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Subject: RFC 8410: Algorithm Identifiers for Ed25519, Ed448, X25519, and X448 for Use in the Internet X.509 Public Key Infrastructure
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>Errata</a>] [<a href=3D"https://www.rfc-editor.org/info/rfc8410" title=3D"=
Info page">Info page</a>]         </span><br><span class=3D"pre noprint doc=
info">                                                                     =
   </span><br><span class=3D"pre noprint docinfo">                         =
                              PROPOSED STANDARD</span><br><span class=3D"pr=
e noprint docinfo">Updated by: <a href=3D"https://www.rfc-editor.org/rfc/rf=
c9295" target=3D"_blank">9295</a>                                          =
  <span style=3D"color: #C00;">Errata Exist</span></span><pre>Internet Engi=
neering Task Force (IETF)                      S. Josefsson
Request for Comments: 8410                                        SJD AB
Category: Standards Track                                      J. Schaad
ISSN: 2070-1721                                           August Cellars
                                                             August 2018


       <span class=3D"h1">Algorithm Identifiers for Ed25519, Ed448, X25519,=
 and X448</span>
        <span class=3D"h1">for Use in the Internet X.509 Public Key Infrast=
ructure</span>

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 <a href=3D"https://www.rfc-editor.org=
/rfc/rfc7841#section-2">Section&nbsp;2 of RFC 7841</a>.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   <a href=3D"https://www.rfc-editor.org/info/rfc8410">https://www.rfc-edit=
or.org/info/rfc8410</a>.

Copyright Notice

   Copyright (c) 2018 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to <a href=3D"https://www.rfc-editor.org/bcp/bc=
p78">BCP 78</a> and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (<a href=3D"https://trustee.ietf.org/license-info">https://trustee.ietf.=
org/license-info</a>) 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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span>


Table of Contents

   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-1">1</a>.  Int=
roduction  . . . . . . . . . . . . . . . . . . . . . . . .   <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-2">2</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-2">2</a>.  Req=
uirements Terminology  . . . . . . . . . . . . . . . . . .   <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-3">3</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-3">3</a>.  Cur=
ve25519 and Curve448 Algorithm Identifiers . . . . . . . .   <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-3">3</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-4">4</a>.  Sub=
ject Public Key Fields . . . . . . . . . . . . . . . . . .   <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-4">4</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-5">5</a>.  Key=
 Usage Bits  . . . . . . . . . . . . . . . . . . . . . . .   <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-5">5</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-6">6</a>.  EdD=
SA Signatures  . . . . . . . . . . . . . . . . . . . . . .   <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-6">6</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-7">7</a>.  Pri=
vate Key Format  . . . . . . . . . . . . . . . . . . . . .   <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-7">7</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-8">8</a>.  Hum=
an-Readable Algorithm Names  . . . . . . . . . . . . . . .   <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-8">8</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-9">9</a>.  ASN=
.1 Module  . . . . . . . . . . . . . . . . . . . . . . . .   <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-9">9</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-10">10</a>. Ex=
amples  . . . . . . . . . . . . . . . . . . . . . . . . . .  <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-11">11</a>
     <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-10.1">10.1</=
a>.  Example Ed25519 Public Key . . . . . . . . . . . . . . .  <a href=3D"h=
ttps://www.rfc-editor.org/rfc/rfc8410#page-11">11</a>
     <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-10.2">10.2</=
a>.  Example X25519 Certificate . . . . . . . . . . . . . . .  <a href=3D"h=
ttps://www.rfc-editor.org/rfc/rfc8410#page-12">12</a>
     <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-10.3">10.3</=
a>.  Examples of Ed25519 Private Key  . . . . . . . . . . . .  <a href=3D"h=
ttps://www.rfc-editor.org/rfc/rfc8410#page-14">14</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-11">11</a>. IA=
NA Considerations . . . . . . . . . . . . . . . . . . . . .  <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-15">15</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-12">12</a>. Se=
curity Considerations . . . . . . . . . . . . . . . . . . .  <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-15">15</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-13">13</a>. Re=
ferences  . . . . . . . . . . . . . . . . . . . . . . . . .  <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-16">16</a>
     <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-13.1">13.1</=
a>.  Normative References . . . . . . . . . . . . . . . . . .  <a href=3D"h=
ttps://www.rfc-editor.org/rfc/rfc8410#page-16">16</a>
     <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#section-13.2">13.2</=
a>.  Informative References . . . . . . . . . . . . . . . . .  <a href=3D"h=
ttps://www.rfc-editor.org/rfc/rfc8410#page-16">16</a>
   <a href=3D"https://www.rfc-editor.org/rfc/rfc8410#appendix-A">Appendix A=
</a>.  Invalid Encodings  . . . . . . . . . . . . . . . . .  <a href=3D"htt=
ps://www.rfc-editor.org/rfc/rfc8410#page-18">18</a>
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  <a hr=
ef=3D"https://www.rfc-editor.org/rfc/rfc8410#page-19">19</a>
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  <a hr=
ef=3D"https://www.rfc-editor.org/rfc/rfc8410#page-20">20</a>

