| Internet-Draft | ML-DSA in Certificates | November 2024 |
| Massimo, et al. | Expires 9 May 2025 | [Page] |
Digital signatures are used within X.509 certificates, Certificate Revocation Lists (CRLs), and to sign messages. This document describes the conventions for using FIPS 204, the Module-Lattice-Based Digital Signature Algorithm (ML-DSA) in Internet X.509 certificates and certificate revocation lists. The conventions for the associated signatures, subject public keys, and private key are also described.¶
This note is to be removed before publishing as an RFC.¶
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The Module-Lattice-Based Digital Signature Algorithm (ML-DSA) is a quantum-resistant digital signature scheme standardized by the US National Institute of Standards and Technology (NIST) PQC project [NIST-PQC] in [FIPS204]. This document specifies the use of the ML-DSA in Public Key Infrastructure X.509 (PKIX) certificates and Certificate Revocation Lists (CRLs) at three security levels: ML-DSA-44, ML-DSA-65, and ML-DSA-87.¶
[FIPS204] defines two variants of ML-DSA: a pure and a prehash variant. Only the former is specified in this document. The pure variant of ML-DSA supports the typical prehash flow: one cryptographic module can compute the hash mu on line 6 of algorithm 7 of [FIPS204] and pass it to a second module to finish the signature. The first module only needs access to the full message and the public key, whereas the second module only needs access to hash mu and the private key.¶
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 OIDs are:¶
id-ml-dsa-44 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithm(4) sigAlgs(3) id-ml-dsa-44(17) }
id-ml-dsa-65 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithm(4) sigAlgs(3) id-ml-dsa-65(18) }
id-ml-dsa-87 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithm(4) sigAlgs(3) id-ml-dsa-87(19) }
¶
The contents of the parameters component for each algorithm MUST be absent.¶
ML-DSA is a digital signature scheme built upon the Fiat-Shamir-with-aborts framework [Fiat-Shamir]. The security is based upon the hardness of lattice problems over module lattices [Dilithium]. ML-DSA provides three parameter sets for the NIST PQC security categories 2, 3 and 5.¶
Signatures are used in a number of different ASN.1 structures. As shown in the ASN.1 representation from [RFC5280] below, in an X.509 certificate, a signature is encoded with an algorithm identifier in the signatureAlgorithm attribute and a signatureValue attribute that contains the actual signature.¶
Certificate ::= SIGNED{ TBSCertificate }
SIGNED{ToBeSigned} ::= SEQUENCE {
toBeSigned ToBeSigned,
algorithmIdentifier SEQUENCE {
algorithm SIGNATURE-ALGORITHM.
&id({SignatureAlgorithms}),
parameters SIGNATURE-ALGORITHM.
&Params({SignatureAlgorithms}
{@algorithmIdentifier.algorithm})
OPTIONAL
},
signature BIT STRING (CONTAINING SIGNATURE-ALGORITHM.&Value(
{SignatureAlgorithms}
{@algorithmIdentifier.algorithm}))
}
¶
Signatures are also used in the CRL list ASN.1 representation from [RFC5280] below. In a X.509 CRL, a signature is encoded with an algorithm identifier in the signatureAlgorithm attribute and a signatureValue attribute that contains the actual signature.¶
CertificateList ::= SIGNED{ TBSCertList }
¶
The identifiers defined in Section 2 can be used as the AlgorithmIdentifier in the signatureAlgorithm field in the sequence Certificate/CertificateList and the signature field in the sequence TBSCertificate/TBSCertList in certificates and CRLs, respectively, [RFC5280]. The parameters of these signature algorithms MUST be absent, as explained in Section 2.¶
The signatureValue field contains the corresponding ML-DSA signature computed upon the ASN.1 DER encoded tbsCertificate/tbsCertList [RFC5280].¶
Conforming Certification Authority (CA) implementations MUST specify the algorithms explicitly by using the OIDs specified in Section 2 when encoding ML-DSA signatures in certificates and CRLs. Conforming client implementations that process certificates and CRLs using ML-DSA MUST recognize the corresponding OIDs. Encoding rules for ML-DSA signature values are specified Section 2.¶
When the id-ml-dsa identifier appears in the algorithm field as an AlgorithmIdentifier, the encoding MUST omit the parameters field. That is, the AlgorithmIdentifier SHALL be a SEQUENCE of one component, the OID id-ml-dsa.¶
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 contains example ML-DSA private keys encoded using the textual encoding defined in [RFC7468].¶
The intended application for the key is indicated in the keyUsage certificate extension; see Section 4.2.1.3 of [RFC5280]. If the keyUsage extension is present in a certificate that indicates id-ml-dsa in the SubjectPublicKeyInfo, then the at least one of following MUST be present:¶
digitalSignature; or nonRepudiation; or keyCertSign; or cRLSign.¶
If the keyUsage extension is present in a certificate that indicates id-ml-dsa in the SubjectPublicKeyInfo, then the following MUST NOT be present:¶
keyEncipherment; or dataEncipherment; or keyAgreement; or encipherOnly; or decipherOnly.¶
Requirements about the keyUsage extension bits defined in [RFC5280] still apply.¶
An ML-DSA private key is encoded by storing its 32-octet seed in the privateKey field as follows.¶
[FIPS204] specifies two formats for an ML-DSA private key: a 32-octet
seed (xi) and an (expanded) private key. The expanded private key (and public key)
is computed from the seed using ML-DSA.KeyGen_internal(xi) (algorithm 6).¶
"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 32-octet seed. The publicKey field SHOULD be omitted because the public key can be computed as noted earlier in this section.¶
Appendix C contains example ML-DSA private keys encoded using the textual encoding defined in [RFC7468].¶
For the ASN.1 module in {asn1}, IANA is requested to assign an object identifier (OID) for the module identifier (TBD1) with a Description of "id-mod-x509-ml-dsa-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).¶
The Security Considerations section of [RFC5280] applies to this specification as well.¶
The digital signature scheme defined within this document are modeled under strongly existentially unforgeable under chosen message attack (SUF-CMA). For the purpose of estimating security strength, it has been assumed that the attacker has access to signatures for no more than 2^{64} chosen messages.¶
ML-DSA offers both deterministic and randomized signing. By default ML-DSA signatures are non-deterministic. The private random seed (rho') for the signature is pseudorandomly derived from the signer’s private key, the message, and a 256-bit string, rnd - where rnd should be generated by an approved RBG. In the deterministic version, rng is instead a 256-bit constant string. The source of randomness in the randomized mode has been "hedged" against sources of poor entropy, by including the signers private key and message into the derivation. The primary purpose of rnd is to facilitate countermeasures to side-channel attacks and fault attacks on deterministic signatures.¶
In the design of ML-DSA, care has been taken to make side-channel resilience easier to achieve. For instance, ML-DSA does not depend on Gaussian sampling. Implementations must still take great care not to leak information via varius side channels. While deliberate design decisions such as these can help to deliver a greater ease of secure implementation - particularly against side-channel attacks - it does not necessarily provide resistance to more powerful attacks such as differential power analysis. Some amount of side-channel leakage has been demonstrated in parts of the signing algorithm (specifically the bit-unpacking function), from which a demonstration of key recovery has been made over a large sample of signatures. Masking countermeasures exist for ML-DSA, but come with a performance overhead.¶
A fundamental security property also associated with digital signatures is non-repudiation. Non-repudiation refers to the assurance that the owner of a signature key pair that was capable of generating an existing signature corresponding to certain data cannot convincingly deny having signed the data. The digital signature scheme ML-DSA possess three security properties beyond unforgeability, that are associated with non-repudiation. These are exclusive ownership, message-bound signatures, and non-resignability. These properties are based tightly on the assumed collision resistance of the hash function used (in this case SHAKE-256).¶
Exclusive ownership is a property in which a signature sigma uniquely determines the public key and message for which it is valid. Message-bound signatures is the property that a valid signature uniquely determines the message for which it is valid, but not necessarily the public key. Non-resignability is the property in which one cannot produce a valid signature under another key given a signature sigma for some unknown message m. These properties are not provided by classical signature schemes such as DSA or ECDSA, and have led to a variety of attacks such as Duplicate-Signature Key Selection (DSKS) attacks , and attacks on the protocols for secure routing. A full discussion of these properties in ML-DSA can be found at [CDFFJ21].¶
These properties are dependent, in part, on unambiguous public key serialization. It for this reason the public key structure defined in Section 4 is intentionally encoded as a single OCTET STRING.¶
This appendix includes the ASN.1 module [X680] for the ML-DSA. Note that as per [RFC5280], certificates use the Distinguished Encoding Rules; see [X690]. This module imports objects from [RFC5912] and [I-D.salter-lamps-cms-ml-dsa].¶
<CODE BEGINS>
X509-ML-DSA-2024
{ iso(1) identified-organization(3) dod(6)
internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-x509-ml-dsa-2024(TBD1) }
DEFINITIONS IMPLICIT TAGS ::=
BEGIN
-- EXPORTS ALL;
IMPORTS
PUBLIC-KEY, SIGNATURE-ALGORITHM
FROM AlgorithmInformation-2009 -- From [RFC5912]
{ iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-algorithmInformation-02(58) }
sa-ml-dsa-44, sa-ml-dsa-65, sa-ml-dsa-87,
pk-ml-dsa-44, pk-ml-dsa-65, pk-ml-dsa-87
FROM ML-DSA-Module-2024 -- From [I-D.salter-lamps-cms-ml-dsa]
{ iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9)
id-smime(16) id-mod(0) id-mod-ml-dsa-2024(TBD2) } ;
--
-- Expand SignatureAlgorithms from RFC 5912
--
SignatureAlgorithms SIGNATURE-ALGORITHM ::= {
sa-ml-dsa-44 |
sa-ml-dsa-65 |
sa-ml-dsa-87,
... }
--
-- Expand SignatureAlgorithms from RFC 5912
--
PublicKeys PUBLIC-KEY ::= {
pk-ml-dsa-44 |
pk-ml-dsa-65 |
pk-ml-dsa-87,
...
