| Network Working Group | S. Josefsson |
| Internet-Draft | SJD AB |
| Intended status: Standards Track | J. Schaad |
| Expires: March 16, 2018 | August Cellars |
| September 12, 2017 |
Algorithm Identifiers for Ed25519, Ed448, X25519 and X448 for use in the Internet X.509 Public Key Infrastructure
draft-ietf-curdle-pkix-06
This document specifies algorithm identifiers and ASN.1 encoding formats for Elliptic Curve constructs using the curve25519 and curve448 curves. The signature algorithms covered are Ed25519 and Ed448. The key agreement algorithm covered are X25519 and X448. The encoding for Public Key, Private Key and EdDSA digital signature structures is provided.
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This Internet-Draft will expire on March 16, 2018.
Copyright (c) 2017 IETF Trust and the persons identified as the document authors. All rights reserved.
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In [RFC7748], the elliptic curves curve25519 and curve448 are described. They are designed with performance and security in mind. The curves may be used for Diffie-Hellman and Digital Signature operations.
[RFC7748] describes the operations on these curves for the Diffie-Hellman operation. A convention has developed that when these two curves are used with the Diffie-Hellman operation, they are referred to as X25519 and X448. This RFC defines the ASN.1 Object Identifiers (OIDs) for the operations X25519 and X448 along with the parameters. The use of these OIDs is described for public and private keys.
In [RFC8032] the elliptic curve signature system Edwards-curve Digital Signature Algorithm (EdDSA) is described along with a recommendation for the use of the curve25519 and curve448. EdDSA has defined two modes, the PureEdDSA mode without pre-hashing, and the HashEdDSA mode with pre-hashing. The convention used for identifying the algorithm/curve combinations are to use the Ed25519 and Ed448 for the PureEdDSA mode. The document does not provide the conventions needed for the pre-hash versions of the signature algorithm. The use of the OIDs is described for public keys, private keys and signatures.
[RFC8032] additionally defined the concept of a context. Contexts can be used to differentiate signatures generated for different purposes with the same key. The use of contexts is not defined in this document for the following reasons:
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119].
Certificates conforming to [RFC5280] can convey a public key for any public key algorithm. The certificate indicates the algorithm through an algorithm identifier. This algorithm identifier is an OID and optionally associated parameters.
The AlgorithmIdentifier type, which is included for convenience, is defined as follows:
AlgorithmIdentifier ::= SEQUENCE {
algorithm OBJECT IDENTIFIER,
parameters ANY DEFINED BY algorithm OPTIONAL
}
The fields in AlgorithmIdentifier have the following meanings:
In this document we defined four new OIDs for identifying the different curve/algorithm pairs. The curves being curve25519 and curve448. The algorithms being ECDH and EdDSA in pure mode. For all of the OIDs, the parameters MUST be absent. Regardless of the defect in the original 1997 syntax, implementations MUST NOT accept a parameters value of NULL.
The same algorithm identifiers are used for identifying a public key, identifying a private key and identifying a signature (for the two EdDSA related OIDs). Additional encoding information is provided below for each of these locations.
id-X25519 OBJECT IDENTIFIER ::= { 1 3 101 110 }
id-X448 OBJECT IDENTIFIER ::= { 1 3 101 111 }
id-Ed25519 OBJECT IDENTIFIER ::= { 1 3 101 112 }
id-Ed448 OBJECT IDENTIFIER ::= { 1 3 101 113 }
In the X.509 certificate, the subjectPublicKeyInfo field has the SubjectPublicKeyInfo type, which has the following ASN.1 syntax:
SubjectPublicKeyInfo ::= SEQUENCE {
algorithm AlgorithmIdentifier,
subjectPublicKey BIT STRING
}
The fields in SubjectPublicKeyInfo have the following meanings:
Both [RFC7748] and [RFC8032] define the public key value as being a byte string. It should be noted that the public key is computed differently for each of these documents, thus the same private key will not produce the same public key.
