 1a 66 2c 7e 3f 96 19 cb d8
: 69 dd 77 1a f3 08 96 cc d5 91 8a c6 cb 77 46 6c
: 5e 77 99 96 d6 7f f9 aa bc 97 50 3f 2c 7b 7e 2d
: 00 0d 86 45 0f b1 80 7c a4 ca bd a4 65 82 5a 31
: c7 89 a1 b7 a4 91 ab 38 72 76 5d 32 0d 0b 71 92
: 0f a2 13 c9 40 93 41 6b 83 b8 12 4e 69 f6 5e 62
: cb 50 00 dc c3 7a a9 a0 ff f7 39 70 c4 77 2f 35
: 7d 24 18 9c a6 f5 30 55 68 c0 e2 37 6a 37 62 a6
: 8c 60 5e 56 3c 5d 20 95 72 e0 fc 75 32 ca 29 47
: 29 53 55 67 b5 fc 41 3c 5e 87 92 d2 46 45 36 cc
: 80 8f 98 ad d7 46 64 f1 41 56 6f 90 16 a9 0a 54
: 18 29 a9 8a 04 64 ce 41 a8 bb 44 c2 d4 fa 3c 2c
: 20 94 60 72 8e f1 4a 1a 7c 4c 9b 98 d1 22 03 b4
: cc 35 29 16 0a 9a b2 d7 83 8f 7f f6 b5 3a e0 5a
: a3 1a 7d 64 6b 7a fa 6c 45 93 25 26 a3 c3 75 56
: 19 be 99 4c 21 1c 2a 31 c0 5b 34 47 83 6c b2 15
: 0b e1 82 9d ae 6b 04 c5 53 5c ff 54 6e 39 2b a7
: 97 41 17 20 f9 24 f4 90 a5 ac 54 95 f2 13 56 d5
: 50 b7 82 a6 4c 16 88 b6 b6 55 bc c7 84 21 97 a4
: 34 c2 f6 56 3b 5b 7f 09 a7 8b cc 48 82 32 78 35
: 61 d1 6f 4c ba b6 75 54 00 05 07 81 57 0c 66 60
: 4b 81 7a d1 25 22 94 73 6e 8b 01 86 1a 4b 5a 74
: 51 9b 8b 6f e5 14 89 a5 07 23 92 e5 87 62 6c 71
: 37 76 57 5d 33 80 6a 1c 8e 27 32 af 97 c2 68 0f
: 51 66 63 31 c4 eb 8b bc 04 31 c4 f9 68 32 da f1
: b3 c4 55 28 fb a1 53 f6 c7 8b 1c 19 87 02 94 7c
: cd 33 77 27 a4 6f b5 3b a1 1d e5 cb 41 91 34 68
: 59 51 6c b6 ad 72 40 0f 3c f2 09 b2 36 ae f3 5a
: 58 0a c8 7e b3 e3 0f af d6 69 73 ca 8a 7d d2 67
: 5a f4 1f 7a 17 b6 14 33 cd 1a f8 0f 77 08 86 9f
: 66 54 88 49 79 80 b1 ac 10 a0 cd cb 63 6a 00 ed
: 86 81 b3 5e 42 91 24 ca 80 35 07 25 b8 5f 83 a5
: ea c3 a4 a3 cc 16 00 90 3e 65 29 35 60 b9 b3 36
: e5 af 0d 52 9d ac 1a 04 81 19 30 2c b7 a9 bc c1
: 10 b9 48 51 bf 02 11 7f 19 9d c4 85 a8 52 b7 47
: 3f 09 b8 31 a6 83 1d 5b 54 c0 b7 90 d2 25 cf 6b
: b9 2d 94 62 a2 6c db 33 dd a5 12 3c 7a af 0e 26
: a0 b8 36 55 ee a2 8b f3 a8 07 47 25 01 8f d6 ba
: e4 b6 01 cf 61 ba ab 71 a7 a3 d3 51 97 a3 43 e7
: 4b 4a 27 2c 12 5d 54 08 96 42 6d 85 b7 95 8d 3b
