Subject: Re: [jose] CFRG ECC in JOSE - thumbprint

From: "Manger, James" <[email-masked]>
Date: Wed, 11 Nov 2015 09:58:16 +1100

How do you calculate a JWK thumbprint [RFC7638] of these keys?

A thumbprint is supposed to cover the "required" members. draft-liusvaara-jose-cfrg-curves implies the thumbprint would cover {alg, crv, kty, x}. That is different from other "kty":"EC" keys, where the thumbprint covers {crv, kty, x, y}. It is different from all other keys that exclude "alg".

Theoretically we can probably have per-curve thumbprint rules, though so far the thumbprint rules have been per-type (per kty value).

Two options could be:
1. Reuse "kty":"EC" but have per-curve thumbprint rules
2. Define a new key type, say, "kty":"EC2" for elliptic curve keys with these thumbprint rules

Either way, draft-liusvaara-jose-cfrg-curves should explicitly state the members covered by a RFC7638 thumbprint.

--
James Manger

-----Original Message-----
From: jose [mailto:[email-masked]] On Behalf Of Ilari Liusvaara
Sent: Wednesday, 11 November 2015 4:56 AM
To: [email-masked]
Subject: [jose] CFRG ECC in JOSE

I cooked up a pre-draft (already circulated privately) about using CFRG
ECC work in JOSE. Encompasses both ECDH and signatures.

Comments (before I attempt to submit this as an I-D)?

-----------------------------------------------------------------------
Network Working Group                                       I. Liusvaara
Internet-Draft                                               Independent
Intended status: Standards Track                        October 17, 2015
Expires: April 19, 2016

                   CFRG curves and signatures in JOSE
                    draft-liusvaara-jose-cfrg-curves

Abstract

   This document defines how to use curves and algorithms from IRTF CFRG
   elliptic curves work (Diffie-Hellman and signatures) in JOSE.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on April 19, 2016.

Copyright Notice

   Copyright (c) 2015 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
   (http://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.

Liusvaara                Expires April 19, 2016                 [Page 1]

Internet-Draft     CFRG curves and signatures in JOSE       October 2015

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements Terminology  . . . . . . . . . . . . . . . .   2
     1.2.  Notation  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Algorithms  . . . . . . . . . . . . . . . . . . . . . . . . .   2
     2.1.  Signatures  . . . . . . . . . . . . . . . . . . . . . . .   3
       2.1.1.  Curves  . . . . . . . . . . . . . . . . . . . . . . .   3
       2.1.2.  Algorithms  . . . . . . . . . . . . . . . . . . . . .   3
       2.1.3.  Signing . . . . . . . . . . . . . . . . . . . . . . .   4
       2.1.4.  Verification  . . . . . . . . . . . . . . . . . . . .   4
     2.2.  ECDH-ES . . . . . . . . . . . . . . . . . . . . . . . . .   4
       2.2.1.  Parameters  . . . . . . . . . . . . . . . . . . . . .   4
       2.2.2.  Performing the ECDH operation . . . . . . . . . . . .   5
   3.  Security considerations . . . . . . . . . . . . . . . . . . .   5
   4.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   6
   5.  IANA considerations . . . . . . . . . . . . . . . . . . . . .   6
   6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   8
     6.1.  Normative References  . . . . . . . . . . . . . . . . . .   8
     6.2.  Informative References  . . . . . . . . . . . . . . . . .   8
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .   9

1.  Introduction

   Internet Research Task Force (IRTF) Crypto Forum Research Group
   (CFRG) selected new elliptic curves and signature algorithms for
   asymmetric key cryptography.  This document defines how those curves
   and algorithms are to be used in JOSE in interoperable manner.

   This extends [RFC7517] and [RFC7518]

1.1.  Requirements Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].

1.2.  Notation

   All inputs to and outputs from the the ECDH and signature functions
   are defined to be octet strings, with the exception of output of
   verfication function, which is a boolean.

2.  Algorithms

Liusvaara                Expires April 19, 2016                 [Page 2]

Internet-Draft     CFRG curves and signatures in JOSE       October 2015

2.1.  Signatures

2.1.1.  Curves

   The following curves are defined for the algorithms are defined here
   (to be applied as values of "crv" parameter):

      crv value:            The curve:
      E255                  Edwards25519
      E448                  Edwards448

   For each of these curves:

   1.  The parameter "kty" MUST be "EC".

   2.  The parameter "crv" MUST be set to appropriate value.

   3.  The parameter "alg" MUST be set to appropriate value.

   4.  The parameter "x" is the base64url [RFC4648] encoded public key
       octet string (note: this is not the same as sec1 encoding).  This
       MUST be present for both public and private keys.

   5.  The parameter "y" MUST NOT be present.  These curves only have
       one public key component.

   6.  The parameter "d" is the base64url encoded private key octet
       string.  This MUST be present for private keys, and MUST NOT be
       present for public keys.

   7.  These curves MUST NOT be used for ECDH-ES.

   8.  If key is private key, and thus both "x" and "d" are present,
       then "x" MUST be the public key corresponding to private key "d".

2.1.2.  Algorithms

   The following signature algorithms are defined here (to be applied as
   values of "alg" parameter):

     alg value:     crv:    The algorithm:
     Ed25519        E255    Ed25519
     Ed25519ph      E255    Ed25519ph
     Ed448          E448    Ed448
     Ed448ph        E448    Ed448ph

Liusvaara                Expires April 19, 2016                 [Page 3]

Internet-Draft     CFRG curves and signatures in JOSE       October 2015

   The key type for these algorithms MUST be "EC", "alg" parameter MUST
   be present and "crv" parameter MUST match the indicated one for each
   algorithm.