}
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 instead elected to define security levels by picking a reference scheme, which NIST expects to offer notable levels of resistance to both quantum and classical attack. To wit, an algorithm that achieves NIST PQC security level 1 must require computational resources to break the relevant security property, which are greater than those required for a brute-force key search on AES-128. Levels 3 and 5 use AES-192 and AES-256 as reference respectively. Levels 2 and 4 use collision search for SHA-256 and SHA-384 as reference.¶
The parameter sets defined for NIST security levels 2, 3 and 5 are listed in the Figure 1, along with the resulting signature size, public key, and private key sizes in bytes.¶
|=======+=======+=====+========+========+========| | Level | (k,l) | eta | Sig. | Public | Private| | | | | (B) | Key(B) | Key(B) | |=======+=======+=====+========+========+========| | 2 | (4,4) | 2 | 2420 | 1312 | 32 | | 3 | (6,5) | 4 | 3309 | 1952 | 32 | | 5 | (8,7) | 2 | 4627 | 2592 | 32 | |=======+=======+=====+========+========+========|
This appendix contains examples of ML-DSA public keys, private keys and certificates.¶
The following is an example of a ML-DSA-44 private key with hex seed 000102…1e1f:¶
-----BEGIN PRIVATE KEY----- MDICAQAwCwYJYIZIAWUDBAMRBCAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob HB0eHw== -----END PRIVATE KEY-----¶
0 49: SEQUENCE {
2 1: INTEGER 0
5 10: SEQUENCE {
7 8: OBJECT IDENTIFIER '2.16.840.1.101.3.4.17'
: }
17 32: 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
: }
¶
The following is an example of a ML-DSA-65 private key with hex seed 000102…1e1f:¶
-----BEGIN PRIVATE KEY----- MDICAQAwCwYJYIZIAWUDBAMSBCAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob HB0eHw== -----END PRIVATE KEY-----¶
0 49: SEQUENCE {
2 1: INTEGER 0
5 10: SEQUENCE {
7 8: OBJECT IDENTIFIER '2.16.840.1.101.3.4.18'
: }
17 32: 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
: }
¶
The following is an example of a ML-DSA-87 private key with hex seed 000102…1e1f:¶
-----BEGIN PRIVATE KEY----- MDICAQAwCwYJYIZIAWUDBAMTBCAAAQIDBAUGBwgJCgsMDQ4PEBESExQVFhcYGRob HB0eHw== -----END PRIVATE KEY-----¶
0 49: SEQUENCE {
2 1: INTEGER 0
5 10: SEQUENCE {
7 8: OBJECT IDENTIFIER '2.16.840.1.101.3.4.19'
: }
17 32: 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
: }
¶
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-DSA algorithm's security strength.¶
The following is the ML-KEM-44 public key corresponding to the private key in the previous section.¶
-----BEGIN PUBLIC KEY----- MIIFMjALBglghkgBZQMEAxEDggUhANeytHJUquDbReeTDUqY0sl9jxOX0Xidr6Fw JLMW6b7JT8mUbULxm3mnQTu6oz5xSctC7VEVaTrAQfrLmIretf4OHYYxGEmVtZLD l9IpTi4U+QqkFLo4JomaxD9MzKy8JumoMrlRGNXLQzy++WYLABOOCBf2HnYsonTD atVU6yKqwRYuSrAay6HjjE79j4C2WzM9D3LlXf5xzpweu5iJ58VhBsD9c4A6Kuz+ r97XqjyyztpU0SvYzTanjPl1lDtHq9JeiArEUuV0LtHo0agq+oblkMdYwVrk0oQN kryhpQkPQElll/yn2LlRPxob2m6VCqqY3kZ1B9Sk9aTwWZIWWCw1cvYu2okFqzWB ZwxKAnd6M+DKcpX9j0/20aCjp2g9ZfX19/xg2gI+gmxfkhRMAvfRuhB1mHVT6pNn /NdtmQt/qZzUWv24g21D5Fn1GH3wWEeXCaAepoNZNfpwRgmQzT3BukAbqUurHd5B rGerMxncrKBgSNTE7vJ+4TqcF9BTj0MPLWQtwkFWYN54h32NirxyUjl4wELkKF9D GYRsRBJiQpdoRMEOVWuiFbWnGeWdDGsqltOYWQcf3MLN51JKe+2uVOhbMY6FTo/i svPt+slxkSgnCq/R5QRMOk/a/Z/zH5B4S46ORZYUSg2vWGUR09mWK56pWvGXtOX8 YPKx7RXeOlvvX4m9x52RBR2bKBbnT6VFMe/cHL501EiFf0drzVjyHAtlOzt2pOB2 plWaMCcYVVzGP3SFmqurkl8COGHKjND3utsocfZ9VTJtdFETWtRfShumkRj7ssij DuyTku8/l3Bmya3VxxDMZHsVFNIX2VjHAXw+kP0gwE5nS5BIbpNwoxoAHTL0c5ee SQZ0nn5Hf6C3RQj4pfI3gxK4PCW9OIygsP/3R4uvQrcWZ+2qyXxGsSlkPlhuWwVa DCEZRtTzbmdb7Vhg+gQqMV2YJhZNapI3w1pfv0lUkKW9TfJIuVxKrneEtgVnMWas QkW1tLCCoJ6TI+YvIHjFt2eDRG3v1zatOjcC1JsImESQCmGDM5e8RBmzDXqXoLOH wZEUdMTUG1PjKpd6y28Op122W7OeWecB52lX3vby1EVZwxp3EitSBOO1whnxaIsU 7QvAuAGz5ugtzUPpwOn0F0TNmBW9G8iCDYuxI/BPrNGxtoXdWisbjbvz7ZM2cPCV oYC08ZLQixC4+rvfzCskUY4y7qCl4MkEyoRHgAg/OwzS0Li2r2e8NVuUlAJdx7Cn j6gOOi2/61EyiFHWB4GY6Uk2Ua54fsAlH5Irow6fUd9iptcnhM890gU5MXbfoySl Er2Ulwo23TSlFKhnkfDrNvAUWwmrZGUbSgMTsplhGiocSIkWJ1mHaKMRQGC6RENI bfUVIqHOiLMJhcIW+ObtF43VZ7MEoNTK+6iCooNC8XqaomrljbYwCD0sNY/fVmw/ XWKkKFZ7yeqM6VyqDzVHSwv6jzOaJQq0388gg76O77wQVeGP4VNw7ssmBWbYP/Br IRquxDyim1TM0A+IFaJGXvC0ZRXMfkHzEk8J7/9zkwmrWLKaFFmgC85QOOk4yWeP cusOTuX9quZtn4Vz/Jf8QrSVn0v4th14Qz6GsDNdbpGRxNi/SHs5BcEIz9asJLDO t9y3z1H4TQ7Wh7lerrHFM8BvDZcCPZKnCCWDe1m6bLfU5WsKh8IDhiro8xW6WSXo 7e+meTaaIgJ2YVHxapZfn4Hs52zAcLVYaeTbl4TPBcgwsyQsgxI= -----END PUBLIC KEY-----¶
