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<pre>Internet Engineering Task Force (IETF) I. Liusvaara
Request for Comments: 8037 Independent
Category: Standards Track January 2017
ISSN: 2070-1721
<span class="h1">CFRG Elliptic Curve Diffie-Hellman (ECDH) and Signatures</span>
<span class="h1">in JSON Object Signing and Encryption (JOSE)</span>
Abstract
This document defines how to use the Diffie-Hellman algorithms
"X25519" and "X448" as well as the signature algorithms "Ed25519" and
"Ed448" from the IRTF CFRG elliptic curves work in JSON Object
Signing and Encryption (JOSE).
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="./rfc7841#section-2">Section 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="http://www.rfc-editor.org/info/rfc8037">http://www.rfc-editor.org/info/rfc8037</a>.
Copyright Notice
Copyright (c) 2017 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to <a href="https://www.rfc-editor.org/bcp/bcp78">BCP 78</a> and the IETF Trust's Legal
Provisions Relating to IETF Documents
(<a href="http://trustee.ietf.org/license-info">http://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.
<span class="grey">Liusvaara Standards Track [Page 1]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-2" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
Table of Contents
<a href="#section-1">1</a>. Introduction . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-2">2</a>
<a href="#section-1.1">1.1</a>. Terminology . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-3">3</a>
<a href="#section-2">2</a>. Key Type "OKP" . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-3">3</a>
<a href="#section-3">3</a>. Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-3.1">3.1</a>. Signatures . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-3.1.1">3.1.1</a>. Signing . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-3.1.2">3.1.2</a>. Verification . . . . . . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-3.2">3.2</a>. ECDH-ES . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-3.2.1">3.2.1</a>. Performing the ECDH Operation . . . . . . . . . . . . <a href="#page-5">5</a>
<a href="#section-4">4</a>. Security Considerations . . . . . . . . . . . . . . . . . . . <a href="#page-5">5</a>
<a href="#section-5">5</a>. IANA Considerations . . . . . . . . . . . . . . . . . . . . . <a href="#page-6">6</a>
<a href="#section-6">6</a>. References . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-8">8</a>
<a href="#section-6.1">6.1</a>. Normative References . . . . . . . . . . . . . . . . . . <a href="#page-8">8</a>
<a href="#section-6.2">6.2</a>. Informative References . . . . . . . . . . . . . . . . . <a href="#page-8">8</a>
<a href="#appendix-A">Appendix A</a>. Examples . . . . . . . . . . . . . . . . . . . . . . <a href="#page-9">9</a>
<a href="#appendix-A.1">A.1</a>. Ed25519 Private Key . . . . . . . . . . . . . . . . . . . <a href="#page-9">9</a>
<a href="#appendix-A.2">A.2</a>. Ed25519 Public Key . . . . . . . . . . . . . . . . . . . <a href="#page-9">9</a>
<a href="#appendix-A.3">A.3</a>. JWK Thumbprint Canonicalization . . . . . . . . . . . . . <a href="#page-9">9</a>
<a href="#appendix-A.4">A.4</a>. Ed25519 Signing . . . . . . . . . . . . . . . . . . . . . <a href="#page-10">10</a>
<a href="#appendix-A.5">A.5</a>. Ed25519 Validation . . . . . . . . . . . . . . . . . . . <a href="#page-11">11</a>
<a href="#appendix-A.6">A.6</a>. ECDH-ES with X25519 . . . . . . . . . . . . . . . . . . . <a href="#page-11">11</a>
<a href="#appendix-A.7">A.7</a>. ECDH-ES with X448 . . . . . . . . . . . . . . . . . . . . <a href="#page-12">12</a>
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-14">14</a>
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-14">14</a>
<span class="h2"><a class="selflink" id="section-1" href="#section-1">1</a>. Introduction</span>
The Internet Research Task Force (IRTF) Crypto Forum Research Group
(CFRG) selected new Diffie-Hellman algorithms ("X25519" and "X448";
[<a href="./rfc7748" title=""Elliptic Curves for Security"">RFC7748</a>]) and signature algorithms ("Ed25519" and "Ed448";
[<a href="./rfc8032" title=""Edwards-Curve Digital Signature Algorithm (EdDSA)"">RFC8032</a>]) for asymmetric key cryptography. This document defines
how to use those algorithms in JOSE in an interoperable manner.