2.1.3.  Signing

   Signing for these is preformed by applying the signing algorithm
   defined in [I-D.irtf-cfrg-eddsa] 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 value.  All inputs and
   outputs are octet strings.

2.1.4.  Verification

   Verification is performed by applying the verification algorithm
   defined in [I-D.irtf-cfrg-eddsa] to the public key (as public key),
   the JWS Signing Input (as message) and the JWS Signature value (as
   signature).  All inputs are octet strings.  If the algorithm accepts,
   the signature is valid, otherwise it is invalid.

2.2.  ECDH-ES

   The following curves are defined for the algorithms are defined here
   (to be applied as values of "crv" parameter):

      crv value:          The curve:
      X255                X25519
      X448                X448

   The key type used with these keys is "EC".

   These curves MUST NOT be used for signatures.

2.2.1.  Parameters

   For each of these curves:

   1.  The "x" parameter is base64url encoding of point octet string
       (note: This is not SEC1 encoding).  This parameter MUST be
       present in both public and private keys.

   2.  The "y" parameter MUST NOT be present.  These functions only have
       one public key component.

   3.  The "d" parameter is base64url encoding of scalar octet string.
       This parameter MUST be present in private keys, and it MUST NOT
       be present in public keys.

Liusvaara                Expires April 19, 2016                 [Page 4]

Internet-Draft     CFRG curves and signatures in JOSE       October 2015

   4.  If key is private key, and thus both "x" and "d" are present,
       then "x" MUST be the output of applying ECDH function to the
       value of "d" (as scalar input) and the standard basepoint (as
       u-coordinate input).

2.2.2.  Performing the ECDH operation

   The "x" parameter of "epk" field is set as follows:

   Apply the appropriate ECDH function to the ephemeral private key (as
   scalar input) and the standard basepoint (as u-coordinate input).
   The output is the value for "x" parameter of "epk" field.  All inputs
   and outputs are octet strings.

   The Z value (raw key agreement output) for key agreement 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.

3.  Security considerations

   Security considerations from [I-D.irtf-cfrg-curves] and
   [I-D.irtf-cfrg-eddsa] apply here.

   The same key MUST NOT be used with multiple algorithms, since some of
   the algorithms defined here interact in bad ways.  For this reason
   "alg" parameters for signature keys are REQUIRED.

   Do not assume that signature also binds the key used for signing, it
   does not (there are also other widespread signature algorithms where
   this binding fails, as such binding is not part of the definition of
   secure signature primitive).  As an example of such failure, the
   Ed25519ph signature of X under key (Ed25519ph,Y) is identical to
   Ed25519 signature of SHA512(X) under key (Ed25519,Y).  And often it
   takes only setting a few bits of message (easy to do by brute force)
   to make the message valid enough to be processed in some very
   surprising way.

   If key generation or batch signature verification is performed, a
   well-seed cryptographical random number generator is REQUIRED.
   Signing and non-batch signature verification are deterministic
   operations do not need random numbers of any kind.

Liusvaara                Expires April 19, 2016                 [Page 5]

Internet-Draft     CFRG curves and signatures in JOSE       October 2015

4.  Acknowledgements

   Mike Jones for comments on initial pre-draft.

5.  IANA considerations

   The following is added to JSON Web Signature and Encryption
   Algorithms Registry:

   o  Algorithm Name: "Ed25519"

   o  Algorithm Description: Ed25519 signature algorithm

   o  Algorithm Usage Location(s): "alg"

   o  JOSE Implementation Requirements: Optional

   o  Change Controller: IESG

   o  Specification Document(s): Section 2.1 of [RFC-THIS]

   o  Algorithm Analysis Documents(s): n/a

   o  Algorithm Name: "Ed25519ph"

   o  Algorithm Description: Ed25519 signature algorithm with prehash

   o  Algorithm Usage Location(s): "alg"

   o  JOSE Implementation Requirements: Optional

   o  Change Controller: IESG

   o  Specification Document(s): Section 2.1 of [RFC-THIS]

   o  Algorithm Analysis Documents(s): n/a

   o  Algorithm Name: "Ed448"

   o  Algorithm Description: Ed448 signature algorithm

   o  Algorithm Usage Location(s): "alg"

   o  JOSE Implementation Requirements: Optional

   o  Change Controller: IESG

Liusvaara                Expires April 19, 2016                 [Page 6]

Internet-Draft     CFRG curves and signatures in JOSE       October 2015

   o  Specification Document(s): Section 2.1 of [RFC-THIS]

   o  Algorithm Analysis Documents(s): n/a

   o  Algorithm Name: "Ed448ph"

   o  Algorithm Description: Ed448 signature algorithm with prehash

   o  Algorithm Usage Location(s): "alg"

   o  JOSE Implementation Requirements: Optional

   o  Change Controller: IESG

   o  Specification Document(s): Section 2.1 of [RFC-THIS]

   o  Algorithm Analysis Documents(s): n/a

   The following is added to JSON Web Key Elliptic Curve Registry:

   o  Curve Name: "X25519"

   o  Curve Description: The X25519 function

   o  JOSE Implementation Requirements: Optional

   o  Change Controller: IESG

   o  Specification Document(s): Section 2.2 of [RFC-THIS]

   o  Curve Name: "X448"

   o  Curve Description: The X448 function

   o  JOSE Implementation Requirements: Optional

   o  Change Controller: IESG

   o  Specification Document(s): Section 2.2 of [RFC-THIS]

   o  Curve Name: "Ed25519"

   o  Curve Description: The Edwards25519 curve

Liusvaara                Expires April 19, 2016                 [Page 7]

Internet-Draft     CFRG curves and signatures in JOSE       October 2015

   o  JOSE Implementation Requirements: Optional

   o  Change Controller: IESG

   o  Specification Document(s): Section 2.1 of [RFC-THIS]

   o  Curve Name: "Ed448"

   o  Curve Description: The Edwards448 curve

   o  JOSE Implementation Requirements: Optional

   o  Change Controller: IESG

   o  Specification Document(s): Section 2.2 of [RFC-THIS]

6.  References

6.1.  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,
              <http://www.rfc-editor.org/info/rfc2119>.