0 1329: SEQUENCE {
4 10: SEQUENCE {
6 8: OBJECT IDENTIFIER '2.16.840.1.101.3.4.17'
: }
16 1313: BIT STRING
00 d7 b2 b4 72 54 aa e0 db 45 e7 93 0d 4a 98 d2
c9 7d 8f 13 97 d1 78 9d af a1 70 24 b3 16 e9 be
c9 4f c9 94 6d 42 f1 9b 79 a7 41 3b ba a3 3e 71
49 cb 42 ed 51 15 69 3a c0 41 fa cb 98 8a de b5
fe 0e 1d 86 31 18 49 95 b5 92 c3 97 d2 29 4e 2e
14 f9 0a a4 14 ba 38 26 89 9a c4 3f 4c cc ac bc
26 e9 a8 32 b9 51 18 d5 cb 43 3c be f9 66 0b 00
13 8e 08 17 f6 1e 76 2c a2 74 c3 6a d5 54 eb 22
aa c1 16 2e 4a b0 1a cb a1 e3 8c 4e fd 8f 80 b6
5b 33 3d 0f 72 e5 5d fe 71 ce 9c 1e bb 98 89 e7
c5 61 06 c0 fd 73 80 3a 2a ec fe af de d7 aa 3c
b2 ce da 54 d1 2b d8 cd 36 a7 8c f9 75 94 3b 47
ab d2 5e 88 0a c4 52 e5 74 2e d1 e8 d1 a8 2a fa
86 e5 90 c7 58 c1 5a e4 d2 84 0d 92 bc a1 a5 09
0f 40 49 65 97 fc a7 d8 b9 51 3f 1a 1b da 6e 95
0a aa 98 de 46 75 07 d4 a4 f5 a4 f0 59 92 16 58
2c 35 72 f6 2e da 89 05 ab 35 81 67 0c 4a 02 77
7a 33 e0 ca 72 95 fd 8f 4f f6 d1 a0 a3 a7 68 3d
65 f5 f5 f7 fc 60 da 02 3e 82 6c 5f 92 14 4c 02
f7 d1 ba 10 75 98 75 53 ea 93 67 fc d7 6d 99 0b
7f a9 9c d4 5a fd b8 83 6d 43 e4 59 f5 18 7d f0
58 47 97 09 a0 1e a6 83 59 35 fa 70 46 09 90 cd
3d c1 ba 40 1b a9 4b ab 1d de 41 ac 67 ab 33 19
dc ac a0 60 48 d4 c4 ee f2 7e e1 3a 9c 17 d0 53
8f 43 0f 2d 64 2d c2 41 56 60 de 78 87 7d 8d 8a
bc 72 52 39 78 c0 42 e4 28 5f 43 19 84 6c 44 12
62 42 97 68 44 c1 0e 55 6b a2 15 b5 a7 19 e5 9d
0c 6b 2a 96 d3 98 59 07 1f dc c2 cd e7 52 4a 7b
ed ae 54 e8 5b 31 8e 85 4e 8f e2 b2 f3 ed fa c9
71 91 28 27 0a af d1 e5 04 4c 3a 4f da fd 9f f3
1f 90 78 4b 8e 8e 45 96 14 4a 0d af 58 65 11 d3
d9 96 2b 9e a9 5a f1 97 b4 e5 fc 60 f2 b1 ed 15
de 3a 5b ef 5f 89 bd c7 9d 91 05 1d 9b 28 16 e7
4f a5 45 31 ef dc 1c be 74 d4 48 85 7f 47 6b cd
58 f2 1c 0b 65 3b 3b 76 a4 e0 76 a6 55 9a 30 27
18 55 5c c6 3f 74 85 9a ab ab 92 5f 02 38 61 ca
8c d0 f7 ba db 28 71 f6 7d 55 32 6d 74 51 13 5a
d4 5f 4a 1b a6 91 18 fb b2 c8 a3 0e ec 93 92 ef
3f 97 70 66 c9 ad d5 c7 10 cc 64 7b 15 14 d2 17
d9 58 c7 01 7c 3e 90 fd 20 c0 4e 67 4b 90 48 6e
93 70 a3 1a 00 1d 32 f4 73 97 9e 49 06 74 9e 7e
47 7f a0 b7 45 08 f8 a5 f2 37 83 12 b8 3c 25 bd
38 8c a0 b0 ff f7 47 8b af 42 b7 16 67 ed aa c9
7c 46 b1 29 64 3e 58 6e 5b 05 5a 0c 21 19 46 d4
f3 6e 67 5b ed 58 60 fa 04 2a 31 5d 98 26 16 4d
6a 92 37 c3 5a 5f bf 49 54 90 a5 bd 4d f2 48 b9
5c 4a ae 77 84 b6 05 67 31 66 ac 42 45 b5 b4 b0
82 a0 9e 93 23 e6 2f 20 78 c5 b7 67 83 44 6d ef
d7 36 ad 3a 37 02 d4 9b 08 98 44 90 0a 61 83 33
97 bc 44 19 b3 0d 7a 97 a0 b3 87 c1 91 14 74 c4
d4 1b 53 e3 2a 97 7a cb 6f 0e a7 5d b6 5b b3 9e
59 e7 01 e7 69 57 de f6 f2 d4 45 59 c3 1a 77 12
2b 52 04 e3 b5 c2 19 f1 68 8b 14 ed 0b c0 b8 01
b3 e6 e8 2d cd 43 e9 c0 e9 f4 17 44 cd 98 15 bd
1b c8 82 0d 8b b1 23 f0 4f ac d1 b1 b6 85 dd 5a
2b 1b 8d bb f3 ed 93 36 70 f0 95 a1 80 b4 f1 92
d0 8b 10 b8 fa bb df cc 2b 24 51 8e 32 ee a0 a5
e0 c9 04 ca 84 47 80 08 3f 3b 0c d2 d0 b8 b6 af
67 bc 35 5b 94 94 02 5d c7 b0 a7 8f a8 0e 3a 2d
bf eb 51 32 88 51 d6 07 81 98 e9 49 36 51 ae 78
7e c0 25 1f 92 2b a3 0e 9f 51 df 62 a6 d7 27 84
cf 3d d2 05 39 31 76 df a3 24 a5 12 bd 94 97 0a
36 dd 34 a5 14 a8 67 91 f0 eb 36 f0 14 5b 09 ab
64 65 1b 4a 03 13 b2 99 61 1a 2a 1c 48 89 16 27
59 87 68 a3 11 40 60 ba 44 43 48 6d f5 15 22 a1
ce 88 b3 09 85 c2 16 f8 e6 ed 17 8d d5 67 b3 04
a0 d4 ca fb a8 82 a2 83 42 f1 7a 9a a2 6a e5 8d
b6 30 08 3d 2c 35 8f df 56 6c 3f 5d 62 a4 28 56
7b c9 ea 8c e9 5c aa 0f 35 47 4b 0b fa 8f 33 9a
25 0a b4 df cf 20 83 be 8e ef bc 10 55 e1 8f e1
53 70 ee cb 26 05 66 d8 3f f0 6b 21 1a ae c4 3c
a2 9b 54 cc d0 0f 88 15 a2 46 5e f0 b4 65 15 cc
7e 41 f3 12 4f 09 ef ff 73 93 09 ab 58 b2 9a 14
59 a0 0b ce 50 38 e9 38 c9 67 8f 72 eb 0e 4e e5
fd aa e6 6d 9f 85 73 fc 97 fc 42 b4 95 9f 4b f8
b6 1d 78 43 3e 86 b0 33 5d 6e 91 91 c4 d8 bf 48
7b 39 05 c1 08 cf d6 ac 24 b0 ce b7 dc b7 cf 51
f8 4d 0e d6 87 b9 5e ae b1 c5 33 c0 6f 0d 97 02