This document defines the conventions to use in the context of
[<a href="./rfc7515" title=""JSON Web Signature (JWS)"">RFC7515</a>], [<a href="./rfc7516" title=""JSON Web Encryption (JWE)"">RFC7516</a>], and [<a href="./rfc7517" title=""JSON Web Key (JWK)"">RFC7517</a>].
While the CFRG also defined two pairs of isogenous elliptic curves
that underlie these algorithms, these curves are not directly
exposed, as the algorithms laid on top are sufficient for the
purposes of JOSE and are much easier to use.
All inputs to and outputs from the Elliptic Curve Diffie-Hellman
(ECDH) and signature functions are defined to be octet strings, with
the exception of outputs of verification functions, which are
booleans.
<span class="grey">Liusvaara Standards Track [Page 2]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-3" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
<span class="h3"><a class="selflink" id="section-1.1" href="#section-1.1">1.1</a>. Terminology</span>
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 [<a href="./rfc2119" title=""Key words for use in RFCs to Indicate Requirement Levels"">RFC2119</a>].
"JWS Signing Input" and "JWS Signature" are defined by [<a href="./rfc7515" title=""JSON Web Signature (JWS)"">RFC7515</a>].
"Key Agreement with Elliptic Curve Diffie-Hellman Ephemeral Static"
is defined by <a href="./rfc7518#section-4.6">Section 4.6 of [RFC7518]</a>.
The JOSE key format ("JSON Web Key (JWK)") is defined by [<a href="./rfc7517" title=""JSON Web Key (JWK)"">RFC7517</a>]
and thumbprints for it ("JSON Web Key (JWK) Thumbprint") in
[<a href="./rfc7638" title=""JSON Web Key (JWK) Thumbprint"">RFC7638</a>].
<span class="h2"><a class="selflink" id="section-2" href="#section-2">2</a>. Key Type "OKP"</span>
A new key type (kty) value "OKP" (Octet Key Pair) is defined for
public key algorithms that use octet strings as private and public
keys. It has the following parameters:
o The parameter "kty" MUST be "OKP".
o The parameter "crv" MUST be present and contain the subtype of the
key (from the "JSON Web Elliptic Curve" registry).
o The parameter "x" MUST be present and contain the public key
encoded using the base64url [<a href="./rfc4648" title=""The Base16, Base32, and Base64 Data Encodings"">RFC4648</a>] encoding.
o The parameter "d" MUST be present for private keys and contain the
private key encoded using the base64url encoding. This parameter
MUST NOT be present for public keys.
Note: Do not assume that there is an underlying elliptic curve,
despite the existence of the "crv" and "x" parameters. (For
instance, this key type could be extended to represent Diffie-Hellman
(DH) algorithms based on hyperelliptic surfaces.)
When calculating JWK Thumbprints [<a href="./rfc7638" title=""JSON Web Key (JWK) Thumbprint"">RFC7638</a>], the three public key
fields are included in the hash input in lexicographic order: "crv",
"kty", and "x".
<span class="grey">Liusvaara Standards Track [Page 3]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-4" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
<span class="h2"><a class="selflink" id="section-3" href="#section-3">3</a>. Algorithms</span>
<span class="h3"><a class="selflink" id="section-3.1" href="#section-3.1">3.1</a>. Signatures</span>
For the purpose of using the Edwards-curve Digital Signature
Algorithm (EdDSA) for signing data using "JSON Web Signature (JWS)"
[<a href="./rfc7515" title=""JSON Web Signature (JWS)"">RFC7515</a>], algorithm "EdDSA" is defined here, to be applied as the
value of the "alg" parameter.