The following is an example of a public key encoded using the textual encoding defined in [RFC7468].
-----BEGIN PUBLIC KEY----- MCowBQYDK2VwAyEAGb9ECWmEzf6FQbrBZ9w7lshQhqowtrbLDFw4rXAxZuE= -----END PUBLIC KEY-----
The intended application for the key is indicated in the keyUsage certificate extension.
If the keyUsage extension is present in a certificate that indicates id-X25519 or id-X448 in SubjectPublicKeyInfo, then the following MUST be present:
keyAgreement;
one of the following MAY also be present:
encipherOnly; or
decipherOnly.
If the keyUsage extension is present in an end-entity certificate that indicates id-Ed25519 or id-Ed448, then the keyUsage extension MUST contain one or both of the following values:
nonRepudiation; and
digitalSignature.
If the keyUsage extension is present in a certification authority certificate that indicates id-Ed25519 or id-Ed448, then the keyUsage extension MUST contain one or more of the following values:
nonRepudiation;
digitalSignature;
keyCertSign; and
cRLSign.
Signatures can be placed in a number of different ASN.1 structures. The top level structure for a certificate is given below as being illustrative of how signatures are frequently encoded with an algorithm identifier and a location for the signature.
Certificate ::= SEQUENCE {
tbsCertificate TBSCertificate,
signatureAlgorithm AlgorithmIdentifier,
signatureValue BIT STRING }
The same algorithm identifiers are used for signatures as are used for public keys. When used to identify signature algorithms, the parameters MUST be absent.
The data to be signed is prepared for EdDSA. Then, a private key operation is performed to generate the signature value. This value is the opaque value ENC(R) || ENC(S) described in section 3.3 of [RFC8032]. The octet string representing the signature is encoded directly in the BIT STRING without adding any additional ASN.1 wrapping. For the Certificate structure, the signature value is wrapped in the "signatureValue" BIT STRING field.
Asymmetric Key Packages describes how encode a private key in a structure that both identifies what algorithm the private key is for, but 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. The algorithm specific details of how a private key is encoded is left for the document describing the algorithm itself.
OneAsymmetricKey ::= SEQUENCE {
version Version,
privateKeyAlgorithm PrivateKeyAlgorithmIdentifier,
privateKey PrivateKey,
attributes [0] IMPLICIT Attributes OPTIONAL,
...,
[[2: publicKey [1] IMPLICIT PublicKey OPTIONAL ]],
...
}
PrivateKey ::= OCTET STRING
PublicKey ::= BIT STRING
For the keys defined in this document, the private key is always an opaque byte sequence. The ASN.1 type CurvePrivateKey is defined in this document to hold the byte sequence. Thus when encoding a OneAsymmetricKey object, the private key is wrapped in an CurvePrivateKey object and wrapped by the OCTET STRING of the "privateKey" field.
CurvePrivateKey ::= OCTET STRING
To encode a EdDSA, X25519 or X448 private key, the "privateKey" field will hold the encoded private key. The "privateKeyAlgorithm" field uses the AlgorithmIdentifier structure. The structure is encoded as defined above. If present, the "publicKey" field will hold the encoded key as defined in [RFC7748] and [RFC8032].
The following is an example of a private key encoded using the textual encoding defined in [RFC7468].
-----BEGIN PRIVATE KEY----- MC4CAQAwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC -----END PRIVATE KEY-----
The following example, in addition to encoding the private key, additionally has an attribute included as well as the public key. As with the prior example, the textual encoding defined in [RFC7468] is used.
-----BEGIN PRIVATE KEY----- MHICAQEwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC oB8wHQYKKoZIhvcNAQkJFDEPDA1DdXJkbGUgQ2hhaXJzgSEAGb9ECWmEzf6FQbrB Z9w7lshQhqowtrbLDFw4rXAxZuE= -----END PRIVATE KEY------
NOTE: There exist some private key import functions that have not picked up the new ASN.1 structure OneAsymmetricKey that is defined in [RFC7748]. This means that they will not accept a private key structure which contains the public key field. This means a balancing act needs to be done between being able to do a consistency check on the key pair and widest ability to import the key.