3d 92 a7 08 25 83 7b 59 ba 6c b7 d4 e5 6b 0a 87
c2 03 86 2a e8 f3 15 ba 59 25 e8 ed ef a6 79 36
9a 22 02 76 61 51 f1 6a 96 5f 9f 81 ec e7 6c c0
70 b5 58 69 e4 db 97 84 cf 05 c8 30 b3 24 2c 83
12
: }
¶
The following is the ML-KEM-65 public key corresponding to the private key in the previous section.¶
-----BEGIN PUBLIC KEY----- MIIHsjALBglghkgBZQMEAxIDggehAEhoPZGXjjHrPd24sEc0gtK4il9iWUn9j1il YeaWvUwn0Fs427Lt8B5mTv2Bvh6ok2iM5oqi1RxZWPi7xutOie5n0sAyCVTVchLK xyKf8dbq8DkovVFRH42I2EdzbH3icw1ZeOVBBxMWCXiGdxG/VTmgv8TDUMK+Vyuv DuLi+xbM/qCAKNmaxJrrt1k33c4RHNq2L/886ouiIz0eVvvFxaHnJt5j+t0q8Bax GRd/o9lxotkncXP85VtndFrwt8IdWX2+uT5qMvNBxJpai+noJQiNHyqkUVXWyK4V Nn5OsAO4/feFEHGUlzn5//CQI+r0UQTSqEpFkG7tRnGkTcKNJ5h7tV32np6FYfYa gKcmmVA4Zf7Zt+5yqOF6GcQIFE9LKa/vcDHDpthXFhC0LJ9CEkWojxl+FoErAxFZ tluWh+Wz6TTFIlrpinm6c9Kzmdc1EO/60Z5TuEUPC6j84QEv2Y0mCnSqqhP64kmg BrHDT1uguILyY3giL7NvIoPCQ/D/618btBSgpw1V49QKVrbLyIrh8Dt7KILZje6i jhRcne39jq8c7y7ZSosFD4lk9G0eoNDCpD4N2mGCrb9PbtF1tnQiV4Wb8i86QX7P H52JMXteU51YevFrnhMT4EUU/6ZLqLP/K4Mh+IEcs/sCLI9kTnCkuAovv+5gSrtz eQkeqObFx038AoNma0DAeThwAoIEoTa/XalWjreY00kDi9sMEeA0ReeEfLUGnHXP KKxgHHeZ2VghDdvLIm5Rr++fHeR7Bzhz1tP5dFa+3ghQgudKKYss1I9LMJMVXzZs j6YBxq+FjfoywISRsqKYh/kDNZSaXW7apnmIKjqV1r9tlwoiH0udPYy/OEr4GqyV 4rMpTgR4msg3J6XcBFWflq9B2KBTUW/u7rxSdG62qygZ4JEIcQ2DXwEfpjBlhyrT NNXN/7KyMQUH6S/Jk64xfal/TzCc2vD2ftmdkCFVdgg4SflTskbX/ts/22dnmFCl rUBOZBR/t89Pau3dBa+0uDSWjR/ogBSWDc5dlCI2Um4SpHjWnl++aXAxCzCMBoRQ GM/HsqtDChOmsax7sCzMuz2RGsLxEGhhP74Cm/3OAs9c04lQ7XLIOUTt+8dWFa+H +GTAUfPFVFbFQShjpAwG0dq1Yr3/BXG408ORe70wCIC7pemYI5uV+pG31kFtTzmL OtvNMJg+01krTZ731CNv0A9Q2YqlOiNaxBcnIPd9lhcmcpgM/o/3pacCeD7cK6Mb IlkBWhEvx/RoqcL5RkA5AC0w72eLTLeYvBFiFr96mnwYugO3tY/QdRXTEVBJ02FL 56B+dEMAdQ3x0sWHUziQWer8PXhczdMcB2SL7cA6XDuK1G0GTVnBPVc3Ryn8TilT YuKlGRIEUwQovBUir6KP9f4WVeMEylvIwnrQ4MajndTfKJVsFLOMyTaCzv5AK71e gtKcRk5E6103tI/FaN/gzG6OFrrqBeUTVZDxkpTnPoNnsCFtu4FQMLneVZE/CAOc QjUcWeVRXdWvjgiaFeYl6Pbe5jk4bEZJfXomMoh3TeWBp96WKbQbRCQUH5ePuDMS CO/ew8bg3jm8VwY/Pc1sRwNzwIiR6inLx8xtZIO4iJCDrOhqp7UbHCz+birRjZfO NvvFbqQvrpfmp6wRSGRHjDZt8eux57EakJhQT9WXW98fSdxwACtjwXOanSY/utQH P2qfbCuK9LTDMqEDoM/6Xe6y0GLKPCFf02ACa+fFFk9KRCTvdJSIBNZvRkh3Msgg LHlUeGR7TqcdYnwIYCTMo1SkHwh3s48Zs3dK0glcjaU7Bp4hx2ri0gB+FnGe1ACA 0zT32lLp9aWZBDnK8IOpW4M/Aq0QoIwabQ8mDAByhb1KL0dwOlrvRlKH0lOxisIl FDFiEP9WaBSxD4eik9bxmdPDlZmQ0MEmi09Q1fn877vyN70MKLgBgtZll0HxTxC/ uyG7oSq2IKojlvVsBoa06pAXmQIkIWsv6K12xKkUju+ahqNjWmqne8Hc+2+6Wad9 /am3Uw3AyoZIyNlzc44Burjwi0kF6EqkZBvWAkEM2XUgJl8vIx8rNeFesvoE0r2U 1ad6uvHg4WEBCpkAh/W0bqmIsrwFEv2g+pI9rdbEXFMB0JSDZzJltasuEPS6Ug9r utVkpcPV4nvbCA99IOEylqMYGVTDnGSclD6+F99cH3quCo/hJsR3WFpdTWSKDQCL avXozTG+aakpbU8/0l7YbyIeS5P2X1kplnUzYkuSNXUMMHB1ULWFNtEJpxMcWlu+ SlcVVnwSU0rsdmB2Huu5+uKJHHdFibgOVmrVV93vc2cZa3In6phw7wnd/seda5MZ poebUgXXa/erpazzOvtZ0X/FTmg4PWvloI6bZtpT3N4Ai7KUuFgr0TLNzEmVn9vC HlJyGIDIrQNSx58DpDu9hMTN/cbFKQBeHnzZo0mnFoo1Vpul3qgYlo1akUZr1uZO IL9iQXGYr8ToHCjdd+1AKCMjmLUvvehryE9HW5AWcQziqrwRoGtNuskB7BbPNlyj 8tU4E5SKaToPk+ecRspdWm3KPSjKUK0YvRP8pVBZ3ZsYX3n5xHGWpOgbIQS8RgoF HgLy6ERP -----END PUBLIC KEY-----¶
0 1969: SEQUENCE {
4 10: SEQUENCE {
6 8: OBJECT IDENTIFIER '2.16.840.1.101.3.4.18'
: }
16 1953: BIT STRING
00 48 68 3d 91 97 8e 31 eb 3d dd b8 b0 47 34 82
d2 b8 8a 5f 62 59 49 fd 8f 58 a5 61 e6 96 bd 4c
27 d0 5b 38 db b2 ed f0 1e 66 4e fd 81 be 1e a8
93 68 8c e6 8a a2 d5 1c 59 58 f8 bb c6 eb 4e 89
ee 67 d2 c0 32 09 54 d5 72 12 ca c7 22 9f f1 d6
ea f0 39 28 bd 51 51 1f 8d 88 d8 47 73 6c 7d e2
73 0d 59 78 e5 41 07 13 16 09 78 86 77 11 bf 55
39 a0 bf c4 c3 50 c2 be 57 2b af 0e e2 e2 fb 16
cc fe a0 80 28 d9 9a c4 9a eb b7 59 37 dd ce 11
1c da b6 2f ff 3c ea 8b a2 23 3d 1e 56 fb c5 c5
a1 e7 26 de 63 fa dd 2a f0 16 b1 19 17 7f a3 d9
71 a2 d9 27 71 73 fc e5 5b 67 74 5a f0 b7 c2 1d
59 7d be b9 3e 6a 32 f3 41 c4 9a 5a 8b e9 e8 25
08 8d 1f 2a a4 51 55 d6 c8 ae 15 36 7e 4e b0 03
b8 fd f7 85 10 71 94 97 39 f9 ff f0 90 23 ea f4
51 04 d2 a8 4a 45 90 6e ed 46 71 a4 4d c2 8d 27
98 7b b5 5d f6 9e 9e 85 61 f6 1a 80 a7 26 99 50
38 65 fe d9 b7 ee 72 a8 e1 7a 19 c4 08 14 4f 4b
29 af ef 70 31 c3 a6 d8 57 16 10 b4 2c 9f 42 12
45 a8 8f 19 7e 16 81 2b 03 11 59 b6 5b 96 87 e5
b3 e9 34 c5 22 5a e9 8a 79 ba 73 d2 b3 99 d7 35
10 ef fa d1 9e 53 b8 45 0f 0b a8 fc e1 01 2f d9
8d 26 0a 74 aa aa 13 fa e2 49 a0 06 b1 c3 4f 5b
a0 b8 82 f2 63 78 22 2f b3 6f 22 83 c2 43 f0 ff
eb 5f 1b b4 14 a0 a7 0d 55 e3 d4 0a 56 b6 cb c8
8a e1 f0 3b 7b 28 82 d9 8d ee a2 8e 14 5c 9d ed
fd 8e af 1c ef 2e d9 4a 8b 05 0f 89 64 f4 6d 1e
a0 d0 c2 a4 3e 0d da 61 82 ad bf 4f 6e d1 75 b6
74 22 57 85 9b f2 2f 3a 41 7e cf 1f 9d 89 31 7b
5e 53 9d 58 7a f1 6b 9e 13 13 e0 45 14 ff a6 4b
a8 b3 ff 2b 83 21 f8 81 1c b3 fb 02 2c 8f 64 4e
70 a4 b8 0a 2f bf ee 60 4a bb 73 79 09 1e a8 e6
c5 c7 4d fc 02 83 66 6b 40 c0 79 38 70 02 82 04
a1 36 bf 5d a9 56 8e b7 98 d3 49 03 8b db 0c 11
e0 34 45 e7 84 7c b5 06 9c 75 cf 28 ac 60 1c 77
99 d9 58 21 0d db cb 22 6e 51 af ef 9f 1d e4 7b
07 38 73 d6 d3 f9 74 56 be de 08 50 82 e7 4a 29
8b 2c d4 8f 4b 30 93 15 5f 36 6c 8f a6 01 c6 af
85 8d fa 32 c0 84 91 b2 a2 98 87 f9 03 35 94 9a
5d 6e da a6 79 88 2a 3a 95 d6 bf 6d 97 0a 22 1f
4b 9d 3d 8c bf 38 4a f8 1a ac 95 e2 b3 29 4e 04
78 9a c8 37 27 a5 dc 04 55 9f 96 af 41 d8 a0 53
51 6f ee ee bc 52 74 6e b6 ab 28 19 e0 91 08 71
0d 83 5f 01 1f a6 30 65 87 2a d3 34 d5 cd ff b2
b2 31 05 07 e9 2f c9 93 ae 31 7d a9 7f 4f 30 9c
da f0 f6 7e d9 9d 90 21 55 76 08 38 49 f9 53 b2
46 d7 fe db 3f db 67 67 98 50 a5 ad 40 4e 64 14
7f b7 cf 4f 6a ed dd 05 af b4 b8 34 96 8d 1f e8
80 14 96 0d ce 5d 94 22 36 52 6e 12 a4 78 d6 9e
5f be 69 70 31 0b 30 8c 06 84 50 18 cf c7 b2 ab
43 0a 13 a6 b1 ac 7b b0 2c cc bb 3d 91 1a c2 f1
10 68 61 3f be 02 9b fd ce 02 cf 5c d3 89 50 ed
72 c8 39 44 ed fb c7 56 15 af 87 f8 64 c0 51 f3
c5 54 56 c5 41 28 63 a4 0c 06 d1 da b5 62 bd ff
05 71 b8 d3 c3 91 7b bd 30 08 80 bb a5 e9 98 23
9b 95 fa 91 b7 d6 41 6d 4f 39 8b 3a db cd 30 98
3e d3 59 2b 4d 9e f7 d4 23 6f d0 0f 50 d9 8a a5
3a 23 5a c4 17 27 20 f7 7d 96 17 26 72 98 0c fe
8f f7 a5 a7 02 78 3e dc 2b a3 1b 22 59 01 5a 11
2f c7 f4 68 a9 c2 f9 46 40 39 00 2d 30 ef 67 8b
4c b7 98 bc 11 62 16 bf 7a 9a 7c 18 ba 03 b7 b5
8f d0 75 15 d3 11 50 49 d3 61 4b e7 a0 7e 74 43
00 75 0d f1 d2 c5 87 53 38 90 59 ea fc 3d 78 5c
cd d3 1c 07 64 8b ed c0 3a 5c 3b 8a d4 6d 06 4d
59 c1 3d 57 37 47 29 fc 4e 29 53 62 e2 a5 19 12
04 53 04 28 bc 15 22 af a2 8f f5 fe 16 55 e3 04
ca 5b c8 c2 7a d0 e0 c6 a3 9d d4 df 28 95 6c 14
b3 8c c9 36 82 ce fe 40 2b bd 5e 82 d2 9c 46 4e
44 eb 5d 37 b4 8f c5 68 df e0 cc 6e 8e 16 ba ea
05 e5 13 55 90 f1 92 94 e7 3e 83 67 b0 21 6d bb
81 50 30 b9 de 55 91 3f 08 03 9c 42 35 1c 59 e5
51 5d d5 af 8e 08 9a 15 e6 25 e8 f6 de e6 39 38
6c 46 49 7d 7a 26 32 88 77 4d e5 81 a7 de 96 29
b4 1b 44 24 14 1f 97 8f b8 33 12 08 ef de c3 c6
e0 de 39 bc 57 06 3f 3d cd 6c 47 03 73 c0 88 91
ea 29 cb c7 cc 6d 64 83 b8 88 90 83 ac e8 6a a7
b5 1b 1c 2c fe 6e 2a d1 8d 97 ce 36 fb c5 6e a4
2f ae 97 e6 a7 ac 11 48 64 47 8c 36 6d f1 eb b1
e7 b1 1a 90 98 50 4f d5 97 5b df 1f 49 dc 70 00
2b 63 c1 73 9a 9d 26 3f ba d4 07 3f 6a 9f 6c 2b
8a f4 b4 c3 32 a1 03 a0 cf fa 5d ee b2 d0 62 ca
3c 21 5f d3 60 02 6b e7 c5 16 4f 4a 44 24 ef 74
94 88 04 d6 6f 46 48 77 32 c8 20 2c 79 54 78 64
7b 4e a7 1d 62 7c 08 60 24 cc a3 54 a4 1f 08 77
b3 8f 19 b3 77 4a d2 09 5c 8d a5 3b 06 9e 21 c7
6a e2 d2 00 7e 16 71 9e d4 00 80 d3 34 f7 da 52
e9 f5 a5 99 04 39 ca f0 83 a9 5b 83 3f 02 ad 10
a0 8c 1a 6d 0f 26 0c 00 72 85 bd 4a 2f 47 70 3a
5a ef 46 52 87 d2 53 b1 8a c2 25 14 31 62 10 ff
56 68 14 b1 0f 87 a2 93 d6 f1 99 d3 c3 95 99 90
d0 c1 26 8b 4f 50 d5 f9 fc ef bb f2 37 bd 0c 28
b8 01 82 d6 65 97 41 f1 4f 10 bf bb 21 bb a1 2a
b6 20 aa 23 96 f5 6c 06 86 b4 ea 90 17 99 02 24
21 6b 2f e8 ad 76 c4 a9 14 8e ef 9a 86 a3 63 5a
6a a7 7b c1 dc fb 6f ba 59 a7 7d fd a9 b7 53 0d
c0 ca 86 48 c8 d9 73 73 8e 01 ba b8 f0 8b 49 05
e8 4a a4 64 1b d6 02 41 0c d9 75 20 26 5f 2f 23
1f 2b 35 e1 5e b2 fa 04 d2 bd 94 d5 a7 7a ba f1
e0 e1 61 01 0a 99 00 87 f5 b4 6e a9 88 b2 bc 05
12 fd a0 fa 92 3d ad d6 c4 5c 53 01 d0 94 83 67
32 65 b5 ab 2e 10 f4 ba 52 0f 6b ba d5 64 a5 c3
d5 e2 7b db 08 0f 7d 20 e1 32 96 a3 18 19 54 c3
9c 64 9c 94 3e be 17 df 5c 1f 7a ae 0a 8f e1 26
c4 77 58 5a 5d 4d 64 8a 0d 00 8b 6a f5 e8 cd 31
be 69 a9 29 6d 4f 3f d2 5e d8 6f 22 1e 4b 93 f6
5f 59 29 96 75 33 62 4b 92 35 75 0c 30 70 75 50
b5 85 36 d1 09 a7 13 1c 5a 5b be 4a 57 15 56 7c