The following key subtypes are defined here for use with EdDSA:
"crv" EdDSA Variant
Ed25519 Ed25519
Ed448 Ed448
The key type used with these keys is "OKP" and the algorithm used for
signing is "EdDSA". These subtypes MUST NOT be used for Elliptic
Curve Diffie-Hellman Ephemeral Static (ECDH-ES).
The EdDSA variant used is determined by the subtype of the key
(Ed25519 for "Ed25519" and Ed448 for "Ed448").
<span class="h4"><a class="selflink" id="section-3.1.1" href="#section-3.1.1">3.1.1</a>. Signing</span>
Signing for these is performed by applying the signing algorithm
defined in [<a href="./rfc8032" title=""Edwards-Curve Digital Signature Algorithm (EdDSA)"">RFC8032</a>] to the private key (as private key), public key
(as public key), and the JWS Signing Input (as message). The
resulting signature is the JWS Signature. All inputs and outputs are
octet strings.
<span class="h4"><a class="selflink" id="section-3.1.2" href="#section-3.1.2">3.1.2</a>. Verification</span>
Verification is performed by applying the verification algorithm
defined in [<a href="./rfc8032" title=""Edwards-Curve Digital Signature Algorithm (EdDSA)"">RFC8032</a>] to the public key (as public key), the JWS
Signing Input (as message), and the JWS Signature (as signature).
All inputs are octet strings. If the algorithm accepts, the
signature is valid; otherwise, the signature is invalid.
<span class="h3"><a class="selflink" id="section-3.2" href="#section-3.2">3.2</a>. ECDH-ES</span>
The following key subtypes are defined here for purpose of "Key
Agreement with Elliptic Curve Diffie-Hellman Ephemeral Static"
(ECDH-ES):
"crv" ECDH Function Applied
X25519 X25519
X448 X448
<span class="grey">Liusvaara Standards Track [Page 4]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-5" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
The key type used with these keys is "OKP". These subtypes MUST NOT
be used for signing.
<a href="./rfc7518#section-4.6">Section 4.6 of [RFC7518]</a> defines the ECDH-ES algorithms
"ECDH-ES+A128KW", "ECDH-ES+A192KW", "ECDH-ES+A256KW", and "ECDH-ES".
<span class="h4"><a class="selflink" id="section-3.2.1" href="#section-3.2.1">3.2.1</a>. Performing the ECDH Operation</span>
The "x" parameter of the "epk" field is set as follows:
Apply the appropriate ECDH function to the ephemeral private key (as
scalar input) and the standard base point (as u-coordinate input).
The base64url encoding of the output is the value for the "x"
parameter of the "epk" field. All inputs and outputs are octet
strings.
The Z value (raw key agreement output) for key agreement (to be used
in subsequent Key Derivation Function (KDF) as per <a href="./rfc7518#section-4.6.2">Section 4.6.2 of
[RFC7518]</a>) is determined as follows:
Apply the appropriate ECDH function to the ephemeral private key (as
scalar input) and receiver public key (as u-coordinate input). The
output is the Z value. All inputs and outputs are octet strings.
<span class="h2"><a class="selflink" id="section-4" href="#section-4">4</a>. Security Considerations</span>
Security considerations from [<a href="./rfc7748" title=""Elliptic Curves for Security"">RFC7748</a>] and [<a href="./rfc8032" title=""Edwards-Curve Digital Signature Algorithm (EdDSA)"">RFC8032</a>] apply here.
Do not separate key material from information about what key subtype
it is for. When using keys, check that the algorithm is compatible
with the key subtype for the key. To do otherwise opens the system
up to attacks via mixing up algorithms. It is particularly dangerous
to mix up signature and Message Authentication Code (MAC) algorithms.
Although for Ed25519 and Ed448, the signature binds the key used for
signing, do not assume this, as there are many signature algorithms
that fail to make such a binding. If key-binding is desired, include
the key used for signing either inside the JWS protected header or
the data to sign.
If key generation or batch signature verification is performed, a
well-seeded cryptographic random number generator is REQUIRED.
Signing and non-batch signature verification are deterministic
operations and do not need random numbers of any kind.
<span class="grey">Liusvaara Standards Track [Page 5]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-6" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
The JSON Web Algorithm (JWA) ECDH-ES KDF construction does not mix
keys into the final shared secret. In key exchange, such mixing
could be a bad mistake; whereas here either the receiver public key
has to be chosen maliciously or the sender has to be malicious in
order to cause problems. In either case, all security evaporates.
The nominal security strengths of X25519 and X448 are ~126 and ~223
bits. Therefore, using 256-bit symmetric encryption (especially key
wrapping and encryption) with X448 is RECOMMENDED.
<span class="h2"><a class="selflink" id="section-5" href="#section-5">5</a>. IANA Considerations</span>
The following has been added to the "JSON Web Key Types" registry:
o "kty" Parameter Value: "OKP"
o Key Type Description: Octet string key pairs
o JOSE Implementation Requirements: Optional
o Change Controller: IESG
o Specification Document(s): <a href="./rfc8037#section-2">Section 2 of RFC 8037</a>
The following has been added to the "JSON Web Key Parameters"
registry:
o Parameter Name: "crv"
o Parameter Description: The subtype of key pair
o Parameter Information Class: Public
o Used with "kty" Value(s): "OKP"
o Change Controller: IESG
o Specification Document(s): <a href="./rfc8037#section-2">Section 2 of RFC 8037</a>
o Parameter Name: "d"
o Parameter Description: The private key
o Parameter Information Class: Private
o Used with "kty" Value(s): "OKP"
o Change Controller: IESG
o Specification Document(s): <a href="./rfc8037#section-2">Section 2 of RFC 8037</a>
o Parameter Name: "x"
o Parameter Description: The public key
o Parameter Information Class: Public
o Used with "kty" Value(s): "OKP"
o Change Controller: IESG
o Specification Document(s): <a href="./rfc8037#section-2">Section 2 of RFC 8037</a>
<span class="grey">Liusvaara Standards Track [Page 6]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-7" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
The following has been added to the "JSON Web Signature and
Encryption Algorithms" registry:
o Algorithm Name: "EdDSA"
o Algorithm Description: EdDSA signature algorithms
o Algorithm Usage Location(s): "alg"
o JOSE Implementation Requirements: Optional
o Change Controller: IESG
o Specification Document(s): <a href="./rfc8037#section-3.1">Section 3.1 of RFC 8037</a>
o Algorithm Analysis Documents(s): [<a href="./rfc8032" title=""Edwards-Curve Digital Signature Algorithm (EdDSA)"">RFC8032</a>]
The following has been added to the "JSON Web Key Elliptic Curve"
registry:
o Curve Name: "Ed25519"
o Curve Description: Ed25519 signature algorithm key pairs
o JOSE Implementation Requirements: Optional
o Change Controller: IESG
o Specification Document(s): <a href="./rfc8037#section-3.1">Section 3.1 of RFC 8037</a>
o Curve Name: "Ed448"
o Curve Description: Ed448 signature algorithm key pairs
o JOSE Implementation Requirements: Optional
o Change Controller: IESG
o Specification Document(s): <a href="./rfc8037#section-3.1">Section 3.1 of RFC 8037</a>
o Curve name: "X25519"
o Curve Description: X25519 function key pairs
o JOSE Implementation Requirements: Optional
o Change Controller: IESG
o Specification Document(s): <a href="./rfc8037#section-3.2">Section 3.2 of RFC 8037</a>
o Analysis Documents(s): [<a href="./rfc7748" title=""Elliptic Curves for Security"">RFC7748</a>]
o Curve Name: "X448"
o Curve Description: X448 function key pairs
o JOSE Implementation Requirements: Optional
o Change Controller: IESG
o Specification Document(s): <a href="./rfc8037#section-3.2">Section 3.2 of RFC 8037</a>
o Analysis Documents(s): [<a href="./rfc7748" title=""Elliptic Curves for Security"">RFC7748</a>]
<span class="grey">Liusvaara Standards Track [Page 7]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-8" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
<span class="h2"><a class="selflink" id="section-6" href="#section-6">6</a>. References</span>
<span class="h3"><a class="selflink" id="section-6.1" href="#section-6.1">6.1</a>. Normative References</span>
[<a id="ref-RFC2119">RFC2119</a>] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", <a href="https://www.rfc-editor.org/bcp/bcp14">BCP 14</a>, <a href="./rfc2119">RFC 2119</a>,
DOI 10.17487/RFC2119, March 1997,
<<a href="http://www.rfc-editor.org/info/rfc2119">http://www.rfc-editor.org/info/rfc2119</a>>.