For the purpose of consistent cross-implementation naming this section establishes human readable names for the algorithms specified in this document. Implementations SHOULD use these names when referring to the algorithms. If there is a strong reason to deviate from these names -- for example, if the implementation has a different naming convention and wants to maintain internal consistency -- it is encouraged to deviate as little as possible from the names given here.
Use the string "ECDH" when referring to a public key of type X25519 or X448 when the curve is not known or relevant.
When the curve is known, use the more specific string of X25519 or X448.
Use the string "EdDSA" when referring to a signing public key or signature when the curve is not known or relevant.
When the curve is known, use a more specific string. For the id-Ed25519 value use the string "Ed25519". For id-Ed448 use "Ed448".
For reference purposes, the ASN.1 syntax is presented as an ASN.1 module here.
-- ASN.1 Module
Safecurves-pkix-0 -- TBD - IANA assigned module OID
DEFINITIONS EXPLICIT TAGS ::=
BEGIN
IMPORTS
SIGNATURE-ALGORITHM, KEY-AGREE, PUBLIC-KEY, KEY-WRAP,
KeyUsage, AlgorithmIdentifier
FROM AlgorithmInformation-2009
{iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) id-mod(0)
id-mod-algorithmInformation-02(58)}
mda-sha512
FROM PKIX1-PSS-OAEP-Algorithms-2009
{ iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-pkix1-rsa-pkalgs-02(54) }
kwa-aes128-wrap, kwa-aes256-wrap
FROM CMSAesRsaesOaep-2009
{ iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9)
smime(16) modules(0) id-mod-cms-aes-02(38) }
;
id-edwards-curve-algs OBJECT IDENTIFIER ::= { 1 3 101 }
id-X25519 OBJECT IDENTIFIER ::= { id-edwards-curve-algs 110 }
id-X448 OBJECT IDENTIFIER ::= { id-edwards-curve-algs 111 }
id-Ed25519 OBJECT IDENTIFIER ::= { id-edwards-curve-algs 112 }
id-Ed448 OBJECT IDENTIFIER ::= { id-edwards-curve-algs 113 }
sa-Ed25519 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-Ed25519
PARAMS ARE absent
PUBLIC-KEYS {pk-Ed25519}
SMIME-CAPS { IDENTIFIED BY id-Ed25519 }
}
pk-Ed25519 PUBLIC-KEY ::= {
IDENTIFIER id-Ed25519
-- KEY no ASN.1 wrapping --
PARAMS ARE absent
CERT-KEY-USAGE {digitalSignature, nonRepudiation,
keyCertSign, cRLSign}
PRIVATE-KEY CurvePrivateKey
}
kaa-X25519 KEY-AGREE ::= {
IDENTIFIER id-X25519
PARAMS ARE absent
PUBLIC-KEYS {pk-X25519}
UKM -- TYPE no ASN.1 wrapping -- ARE preferredPresent
SMIME-CAPS {
TYPE AlgorithmIdentifier{KEY-WRAP, {KeyWrapAlgorithms}}
IDENTIFIED BY id-X25519 }
}
pk-X25519 PUBLIC-KEY ::= {
IDENTIFIER id-X25519
-- KEY no ASN.1 wrapping --
PARAMS ARE absent
CERT-KEY-USAGE { keyAgreement }
PRIVATE-KEY CurvePrivateKey
}
KeyWrapAlgorithms KEY-WRAP ::= {
kwa-aes128-wrap | kwa-aes256-wrap,
...
}
kaa-X448 KEY-AGREE ::= {
IDENTIFIER id-X448
PARAMS ARE absent
PUBLIC-KEYS {pk-X448}
UKM -- TYPE no ASN.1 wrapping -- ARE preferredPresent
SMIME-CAPS {
TYPE AlgorithmIdentifier{KEY-WRAP, {KeyWrapAlgorithms}}
IDENTIFIED BY id-X448 }
}
pk-X448 PUBLIC-KEY ::= {
IDENTIFIER id-X448
-- KEY no ASN.1 wrapping --
PARAMS ARE absent
CERT-KEY-USAGE { keyAgreement }
PRIVATE-KEY CurvePrivateKey
}
CurvePrivateKey ::= OCTET STRING
END
This section contains illustrations of EdDSA public keys and certificates, illustrating parameter choices.
An example of a Ed25519 public key:
Public Key Information:
Public Key Algorithm: Ed25519
Algorithm Security Level: High
Public Key Usage:
Public Key ID: 9b1f5eeded043385e4f7bc623c5975b90bc8bb3b
-----BEGIN PUBLIC KEY-----
MCowBQYDK2VwAyEAGb9ECWmEzf6FQbrBZ9w7lshQhqowtrbLDFw4rXAxZuE=
-----END PUBLIC KEY-----
An example of a self issued PKIX certificate using Ed25519 to sign a X25519 public key would be:
0 300: SEQUENCE {
4 223: SEQUENCE {
7 3: [0] {
9 1: INTEGER 2
: }
12 8: INTEGER 56 01 47 4A 2A 8D C3 30
22 5: SEQUENCE {
24 3: OBJECT IDENTIFIER
: Ed 25519 signature algorithm { 1 3 101 112 }
: }
29 25: SEQUENCE {
31 23: SET {
33 21: SEQUENCE {
35 3: OBJECT IDENTIFIER commonName (2 5 4 3)
40 14: UTF8String 'IETF Test Demo'
: }
: }
: }
56 30: SEQUENCE {
58 13: UTCTime 01/08/2016 12:19:24 GMT
73 13: UTCTime 31/12/2040 23:59:59 GMT
: }
88 25: SEQUENCE {
90 23: SET {
92 21: SEQUENCE {
94 3: OBJECT IDENTIFIER commonName (2 5 4 3)
99 14: UTF8String 'IETF Test Demo'
: }
: }
: }
115 42: SEQUENCE {
117 5: SEQUENCE {
119 3: OBJECT IDENTIFIER
: ECDH 25519 key agreement { 1 3 101 110 }
: }
124 33: BIT STRING
: 85 20 F0 09 89 30 A7 54 74 8B 7D DC B4 3E F7 5A
: 0D BF 3A 0D 26 38 1A F4 EB A4 A9 8E AA 9B 4E 6A
: }
159 69: [3] {
161 67: SEQUENCE {
163 15: SEQUENCE {
165 3: OBJECT IDENTIFIER basicConstraints (2 5 29 19)
170 1: BOOLEAN TRUE
173 5: OCTET STRING, encapsulates {
175 3: SEQUENCE {
177 1: BOOLEAN FALSE
: }
: }
: }
180 14: SEQUENCE {
182 3: OBJECT IDENTIFIER keyUsage (2 5 29 15)
187 1: BOOLEAN FALSE
190 4: OCTET STRING, encapsulates {
192 2: BIT STRING 3 unused bits
: '10000'B (bit 4)
: }
: }
196 32: SEQUENCE {
198 3: OBJECT IDENTIFIER subjectKeyIdentifier (2 5 29 14)
203 1: BOOLEAN FALSE
206 22: OCTET STRING, encapsulates {
208 20: OCTET STRING
: 9B 1F 5E ED ED 04 33 85 E4 F7 BC 62 3C 59 75
: B9 0B C8 BB 3B
: }
: }
: }
: }
: }
230 5: SEQUENCE {
232 3: OBJECT IDENTIFIER
: Ed 25519 signature algorithm { 1 3 101 112 }
: }