   [RFC4648]  Josefsson, S., "The Base16, Base32, and Base64 Data
              Encodings", RFC 4648, DOI 10.17487/RFC4648, October 2006,
              <http://www.rfc-editor.org/info/rfc4648>.

   [I-D.irtf-cfrg-curves]
              Langley, A. and M. Hamburg, "Elliptic Curves for
              Security", draft-irtf-cfrg-curves-09 (work in progress),
              September 2015.

   [I-D.irtf-cfrg-eddsa]
              Josefsson, S. and I. Liusvaara, "Edwards-curve Digital
              Signature Algorithm (EdDSA)", draft-irtf-cfrg-eddsa-00
              (work in progress), October 2015.

6.2.  Informative References

   [RFC7517]  Jones, M., "JSON Web Key (JWK)", RFC 7517, DOI 10.17487/
              RFC7517, May 2015,
              <http://www.rfc-editor.org/info/rfc7517>.

Liusvaara                Expires April 19, 2016                 [Page 8]

Internet-Draft     CFRG curves and signatures in JOSE       October 2015

   [RFC7518]  Jones, M., "JSON Web Algorithms (JWA)", RFC 7518, DOI
              10.17487/RFC7518, May 2015,
              <http://www.rfc-editor.org/info/rfc7518>.

Author's Address

   Ilari Liusvaara
   Independent

   Email: [email-masked]

Liusvaara                Expires April 19, 2016                 [Page 9]

-----------------------------------------------------------------------

-Ilari

_______________________________________________
jose mailing list
[email-masked]
https://www.ietf.org/mailman/listinfo/jose

---

From: Justin Richer <[email-masked]>
Date: Tue, 10 Nov 2015 20:22:53 -0500

I would lean toward using a new “kty” value for these as the syntax is different from existing ones. This will help parsers and existing implementations add this in without adding special processing rules: code is already set up to branch on “kty” so let’s keep that behavior. Note you can still reuse parts of the key definition (like “d” is found in both RSA and EC keypairs) without having to overload a new syntax since the kty defines a new namespace, effectively. I suggest a value of “ED” since they’re all “edwards” curves from my quick read.

 — Justin

> On Nov 10, 2015, at 5:58 PM, Manger, James <[email-masked]> wrote:
>

---

From: Anders Rundgren <[email-masked]>
Date: Wed, 11 Nov 2015 06:59:38 +0100

> I would lean toward using a new “kty” value for these as the syntax is different from existing ones. This will help parsers and existing implementations add this in without adding special processin…

It would IMO be great if this issue is coordinated with the integration of these curves in PKI(X).

Anders

---

From: Ilari Liusvaara <[email-masked]>
Date: Wed, 11 Nov 2015 10:37:33 +0200

On Tue, Nov 10, 2015 at 08:22:53PM -0500, Justin Richer wrote:
> I would lean toward using a new “kty” value for these as the syntax
> is different from existing ones. This will help parsers and existing
> implementations add this in without adding special processing rules:
> code is already set up to branch on “kty” so let’s keep that
> behavior. Note you can still reuse parts of the key definition
> (like “d” is found in both RSA and EC keypairs) without having to
> overload a new syntax since the kty defines a new namespace,
> effectively. I suggest a value of “ED” since they’re all “edwards”
> curves from my quick read.

1) Actually, I think "okp" (Octet Key Pair) or something like that
might be more descriptive, since these are keypairs with no structure
outside the box ("oct" or whatever won't do, since that's symmetric,
not asymmetric). This also holds for X25519 and X448.

2) IIRC, the definition of "EC" talks about all defined curves having
"y", but not necressarily all curves having "y". Might be bad idea
implementation-wise to use that option however (I did encounter
comments about this pre-draft that indicated that options realistically
available are less than what JWK provodes).

3) I think it is a bad idea not to vary key fingerprint on algorithm.
However, that ship has already sailed.

-Ilari

---

From: Brian Campbell <[email-masked]>
Date: Wed, 11 Nov 2015 05:53:28 -0700

FWIW, JWA §6.2.1 <http://tools.ietf.org/html/rfc7518#section-6.2.1> defines
the "y" parameter as required for "the three curves defined [therein]"
which does implies that it may not be required for other curves and the
thumbprint rules follow logically.

---

From: Ilari Liusvaara <[email-masked]>
Date: Sat, 14 Nov 2015 15:10:22 +0200

> not asymmetric). This also holds for X25519 and X448.

Well, here is a pre-draft version using new key type (for algorithms
using octet-string key pairs). I named the analog of the EC "curve"
parameter as "key algorithm group".

The crypto material in examples are either from CFRG document examples
or from my vector generator for Ed25519.

The naming could probably be improved...