<span class=3D"h2"><a class=3D"selflink" id=3D"section-1" href=3D"https://w=
ww.rfc-editor.org/rfc/rfc8410#section-1">1</a>.  Introduction</span>

   In [<a href=3D"https://www.rfc-editor.org/rfc/rfc7748" title=3D"&quot;El=
liptic Curves for Security&quot;">RFC7748</a>], the elliptic curves curve25=
519 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.

   [<a id=3D"ref-RFC7748">RFC7748</a>] describes the operations on these cu=
rves 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 [<a href=3D"https://www.rfc-editor.org/rfc/rfc8032" title=3D"&quot;Ed=
wards-Curve Digital Signature Algorithm (EdDSA)&quot;">RFC8032</a>] the ell=
iptic 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.

   [<a id=3D"ref-RFC8032">RFC8032</a>] 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.

<span class=3D"h2"><a class=3D"selflink" id=3D"section-2" href=3D"https://w=
ww.rfc-editor.org/rfc/rfc8410#section-2">2</a>.  Requirements Terminology</=
span>

   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
   <a href=3D"https://www.rfc-editor.org/bcp/bcp14">BCP 14</a> [<a href=3D"=
https://www.rfc-editor.org/rfc/rfc2119" title=3D"&quot;Key words for use in=
 RFCs to Indicate Requirement Levels&quot;">RFC2119</a>] [<a href=3D"https:=
//www.rfc-editor.org/rfc/rfc8174" title=3D"&quot;Ambiguity of Uppercase vs =
Lowercase in RFC 2119 Key Words&quot;">RFC8174</a>] when, and only when, th=
ey appear in all
   capitals, as shown here.

<span class=3D"h2"><a class=3D"selflink" id=3D"section-3" href=3D"https://w=
ww.rfc-editor.org/rfc/rfc8410#section-3">3</a>.  Curve25519 and Curve448 Al=
gorithm Identifiers</span>

   Certificates conforming to [<a href=3D"https://www.rfc-editor.org/rfc/rf=
c5280" title=3D"&quot;Internet X.509 Public Key Infrastructure Certificate =
and Certificate Revocation List (CRL) Profile&quot;">RFC5280</a>] can conve=
y 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  ::=3D  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 ::=3D { 1 3 101 110 }
   id-X448      OBJECT IDENTIFIER ::=3D { 1 3 101 111 }
   id-Ed25519   OBJECT IDENTIFIER ::=3D { 1 3 101 112 }
   id-Ed448     OBJECT IDENTIFIER ::=3D { 1 3 101 113 }

<span class=3D"h2"><a class=3D"selflink" id=3D"section-4" href=3D"https://w=
ww.rfc-editor.org/rfc/rfc8410#section-4">4</a>.  Subject Public Key Fields<=
/span>

   In the X.509 certificate, the subjectPublicKeyInfo field has the
   SubjectPublicKeyInfo type, which has the following ASN.1 syntax:

   SubjectPublicKeyInfo  ::=3D  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 [<a href=3D"https://www.rfc-editor.org/rfc/rfc7748" title=3D"&quot;=
Elliptic Curves for Security&quot;">RFC7748</a>] and [<a href=3D"https://ww=
w.rfc-editor.org/rfc/rfc8032" title=3D"&quot;Edwards-Curve Digital Signatur=
e Algorithm (EdDSA)&quot;">RFC8032</a>] define the public key value as bein=
g 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 [<a href=3D"https://www.rfc-editor.org/rfc/rfc7468" =
title=3D"&quot;Textual Encodings of PKIX, PKCS, and CMS Structures&quot;">R=
FC7468</a>].

   -----BEGIN PUBLIC KEY-----
   MCowBQYDK2VwAyEAGb9ECWmEzf6FQbrBZ9w7lshQhqowtrbLDFw4rXAxZuE=3D
   -----END PUBLIC KEY-----

<span class=3D"h2"><a class=3D"selflink" id=3D"section-5" href=3D"https://w=
ww.rfc-editor.org/rfc/rfc8410#section-5">5</a>.  Key Usage Bits</span>

   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.

<span class=3D"h2"><a class=3D"selflink" id=3D"section-6" href=3D"https://w=
ww.rfc-editor.org/rfc/rfc8410#section-6">6</a>.  EdDSA Signatures</span>

   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  ::=3D  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 <a href=3D"https://www=
.rfc-editor.org/rfc/rfc8032#section-3.3">Section&nbsp;3.3 of
   [RFC8032]</a>.  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"></span>
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span>


<span class=3D"h2"><a class=3D"selflink" id=3D"section-7" href=3D"https://w=
ww.rfc-editor.org/rfc/rfc8410#section-7">7</a>.  Private Key Format</span>

   "Asymmetric Key Packages" [<a href=3D"https://www.rfc-editor.org/rfc/rfc=
5958" title=3D"&quot;Asymmetric Key Packages&quot;">RFC5958</a>] 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 ::=3D SEQUENCE {
      version Version,
      privateKeyAlgorithm PrivateKeyAlgorithmIdentifier,
      privateKey PrivateKey,
      attributes [0] IMPLICIT Attributes OPTIONAL,
      ...,
      [[2: publicKey [1] IMPLICIT PublicKey OPTIONAL ]],
      ...
   }

   PrivateKey ::=3D OCTET STRING

   PublicKey ::=3D 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 ::=3D 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 [<a href=3D"https://www.rfc-editor.or=
g/rfc/rfc7748" title=3D"&quot;Elliptic Curves for Security&quot;">RFC7748</=
a>] and [<a href=3D"https://www.rfc-editor.org/rfc/rfc8032" title=3D"&quot;=
Edwards-Curve Digital Signature Algorithm (EdDSA)&quot;">RFC8032</a>].













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              [Page 7]</span></pre>
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-8"></span>
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span>


   The following is an example of a private key encoded using the
   textual encoding defined in [<a href=3D"https://www.rfc-editor.org/rfc/r=
fc7468" title=3D"&quot;Textual Encodings of PKIX, PKCS, and CMS Structures&=
quot;">RFC7468</a>].

   -----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 [<a href=3D"https://www.rfc-edi=
tor.org/rfc/rfc7468" title=3D"&quot;Textual Encodings of PKIX, PKCS, and CM=
S Structures&quot;">RFC7468</a>] is used.

   -----BEGIN PRIVATE KEY-----
   MHICAQEwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC
   oB8wHQYKKoZIhvcNAQkJFDEPDA1DdXJkbGUgQ2hhaXJzgSEAGb9ECWmEzf6FQbrB
   Z9w7lshQhqowtrbLDFw4rXAxZuE=3D
   -----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
   [<a href=3D"https://www.rfc-editor.org/rfc/rfc7748" title=3D"&quot;Ellip=
tic Curves for Security&quot;">RFC7748</a>].  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.

<span class=3D"h2"><a class=3D"selflink" id=3D"section-8" href=3D"https://w=
ww.rfc-editor.org/rfc/rfc8410#section-8">8</a>.  Human-Readable Algorithm N=
ames</span>

   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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              [Page 8]</span></pre>
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-9"></span>
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 8410</a>                  Safe Curves for X.509              August 2018</=
span>


<span class=3D"h2"><a class=3D"selflink" id=3D"section-9" href=3D"https://w=
ww.rfc-editor.org/rfc/rfc8410#section-9">9</a>.  ASN.1 Module</span>

   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 ::=3D
   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 ::=3D { 1 3 101 }

   id-X25519        OBJECT IDENTIFIER ::=3D { id-edwards-curve-algs 110 }
   id-X448          OBJECT IDENTIFIER ::=3D { id-edwards-curve-algs 111 }
   id-Ed25519       OBJECT IDENTIFIER ::=3D { id-edwards-curve-algs 112 }
   id-Ed448         OBJECT IDENTIFIER ::=3D { id-edwards-curve-algs 113 }









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              [Page 9]</span></pre>
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-10"></span>
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span>


    sa-Ed25519 SIGNATURE-ALGORITHM ::=3D {
       IDENTIFIER id-Ed25519
        PARAMS ARE absent
        PUBLIC-KEYS {pk-Ed25519}
        SMIME-CAPS { IDENTIFIED BY id-Ed25519 }
    }

    pk-Ed25519 PUBLIC-KEY ::=3D {
        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 ::=3D {
        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 ::=3D {
        IDENTIFIER id-X25519
        -- KEY no ASN.1 wrapping --
        PARAMS ARE absent
        CERT-KEY-USAGE { keyAgreement }
        PRIVATE-KEY CurvePrivateKey
    }

    KeyWrapAlgorithms KEY-WRAP ::=3D {
        kwa-aes128-wrap | kwa-aes256-wrap,
        ...
    }

    kaa-X448 KEY-AGREE ::=3D {
        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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             [Page 10]</span></pre>
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span>


    pk-X448 PUBLIC-KEY ::=3D {
        IDENTIFIER id-X448
        -- KEY no ASN.1 wrapping --
        PARAMS ARE absent
        CERT-KEY-USAGE { keyAgreement }
        PRIVATE-KEY CurvePrivateKey
    }

   CurvePrivateKey ::=3D OCTET STRING


   END

<span class=3D"h2"><a class=3D"selflink" id=3D"section-10" href=3D"https://=
www.rfc-editor.org/rfc/rfc8410#section-10">10</a>.  Examples</span>

   This section contains illustrations of EdDSA public keys and
   certificates, illustrating parameter choices.

<span class=3D"h3"><a class=3D"selflink" id=3D"section-10.1" href=3D"https:=
//www.rfc-editor.org/rfc/rfc8410#section-10.1">10.1</a>.  Example Ed25519 P=
ublic Key</span>

   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=3D
         -----END PUBLIC KEY-----


















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-12"></span>
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span>


<span class=3D"h3"><a class=3D"selflink" id=3D"section-10.2" href=3D"https:=
//www.rfc-editor.org/rfc/rfc8410#section-10.2">10.2</a>.  Example X25519 Ce=
rtificate</span>

   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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             [Page 12]</span></pre>
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span>


   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=3D=3D
   -----END CERTIFICATE-----




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             [Page 13]</span></pre>
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-14"></span>
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 8410</a>                  Safe Curves for X.509              August 2018</=
span>


<span class=3D"h3"><a class=3D"selflink" id=3D"section-10.3" href=3D"https:=
//www.rfc-editor.org/rfc/rfc8410#section-10.3">10.3</a>.  Examples of Ed255=
19 Private Key</span>

   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=3D
   -----END PRIVATE KEY-----
















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-15"></span>
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span>


   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
          :   }

<span class=3D"h2"><a class=3D"selflink" id=3D"section-11" href=3D"https://=
www.rfc-editor.org/rfc/rfc8410#section-11">11</a>.  IANA Considerations</sp=
an>

   For the ASN.1 module in <a href=3D"https://www.rfc-editor.org/rfc/rfc841=
0#section-9">Section 9</a>, 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 [<a href=3D"https://www.rfc-ed=
itor.org/rfc/rfc8411" title=3D"&quot;IANA Registration for the Cryptographi=
c Algorithm Object Identifier Range&quot;">RFC8411</a>].