237 65: BIT STRING
: AF 23 01 FE DD C9 E6 FF C1 CC A7 3D 74 D6 48 A4
: 39 80 82 CD DB 69 B1 4E 4D 06 EC F8 1A 25 CE 50
: D4 C2 C3 EB 74 6C 4E DD 83 46 85 6E C8 6F 3D CE
: 1A 18 65 C5 7A C2 7B 50 A0 C3 50 07 F5 E7 D9 07
: }
-----BEGIN CERTIFICATE-----
MIIBLDCB36ADAgECAghWAUdKKo3DMDAFBgMrZXAwGTEXMBUGA1UEAwwOSUVURiBUZX
N0IERlbW8wHhcNMTYwODAxMTIxOTI0WhcNNDAxMjMxMjM1OTU5WjAZMRcwFQYDVQQD
DA5JRVRGIFRlc3QgRGVtbzAqMAUGAytlbgMhAIUg8AmJMKdUdIt93LQ+91oNvzoNJj
ga9OukqY6qm05qo0UwQzAPBgNVHRMBAf8EBTADAQEAMA4GA1UdDwEBAAQEAwIDCDAg
BgNVHQ4BAQAEFgQUmx9e7e0EM4Xk97xiPFl1uQvIuzswBQYDK2VwA0EAryMB/t3J5v
/BzKc9dNZIpDmAgs3babFOTQbs+BolzlDUwsPrdGxO3YNGhW7Ibz3OGhhlxXrCe1Cg
w1AH9efZBw==
-----END CERTIFICATE-----
An example of an Ed25519 private key without the public key:
-----BEGIN PRIVATE KEY----- MC4CAQAwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC -----END PRIVATE KEY-----
The same item dumped as asn1 yields:
0 30 46: SEQUENCE {
2 02 1: INTEGER 0
5 30 5: SEQUENCE {
7 06 3: OBJECT IDENTIFIER
: Ed 25519 signature algorithm { 1 3 101 112 }
: }
12 04 34: OCTET STRING
: 04 20 D4 EE 72 DB F9 13 58 4A D5 B6 D8 F1 F7 69
: F8 AD 3A FE 7C 28 CB F1 D4 FB E0 97 A8 8F 44 75
: 58 42
: }
Note that the value of the private key is:
D4 EE 72 DB F9 13 58 4A D5 B6 D8 F1 F7 69 F8 AD 3A FE 7C 28 CB F1 D4 FB E0 97 A8 8F 44 75 58 42
An example of the same Ed25519 private key encoded with an attribute and the public key:
-----BEGIN PRIVATE KEY----- MHICAQEwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC oB8wHQYKKoZIhvcNAQkJFDEPDA1DdXJkbGUgQ2hhaXJzgSEAGb9ECWmEzf6FQbrB Z9w7lshQhqowtrbLDFw4rXAxZuE= -----END PRIVATE KEY-----
The same item dumped as asn1 yields:
0 114: SEQUENCE {
2 1: INTEGER 1
5 5: SEQUENCE {
7 3: OBJECT IDENTIFIER '1 3 101 112'
: }
12 34: OCTET STRING, encapsulates {
14 32: OCTET STRING D4 EE 72 DB F9 13 58 4A D5 B6 D8 F1 F7
69 F8 AD 3A FE 7C 28 CB F1 D4 FB E0 97 A8 8F 44
75 58 42
: }
48 31: [0] {
50 29: SEQUENCE {
52 10: OBJECT IDENTIFIER '1 2 840 113549 1 9 9 20'
64 15: SET {
66 13: UTF8String 'Curdle Chairs'
: }
: }
: }
81 33: [1] 00 19 BF 44 09 69 84 CD FE 85 41 BA C1 67 DC 3B
96 C8 50 86 AA 30 B6 B6 CB 0C 5C 38 AD 70 31 66
E1
: }
Text and/or inspiration were drawn from [RFC5280], [RFC3279], [RFC4055], [RFC5480], and [RFC5639].
The following people discussed the document and provided feedback: Klaus Hartke, Ilari Liusvaara, Erwann Abalea, Rick Andrews, Rob Stradling, James Manger, Nikos Mavrogiannopoulos, Russ Housley, David Benjamin, Brian Smith, and Alex Wilson.