-----------------------------------------------------------------------
Network Working Group                                       I. Liusvaara
Internet-Draft                                               Independent
Intended status: Standards Track                       November 14, 2015
Expires: May 17, 2016

Abstract

Status of This Memo

   This Internet-Draft will expire on May 17, 2016.

Copyright Notice

Liusvaara                 Expires May 17, 2016                  [Page 1]

Internet-Draft     CFRG curves and signatures in JOSE      November 2015

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements Terminology  . . . . . . . . . . . . . . . .   2
     1.2.  Notation  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Key type 'OKP'  . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  Algorithms  . . . . . . . . . . . . . . . . . . . . . . . . .   3
     3.1.  Signatures  . . . . . . . . . . . . . . . . . . . . . . .   3
       3.1.1.  Algorithms  . . . . . . . . . . . . . . . . . . . . .   3
       3.1.2.  Signing . . . . . . . . . . . . . . . . . . . . . . .   3
       3.1.3.  Verification  . . . . . . . . . . . . . . . . . . . .   4
     3.2.  ECDH-ES . . . . . . . . . . . . . . . . . . . . . . . . .   4
       3.2.1.  Performing the ECDH operation . . . . . . . . . . . .   4
   4.  Security considerations . . . . . . . . . . . . . . . . . . .   4
   5.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   5
   6.  IANA considerations . . . . . . . . . . . . . . . . . . . . .   5
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   7
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .   7
     7.2.  Informative References  . . . . . . . . . . . . . . . . .   7
   Appendix A.  Examples . . . . . . . . . . . . . . . . . . . . . .   8
     A.1.  Ed25519 private key . . . . . . . . . . . . . . . . . . .   8
     A.2.  Ed25519 public key  . . . . . . . . . . . . . . . . . . .   8
     A.3.  JWK thumbprint canonicalization . . . . . . . . . . . . .   8
     A.4.  Ed25519 Signing . . . . . . . . . . . . . . . . . . . . .   9
     A.5.  Ed25519 Validation  . . . . . . . . . . . . . . . . . . .   9
     A.6.  ECDH-ES with X25519 . . . . . . . . . . . . . . . . . . .  10
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  11

1.  Introduction

1.2.  Notation

Liusvaara                 Expires May 17, 2016                  [Page 2]

Internet-Draft     CFRG curves and signatures in JOSE      November 2015

2.  Key type 'OKP'

   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 "kag" MUST be present, and contain the key algorithm
      group (from JSON Web Signature and Encryption Algorithms).

   o  The parameter "p" MUST be present, and contain the public key
      encoded using base64url [RFC4648] encoding.

   o  The parameter "d" MUST be present for private keys, and contain
      the private key encoded using base64url encoding.  This parameter
      MUST NOT be present for public keys.

   When calculating thumbprints [RFC7638], the three public key fields
   are included in the hash.  That is, in lexographic order: "kag",
   "kty" and "p".

3.  Algorithms

3.1.  Signatures

3.1.1.  Algorithms

   The following signature algorithms are defined here (to be applied as
   values of "alg" parameter).  All these have keys with algorithm group
   of the same name:

     alg/kag value:     The algorithm:
     Ed25519            Ed25519
     Ed25519ph          Ed25519ph
     Ed448              Ed448
     Ed448ph            Ed448ph

   The key type for these keys is "OKP" and key algorithm group for
   these algorithms MUST be the same as the algorithm name.

3.1.2.  Signing

Liusvaara                 Expires May 17, 2016                  [Page 3]

Internet-Draft     CFRG curves and signatures in JOSE      November 2015

3.1.3.  Verification

3.2.  ECDH-ES

   The following key algorithm groups are defined here for purpose of
   ECDH-ES:

      algorithm group:  ECDH Function:
      X25519            X25519
      X448              X448

   The key type used with these keys is "OKP".

3.2.1.  Performing the ECDH operation

   The "p" parameter of "epk" field is set as follows:

   Apply the appropriate ECDH function to the ephemeral private key (as
   scalar input) and the standard basepoint (as u-coordinate input).
   The output is the value for "p" parameter of "epk" field.  All inputs
   and outputs are octet strings.

4.  Security considerations

   Some algorithms interact in bad ways (e.g.  "Ed25519" and
   "Ed25519ph").  For this reason, those algorithms have different
   algorithm groups, so keys for each are not mixed up.

   Do not separate key material from information what key algorithm
   group it is for.  When using keys, check that the algorithm is
   compatible with the key algorithm group for the key.  To do otherwise

Liusvaara                 Expires May 17, 2016                  [Page 4]

Internet-Draft     CFRG curves and signatures in JOSE      November 2015

   opens system up to attacks via mixing up algorithms.  It is
   practicularly dangerous to mix up signature and MAC algorithms.

   If key generation or batch signature verification is performed, a
   well-seed cryptographical random number generator is REQUIRED.
   Signing and non-batch signature verification are deterministic
   operations and do not need random numbers of any kind.