: 38 a6 ba 98 7e c3 72 25 c7 b4 4c db 12 dd e4 53
: 9b 4a b0 82 36 36 83 f0 4b f7 a0 9c c5 c4 1d fe
: 83 0a 1b 16 2e 0b 32 43 34 36 2f 08 4a 14 46 77
: 23 34 4b ad d0 00 f8 d8 c5 37 c4 8f 99 8f 05 30
: 7c eb d1 ed e0 b8 1c 3b c5 9a 06 5a 1b 6d 63 b2
: 6c
: }
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-----
0 1202: SEQUENCE {
4 11: SEQUENCE {
6 9: OBJECT IDENTIFIER '2.16.840.1.101.3.4.4.2'
: }
17 801: BIT STRING
: 00 29 8a a1 0d 42 3c 8d da 06 9d 02 bc 59 e6 cd
: f0 3a 09 6b 8b 3d a4 ca b9 b8 0c a4 a1 49 07 67
: 2c ce f1 ec 4f af 23 4a 0b c5 b7 e9 d4 73 f2 b3
: 13 3b 3b 26 a1 d1 75 cb 67 a7 80 59 19 69 9c 02
: f7 65 31 b9 9c 5f 89 18 07 04 bb 4c a4 53 5c 5b
: 89 72 67 9c 66 0a 07 c5 e5 14 b8 70 09 c8 62 eb
: 8f 51 57 69 5e fb 3f c4 0a 9d ef 6b 81 c1 cc 02
: a2 49 ae 4f 09 4a d0 d9 bd 34 85 c1 c1 c6 80 80
: 52 0a 7c 8c 63 20 32 ce e7 38 15 4e 5c 51 76 c0
: 7d a5 60 24 77 6a 43 0f e7 6e ac f6 65 a3 f7 b8
: 32 10 22 15 bc 82 f1 09 39 c8 35 57 04 33 6a 8f
: ac 1d 81 e4 bb 04 85 aa 5d 7c 74 d6 b5 9b be 5c
: 5e 97 2a 0d 8b ac 41 1b 55 b5 d5 55 7c d6 80 a1
: a8 f7 1b 4e b8 6b c4 8c 9a 05 09 73 1a 54 bd 9d
: 72 90 b2 79 63 e4 37 2d c9 b1 99 cf dc ac 0b 01
: ac d2 8a 62 39 51 12 e4 c4 36 48 d6 22 c4 8c 82
: 34 d0 14 40 e8 cc 37 6c 92 7f 23 a5 af c9 ac 04
: 74 c6 62 27 4e 42 45 25 c8 55 2e ce 3b 3f e2 65
: 16 de 90 1b c7 d5 15 bd e8 95 58 e6 26 c9 5c 80
: b9 33 42 f8 01 00 04 f3 9e 6c 6c 94 87 1c 5e 34
: 4c ab 39 66 c8 35 f9 a9 6a 59 af d3 1c 40 28 6b
: 38 b1 c1 a7 84 70 ba b9 47 51 89 34 45 3c e8 67
: 36 a9 19 f1 f5 a6 d5 10 a8 6f 54 54 fc 39 80 cb
: 5c 76 5b d2 bd 5f 7b 36 b1 41 0d 66 35 c8 ce b4
: 7c 4d da 0d 76 a2 8e ac 93 9c 71 c3 02 48 04 86
: 6c 71 62 66 58 44 21 63 c2 c2 21 17 e5 0a ce fc
: e6 37 8a 98 56 52 30 2a 4e f0 c2 ce 0c c7 16 b7
: 79 6e 2b 6b 2e 37 77 df a1 ac 3d a2 59 a3 1b 5a
: 9b 53 0f 8c b6 38 a8 1a 62 ac 30 18 49 ab af 95
: a7 30 1b da 30 06 89 09 bf db 7e 67 db cc bb 38
: a5 55 1a 25 b1 a3 a0 f6 85 74 8a d5 75 3d 88 80
: f0 01 6c 62 74 86 16 63 84 c5 57 1f e2 36 59 00