[<a id="ref-RFC4648">RFC4648</a>] Josefsson, S., "The Base16, Base32, and Base64 Data
Encodings", <a href="./rfc4648">RFC 4648</a>, DOI 10.17487/RFC4648, October 2006,
<<a href="http://www.rfc-editor.org/info/rfc4648">http://www.rfc-editor.org/info/rfc4648</a>>.
[<a id="ref-RFC7515">RFC7515</a>] Jones, M., Bradley, J., and N. Sakimura, "JSON Web
Signature (JWS)", <a href="./rfc7515">RFC 7515</a>, DOI 10.17487/RFC7515, May
2015, <<a href="http://www.rfc-editor.org/info/rfc7515">http://www.rfc-editor.org/info/rfc7515</a>>.
[<a id="ref-RFC7517">RFC7517</a>] Jones, M., "JSON Web Key (JWK)", <a href="./rfc7517">RFC 7517</a>,
DOI 10.17487/RFC7517, May 2015,
<<a href="http://www.rfc-editor.org/info/rfc7517">http://www.rfc-editor.org/info/rfc7517</a>>.
[<a id="ref-RFC7518">RFC7518</a>] Jones, M., "JSON Web Algorithms (JWA)", <a href="./rfc7518">RFC 7518</a>,
DOI 10.17487/RFC7518, May 2015,
<<a href="http://www.rfc-editor.org/info/rfc7518">http://www.rfc-editor.org/info/rfc7518</a>>.
[<a id="ref-RFC7638">RFC7638</a>] Jones, M. and N. Sakimura, "JSON Web Key (JWK)
Thumbprint", <a href="./rfc7638">RFC 7638</a>, DOI 10.17487/RFC7638, September
2015, <<a href="http://www.rfc-editor.org/info/rfc7638">http://www.rfc-editor.org/info/rfc7638</a>>.
[<a id="ref-RFC7748">RFC7748</a>] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", <a href="./rfc7748">RFC 7748</a>, DOI 10.17487/RFC7748, January
2016, <<a href="http://www.rfc-editor.org/info/rfc7748">http://www.rfc-editor.org/info/rfc7748</a>>.
[<a id="ref-RFC8032">RFC8032</a>] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
Signature Algorithm (EdDSA)", <a href="./rfc8032">RFC 8032</a>,
DOI 10.17487/RFC8032, January 2017,
<<a href="http://www.rfc-editor.org/info/rfc8032">http://www.rfc-editor.org/info/rfc8032</a>>.
<span class="h3"><a class="selflink" id="section-6.2" href="#section-6.2">6.2</a>. Informative References</span>
[<a id="ref-RFC7516">RFC7516</a>] Jones, M. and J. Hildebrand, "JSON Web Encryption (JWE)",
<a href="./rfc7516">RFC 7516</a>, DOI 10.17487/RFC7516, May 2015,
<<a href="http://www.rfc-editor.org/info/rfc7516">http://www.rfc-editor.org/info/rfc7516</a>>.