5.  Acknowledgements

6.  IANA considerations

   The following is added to 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): Section 2 of [RFC-THIS]

   The following is added to JSON Web Key Parameters Registry:

   o  Parameter Name: "kag"
   o  Parameter Description: The algorithm group of keypair
   o  Parameter Information Class: Public
   o  Used with "kty" Value(s): "OKP"
   o  Change Controller: IESG
   o  Specification Document(s): Section 2 of [RFC-THIS]

   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): Section 2 of [RFC-THIS]

Liusvaara                 Expires May 17, 2016                  [Page 5]

Internet-Draft     CFRG curves and signatures in JOSE      November 2015

   The following is added to JSON Web Key Parameters Registry:

   o  Parameter Name: "p"
   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): Section 2 of [RFC-THIS]

   o  Algorithm Name: "Ed25519"
   o  Algorithm Description: Ed25519 signature algorithm and its
      keypairs
   o  Algorithm Usage Location(s): "alg", "kag"
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.1 of [RFC-THIS]
   o  Algorithm Analysis Documents(s): [I-D.irtf-cfrg-eddsa]

   o  Algorithm Name: "Ed25519ph"
   o  Algorithm Description: Ed25519 signature algorithm with prehash
      and its keypairs
   o  Algorithm Usage Location(s): "alg", "kag"
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.1 of [RFC-THIS]
   o  Algorithm Analysis Documents(s): [I-D.irtf-cfrg-eddsa]

   o  Algorithm Name: "Ed448"
   o  Algorithm Description: Ed448 signature algorithm and its keypairs
   o  Algorithm Usage Location(s): "alg", "kag"
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.1 of [RFC-THIS]
   o  Algorithm Analysis Documents(s): [I-D.irtf-cfrg-eddsa]

   o  Algorithm Name: "Ed448ph"
   o  Algorithm Description: Ed448 signature algorithm with prehash and
      its keypairs
   o  Algorithm Usage Location(s): "alg", "kag"
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.1 of [RFC-THIS]
   o  Algorithm Analysis Documents(s): [I-D.irtf-cfrg-eddsa]

Liusvaara                 Expires May 17, 2016                  [Page 6]

Internet-Draft     CFRG curves and signatures in JOSE      November 2015

   o  Algorithm Name: "X25519"
   o  Algorithm Description: X25519 function keypairs
   o  Algorithm Usage Location(s): "kag"
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.2 of [RFC-THIS]
   o  Algorithm Analysis Documents(s): [I-D.irtf-cfrg-curves]

   o  Class Name: "X448"
   o  Class Description: X448 function keypairs
   o  JOSE Implementation Requirements: Optional
   o  Algorithm Usage Location(s): "kag"
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.2 of [RFC-THIS]
   o  Algorithm Analysis Documents(s): [I-D.irtf-cfrg-curves]

7.  References

7.1.  Normative References

   [I-D.irtf-cfrg-curves]

   [I-D.irtf-cfrg-eddsa]

7.2.  Informative References

Liusvaara                 Expires May 17, 2016                  [Page 7]

Internet-Draft     CFRG curves and signatures in JOSE      November 2015

   [RFC7638]  Jones, M. and N. Sakimura, "JSON Web Key (JWK)
              Thumbprint", RFC 7638, DOI 10.17487/RFC7638, September
              2015, <http://www.rfc-editor.org/info/rfc7638>.

Appendix A.  Examples

   To the extent possible, the examples use material lifted from test
   vectors of [I-D.irtf-cfrg-curves] and [I-D.irtf-cfrg-eddsa]

A.1.  Ed25519 private key

   {"kty":"OKP","kag":"Ed25519",
   "d":"nWGxne_9WmC6hEr0kuwsxERJxWl7MmkZcDusAxyuf2A"
   "p":"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:

   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

A.2.  Ed25519 public key

   This is the public parts of the previous private key (just omits
   "d"):

   {"kty":"OKP","kag":"Ed25519",
   "p":"11qYAYKxCrfVS_7TyWQHOg7hcvPapiMlrwIaaPcHURo"}

A.3.  JWK thumbprint canonicalization

   The JWK thumbprint canonicalization of the two above examples is
   (linebreak inserted for formatting reasons)

   {"kag":"Ed25519","kty":"OKP","p":"11qYAYKxCrfVS_7TyWQHOg7hcvPapiMlrwI
   aaPcHURo"}

   Which has the SHA-256 hash of:
   9b4dece50b24e8008ea629f8b0443f785c910fe2d6fd9c058a8032a54ae8ed97

Liusvaara                 Expires May 17, 2016                  [Page 8]

Internet-Draft     CFRG curves and signatures in JOSE      November 2015

A.4.  Ed25519 Signing

   The JWS protected header is:

   {"alg":"Ed25519"}

   This has base64url encoding of:

   eyJhbGciOiJFZDI1NTE5In0

   The payload is (text):

   Example of Ed25519 signing

   This has base64url encoding of:

   RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc

   The JWS signing input is (concatenation of base64url encoding of the
   (protected) header, a dot and base64url encoding of the payload) is:

   eyJhbGciOiJFZDI1NTE5In0.RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc

   Applying Ed25519 signing algorithm to the private key, public key and
   the JWS signing input yields signature (hex):

   53 18 48 60 b1 c6 83 7f 4d 54 22 e9 40 05 43 fd
   47 1f 3a 69 c6 48 2c cb 15 9a 17 62 42 e2 21 b1
   5c 72 63 9b fe a3 9b b2 08 f3 2c ab 1f 27 0f b8
   36 57 1c 52 0b d8 ac 41 eb 45 b3 55 d0 77 19 01

   Converting this to base64url yields:

   UxhIYLHGg39NVCLpQAVD_UcfOmnGSCzLFZoXYkLiIbFccmOb_qObsgjzLKsfJw-4NlccU
   gvYrEHrRbNV0HcZAQ

   So the compact serialization of JWS is (concatenation of signing
   input, a dot and base64url encoding of the signature:

   eyJhbGciOiJFZDI1NTE5In0.RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc.UxhIYLHGg
   39NVCLpQAVD_UcfOmnGSCzLFZoXYkLiIbFccmOb_qObsgjzLKsfJw-4NlccUgvYrEHrRb
   NV0HcZAQ