12 53 4a ec 76 60 76 1e eb b9 fa e2 89 1c 77 45
89 b8 0e 56 6a d5 57 dd ef 73 67 19 6b 72 27 ea
98 70 ef 09 dd fe c7 9d 6b 93 19 a6 87 9b 52 05
d7 6b f7 ab a5 ac f3 3a fb 59 d1 7f c5 4e 68 38
3d 6b e5 a0 8e 9b 66 da 53 dc de 00 8b b2 94 b8
58 2b d1 32 cd cc 49 95 9f db c2 1e 52 72 18 80
c8 ad 03 52 c7 9f 03 a4 3b bd 84 c4 cd fd c6 c5
29 00 5e 1e 7c d9 a3 49 a7 16 8a 35 56 9b a5 de
a8 18 96 8d 5a 91 46 6b d6 e6 4e 20 bf 62 41 71
98 af c4 e8 1c 28 dd 77 ed 40 28 23 23 98 b5 2f
bd e8 6b c8 4f 47 5b 90 16 71 0c e2 aa bc 11 a0
6b 4d ba c9 01 ec 16 cf 36 5c a3 f2 d5 38 13 94
8a 69 3a 0f 93 e7 9c 46 ca 5d 5a 6d ca 3d 28 ca
50 ad 18 bd 13 fc a5 50 59 dd 9b 18 5f 79 f9 c4
71 96 a4 e8 1b 21 04 bc 46 0a 05 1e 02 f2 e8 44
4f
: }
¶
The following is the ML-KEM-87 public key corresponding to the private key in the previous section.¶
-----BEGIN PUBLIC KEY----- MIIKMjALBglghkgBZQMEAxMDggohAJeSvOwvJDBoaoL8zzwvX/Zl53HXq0G5AljP p+kOyXEkpzsyO5uiGrZNdnxDP1pSHv/hj4bkahiJUsRGfgSLcp5/xNEV5+SNoYlt X+EZsQ3N3vYssweVQHS0IzblKDbeYdqUH4036misgQb6vhkHBnmvYAhTcSD3B5O4 6pzA5ue3tMmlx0IcYPJEUboekz2xou4Wx5VZ8hs9G4MFhQqkKvuxPx9NW59INfnY ffzrFi0O9Kf9xMuhdDzRyHu0ln2hbMh2S2Vp347lvcv/6aTgV0jm/fIlr55O63dz ti6Phfm1a1SJRVUYRPvYmAakrDab7S0lYQD2iKatXgpwmCbcREnpHiPFUG5kI2Hv WjE3EvebxLMYaGHKhaS6sX5/lD0bijM6o6584WtEDWAY+eBNr1clx/GpP60aWie2 eJW9JJqpFoXeIK8yyLfiaMf5aHfQyFABE1pPCo8bgmT6br5aNJ2K7K0aFimczy/Z x7hbrOLO06oSdrph7njtflyltnzdRYqTVAMOaru6v1agojFv7J26g7UdQv0xZ/Hg +QhV1cZlCbIQJl3B5U7ES0O6fPmu8Ri0TYCRLOdRZqZlHhFs6+SSKacGLAmTH3Gr 0ik/dvfvwyFbqXgAA35Y5HC9u7Q8GwQ56vecVNk7RKrJ7+n74VGHTPsqZMvuKMxM D+d3Xl2HDxwC5bLjxQBMmV8kybd5y3U6J30Ocf1CXra8LKVs4SnbUfcHQPMeY5dr UMcxLpeX14xbGsJKX6NHzJFuCoP1w7Z1zTC4Hj+hC5NETgc5dXHM6Yso2lHbkFa8 coxbCxGB4vvTh7THmrGl/v7ONxZ693LdrRTrTDmC2lpZ0OnrFz7GMVCRFwAno6te 9qoSnLhYVye5NYooUB1xOnLz8dsxcUKG+bZAgBOvBgRddVkvwLfdR8c+2cdbEenX xp98rfwygKkGLFJzxDvhw0+HRIhkzqe1yX1tMvWb1fJThGU7tcT6pFvqi4lAKEPm Rba5Jp4r2YjdrLAzMo/7BgRQ998IAFPmlpslHodezsMs/FkoQNaatpp14Gs3nFNd lSZrCC9PCckxYrM7DZ9zB6TqqlIQRDf+1m+O4+q71F1nslqBM/SWRotSuv/b+tk+ 7xqYGLXkLscieIo9jTUp/Hd9K6VwgB364B7IgwKDfB+54DVXJ2Re4QRsP5Ffaugt rU+2sDVqRlGP/INBVcO0/m2vpsyKXM9TxzoISdjUT33PcnVOcOG337RHu070nRpx j2Fxu84gCVDgzpJhBrFRo+hx1c5JcxvWZQqbDKly2hxfE21Egg6mODwI87OEzyM4 54nFE/YYzFaUpvDO4QRRHh7XxfI6Hr/YoNuEJFUyQBVtv2IoMbDGQ9HFUbbz96mN KbhcLeBaZfphXu4WSVvZBzdnIRW1PpHF2QAozz8ak5U6FT3lO0QITpzP9rc2aTkm 2u/rstd6pa1om5LzFoZmnfFtFxXMWPeiz7ct0aUekvglmTp0Aivn6etgVGVEVwlN FJKPICFeeyIqxWtRrb7I2L22mDl5p+OiG0S10VGMqX0LUZX1HtaiQ1DIl0fh7epR tEjj6RRwVM6SeHPJDbOU2GiI4H3/F3WT1veeFSMCIErrA74jhq8+JAeL0CixaJ9e FHyfRSyM6wLsWcydtjoDV2zur+mCOQI4l9oCNmMKU8Def0NaGYaXkvqzbnueY1dg 8JBp5kMucAA1rCoCh5//Ch4b7FIgRxk9lOtd8e/VPuoRRMp4lAhS9eyXJ5BLNm7e T14tMx+tX8KC6ixH6SMUJ3HD3XWoc1dIfe+Z5fGOnZ7WI8F10CiIxR+CwHqA1UcW s8PCvb4unwqbuq6+tNUpNodkBvXADo5LvQpewFeX5iB8WrbIjxpohCG9BaEU9Nfe KsJB+g6L7f9H92Ldy+qpEAT40x6FCVyBBUmUrTgm40S6lgQIEPwLKtHeSM+t4ALG LlpJoHMas4NEvBY23xa/YH1WhV5W1oQAPHGOS62eWgmZefzd7rHEp3ds03o0F8sO GE4p75vA6HR1umY74J4Aq1Yut8D3Fl+WmptCQUGYzPG/8qLI1omkFOznZiknZlaJ 6U25YeuuxWFcvBp4lcaFGslhQy/xEY1GB9Mu+dxzLVEzO+S00OMN3qeE7Ki+R+dB vpwZYx3EcKUu9NwTpPNjP9Q014fBcJd7QX31mOHQ3eUGu3HW8LwX7HDjsDzcGWXL Npk/YzsEcuUNCSOsbGb98dPmRZzBIfD1+U0J6dvPXWkOIyM4OKC6y3xjjRsmUKQw jNFxtoVRJtHaZypu2FqNeMKG+1b0qz0hSXUoBFxjJiyKQq8vmALFO3u4vijnj+C1 zkX7t6GvGjsoqNlLeJDjyILjm8mOnwrXYCW/DdLwApjnFBoiaz187kFPYE0eC6VN EdX+WLzOpq13rS6MHKrPMkWQFLe5EAGx76itFypSP7jjZbV3Ehv5/Yiixgwh6CHX tqy0elqZXkDKztXCI7j+beXhjp0uWJOu/rt6rn/xoUYmDi8RDpOVKCE6ACWjjsea q8hhsl68UJpGdMEyqqy34BRvFO/RHPyvTKpPd1pxbOMl4KQ1pNNJ1yC88TdFCvxF BG/Bofg6nTKXd6cITkqtrnEizpcAWTBSjrPH9/ESmzcoh6NxFVo7ogGiXL8dy2Tn ze4JLDFB+1VQ/j0N2C6HDleLK0ZQCBgRO49laXc8Z3OFtppCt33Lp6z/2V/URS4j qqHTfh2iFR6mWNQKNZayesn4Ep3GzwZDdyYktZ9PRhIw30ccomCHw5QtXGaH32CC g1k1o/h8t2Kww7HQ3aSmUzllvvG3uCkuJUwBTQkP7YV8RMGDnGlMCmTj+tkKEfU0 citu4VdPLhSdVddE3kiHAk4IURQxwGJ1DhbHSrnzJC8ts/+xKo1hB/qiKdb2NzsH 8205MrO9sEwZ3WTq3X+Tw8Vkw1ihyB3PHJwx5bBlaPl1RMF9wVaYxcs4mDqa/EJ4 P6p3OlLJ2CYGkL6eMVaqW8FQneo/aVh2lc1v8XK6g+am2KfWu+u7zaNnJzGYP4m8 WDHcN8PzxcVvrMaX88sgvV2629cC5UhErC9iaQH+FZ25Pf1Hc9j+c1YrhGwfyFbR gCdihA68cteYi951y8pw0xnTLODMAlO7KtRVcj7gx/RzbObmZlxayjKkgcU4Obwl kWewE9BCM5Xuuaqu4yBhSafVUNZ/xf3+SopcNdJRC2ZDeauPcoVaKvR6vOKmMgSO r4nly0qI3rxTpZUQOszk8c/xis/wev4etXFqoeQLYxNMOjrpV5+of1Fb4JPC0p22 1rZck2YeAGNrWScE0JPMZxbCNC6xhT1IyFxjrIooVEYse3fn470erFvKKP+qALXT SfilR62HW5aowrKRDJMBMJo/kTilaTER9Vs8AJypR8Od/ILZjrHKpKnL6IX3hvqG 5VvgYiIvi6kKl0BzMmsxISrs4KNKYA== -----END PUBLIC KEY-----¶