<span class=3D"h2"><a class=3D"selflink" id=3D"section-12" href=3D"https://=
www.rfc-editor.org/rfc/rfc8410#section-12">12</a>.  Security Considerations=
</span>

   The security considerations of [<a href=3D"https://www.rfc-editor.org/rf=
c/rfc5280" title=3D"&quot;Internet X.509 Public Key Infrastructure Certific=
ate and Certificate Revocation List (CRL) Profile&quot;">RFC5280</a>], [<a =
href=3D"https://www.rfc-editor.org/rfc/rfc7748" title=3D"&quot;Elliptic Cur=
ves for Security&quot;">RFC7748</a>], and [<a href=3D"https://www.rfc-edito=
r.org/rfc/rfc8032" title=3D"&quot;Edwards-Curve Digital Signature Algorithm=
 (EdDSA)&quot;">RFC8032</a>]
   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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-16"></span>
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span>


<span class=3D"h2"><a class=3D"selflink" id=3D"section-13" href=3D"https://=
www.rfc-editor.org/rfc/rfc8410#section-13">13</a>.  References</span>

<span class=3D"h3"><a class=3D"selflink" id=3D"section-13.1" href=3D"https:=
//www.rfc-editor.org/rfc/rfc8410#section-13.1">13.1</a>.  Normative Referen=
ces</span>

   [<a id=3D"ref-RFC2119">RFC2119</a>]  Bradner, S., "Key words for use in =
RFCs to Indicate
              Requirement Levels", <a href=3D"https://www.rfc-editor.org/bc=
p/bcp14">BCP 14</a>, <a href=3D"https://www.rfc-editor.org/rfc/rfc2119">RFC=
 2119</a>,
              DOI 10.17487/RFC2119, March 1997,
              &lt;<a href=3D"https://www.rfc-editor.org/info/rfc2119">https=
://www.rfc-editor.org/info/rfc2119</a>&gt;.

   [<a id=3D"ref-RFC5280">RFC5280</a>]  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", <a href=3D"https://www.rfc-editor.org/rfc/rfc=
5280">RFC 5280</a>, DOI 10.17487/RFC5280, May 2008,
              &lt;<a href=3D"https://www.rfc-editor.org/info/rfc5280">https=
://www.rfc-editor.org/info/rfc5280</a>&gt;.

   [<a id=3D"ref-RFC5480">RFC5480</a>]  Turner, S., Brown, D., Yiu, K., Hou=
sley, R., and T. Polk,
              "Elliptic Curve Cryptography Subject Public Key
              Information", <a href=3D"https://www.rfc-editor.org/rfc/rfc54=
80">RFC 5480</a>, DOI 10.17487/RFC5480, March 2009,
              &lt;<a href=3D"https://www.rfc-editor.org/info/rfc5480">https=
://www.rfc-editor.org/info/rfc5480</a>&gt;.

   [<a id=3D"ref-RFC5958">RFC5958</a>]  Turner, S., "Asymmetric Key Package=
s", <a href=3D"https://www.rfc-editor.org/rfc/rfc5958">RFC 5958</a>,
              DOI 10.17487/RFC5958, August 2010,
              &lt;<a href=3D"https://www.rfc-editor.org/info/rfc5958">https=
://www.rfc-editor.org/info/rfc5958</a>&gt;.

   [<a id=3D"ref-RFC7748">RFC7748</a>]  Langley, A., Hamburg, M., and S. Tu=
rner, "Elliptic Curves
              for Security", <a href=3D"https://www.rfc-editor.org/rfc/rfc7=
748">RFC 7748</a>, DOI 10.17487/RFC7748, January
              2016, &lt;<a href=3D"https://www.rfc-editor.org/info/rfc7748"=
>https://www.rfc-editor.org/info/rfc7748</a>&gt;.

   [<a id=3D"ref-RFC8032">RFC8032</a>]  Josefsson, S. and I. Liusvaara, "Ed=
wards-Curve Digital
              Signature Algorithm (EdDSA)", <a href=3D"https://www.rfc-edit=
or.org/rfc/rfc8032">RFC 8032</a>,
              DOI 10.17487/RFC8032, January 2017,
              &lt;<a href=3D"https://www.rfc-editor.org/info/rfc8032">https=
://www.rfc-editor.org/info/rfc8032</a>&gt;.

   [<a id=3D"ref-RFC8174">RFC8174</a>]  Leiba, B., "Ambiguity of Uppercase =
vs Lowercase in <a href=3D"https://www.rfc-editor.org/rfc/rfc2119">RFC</a>
              <a href=3D"https://www.rfc-editor.org/rfc/rfc2119">2119</a> K=
ey Words", <a href=3D"https://www.rfc-editor.org/bcp/bcp14">BCP 14</a>, <a =
href=3D"https://www.rfc-editor.org/rfc/rfc8174">RFC 8174</a>, DOI 10.17487/=
RFC8174,
              May 2017, &lt;<a href=3D"https://www.rfc-editor.org/info/rfc8=
174">https://www.rfc-editor.org/info/rfc8174</a>&gt;.

<span class=3D"h3"><a class=3D"selflink" id=3D"section-13.2" href=3D"https:=
//www.rfc-editor.org/rfc/rfc8410#section-13.2">13.2</a>.  Informative Refer=
ences</span>

   [<a id=3D"ref-RFC3279">RFC3279</a>]  Bassham, L., Polk, W., and R. Housl=
ey, "Algorithms and
              Identifiers for the Internet X.509 Public Key
              Infrastructure Certificate and Certificate Revocation List
              (CRL) Profile", <a href=3D"https://www.rfc-editor.org/rfc/rfc=
3279">RFC 3279</a>, DOI 10.17487/RFC3279, April
              2002, &lt;<a href=3D"https://www.rfc-editor.org/info/rfc3279"=
>https://www.rfc-editor.org/info/rfc3279</a>&gt;.







<span class=3D"grey">Josefsson &amp; Schaad           Standards Track      =
             [Page 16]</span></pre>
<hr class=3D"noprint"><!--NewPage--><pre class=3D"newpage"><span id=3D"page=
-17"></span>
<span class=3D"grey"><a href=3D"https://www.rfc-editor.org/rfc/rfc8410">RFC=
 8410</a>                  Safe Curves for X.509              August 2018</=
span>


   [<a id=3D"ref-RFC4055">RFC4055</a>]  Schaad, J., Kaliski, B., and R. Hou=
sley, "Additional
              Algorithms and Identifiers for RSA Cryptography for use in
              the Internet X.509 Public Key Infrastructure Certificate
              and Certificate Revocation List (CRL) Profile", <a href=3D"ht=
tps://www.rfc-editor.org/rfc/rfc4055">RFC 4055</a>,
              DOI 10.17487/RFC4055, June 2005,
              &lt;<a href=3D"https://www.rfc-editor.org/info/rfc4055">https=
://www.rfc-editor.org/info/rfc4055</a>&gt;.

   [<a id=3D"ref-RFC5639">RFC5639</a>]  Lochter, M. and J. Merkle, "Ellipti=
c Curve Cryptography
              (ECC) Brainpool Standard Curves and Curve Generation",
              <a href=3D"https://www.rfc-editor.org/rfc/rfc5639">RFC 5639</=
a>, DOI 10.17487/RFC5639, March 2010,
              &lt;<a href=3D"https://www.rfc-editor.org/info/rfc5639">https=
://www.rfc-editor.org/info/rfc5639</a>&gt;.

   [<a id=3D"ref-RFC7468">RFC7468</a>]  Josefsson, S. and S. Leonard, "Text=
ual Encodings of PKIX,
              PKCS, and CMS Structures", <a href=3D"https://www.rfc-editor.=
org/rfc/rfc7468">RFC 7468</a>, DOI 10.17487/RFC7468,
              April 2015, &lt;<a href=3D"https://www.rfc-editor.org/info/rf=
c7468">https://www.rfc-editor.org/info/rfc7468</a>&gt;.

   [<a id=3D"ref-RFC8411">RFC8411</a>]  Schaad, J. and R. Andrews, "IANA Re=
gistration for the
              Cryptographic Algorithm Object Identifier Range",
              <a href=3D"https://www.rfc-editor.org/rfc/rfc8411">RFC 8411</=
a>, DOI 10.17487/RFC8411, August 2018,
              &lt;<a href=3D"https://www.rfc-editor.org/info/rfc8411">http:=
//www.rfc-editor.org/info/rfc8411</a>&gt;.