A.5.  Ed25519 Validation

   The JWS from above example is:

Liusvaara                 Expires May 17, 2016                  [Page 9]

Internet-Draft     CFRG curves and signatures in JOSE      November 2015

   eyJhbGciOiJFZDI1NTE5In0.RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc.UxhIYLHGg
   39NVCLpQAVD_UcfOmnGSCzLFZoXYkLiIbFccmOb_qObsgjzLKsfJw-4NlccUgvYrEHrRb
   NV0HcZAQ

   This has 2 dots in it, so it might be valid JWS.  Base64url decoding
   the protected header yields:

   {"alg":"Ed25519"}

   So this is Ed25519 signature.  Now the key has: "kty":"OKP" and
   "kag":"Ed25519", so the key is valid for the algorithm (if it had
   other values, the validation would have failed).

   The signing input is the part before second dot:

   eyJhbGciOiJFZDI1NTE5In0.RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc

   Applying Ed25519 verification algorithm to the public key, JWS
   signing input and the signature yields true.  So the signature is
   valid.  The message is base64 decoding of the part between the dots:

   Example of Ed25519 signing

A.6.  ECDH-ES with X25519

   The public key to encrypt to is:

   {"kty":"OKP","kag":"X25519","kid":"Bob"
   "p":"3p7bfXt9wbTTW2HC7OQ1Nz-DQ8hbeGdNrfx-FG-IK08"}

   The public key from 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

   This is packed into ephemeral public key value:

Liusvaara                 Expires May 17, 2016                 [Page 10]

Internet-Draft     CFRG curves and signatures in JOSE      November 2015

   {"kty":"OKP","kag":"X25519",
   "p":"hSDwCYkwp1R0i33ctD73Wg2_Og0mOBr066SpjqqbTmo"}

   So the protected header could for example be:

   {"alg":"ECDH-ES+A128KW","epk":{"kty":"OKP","kag":"X25519",
   "p":"hSDwCYkwp1R0i33ctD73Wg2_Og0mOBr066SpjqqbTmo"},
   "enc":"A128GCM","kid":"Bob"}

   And sender computes as 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 as 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

   Which is the same as sender's value (the both sides run this through
   KDF before using as AES128-KW key).

Author's Address

   Ilari Liusvaara
   Independent

Liusvaara                 Expires May 17, 2016                 [Page 11]
-----------------------------------------------------------------------

-Ilari

---

From: Anders Rundgren <[email-masked]>
Date: Sat, 14 Nov 2015 16:43:27 +0100

Hi Ilari,

If these curves are generally recognized as "Edwards" (?) I would personally prefer
that "kty" refer to something Edward-ish like "ED" although this is (of course)
entirely unimportant.

However, for the other parameters I don't see much value in creating new JOSE
"keywords" unless we are dealing with things that have no previous counterpart.

Simon's PKIX I-Ds talk about "curves" so "crv" should IMHO apply here as well.

Reusing "x" wouldn't be a crime either since each "kty" must be treated separately anyway.

Anders
for the "art club" :-)

---

From: Ilari Liusvaara <[email-masked]>
Date: Sat, 14 Nov 2015 20:35:26 +0200

> that "kty" refer to something Edward-ish like "ED" although this is (of course)

These things are not Edwards curves. These things are abstract public-key
algorithms.

If you truly had Edwards curve over prime field[1], there would be no
problem presenting it in standard "EC" notation, as these things have
well-defined curve and both x and y coordinates that are in Z_p.

And yes, I did consider reusing "crv" and "x", but decided that looks
pretty odd (there is no guarantee that these things are in any way
based on elliptic curves, nor that even if they are, "x" is actually
x coordinate of the curve.

[1] But this fails for Edwards curves over prime squared fields, since
each co-ordinate has two subcomponents (AFAIK, higher powers give
weak-for-ECC fields). 

-Ilari

---

From: Mike Jones <[email-masked]>
Date: Wed, 18 Nov 2015 00:27:12 +0000

I would strongly argue for using "crv" and "x" to characterize these algorithms.  Developers will be unpleasantly surprised if we don't and more than likely unnecessarily confused as well.

I'm on the fence about whether to use "kty":"EC" or a new key type value, such as "EC1" (Elliptic Curve with one coordinate).  I'll note that "EC" is already designed to allow curves whose representations use "x" but not "y", so there's strictly speaking no need for a new key type.  But I understand the argument that since "x" isn't represented in SEC1 format for these curves, that a different "kty" value may be appropriate.

				-- Mike

-----Original Message-----
From: jose [mailto:[email-masked]] On Behalf Of Ilari Liusvaara
Sent: Saturday, November 14, 2015 10:35 AM
To: Anders Rundgren
Cc: [email-masked]
Subject: Re: [jose] CFRG ECC in JOSE - thumbprint

On Sat, Nov 14, 2015 at 04:43:27PM +0100, Anders Rundgren wrote:
> Hi Ilari,
> 
> If these curves are generally recognized as "Edwards" (?) I would 
> personally prefer that "kty" refer to something Edward-ish like "ED" 
> although this is (of course) entirely unimportant.

These things are not Edwards curves. These things are abstract public-key algorithms.

If you truly had Edwards curve over prime field[1], there would be no problem presenting it in standard "EC" notation, as these things have well-defined curve and both x and y coordinates that are in Z_p.