: 36 4d 03 83 11 e2 d8 75 db 36 66 86 93 2b 5e c6
: 02 43 0a 36 9e 87 a6 ef 5c 33 87 86 65 78 25 bd
: 4c 05 7a ce b9 23 eb 09 35 e6 90 5e 63 b4 ce d7
: f8 08 57 a7 73 dd 64 b1 50 d2 66 12 ea 9a c1 20
: 52 db 20 17 bf 18 43 cc b4 b3 28 1b 69 0d c7 28
: ad fa 85 c0 02 81 b8 e3 c0 92 87 33 5f 85 6b 4f
: c2 89 2f 69 a2 f5 79 21 ad a0 19 14 c4 09 88 66
: 2d 57 76 96 62 a7 86 35 1b 9b 66 49 3d ab 79 59
: 4d 98 6d e2 10 0d 65 ba 0f f4 ea 58 b8 15 38 d2
: 4a 44 35 a2 58 fa c2 54 04 aa 7f 41 f6 58 b1 38
: 50 65 e1 58 dc b6 01 15 73 27 20 f4 04 59 aa ac
: 15 e4 06 95 3a 90 ac 52 99 7d 1c cd 07 00 60 ef
: c6 5d b9 e6 53 35 44 67 fa d5 6e c7 13 c8 6e 75
: 40 c4 23 ac f2 66 9f 52 fa 6f 4a c6 88 8d 87 1e
: f3 e8 47 c0 29 a8 aa fb b9 2e 17 b2 4a a0 79 b1
: f4 19 ba 61 75 b4 42 af b1 19 09 d4 a5 6b 70 a0
: 33 5b 28 73 92 18 aa 7c 93 48 e2 c3 c2 f3 eb 3d
: 15 a4 1e 64 17 c0 dd 94 bf eb 21 41 9b 31 1a 7b
: b1 3a 18 0b be 83 32 18 a9 a6 b1 74 47 cc 85 f2
: 25 85 95 87 a7 30 77 04 9a cb cf d4 4d 0f 02 54
: 38 e1 5d 15 38 27 0d 58 6e 1b f8 31 92 a9 45 9c
: f6 3c 0e 97 2f 85 29 76 79 83 1e cf 12 15 09 85
: 1c b8 34 0f 6f 10 7b 0f a1 a0 ef d1 b3 6a 81 89
: bc 08 5c 4f 5c b7 84 e5 53 f4 1b 91 8f 80 39 7c
: e1 95 6f 78 5b ee 37 7c a9 aa 8b e6 99 8a da 30
: c2 6b 7c 3d 8c 6b 55 25 4c c9 62 03 b2 0c 42 ae
: e0 ac 4e 1e bb 40 8e 49 a9 e3 f8 79 d0 ab 07 85
: eb 70 25 42 5d 13 05 a2 29 9c 01 5e 12 0d 16 3b
: 0e 19 49 4c e5 72 53 d0 24 6d 18 27 45 cb 81 97
: ab 74 38 b3 c1 bb 79 72 be c5 a3 06 eb a3 56 78
: 55 c0 14 69 9f ef 65 ae 54 c7 70 a0 d8 5c 18 40
: 0c f6 42 ae dc 66 07 77 ba 4b 13 85 02 bd 5a 78
: 12 f6 21 f8 4a 48 29 6b 98 dd 43 22 b6 f1 58 28
: b8 a8 f0 e0 0a 8b a4 4a 53 c3 a8 b1 43 57 1b 07
: 40 ab d5 67 da f1 cd e9 c7 9c 20 4b 6d 5e 25 9d
: 17 66 a3 1b bb cb 4e 6a 05 cf 45 02 17 6b 30 1c
: 1c 2f 41 24 77 50 15 7b ce c8 5e 80 9b 30 a4 d6
: 0d 77 47 cd d0 f5 b9 9a a8 c8 26 98 75 17 79 3a
: aa 80 80 a0 b1 24 a8 55 8d f7 2b be 37 b7 5f 4e