<span class="grey">Liusvaara Standards Track [Page 8]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-9" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
<span class="h2"><a class="selflink" id="appendix-A" href="#appendix-A">Appendix A</a>. Examples</span>
To the extent possible, these examples use material taken from test
vectors of [<a href="./rfc7748" title=""Elliptic Curves for Security"">RFC7748</a>] and [<a href="./rfc8032" title=""Edwards-Curve Digital Signature Algorithm (EdDSA)"">RFC8032</a>].
<span class="h3"><a class="selflink" id="appendix-A.1" href="#appendix-A.1">A.1</a>. Ed25519 Private Key</span>
{"kty":"OKP","crv":"Ed25519",
"d":"nWGxne_9WmC6hEr0kuwsxERJxWl7MmkZcDusAxyuf2A",
"x":"11qYAYKxCrfVS_7TyWQHOg7hcvPapiMlrwIaaPcHURo"}
The hexadecimal dump of private key is:
9d 61 b1 9d ef fd 5a 60 ba 84 4a f4 92 ec 2c c4
44 49 c5 69 7b 32 69 19 70 3b ac 03 1c ae 7f 60
And of the public key is:
d7 5a 98 01 82 b1 0a b7 d5 4b fe d3 c9 64 07 3a
0e e1 72 f3 da a6 23 25 af 02 1a 68 f7 07 51 1a
<span class="h3"><a class="selflink" id="appendix-A.2" href="#appendix-A.2">A.2</a>. Ed25519 Public Key</span>
This is the public part of the previous private key (which just omits
"d"):
{"kty":"OKP","crv":"Ed25519",
"x":"11qYAYKxCrfVS_7TyWQHOg7hcvPapiMlrwIaaPcHURo"}
<span class="h3"><a class="selflink" id="appendix-A.3" href="#appendix-A.3">A.3</a>. JWK Thumbprint Canonicalization</span>
The JWK Thumbprint canonicalization of the two examples above (with a
linebreak inserted for formatting reasons) is:
{"crv":"Ed25519","kty":"OKP","x":"11qYAYKxCrfVS_7TyWQHOg7hcvPapiMlrwI
aaPcHURo"}
Which has the SHA-256 hash (in hexadecimal) of
90facafea9b1556698540f70c0117a22ea37bd5cf3ed3c47093c1707282b4b89,
which results in the base64url encoded JWK Thumbprint representation
of "kPrK_qmxVWaYVA9wwBF6Iuo3vVzz7TxHCTwXBygrS4k".
<span class="grey">Liusvaara Standards Track [Page 9]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-10" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
<span class="h3"><a class="selflink" id="appendix-A.4" href="#appendix-A.4">A.4</a>. Ed25519 Signing</span>
The JWS protected header is:
{"alg":"EdDSA"}
This has the base64url encoding of:
eyJhbGciOiJFZERTQSJ9
The payload is (text):
Example of Ed25519 signing
This has the base64url encoding of:
RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc
The JWS signing input is (a concatenation of base64url encoding of
the (protected) header, a dot, and base64url encoding of the payload)
is:
eyJhbGciOiJFZERTQSJ9.RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc
Applying the Ed25519 signing algorithm using the private key, public
key, and the JWS signing input yields the signature (hex):
86 0c 98 d2 29 7f 30 60 a3 3f 42 73 96 72 d6 1b
53 cf 3a de fe d3 d3 c6 72 f3 20 dc 02 1b 41 1e
9d 59 b8 62 8d c3 51 e2 48 b8 8b 29 46 8e 0e 41
85 5b 0f b7 d8 3b b1 5b e9 02 bf cc b8 cd 0a 02
Converting this to base64url yields:
hgyY0il_MGCjP0JzlnLWG1PPOt7-09PGcvMg3AIbQR6dWbhijcNR4ki4iylGjg5BhVsPt