And yes, I did consider reusing "crv" and "x", but decided that looks pretty odd (there is no guarantee that these things are in any way based on elliptic curves, nor that even if they are, "x" is actually x coordinate of the curve.

[1] But this fails for Edwards curves over prime squared fields, since each co-ordinate has two subcomponents (AFAIK, higher powers give weak-for-ECC fields). 

-Ilari

---

From: Anders Rundgren <[email-masked]>
Date: Wed, 18 Nov 2015 09:49:27 +0100

On 2015-11-18 01:27, Mike Jones wrote:
> I would strongly argue for using "crv" and "x" to characterize these algorithms.
 > Developers will be unpleasantly surprised if we don't and more than likely unnecessarily confused as well.

I agree.  In the case "crv" isn't a curve it would still at least be an algorithm.

> I'm on the fence about whether to use "kty":"EC" or a new key type value,
 > such as "EC1" (Elliptic Curve with one coordinate).  I'll note that "EC"
 > is already designed to allow curves whose representations use
 > "x" but not "y", so there's strictly speaking no need for a new key type.
 > But I understand the argument that since "x" isn't represented in SEC1
 > format for these curves, that a different "kty" value may be appropriate.

IMO, the fact that quite a bunch of popular cryptographic libraries build on
"hardcoded" EC and RSA key-types, motivate a *new name*.  It seems that
JWK parsing would be more straightforward as well.

The actual name is fairly unimportant but "EC1" doesn't sound too bad :-)
It fits the algorithms/curves currently on the table, doesn't it?

Anders

---

From: Ilari Liusvaara <[email-masked]>
Date: Wed, 18 Nov 2015 21:31:27 +0200

On Wed, Nov 18, 2015 at 12:27:12AM +0000, Mike Jones wrote:
> I would strongly argue for using "crv" and "x" to characterize these
> algorithms.  Developers will be unpleasantly surprised if we don't
> and more than likely unnecessarily confused as well.

Well, I changed the text to use "crv" and "x" instead of "kag" and "p"
(and also changed "key algorithm group" to "key subtype", now from
EC registry, instead of algorithm registry).

As to confusion potential, I would say this is more confusing as it
uses the same parameter name for two quite different uses. 

> I'm on the fence about whether to use "kty":"EC" or a new key type
> value, such as "EC1" (Elliptic Curve with one coordinate).  I'll
> note that "EC" is already designed to allow curves whose
> representations use "x" but not "y", so there's strictly speaking no
> need for a new key type.  But I understand the argument that since
> "x" isn't represented in SEC1 format for these curves, that a
> different "kty" value may be appropriate.

Well, I kept the "OKP" name as I think it better describes what these
things are about than "EC1".

As for "EC", there is no guarantee these work for various ECC
algorithms one would expect to work for every curve (e.g. X25519 won't
work for signing, Ed25519 won't work for anything that presently
exists).

-----------------------------------------------------------------------
Network Working Group                                       I. Liusvaara
Internet-Draft                                               Independent
Intended status: Standards Track                       November 18, 2015
Expires: May 21, 2016

Abstract

Status of This Memo

   This Internet-Draft will expire on May 21, 2016.

Copyright Notice

Liusvaara                 Expires May 21, 2016                  [Page 1]


Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements Terminology  . . . . . . . . . . . . . . . .   2
     1.2.  Notation  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Key type 'OKP'  . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  Algorithms  . . . . . . . . . . . . . . . . . . . . . . . . .   3
     3.1.  Signatures  . . . . . . . . . . . . . . . . . . . . . . .   3
       3.1.1.  Algorithms  . . . . . . . . . . . . . . . . . . . . .   3
       3.1.2.  Signing . . . . . . . . . . . . . . . . . . . . . . .   4
       3.1.3.  Verification  . . . . . . . . . . . . . . . . . . . .   4
     3.2.  ECDH-ES . . . . . . . . . . . . . . . . . . . . . . . . .   4
       3.2.1.  Performing the ECDH operation . . . . . . . . . . . .   4
   4.  Security considerations . . . . . . . . . . . . . . . . . . .   4
   5.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   5
   6.  IANA considerations . . . . . . . . . . . . . . . . . . . . .   5
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   8
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .   8
     7.2.  Informative References  . . . . . . . . . . . . . . . . .   8
   Appendix A.  Examples . . . . . . . . . . . . . . . . . . . . . .   8
     A.1.  Ed25519 private key . . . . . . . . . . . . . . . . . . .   8
     A.2.  Ed25519 public key  . . . . . . . . . . . . . . . . . . .   9
     A.3.  JWK thumbprint canonicalization . . . . . . . . . . . . .   9
     A.4.  Ed25519 Signing . . . . . . . . . . . . . . . . . . . . .   9
     A.5.  Ed25519 Validation  . . . . . . . . . . . . . . . . . . .  10
     A.6.  ECDH-ES with X25519 . . . . . . . . . . . . . . . . . . .  11
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  12

1.  Introduction

1.2.  Notation

Liusvaara                 Expires May 21, 2016                  [Page 2]


2.  Key type 'OKP'

   o  The parameter "crv" MUST be present, and contain the subtype of
      the key (from "JSON Web Elliptic curve" registry).

   o  The parameter "x" MUST be present, and contain the public key
      encoded using base64url [RFC4648] encoding.

   Note: Do not assume that there is an underlying elliptic curve,
   despite the existence of the "crv" and "x" parameters.

   When calculating thumbprints [RFC7638], the three public key fields
   are included in the hash.  That is, in lexographic order: "crv",
   "kty" and "x".

3.  Algorithms

3.1.  Signatures

3.1.1.  Algorithms

   The following signature algorithms are defined here (to be applied as
   values of "alg" parameter).  All these have keys with subtype of the
   same name:

     alg value:  subtype:     The algorithm:
     Ed25519     Ed25519      Ed25519
     Ed25519ph   Ed25519ph    Ed25519ph
     Ed448       Ed448        Ed448
     Ed448ph     Ed448ph      Ed448ph

   The key type for these keys is "OKP" and key subtype for these
   algorithms MUST be the same as the algorithm name.

   The keys of these subtypes MUST NOT be used for ECDH-ES.

Liusvaara                 Expires May 21, 2016                  [Page 3]


3.1.2.  Signing

3.1.3.  Verification

3.2.  ECDH-ES

   The following key subtypes defined here for purpose of ECDH-ES:

      subtype:          ECDH Function:
      X25519            X25519
      X448              X448

   The key type used with these keys is "OKP".  These subtypes MUST NOT
   be used for signing.

Liusvaara                 Expires May 21, 2016                  [Page 4]


   Some algorithms interact in bad ways (e.g.  "Ed25519" and
   "Ed25519ph").  For this reason, those algorithms have different
   subtypes, so keys for each are not mixed up.

5.  Acknowledgements

6.  IANA considerations

   o  Parameter Name: "crv"

Liusvaara                 Expires May 21, 2016                  [Page 5]


   o  Parameter Name: "d"

   o  Parameter Name: "x"

Liusvaara                 Expires May 21, 2016                  [Page 6]


   o  Curve Name: "Ed25519"
   o  Curve Description: Ed25519 signature algorithm keypairs
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.1 of [RFC-THIS]

   o  Curve Name: "Ed25519ph"
   o  Curve Description: Ed25519 signature algorithm with prehash
      keypairs
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.1 of [RFC-THIS]

   o  Curve Name: "Ed448"
   o  Curve Description: Ed448 signature algorithm keypairs
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.1 of [RFC-THIS]

   o  Curve Name: "Ed448ph"
   o  Curve Description: Ed448 signature algorithm with prehash keypairs
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.1 of [RFC-THIS]

   o  Curve name: "X25519"
   o  Curve Description: X25519 function keypairs
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.2 of [RFC-THIS]
   o  Analysis Documents(s): [I-D.irtf-cfrg-curves]

   o  Curve Name: "X448"
   o  Curve Description: X448 function keypairs
   o  JOSE Implementation Requirements: Optional
   o  Change Controller: IESG
   o  Specification Document(s): Section 3.2 of [RFC-THIS]
   o  Analysis Documents(s): [I-D.irtf-cfrg-curves]

Liusvaara                 Expires May 21, 2016                  [Page 7]


7.  References

   [I-D.irtf-cfrg-curves]

   [I-D.irtf-cfrg-eddsa]

Appendix A.  Examples

A.1.  Ed25519 private key

   {"kty":"OKP","crv":"Ed25519",
   "d":"nWGxne_9WmC6hEr0kuwsxERJxWl7MmkZcDusAxyuf2A"
   "x":"11qYAYKxCrfVS_7TyWQHOg7hcvPapiMlrwIaaPcHURo"}

Liusvaara                 Expires May 21, 2016                  [Page 8]


   And of the public key:

A.2.  Ed25519 public key

   {"kty":"OKP","crv":"Ed25519",
   "x":"11qYAYKxCrfVS_7TyWQHOg7hcvPapiMlrwIaaPcHURo"}

   {"crv":"Ed25519","kty":"OKP","x":"11qYAYKxCrfVS_7TyWQHOg7hcvPapiMlrwI
   aaPcHURo"}

   Which has the SHA-256 hash of:
   90facafea9b1556698540f70c0117a22ea37bd5cf3ed3c47093c1707282b4b89

A.4.  Ed25519 Signing

   {"alg":"Ed25519"}

   eyJhbGciOiJFZDI1NTE5In0

   The payload is (text):

Liusvaara                 Expires May 21, 2016                  [Page 9]


A.5.  Ed25519 Validation

   {"alg":"Ed25519"}

   So this is Ed25519 signature.  Now the key has: "kty":"OKP" and
   "crv":"Ed25519", so the key is valid for the algorithm (if it had
   other values, the validation would have failed).

Liusvaara                 Expires May 21, 2016                 [Page 10]


A.6.  ECDH-ES with X25519

   {"kty":"OKP","crv":"X25519","kid":"Bob"
   "x":"3p7bfXt9wbTTW2HC7OQ1Nz-DQ8hbeGdNrfx-FG-IK08"}

   {"kty":"OKP","crv":"X25519",
   "x":"hSDwCYkwp1R0i33ctD73Wg2_Og0mOBr066SpjqqbTmo"}

   {"alg":"ECDH-ES+A128KW","epk":{"kty":"OKP","crv":"X25519",
   "x":"hSDwCYkwp1R0i33ctD73Wg2_Og0mOBr066SpjqqbTmo"},
   "enc":"A128GCM","kid":"Bob"}

Liusvaara                 Expires May 21, 2016                 [Page 11]


Author's Address

   Ilari Liusvaara
   Independent

Liusvaara                 Expires May 21, 2016                 [Page 12]
-----------------------------------------------------------------------

-Ilari

---

From: Anders Rundgren <[email-masked]>
Date: Wed, 18 Nov 2015 20:40:34 +0100

Confusing or not, I like it and hope to implement at least
Ed25519 in the next couple of months.

Anders