| Internet-Draft | ML-KEM in Certificates | November 2024 |
| Turner, et al. | Expires 7 May 2025 | [Page] |
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.¶
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/.¶
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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.¶
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].¶
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.¶
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
}
¶
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.¶
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.¶
Appendix C.2 contains examples for ML-KEM public keys encoded using the textual encoding defined in [RFC7468].¶
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,
...
}
¶
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].¶
The Security Considerations section of [RFC5280] applies to this specification as well.¶
For the ASN.1 Module in Appendix A, IANA is requested to assign an object identifier (OID) for the module identifier (TBD2) 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).¶
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(TBD2) }
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>¶
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.¶
| 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 |
This appendix contains examples of ML-KEM public keys, private keys and certificates.¶
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 '2.16.840.1.101.3.4.4.2'
: }
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 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----- 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-----¶
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----- 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-----¶
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-------¶
TODO insert ASN.1 Pretty Print¶
-----BEGIN CERTIFICATE----- TODO Certificate -----END CERTIFICATE-------¶
TODO acknowledge.¶