A big thank you to Symantec for kindly donating the OIDs used in this draft.
IANA is requested to assign a module OID from the "SMI for PKIX Module Identifier" registry for the ASN.1 module in Section 9.
The security considerations of [RFC5280], [RFC7748], and [RFC8032] apply accordingly.
The procedures for going from a private key to a public key are different for when used with Diffie-Hellman and when used with Edwards Signatures. This means that the same public key cannot be used for both ECDH and EdDSA.
| [RFC2119] | Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997. |
| [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. |
| [RFC5480] | Turner, S., Brown, D., Yiu, K., Housley, R. and T. Polk, "Elliptic Curve Cryptography Subject Public Key Information", RFC 5480, DOI 10.17487/RFC5480, March 2009. |
| [RFC5958] | Turner, S., "Asymmetric Key Packages", RFC 5958, DOI 10.17487/RFC5958, August 2010. |
| [RFC7748] | Langley, A., Hamburg, M. and S. Turner, "Elliptic Curves for Security", RFC 7748, DOI 10.17487/RFC7748, January 2016. |
| [RFC8032] | Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital Signature Algorithm (EdDSA)", RFC 8032, DOI 10.17487/RFC8032, January 2017. |
| [RFC3279] | Bassham, L., Polk, W. and R. Housley, "Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 3279, DOI 10.17487/RFC3279, April 2002. |
| [RFC4055] | Schaad, J., Kaliski, B. and R. Housley, "Additional Algorithms and Identifiers for RSA Cryptography for use in the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 4055, DOI 10.17487/RFC4055, June 2005. |
| [RFC5639] | Lochter, M. and J. Merkle, "Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation", RFC 5639, DOI 10.17487/RFC5639, March 2010. |
| [RFC7468] | Josefsson, S. and S. Leonard, "Textual Encodings of PKIX, PKCS, and CMS Structures", RFC 7468, DOI 10.17487/RFC7468, April 2015. |
There are a number of things that need to be dealt with when a new key part is decoded and imported into the system. A partial list of these includes:
Some systems are also going to be stricter on what they accept. As stated in [RFC5958], BER decoding of OneAsymmetricKey objects is a requirement for compliance. Despite this requirement, some acceptors will only decode DER formats. The following is a BER encoding of a private key, as such is is valid, but it may not be accepted by many systems.
-----BEGIN PRIVATE KEY-----
MIACAQAwgAYDK2VwAAAEIgQg1O5y2/kTWErVttjx92n4rTr+fCjL8dT74Jeoj0R1W
EIAAA==
-----END PRIVATE KEY-----
What follows here is a brief sampling of some incorrect keys.
In the following example, the private key does not match the masking requirements for X25519. For this example the top bits are set to zero and the bottom three bits are set to 001.
-----BEGIN PRIVATE KEY-----
MFMCAQEwBQYDK2VuBCIEIPj///////////////////////////////////////8/oS
MDIQCEfA0sN1I082XmYJVRh6NzWg92E9FgnTpqTYxTrqpaIg==
-----END PRIVATE KEY-----
In the following examples, the key is the wrong length because an all zero byte has been removed. In one case the first byte has been removed, in the other case the last byte has been removed.
-----BEGIN PRIVATE KEY-----
MFICAQEwBQYDK2VwBCIEIC3GfeUYbZGTAhwLEE2cbvJL7ivTlcy17VottfN6L8HwoS
IDIADBfk2Lv/J8H7YYwj/OmIcDx++jzVkKrKwS0/HjyQyM
-----END PRIVATE KEY-----
-----BEGIN PRIVATE KEY-----
MFICAQEwBQYDK2VwBCIEILJXn1VaLqvausjUaZexwI/ozmOFjfEk78KcYN+7hsNJoS
IDIACdQhJwzi/MCGcsQeQnIUh2JFybDxSrZxuLudJmpJLk
-----END PRIVATE KEY-----