Network Working Group I. Liusvaara
Internet-Draft Independent
Intended status: Standards Track July 1, 2016
Expires: January 2, 2017

CFRG ECDH and signatures in JOSE


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 JOSE.

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Table of Contents

1. Introduction

Internet Research Task Force (IRTF) Crypto Forum Research Group (CFRG) selected new Diffie-Hellman algorithms ("X25519" and "X448"; [RFC7748]) and signature algorithms ("Ed25519" and "Ed448"; [I-D.irtf-cfrg-eddsa]) for asymmetric key cryptography. This document defines how those algorithms are to be used in JOSE in interoperable manner.

This document defines the conventions to be used in the context of [RFC7517] and [RFC7518].

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. (Trying to apply ECDSA to those curves leads to nasty corner-cases and produces odd results.)

All inputs to and outputs from the the ECDH and signature functions are defined to be octet strings, with the exception of outputs of verification function, which are booleans.

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].

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:

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 DH algorithms based on hyperelliptic surfaces.)

When calculating JWK Thumbprints [RFC7638], the three public key fields are included in the hash input lexicographic order: "crv", "kty", and "x".

3. Algorithms

3.1. Signatures

3.1.1. Algorithms

For EdDSA signatures, algorithm "EdDSA" is defined here, to be applied as value of "alg" parameter.

   "crv"             EdDSA Variant
   Ed25519           Ed25519
   Ed448             Ed448

The key type for these keys is "OKP" and key subtype for these keys MUST be "Ed25519" for Ed25519 and "Ed448" for Ed448. The keys of these subtypes MUST NOT be used for ECDH-ES.

3.1.2. 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.

3.1.3. 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, the signature is invalid.

3.2. ECDH-ES

The following key subtypes defined here for purpose of "Key Agreement with Elliptic Curve Diffie-Hellman Ephemeral Static" (ECDH-ES).

   "crv"             ECDH Function Applied
   X25519            X25519
   X448              X448

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

[RFC7518] Section 4.6 defines the ECDH-ES algorithms "ECDH-ES+A128KW", "ECDH-ES+A192KW", "ECDH-ES+A256KW" and "ECDH-ES".

3.2.1. Performing the ECDH Operation

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 basepoint (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 KDF as per [RFC7518] section 4.6.2) 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.

4. Security considerations

Security considerations from [RFC7748] and [I-D.irtf-cfrg-eddsa] 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 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.

The JWA ECDH-ES KDF construction does not mix keys into the final shared secret. While in key exchange such could be a bad mistake, 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.

5. Acknowledgements

Thanks to Michael B. Jones for his comments on an initial pre-draft and editorial help.

6. IANA considerations

The following is added to the "JSON Web Key Types" registry:

The following is added to the "JSON Web Key Parameters" registry:

The following is added to the "JSON Web Signature and Encryption Algorithms" registry:

The following is added to the "JSON Web Key Elliptic Curve" registry:

7. References

7.1. 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.
[RFC4648] Josefsson, S., "The Base16, Base32, and Base64 Data Encodings", RFC 4648, DOI 10.17487/RFC4648, October 2006.
[RFC7748] Langley, A., Hamburg, M. and S. Turner, "Elliptic Curves for Security", RFC 7748, DOI 10.17487/RFC7748, January 2016.
[I-D.irtf-cfrg-eddsa] Josefsson, S. and I. Liusvaara, "Edwards-curve Digital Signature Algorithm (EdDSA)", Internet-Draft draft-irtf-cfrg-eddsa-05, March 2016.

7.2. Informative References

[RFC7517] Jones, M., "JSON Web Key (JWK)", RFC 7517, DOI 10.17487/RFC7517, May 2015.
[RFC7518] Jones, M., "JSON Web Algorithms (JWA)", RFC 7518, DOI 10.17487/RFC7518, May 2015.
[RFC7638] Jones, M. and N. Sakimura, "JSON Web Key (JWK) Thumbprint", RFC 7638, DOI 10.17487/RFC7638, September 2015.

Appendix A. Examples

To the extent possible, the examples use material taken from test vectors of [RFC7748] and [I-D.irtf-cfrg-eddsa].

A.1. Ed25519 Private Key


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

A.2. Ed25519 Public Key

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


A.3. JWK Thumbprint Canonicalization

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


Which has the SHA-256 hash (in hexadecimal) of 90facafea9b1556698540f70c0117a22ea37bd5cf3ed3c47093c1707282b4b89, which results in the base64url encoded JWK Thumbprint representation of "kPrK_qmxVWaYVA9wwBF6Iuo3vVzz7TxHCTwXBygrS4k".

A.4. Ed25519 Signing

The JWS protected header is:


This has the base64url encoding of:


The payload is (text):

Example of Ed25519 signing

This has the base64url encoding of:


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


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:


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


A.5. Ed25519 Validation

The JWS from above example is:


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


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 second dot:


Applying 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

A.6. ECDH-ES with X25519

The public key to encrypt to is:


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

This is represented as the ephemeral public key value:


So the protected header could, for example, be:


And the 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 the sender's value (the both sides run this through the KDF before using it as a direct encryption key or AES128-KW key).

A.7. ECDH-ES with X448

The public key to encrypt to (with linebreak inserted for formatting reasons) is:


The public key from 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

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 ephemeral public key value (linebreak inserted for formatting purposes):


So the protected header could for example be (linebreak inserted for formatting purposes):


And the sender computes as 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 as 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

Which is the same as the sender's value (the both sides run this through KDF before using as direct encryption key or AES256-KW key).

Author's Address

Ilari Liusvaara Independent EMail: