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PROPOSED STANDARD
Errata Exist
Internet Engineering Task Force (IETF) S. Josefsson
Request for Comments: 8410 SJD AB
Category: Standards Track J. Schaad
ISSN: 2070-1721 August Cellars
August 2018
Algorithm Identifiers for Ed25519, Ed448, X25519, and X448
for Use in the Internet X.509 Public Key Infrastructure
Abstract
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 algorithms covered are X25519 and X448.
The encoding for public key, private key, and Edwards-curve Digital
Signature Algorithm (EdDSA) structures is provided.
Status of This Memo
This is an Internet Standards Track document.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Further information on
Internet Standards is available in Section 2 of RFC 7841.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
https://www.rfc-editor.org/info/rfc8410.
Copyright Notice
Copyright (c) 2018 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(https://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document. Code Components extracted from this document must
include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Requirements Terminology . . . . . . . . . . . . . . . . . . 3
3. Curve25519 and Curve448 Algorithm Identifiers . . . . . . . . 3
4. Subject Public Key Fields . . . . . . . . . . . . . . . . . . 4
5. Key Usage Bits . . . . . . . . . . . . . . . . . . . . . . . 5
6. EdDSA Signatures . . . . . . . . . . . . . . . . . . . . . . 6
7. Private Key Format . . . . . . . . . . . . . . . . . . . . . 7
8. Human-Readable Algorithm Names . . . . . . . . . . . . . . . 8
9. ASN.1 Module . . . . . . . . . . . . . . . . . . . . . . . . 9
10. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 11
10.1. Example Ed25519 Public Key . . . . . . . . . . . . . . . 11
10.2. Example X25519 Certificate . . . . . . . . . . . . . . . 12
10.3. Examples of Ed25519 Private Key . . . . . . . . . . . . 14
11. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 15
12. Security Considerations . . . . . . . . . . . . . . . . . . . 15
13. References . . . . . . . . . . . . . . . . . . . . . . . . . 16
13.1. Normative References . . . . . . . . . . . . . . . . . . 16
13.2. Informative References . . . . . . . . . . . . . . . . . 16
Appendix A. Invalid Encodings . . . . . . . . . . . . . . . . . 18
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 19
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 20
1. Introduction
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 associated
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 prehashing and the
HashEdDSA mode with prehashing. The convention used for identifying
the algorithm/curve combinations is to use "Ed25519" and "Ed448" for
the PureEdDSA mode. This document does not provide the conventions
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needed for the prehash versions of the signature algorithm. The use
of the OIDs is described for public keys, private keys and
signatures.
[RFC8032] additionally defines 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:
o The current implementations of Ed25519 do not support the use of
contexts; thus, if specified, it will potentially delay the use of
these algorithms further.
o EdDSA is the only IETF algorithm that currently supports the use
of contexts; however, there is a possibility that there will be
confusion between which algorithms need to have separate keys and
which do not. This may result in a decrease of security for those
other algorithms.
o There are still ongoing discussions among the cryptographic
community about how effective the use of contexts is for
preventing attacks.
o There needs to be discussions about the correct way to identify
when context strings are to be used. It is not clear if different
OIDs should be used for different contexts or the OID should
merely note that a context string needs to be provided.
2. Requirements Terminology
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. Curve25519 and Curve448 Algorithm Identifiers
Certificates conforming to [RFC5280] can convey a public key for any
public key algorithm. The certificate indicates the algorithm
through an algorithm identifier. An algorithm identifier consists of
an OID and optional parameters.
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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:
o algorithm identifies the cryptographic algorithm with an object
identifier. Four such OIDs are defined below.
o parameters, which are optional, are the associated parameters for
the algorithm identifier in the algorithm field.
In this document, we define four new OIDs for identifying the
different curve/algorithm pairs: the curves being curve25519 and
curve448 and the algorithms being ECDH and EdDSA in pure mode. For
all of the OIDs, the parameters MUST be absent.
It is possible to find systems that require the parameters to be
present. This can be due to either a defect in the original 1997
syntax or a programming error where developers never got input where
this was not true. The optimal solution is to fix these systems;
where this is not possible, the problem needs to be restricted to
that subsystem and not propagated to the Internet.
The same algorithm identifiers are used for identifying a public key,
a private key, and 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 }
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 ::= SEQUENCE {
algorithm AlgorithmIdentifier,
subjectPublicKey BIT STRING
}
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The fields in SubjectPublicKeyInfo have the following meanings:
o algorithm is the algorithm identifier and parameters for the
public key (see above).
o subjectPublicKey contains the byte stream of the public key. The
algorithms defined in this document always encode the public key
as an exact multiple of 8 bits.
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-----
5. Key Usage Bits
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.
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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.
6. EdDSA Signatures
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.
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7. Private Key Format
"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. The algorithm-
specific details of how a private key is encoded are 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 a
CurvePrivateKey object and wrapped by the OCTET STRING of the
"privateKey" field.
CurvePrivateKey ::= OCTET STRING
To encode an 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].
Josefsson & Schaad Standards Track [Page 7]
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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, 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 that 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.
8. Human-Readable Algorithm Names
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".
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9. ASN.1 Module
For reference purposes, the ASN.1 syntax is presented as an ASN.1
module here.
-- ASN.1 Module
Safecurves-pkix-18
{ iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-safecurves-pkix(93) }
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 }
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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 }
}
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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
10. Examples
This section contains illustrations of EdDSA public keys and
certificates, illustrating parameter choices.
10.1. Example Ed25519 Public Key
An example of an 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-----
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10.2. Example X25519 Certificate
An example of a self-issued PKIX certificate using Ed25519 to sign an
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)
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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-----
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10.3. Examples of Ed25519 Private Key
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 ASN.1 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-----
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The same item dumped as ASN.1 yields:
0 114: SEQUENCE {
2 1: INTEGER 1
5 5: SEQUENCE {
7 3: OBJECT IDENTIFIER '1 3 101 112'
: }
12 34: OCTET STRING, encapsulates {
: 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
: }
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
: }
11. IANA Considerations
For the ASN.1 module in Section 9, IANA has registered value 93 for
"id-mod-safecurves-pkix" in the "SMI Security for PKIX Module
Identifier" (1.3.6.1.5.5.7.0) registry.
The OIDs are being independently registered in the IANA registry "SMI
Security for Cryptographic Algorithms" in [RFC8411].
12. Security Considerations
The security considerations of [RFC5280], [RFC7748], and [RFC8032]
apply accordingly.
The procedures for going from a private key to a public key are
different when used with Diffie-Hellman versus when used with Edwards
Signatures. This means that the same public key cannot be used for
both ECDH and EdDSA.
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13. References
13.1. Normative References
[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/info/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/info/rfc5280>.
[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,
<https://www.rfc-editor.org/info/rfc5480>.
[RFC5958] Turner, S., "Asymmetric Key Packages", RFC 5958,
DOI 10.17487/RFC5958, August 2010,
<https://www.rfc-editor.org/info/rfc5958>.
[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <https://www.rfc-editor.org/info/rfc7748>.
[RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
Signature Algorithm (EdDSA)", RFC 8032,
DOI 10.17487/RFC8032, January 2017,
<https://www.rfc-editor.org/info/rfc8032>.
[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/info/rfc8174>.
13.2. Informative References
[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, <https://www.rfc-editor.org/info/rfc3279>.
Josefsson & Schaad Standards Track [Page 16]
RFC 8410 Safe Curves for X.509 August 2018
[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,
<https://www.rfc-editor.org/info/rfc4055>.
[RFC5639] Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
(ECC) Brainpool Standard Curves and Curve Generation",
RFC 5639, DOI 10.17487/RFC5639, March 2010,
<https://www.rfc-editor.org/info/rfc5639>.
[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/info/rfc7468>.
[RFC8411] Schaad, J. and R. Andrews, "IANA Registration for the
Cryptographic Algorithm Object Identifier Range",
RFC 8411, DOI 10.17487/RFC8411, August 2018,
<http://www.rfc-editor.org/info/rfc8411>.
Josefsson & Schaad Standards Track [Page 17]
RFC 8410 Safe Curves for X.509 August 2018
Appendix A. Invalid Encodings
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:
o ASN.1 encoding errors: Two items are highlighted here. First, the
use of an OCTET STRING rather than a BIT STRING for the public
key. The use of OCTET STRING was a copy error that existed in a
previous draft version of this document; the structure is correct
in [RFC5958]. However, any early implementation may have this
wrong. Second, the value of the version field is required to be 0
if the publicKey is absent and 1 if present. This is called out
in [RFC5958], but was not duplicated above.
o Key encoding errors: Both [RFC7748] and [RFC8032] have formatting
requirements for keys that need to be enforced. In some cases,
the enforcement is done at the time of importing, for example,
doing masking or a mod p operation. In other cases, the
enforcement is done by rejecting the keys and having an import
failure.
o Key mismatch errors: If a public key is provided, it may not agree
with the private key because either it is wrong or the wrong
algorithm was used.
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; it 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-----
Josefsson & Schaad Standards Track [Page 18]
RFC 8410 Safe Curves for X.509 August 2018
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-----
Acknowledgments
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
document.
Josefsson & Schaad Standards Track [Page 19]
RFC 8410 Safe Curves for X.509 August 2018
Authors' Addresses
Simon Josefsson
SJD AB
Email: simon@josefsson.org
Jim Schaad
August Cellars
Email: ietf@augustcellars.com
Josefsson & Schaad Standards Track [Page 20]
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