: db b6 be 82 16 d6 c6 33 fb 2b 22 80 e2 51 13 d8
: 69 5e 43 48 1c 3e eb 39 7e b1 92 50 52 29 b6 7a
: 20 1e a8 93 c3 e2 cb 32 da 8b c3 42 fa 4d ea 05
: 78
: }
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-----
0 1586: SEQUENCE {
4 11: SEQUENCE {
6 9: OBJECT IDENTIFIER '2.16.840.1.101.3.4.4.3'
: }
17 1569: BIT STRING
: 00 4b 94 c2 94 50 11 11 91 82 3b 35 14 c9 ac 1e
: a3 d9 82 5c cb 86 39 3a 2d fb 04 65 4f a2 19 2d
: 37 bf ad 1c 49 7c 65 02 ee e5 ca 80 a7 3b fc e0
: ba f5 a5 4a 88 58 5a 40 13 97 a3 d2 32 f4 26 a7
: af b0 82 bc 21 a4 43 17 09 0e aa c7 59 2c 2e a8
: 8a 65 3c 44 91 ea 19 39 31 33 5f 52 e9 89 a3 c4
: cc 56 d9 c5 53 73 2d 57 c4 70 fb 41 ab 75 9b 65
: d2 d0 44 45 38 2f cd 9c 4e 34 4a 11 28 fa 9e 11
: e0 43 58 e1 92 ed 01 4b 23 23 2a 7e e2 b2 2e 23
: 71 7f 44 11 1e e3 35 75 39 9c 37 64 6d a9 81 3e
: c9 b2 12 af e9 4e 5d c5 c2 33 0a 72 94 cc 1f 42
: 34 a6 d3 fb b4 f1 68 5a b8 89 2c 04 ac b1 7c d1
: c1 70 d7 b0 61 1b 6a 71 76 c7 94 cc 8c 67 f5 5f
: c9 23 c2 ad 20 31 00 f3 65 99 18 82 c3 02 43 d7
: 78 13 84 3b 5e c7 c9 64 03 22 63 70 60 92 ec f0
: 0c 75 16 be 64 e4 59 8c a4 22 6c 06 9b b5 e6 7e
: 41 75 cf 22 86 c8 dd 5c 48 8a 6c 58 61 f3 1b aa
: 0b d0 26 94 70 e8 b5 51 dd 3b cd 38 c8 6c 12 f9
: cd b1 76 c7 7d c8 b6 c0 2a 70 1f 47 89 02 c8 55
: 3f 69 4c 0d 82 72 7b 4c 4a 5c 2c 10 41 21 2a a1
: 27 48 08 b8 21 11 b3 77 ec 75 21 4e 9b 19 78 f7
: 60 04 d4 13 9d 98 61 3f 4b 8e 98 d2 0a f7 b5 34
: 07 3a 50 9a 95 9b 7a 75 64 f9 b4 0c a2 18 bf 61
: 82 93 20 a8 50 20 17 95 4d 32 8d 7a c6 c7 69 ec
: 29 70 07 56 e7 b0 68 5b 34 0d 5e 11 80 59 50 4a
: 49 a9 a5 0a 10 19 8e b1 0a 57 84 67 8e b4 27 d7
: b4 ba bb 95 52 93 3b 06 28 97 97 3e 13 18 ea f0
: a0 ea c3 75 84 a6 54 01 b1 70 3e 04 2a cc d8 37
: 53 14 83 f2 41 ca dc d1 c1 d3 78 11 9e 69 44 29
: db 19 9a c8 91 e4 c5 34 37 57 08 5b b3 ae 78 36
: 67 35 0c 44 58 d9 76 72 e8 61 e8 0b 1d 26 79 51
: 0e a3 a6 f2 36 0c 77 a4 69 42 c7 a0 6a 55 4d 22
: 80 80 c8 4b 47 ae f1 4d b1 76 20 cb 16 c0 6a b3
: 0a 1b e4 cd a7 08 2b e9 f8 7e 9c 21 1c 46 91 63
: 49 a5 ba 8e aa 52 01 c7 29 4a 3c 08 85 b5 3b 65
: 74 52 10 88 25 ec 64 6c 90 a0 46 12 32 4e e7 d0
: 31 af e5 34 31 32 cb ef 67 b6 ef b1 a5 ec 28 09
: b7 73 53 8c e7 7b 3d 8b 04 eb 0b 3c 22 56 01 1e
: 4c 71 6c 19 a8 ba 07 52 bf 71 49 21 17 64 9f 06
: 15 c3 29 0f c2 9a 46 fd e4 bd 52 db 92 86 d6 03
: 38 82 44 25 9c 15 a7 ac 2b 64 0a 60 cc 03 37 6a
: 58 41 a3 fb 8a 47 35 68 fa 9b 1a 26 72 15 f3 4c
: 01 69 7b 0f 0e 62 71 75 d7 21 05 b7 70 7c 29 b9
: e6 14 bd c3 3a 6f 6c 81 8a 95 37 0b 42 78 82 d7
: b4 76 79 6a 9e c6 eb 99 32 74 cd 9b 23 91 a8 2b
: a4 5e 33 93 d2 e9 ae 97 21 ca 9d 6c 1b 98 8b 58
: 27 71 3f 90 a6 58 5d e9 43 35 28 c0 2b 03 ce 10
: bb 5f 72 01 38 d0 fb b4 c3 0c 12 66 b9 18 e5 29
: 25 df e1 7b 37 f9 5d 22 bc a5 4f 47 59 19 ac 85
: 90 98 c0 f0 d0 8a c5 87 5e f2 9b 56 fd 14 1e 6e
: f1 5f 70 0a 0b 66 f3 95 95 c5 88 17 73 73 c4 66
: 9b 21 bc 07 1e 4c 3a a5 f0 b4 a3 1b 62 58 f3 5d
: a2 4a c3 cd 29 c7 f2 09 24 10 c5 07 83 55 b1 38
: fb 53 a6 b9 ae 6e 0b 9c 08 24 3e 7b aa 45 c4 73
: 76 eb 8c 7f 13 d4 cf 51 aa 73 6f a3 15 40 c9 24
: 1f 37 0d a5 44 bf 9f 9c 28 d9 a5 7e 2f 2a 7c a9
: 5a 4e 4b 46 6e 64 1a b3 bc c7 6a df 11 39 d5 67
: a6 f1 2b 52 f3 a6 5e 7e c0 aa e2 6b ca a8 c5 58
: 33 b0 4e 59 99 8e bc 9a 19 30 fb b6 d2 23 3c 53
: d2 c1 f8 b9 51 8e 3c 2d e7 3a 19 de e6 b3 80 a5
: b3 29 71 cf 64 e1 29 fd 6c 1f a6 e7 5d 4a 23 45
: 01 e9 66 dd 3a 54 0a f5 c8 f4 f3 4a 6b 4a 25 3e
: e2 84 92 56 6d 5e 67 c6 f5 58 55 fc b0 50 6f b0
: 6c 15 67 44 d9 a0 3a 31 a2 6f a9 4c ad 14 f1 57
: b7 f3 03 d0 7a 69 c7 73 76 8f cb 4d 07 9c 09 05
: 97 03 a0 c3 a9 4d e4 b9 9e a3 a2 f1 65 83 d0 f9
: 17 0a 39 50 db 07 b4 f0 bc 30 80 29 27 f9 f7 96
: 1b 62 59 89 26 36 a9 50 2a 27 05 30 36 37 79 9d
: d3 44 da 45 1c 1c f7 bf 67 84 0c eb 30 79 ab 8c
: 6b 8c 19 27 f6 40 53 c6 12 45 0c 45 c9 e6 03 bc
: 16 66 6e 59 6b 34 71 e1 03 b6 f1 54 47 42 4d 17
: 02 20 48 11 1f fb d3 7e 1c 67 0f 64 f1 4b 8a 7b
: 32 b9 4c 1a 49 b4 5d d2 fc 38 cd 52 89 d9 10 ad
: 63 60 2c f5 e1 30 42 c6 4a c6 79 7b 89 fb 55 1a
: d0 8e 05 a9 2d 20 0c cc b7 e7 12 ef 23 c9 31 2c
: b3 50 f0 29 ab 53 7e 28 73 47 fd 30 75 ac 10 90
: 6a 78 3f 1c 6c 07 cc b8 8f 41 22 8c 4b e1 c6 40
: f7 90 b5 c3 a5 d5 d3 ca 79 24 95 d7 4b c4 61 56
: 26 58 c0 7a c6 00 27 6b 92 4a b5 bc 9b e1 f0 49
: 4c b7 6f 82 f4 60 a7 48 09 72 66 33 81 e1 69 99
: 60 61 d7 99 85 9e c5 4d 4f 5c a5 c4 11 c0 1d b1
: 59 7b 16 59 77 66 9d e1 3a 92 8a 34 af ba c2 58
: fe a8 c4 76 42 39 c9 42 1d c3 11 9b f5 b4 76 99
: 20 69 78 32 7b 1c 53 45 ef 74 6a 79 83 84 1f 05
: 6e 25 34 10 0a b2 4d 4e 9a bb d0 b1 7c 6a 95 bd
: 4c 3c 0e 40 f6 9e 16 12 ac ee b2 8b 99 08 6c 95
: 11 6e 72 04 27 38 93 39 0b f4 6b 89 9b 36 28 6b
: 0e bf 19 47 bb 98 84 f7 32 ca 27 da 82 b1 9b 5d
: c0 cc 7f 88 85 71 49 10 88 8b 23 10 c4 f9 31 9d
: 41 0b 34 e6 43 3b 90 03 e2 17 6b b9 95 25 74 56
: 10 6e 89 52 16 3b 8b a5 92 53 0c c5 aa 0a eb 43
: ad 39 8f e9 e9 7b aa 52 3d 7a 44 31 67 7c 3d 3a
: f0 71 9e 47 5d b8 5c a9 5a f5 08 9b ea be b0 5b
: 2f aa b4 89 6b a6 0f 81 c8 84 72 a5 7b 46 a8 28
: 82 6a 0c df b4 46 f8 18 91 82 d2 bf 5e ac 4e c1
: cc 5d ea f5 99 c8 a1 3e 48 23 54 06 d1 7f fd dc
: 83 44 b6 c6 69 84 a8 68 aa 92 fa 02 22 7a 08 69
: 50 eb 0c 87 01 ed 58 dc 62 87 76 b9 83 88 2e 11
: 75
: }
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 Certificate
TODO insert ASN.1 Pretty Print
-----BEGIN CERTIFICATE-----
TODO Certificate
-----END CERTIFICATE-------
Acknowledgments
TODO acknowledge.
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
Datatracker
draft-ietf-lamps-kyber-certificates-06
This is an older version of an Internet-Draft whose latest revision state is "Active".
| Document | Document type |
This is an older version of an Internet-Draft whose latest revision state is "Active".
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| Authors | Sean Turner , Panos Kampanakis , Jake Massimo , Bas Westerbaan | ||
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| Additional resources | Mailing list discussion |