9g7sVvpAr_MuM0KAg
So the compact serialization of the JWS is (a concatenation of
signing input, a dot, and base64url encoding of the signature):
eyJhbGciOiJFZERTQSJ9.RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc.hgyY0il_MGCj
P0JzlnLWG1PPOt7-09PGcvMg3AIbQR6dWbhijcNR4ki4iylGjg5BhVsPt9g7sVvpAr_Mu
M0KAg
<span class="grey">Liusvaara Standards Track [Page 10]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-11" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
<span class="h3"><a class="selflink" id="appendix-A.5" href="#appendix-A.5">A.5</a>. Ed25519 Validation</span>
The JWS from the example above is:
eyJhbGciOiJFZERTQSJ9.RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc.hgyY0il_MGCj
P0JzlnLWG1PPOt7-09PGcvMg3AIbQR6dWbhijcNR4ki4iylGjg5BhVsPt9g7sVvpAr_Mu
M0KAg
This has 2 dots in it, so it might be valid a JWS. Base64url
decoding the protected header yields:
{"alg":"EdDSA"}
So this is an EdDSA signature. Now the key has: "kty":"OKP" and
"crv":"Ed25519", so the signature is Ed25519 signature.
The signing input is the part before the second dot:
eyJhbGciOiJFZERTQSJ9.RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc
Applying the Ed25519 verification algorithm to the public key, JWS
signing input, and the signature yields true. So the signature is
valid. The message is the base64url decoding of the part between the
dots:
Example of Ed25519 Signing
<span class="h3"><a class="selflink" id="appendix-A.6" href="#appendix-A.6">A.6</a>. ECDH-ES with X25519</span>
The public key to encrypt to is:
{"kty":"OKP","crv":"X25519","kid":"Bob",
"x":"3p7bfXt9wbTTW2HC7OQ1Nz-DQ8hbeGdNrfx-FG-IK08"}
The public key from the target key is (hex):
de 9e db 7d 7b 7d c1 b4 d3 5b 61 c2 ec e4 35 37
3f 83 43 c8 5b 78 67 4d ad fc 7e 14 6f 88 2b 4f
The ephemeral secret happens to be (hex):
77 07 6d 0a 73 18 a5 7d 3c 16 c1 72 51 b2 66 45
df 4c 2f 87 eb c0 99 2a b1 77 fb a5 1d b9 2c 2a
So the ephemeral public key is X25519(ephkey, G) (hex):
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
<span class="grey">Liusvaara Standards Track [Page 11]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-12" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
This is represented as the ephemeral public key value:
{"kty":"OKP","crv":"X25519",
"x":"hSDwCYkwp1R0i33ctD73Wg2_Og0mOBr066SpjqqbTmo"}
So the protected header could be, for example:
{"alg":"ECDH-ES+A128KW","epk":{"kty":"OKP","crv":"X25519",
"x":"hSDwCYkwp1R0i33ctD73Wg2_Og0mOBr066SpjqqbTmo"},
"enc":"A128GCM","kid":"Bob"}
And the sender computes the DH Z value as X25519(ephkey, recv_pub)
(hex):
4a 5d 9d 5b a4 ce 2d e1 72 8e 3b f4 80 35 0f 25
e0 7e 21 c9 47 d1 9e 33 76 f0 9b 3c 1e 16 17 42
The receiver computes the DH Z value as X25519(seckey, ephkey_pub)
(hex):
4a 5d 9d 5b a4 ce 2d e1 72 8e 3b f4 80 35 0f 25
e0 7e 21 c9 47 d1 9e 33 76 f0 9b 3c 1e 16 17 42
This is the same as the sender's value (both sides run this through
the KDF before using it as a direct encryption key or AES128-KW key).