<span class=3D"grey">Josefsson &amp; Schaad           Standards Track      =
             [Page 17]</span></pre>
<hr class=3D"noprint"><!--NewPage--><pre class=3D"newpage"><span id=3D"page=
-18"></span>
<span class=3D"grey"><a href=3D"https://www.rfc-editor.org/rfc/rfc8410">RFC=
 8410</a>                  Safe Curves for X.509              August 2018</=
span>


<span class=3D"h2"><a class=3D"selflink" id=3D"appendix-A" href=3D"https://=
www.rfc-editor.org/rfc/rfc8410#appendix-A">Appendix A</a>.  Invalid Encodin=
gs</span>

   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 [<a href=3D"https://www.rfc-editor.org/rfc/rfc5958" title=3D"&quot=
;Asymmetric Key Packages&quot;">RFC5958</a>].  However, any early implement=
ation 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 [<a href=3D"https://www.rfc-editor.org/rfc/rfc5958" title=3D"&quot=
;Asymmetric Key Packages&quot;">RFC5958</a>], but was not duplicated above.

   o  Key encoding errors: Both [<a href=3D"https://www.rfc-editor.org/rfc/=
rfc7748" title=3D"&quot;Elliptic Curves for Security&quot;">RFC7748</a>] an=
d [<a href=3D"https://www.rfc-editor.org/rfc/rfc8032" title=3D"&quot;Edward=
s-Curve Digital Signature Algorithm (EdDSA)&quot;">RFC8032</a>] have format=
ting
      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 [<a href=3D"https://www.rfc-editor.org/rfc/rfc5958" title=3D"&=
quot;Asymmetric Key Packages&quot;">RFC5958</a>], BER decoding of OneAsymme=
tricKey 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=3D=3D
   -----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=3D=3D
   -----END PRIVATE KEY-----




<span class=3D"grey">Josefsson &amp; Schaad           Standards Track      =
             [Page 18]</span></pre>
<hr class=3D"noprint"><!--NewPage--><pre class=3D"newpage"><span id=3D"page=
-19"></span>
<span class=3D"grey"><a href=3D"https://www.rfc-editor.org/rfc/rfc8410">RFC=
 8410</a>                  Safe Curves for X.509              August 2018</=
span>


   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 [<a href=3D"https://www.rfc-edit=
or.org/rfc/rfc5280" title=3D"&quot;Internet X.509 Public Key Infrastructure=
 Certificate and Certificate Revocation List (CRL) Profile&quot;">RFC5280</=
a>], [<a href=3D"https://www.rfc-editor.org/rfc/rfc3279" title=3D"&quot;Alg=
orithms and Identifiers for the Internet X.509 Public Key Infrastructure Ce=
rtificate and Certificate Revocation List (CRL) Profile&quot;">RFC3279</a>]=
,
   [<a href=3D"https://www.rfc-editor.org/rfc/rfc4055" title=3D"&quot;Addit=
ional Algorithms and Identifiers for RSA Cryptography for use in the Intern=
et X.509 Public Key Infrastructure Certificate and Certificate Revocation L=
ist (CRL) Profile&quot;">RFC4055</a>], [<a href=3D"https://www.rfc-editor.o=
rg/rfc/rfc5480" title=3D"&quot;Elliptic Curve Cryptography Subject Public K=
ey Information&quot;">RFC5480</a>], and [<a href=3D"https://www.rfc-editor.=
org/rfc/rfc5639" title=3D"&quot;Elliptic Curve Cryptography (ECC) Brainpool=
 Standard Curves and Curve Generation&quot;">RFC5639</a>].

   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.

























<span class=3D"grey">Josefsson &amp; Schaad           Standards Track      =
             [Page 19]</span></pre>
<hr class=3D"noprint"><!--NewPage--><pre class=3D"newpage"><span id=3D"page=
-20"></span>
<span class=3D"grey"><a href=3D"https://www.rfc-editor.org/rfc/rfc8410">RFC=
 8410</a>                  Safe Curves for X.509              August 2018</=
span>


Authors' Addresses

   Simon Josefsson
   SJD AB

   Email: simon@josefsson.org


   Jim Schaad
   August Cellars

   Email: ietf@augustcellars.com







































Josefsson &amp; Schaad           Standards Track                   [Page 20=
]
</pre>




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