0 2609: SEQUENCE {
4 10: SEQUENCE {
6 8: OBJECT IDENTIFIER '2.16.840.1.101.3.4.18'
: }
16 2593: BIT STRING
00 97 92 bc ec 2f 24 30 68 6a 82 fc cf 3c 2f 5f
f6 65 e7 71 d7 ab 41 b9 02 58 cf a7 e9 0e c9 71
24 a7 3b 32 3b 9b a2 1a b6 4d 76 7c 43 3f 5a 52
1e ff e1 8f 86 e4 6a 18 89 52 c4 46 7e 04 8b 72
9e 7f c4 d1 15 e7 e4 8d a1 89 6d 5f e1 19 b1 0d
cd de f6 2c b3 07 95 40 74 b4 23 36 e5 28 36 de
61 da 94 1f 8d 37 ea 68 ac 81 06 fa be 19 07 06
79 af 60 08 53 71 20 f7 07 93 b8 ea 9c c0 e6 e7
b7 b4 c9 a5 c7 42 1c 60 f2 44 51 ba 1e 93 3d b1
a2 ee 16 c7 95 59 f2 1b 3d 1b 83 05 85 0a a4 2a
fb b1 3f 1f 4d 5b 9f 48 35 f9 d8 7d fc eb 16 2d
0e f4 a7 fd c4 cb a1 74 3c d1 c8 7b b4 96 7d a1
6c c8 76 4b 65 69 df 8e e5 bd cb ff e9 a4 e0 57
48 e6 fd f2 25 af 9e 4e eb 77 73 b6 2e 8f 85 f9
b5 6b 54 89 45 55 18 44 fb d8 98 06 a4 ac 36 9b
ed 2d 25 61 00 f6 88 a6 ad 5e 0a 70 98 26 dc 44
49 e9 1e 23 c5 50 6e 64 23 61 ef 5a 31 37 12 f7
9b c4 b3 18 68 61 ca 85 a4 ba b1 7e 7f 94 3d 1b
8a 33 3a a3 ae 7c e1 6b 44 0d 60 18 f9 e0 4d af
57 25 c7 f1 a9 3f ad 1a 5a 27 b6 78 95 bd 24 9a
a9 16 85 de 20 af 32 c8 b7 e2 68 c7 f9 68 77 d0
c8 50 01 13 5a 4f 0a 8f 1b 82 64 fa 6e be 5a 34
9d 8a ec ad 1a 16 29 9c cf 2f d9 c7 b8 5b ac e2
ce d3 aa 12 76 ba 61 ee 78 ed 7e 5c a5 b6 7c dd
45 8a 93 54 03 0e 6a bb ba bf 56 a0 a2 31 6f ec
9d ba 83 b5 1d 42 fd 31 67 f1 e0 f9 08 55 d5 c6
65 09 b2 10 26 5d c1 e5 4e c4 4b 43 ba 7c f9 ae
f1 18 b4 4d 80 91 2c e7 51 66 a6 65 1e 11 6c eb
e4 92 29 a7 06 2c 09 93 1f 71 ab d2 29 3f 76 f7
ef c3 21 5b a9 78 00 03 7e 58 e4 70 bd bb b4 3c
1b 04 39 ea f7 9c 54 d9 3b 44 aa c9 ef e9 fb e1
51 87 4c fb 2a 64 cb ee 28 cc 4c 0f e7 77 5e 5d
87 0f 1c 02 e5 b2 e3 c5 00 4c 99 5f 24 c9 b7 79
cb 75 3a 27 7d 0e 71 fd 42 5e b6 bc 2c a5 6c e1
29 db 51 f7 07 40 f3 1e 63 97 6b 50 c7 31 2e 97
97 d7 8c 5b 1a c2 4a 5f a3 47 cc 91 6e 0a 83 f5
c3 b6 75 cd 30 b8 1e 3f a1 0b 93 44 4e 07 39 75
71 cc e9 8b 28 da 51 db 90 56 bc 72 8c 5b 0b 11
81 e2 fb d3 87 b4 c7 9a b1 a5 fe fe ce 37 16 7a
f7 72 dd ad 14 eb 4c 39 82 da 5a 59 d0 e9 eb 17
3e c6 31 50 91 17 00 27 a3 ab 5e f6 aa 12 9c b8
58 57 27 b9 35 8a 28 50 1d 71 3a 72 f3 f1 db 31
71 42 86 f9 b6 40 80 13 af 06 04 5d 75 59 2f c0
b7 dd 47 c7 3e d9 c7 5b 11 e9 d7 c6 9f 7c ad fc
32 80 a9 06 2c 52 73 c4 3b e1 c3 4f 87 44 88 64
ce a7 b5 c9 7d 6d 32 f5 9b d5 f2 53 84 65 3b b5
c4 fa a4 5b ea 8b 89 40 28 43 e6 45 b6 b9 26 9e
2b d9 88 dd ac b0 33 32 8f fb 06 04 50 f7 df 08
00 53 e6 96 9b 25 1e 87 5e ce c3 2c fc 59 28 40
d6 9a b6 9a 75 e0 6b 37 9c 53 5d 95 26 6b 08 2f
4f 09 c9 31 62 b3 3b 0d 9f 73 07 a4 ea aa 52 10
44 37 fe d6 6f 8e e3 ea bb d4 5d 67 b2 5a 81 33
f4 96 46 8b 52 ba ff db fa d9 3e ef 1a 98 18 b5
e4 2e c7 22 78 8a 3d 8d 35 29 fc 77 7d 2b a5 70
80 1d fa e0 1e c8 83 02 83 7c 1f b9 e0 35 57 27
64 5e e1 04 6c 3f 91 5f 6a e8 2d ad 4f b6 b0 35
6a 46 51 8f fc 83 41 55 c3 b4 fe 6d af a6 cc 8a
5c cf 53 c7 3a 08 49 d8 d4 4f 7d cf 72 75 4e 70
e1 b7 df b4 47 bb 4e f4 9d 1a 71 8f 61 71 bb ce
20 09 50 e0 ce 92 61 06 b1 51 a3 e8 71 d5 ce 49
73 1b d6 65 0a 9b 0c a9 72 da 1c 5f 13 6d 44 82
0e a6 38 3c 08 f3 b3 84 cf 23 38 e7 89 c5 13 f6
18 cc 56 94 a6 f0 ce e1 04 51 1e 1e d7 c5 f2 3a
1e bf d8 a0 db 84 24 55 32 40 15 6d bf 62 28 31
b0 c6 43 d1 c5 51 b6 f3 f7 a9 8d 29 b8 5c 2d e0
5a 65 fa 61 5e ee 16 49 5b d9 07 37 67 21 15 b5
3e 91 c5 d9 00 28 cf 3f 1a 93 95 3a 15 3d e5 3b
44 08 4e 9c cf f6 b7 36 69 39 26 da ef eb b2 d7
7a a5 ad 68 9b 92 f3 16 86 66 9d f1 6d 17 15 cc
58 f7 a2 cf b7 2d d1 a5 1e 92 f8 25 99 3a 74 02
2b e7 e9 eb 60 54 65 44 57 09 4d 14 92 8f 20 21
5e 7b 22 2a c5 6b 51 ad be c8 d8 bd b6 98 39 79
a7 e3 a2 1b 44 b5 d1 51 8c a9 7d 0b 51 95 f5 1e
d6 a2 43 50 c8 97 47 e1 ed ea 51 b4 48 e3 e9 14
70 54 ce 92 78 73 c9 0d b3 94 d8 68 88 e0 7d ff
17 75 93 d6 f7 9e 15 23 02 20 4a eb 03 be 23 86
af 3e 24 07 8b d0 28 b1 68 9f 5e 14 7c 9f 45 2c
8c eb 02 ec 59 cc 9d b6 3a 03 57 6c ee af e9 82