<span class="h3"><a class="selflink" id="appendix-A.7" href="#appendix-A.7">A.7</a>. ECDH-ES with X448</span>
The public key to encrypt to (with a linebreak inserted for
formatting reasons) is:
{"kty":"OKP","crv":"X448","kid":"Dave",
"x":"PreoKbDNIPW8_AtZm2_sz22kYnEHvbDU80W0MCfYuXL8PjT7QjKhPKcG3LV67D2
uB73BxnvzNgk"}
The public key from the target key is (hex):
3e b7 a8 29 b0 cd 20 f5 bc fc 0b 59 9b 6f ec cf
6d a4 62 71 07 bd b0 d4 f3 45 b4 30 27 d8 b9 72
fc 3e 34 fb 42 32 a1 3c a7 06 dc b5 7a ec 3d ae
07 bd c1 c6 7b f3 36 09
The ephemeral secret happens to be (hex):
9a 8f 49 25 d1 51 9f 57 75 cf 46 b0 4b 58 00 d4
ee 9e e8 ba e8 bc 55 65 d4 98 c2 8d d9 c9 ba f5
74 a9 41 97 44 89 73 91 00 63 82 a6 f1 27 ab 1d
9a c2 d8 c0 a5 98 72 6b
<span class="grey">Liusvaara Standards Track [Page 12]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-13" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
So the ephemeral public key is X448(ephkey, G) (hex):
9b 08 f7 cc 31 b7 e3 e6 7d 22 d5 ae a1 21 07 4a
27 3b d2 b8 3d e0 9c 63 fa a7 3d 2c 22 c5 d9 bb
c8 36 64 72 41 d9 53 d4 0c 5b 12 da 88 12 0d 53
17 7f 80 e5 32 c4 1f a0
This is packed into the ephemeral public key value (a linebreak
inserted for formatting purposes):
{"kty":"OKP","crv":"X448",
"x":"mwj3zDG34-Z9ItWuoSEHSic70rg94Jxj-qc9LCLF2bvINmRyQdlT1AxbEtqIEg1
TF3-A5TLEH6A"}
So the protected header could be, for example (a linebreak inserted
for formatting purposes):
{"alg":"ECDH-ES+A256KW","epk":{"kty":"OKP","crv":"X448",
"x":"mwj3zDG34-Z9ItWuoSEHSic70rg94Jxj-qc9LCLF2bvINmRyQdlT1AxbEtqIEg1
TF3-A5TLEH6A"},"enc":"A256GCM","kid":"Dave"}
And the sender computes the DH Z value as X448(ephkey,recv_pub)
(hex):
07 ff f4 18 1a c6 cc 95 ec 1c 16 a9 4a 0f 74 d1
2d a2 32 ce 40 a7 75 52 28 1d 28 2b b6 0c 0b 56
fd 24 64 c3 35 54 39 36 52 1c 24 40 30 85 d5 9a
44 9a 50 37 51 4a 87 9d
The receiver computes the DH Z value as X448(seckey, ephkey_pub)
(hex):
07 ff f4 18 1a c6 cc 95 ec 1c 16 a9 4a 0f 74 d1
2d a2 32 ce 40 a7 75 52 28 1d 28 2b b6 0c 0b 56
fd 24 64 c3 35 54 39 36 52 1c 24 40 30 85 d5 9a
44 9a 50 37 51 4a 87 9d
This is the same as the sender's value (both sides run this through
KDF before using it as the direct encryption key or AES256-KW key).
<span class="grey">Liusvaara Standards Track [Page 13]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-14" ></span>
<span class="grey"><a href="./rfc8037">RFC 8037</a> CFRG ECDH and Signatures in JOSE January 2017</span>
Acknowledgements
Thanks to Michael B. Jones for his comments on an initial draft of
this document and editorial help.
Thanks to Matt Miller for some editorial help.
Author's Address
Ilari Liusvaara
Independent
Email: ilariliusvaara@welho.com
Liusvaara Standards Track [Page 14]
</pre>
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