39 02 38 97 da 02 36 63 0a 53 c0 de 7f 43 5a 19
86 97 92 fa b3 6e 7b 9e 63 57 60 f0 90 69 e6 43
2e 70 00 35 ac 2a 02 87 9f ff 0a 1e 1b ec 52 20
47 19 3d 94 eb 5d f1 ef d5 3e ea 11 44 ca 78 94
08 52 f5 ec 97 27 90 4b 36 6e de 4f 5e 2d 33 1f
ad 5f c2 82 ea 2c 47 e9 23 14 27 71 c3 dd 75 a8
73 57 48 7d ef 99 e5 f1 8e 9d 9e d6 23 c1 75 d0
28 88 c5 1f 82 c0 7a 80 d5 47 16 b3 c3 c2 bd be
2e 9f 0a 9b ba ae be b4 d5 29 36 87 64 06 f5 c0
0e 8e 4b bd 0a 5e c0 57 97 e6 20 7c 5a b6 c8 8f
1a 68 84 21 bd 05 a1 14 f4 d7 de 2a c2 41 fa 0e
8b ed ff 47 f7 62 dd cb ea a9 10 04 f8 d3 1e 85
09 5c 81 05 49 94 ad 38 26 e3 44 ba 96 04 08 10
fc 0b 2a d1 de 48 cf ad e0 02 c6 2e 5a 49 a0 73
1a b3 83 44 bc 16 36 df 16 bf 60 7d 56 85 5e 56
d6 84 00 3c 71 8e 4b ad 9e 5a 09 99 79 fc dd ee
b1 c4 a7 77 6c d3 7a 34 17 cb 0e 18 4e 29 ef 9b
c0 e8 74 75 ba 66 3b e0 9e 00 ab 56 2e b7 c0 f7
16 5f 96 9a 9b 42 41 41 98 cc f1 bf f2 a2 c8 d6
89 a4 14 ec e7 66 29 27 66 56 89 e9 4d b9 61 eb
ae c5 61 5c bc 1a 78 95 c6 85 1a c9 61 43 2f f1
11 8d 46 07 d3 2e f9 dc 73 2d 51 33 3b e4 b4 d0
e3 0d de a7 84 ec a8 be 47 e7 41 be 9c 19 63 1d
c4 70 a5 2e f4 dc 13 a4 f3 63 3f d4 34 d7 87 c1
70 97 7b 41 7d f5 98 e1 d0 dd e5 06 bb 71 d6 f0
bc 17 ec 70 e3 b0 3c dc 19 65 cb 36 99 3f 63 3b
04 72 e5 0d 09 23 ac 6c 66 fd f1 d3 e6 45 9c c1
21 f0 f5 f9 4d 09 e9 db cf 5d 69 0e 23 23 38 38
a0 ba cb 7c 63 8d 1b 26 50 a4 30 8c d1 71 b6 85
51 26 d1 da 67 2a 6e d8 5a 8d 78 c2 86 fb 56 f4
ab 3d 21 49 75 28 04 5c 63 26 2c 8a 42 af 2f 98
02 c5 3b 7b b8 be 28 e7 8f e0 b5 ce 45 fb b7 a1
af 1a 3b 28 a8 d9 4b 78 90 e3 c8 82 e3 9b c9 8e
9f 0a d7 60 25 bf 0d d2 f0 02 98 e7 14 1a 22 6b
3d 7c ee 41 4f 60 4d 1e 0b a5 4d 11 d5 fe 58 bc
ce a6 ad 77 ad 2e 8c 1c aa cf 32 45 90 14 b7 b9
10 01 b1 ef a8 ad 17 2a 52 3f b8 e3 65 b5 77 12
1b f9 fd 88 a2 c6 0c 21 e8 21 d7 b6 ac b4 7a 5a
99 5e 40 ca ce d5 c2 23 b8 fe 6d e5 e1 8e 9d 2e
58 93 ae fe bb 7a ae 7f f1 a1 46 26 0e 2f 11 0e
93 95 28 21 3a 00 25 a3 8e c7 9a ab c8 61 b2 5e
bc 50 9a 46 74 c1 32 aa ac b7 e0 14 6f 14 ef d1
1c fc af 4c aa 4f 77 5a 71 6c e3 25 e0 a4 35 a4
d3 49 d7 20 bc f1 37 45 0a fc 45 04 6f c1 a1 f8
3a 9d 32 97 77 a7 08 4e 4a ad ae 71 22 ce 97 00
59 30 52 8e b3 c7 f7 f1 12 9b 37 28 87 a3 71 15
5a 3b a2 01 a2 5c bf 1d cb 64 e7 cd ee 09 2c 31
41 fb 55 50 fe 3d 0d d8 2e 87 0e 57 8b 2b 46 50
08 18 11 3b 8f 65 69 77 3c 67 73 85 b6 9a 42 b7
7d cb a7 ac ff d9 5f d4 45 2e 23 aa a1 d3 7e 1d
a2 15 1e a6 58 d4 0a 35 96 b2 7a c9 f8 12 9d c6
cf 06 43 77 26 24 b5 9f 4f 46 12 30 df 47 1c a2
60 87 c3 94 2d 5c 66 87 df 60 82 83 59 35 a3 f8
7c b7 62 b0 c3 b1 d0 dd a4 a6 53 39 65 be f1 b7
b8 29 2e 25 4c 01 4d 09 0f ed 85 7c 44 c1 83 9c
69 4c 0a 64 e3 fa d9 0a 11 f5 34 72 2b 6e e1 57
4f 2e 14 9d 55 d7 44 de 48 87 02 4e 08 51 14 31
c0 62 75 0e 16 c7 4a b9 f3 24 2f 2d b3 ff b1 2a
8d 61 07 fa a2 29 d6 f6 37 3b 07 f3 6d 39 32 b3
bd b0 4c 19 dd 64 ea dd 7f 93 c3 c5 64 c3 58 a1
c8 1d cf 1c 9c 31 e5 b0 65 68 f9 75 44 c1 7d c1
56 98 c5 cb 38 98 3a 9a fc 42 78 3f aa 77 3a 52
c9 d8 26 06 90 be 9e 31 56 aa 5b c1 50 9d ea 3f
69 58 76 95 cd 6f f1 72 ba 83 e6 a6 d8 a7 d6 bb
eb bb cd a3 67 27 31 98 3f 89 bc 58 31 dc 37 c3
f3 c5 c5 6f ac c6 97 f3 cb 20 bd 5d ba db d7 02
e5 48 44 ac 2f 62 69 01 fe 15 9d b9 3d fd 47 73
d8 fe 73 56 2b 84 6c 1f c8 56 d1 80 27 62 84 0e
bc 72 d7 98 8b de 75 cb ca 70 d3 19 d3 2c e0 cc
02 53 bb 2a d4 55 72 3e e0 c7 f4 73 6c e6 e6 66
5c 5a ca 32 a4 81 c5 38 39 bc 25 91 67 b0 13 d0
42 33 95 ee b9 aa ae e3 20 61 49 a7 d5 50 d6 7f
c5 fd fe 4a 8a 5c 35 d2 51 0b 66 43 79 ab 8f 72
85 5a 2a f4 7a bc e2 a6 32 04 8e af 89 e5 cb 4a
88 de bc 53 a5 95 10 3a cc e4 f1 cf f1 8a cf f0
7a fe 1e b5 71 6a a1 e4 0b 63 13 4c 3a 3a e9 57
9f a8 7f 51 5b e0 93 c2 d2 9d b6 d6 b6 5c 93 66
1e 00 63 6b 59 27 04 d0 93 cc 67 16 c2 34 2e b1
85 3d 48 c8 5c 63 ac 8a 28 54 46 2c 7b 77 e7 e3
bd 1e ac 5b ca 28 ff aa 00 b5 d3 49 f8 a5 47 ad
87 5b 96 a8 c2 b2 91 0c 93 01 30 9a 3f 91 38 a5
69 31 11 f5 5b 3c 00 9c a9 47 c3 9d fc 82 d9 8e
b1 ca a4 a9 cb e8 85 f7 86 fa 86 e5 5b e0 62 22
2f 8b a9 0a 97 40 73 32 6b 31 21 2a ec e0 a3 4a
60
: }
¶
TODO: Add an example¶
TODO: Add pretty print¶
We would like to thank ... for their insightful comments.¶