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
draft-ietf-jose-cfrg-curves-03
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 JOSE.
Status of This Memo
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provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on January 2, 2017.
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Copyright (c) 2016 IETF Trust and the persons identified as the
document authors. All rights reserved.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Requirements Terminology . . . . . . . . . . . . . . . . 3
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 . . . . . . . . . . . . . . . . . . . 5
5. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 5
6. IANA considerations . . . . . . . . . . . . . . . . . . . . . 6
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 7
7.1. Normative References . . . . . . . . . . . . . . . . . . 7
7.2. Informative References . . . . . . . . . . . . . . . . . 8
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 . . . . . . . . . . . . . . . . . . . 10
A.6. ECDH-ES with X25519 . . . . . . . . . . . . . . . . . . . 10
A.7. ECDH-ES with X448 . . . . . . . . . . . . . . . . . . . . 11
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 13
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.)
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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:
o The parameter "kty" MUST be "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 the base64url [RFC4648] 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 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.
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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.
"crv" EdDSA Variant
Ed25519 Ed25519
Ed448 Ed448
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.
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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.
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6. IANA considerations
The following is 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): Section 2 of [RFC-THIS]
The following is added to the "JSON Web Key Parameters" registry:
o Parameter Name: "crv"
o Parameter Description: The subtype 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]
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): Section 2 of [RFC-THIS]
The following is 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): Section 3 of [RFC-THIS]
o Algorithm Analysis Documents(s): [I-D.irtf-cfrg-eddsa]
The following is added to the "JSON Web Key Elliptic Curve" registry:
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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 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 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): [RFC7748]
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): [RFC7748]
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,
<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>.
[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <http://www.rfc-editor.org/info/rfc7748>.
[I-D.irtf-cfrg-eddsa]
Josefsson, S. and I. Liusvaara, "Edwards-curve Digital
Signature Algorithm (EdDSA)", draft-irtf-cfrg-eddsa-05
(work in progress), March 2016.
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7.2. Informative References
[RFC7517] Jones, M., "JSON Web Key (JWK)", RFC 7517,
DOI 10.17487/RFC7517, May 2015,
<http://www.rfc-editor.org/info/rfc7517>.
[RFC7518] Jones, M., "JSON Web Algorithms (JWA)", RFC 7518,
DOI 10.17487/RFC7518, May 2015,
<http://www.rfc-editor.org/info/rfc7518>.
[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 taken from test
vectors of [RFC7748] and [I-D.irtf-cfrg-eddsa].
A.1. Ed25519 Private Key
{"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
A.2. Ed25519 Public Key
This is the public parts of the previous private key (which just
omits "d"):
{"kty":"OKP","crv":"Ed25519",
"x":"11qYAYKxCrfVS_7TyWQHOg7hcvPapiMlrwIaaPcHURo"}
A.3. JWK Thumbprint Canonicalization
The JWK Thumbprint canonicalization of the two above examples (with
linebreak inserted for formatting reasons) is:
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{"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".
A.4. Ed25519 Signing
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 (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 (concatenation of signing
input, a dot, and base64url encoding of the signature):
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eyJhbGciOiJFZERTQSJ9.RXhhbXBsZSBvZiBFZDI1NTE5IHNpZ25pbmc.hgyY0il_MGCj
P0JzlnLWG1PPOt7-09PGcvMg3AIbQR6dWbhijcNR4ki4iylGjg5BhVsPt9g7sVvpAr_Mu
M0KAg
A.5. Ed25519 Validation
The JWS from above example 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 second dot:
eyJhbGciOiJFZERTQSJ9.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 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:
{"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
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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:
{"kty":"OKP","crv":"X25519",
"x":"hSDwCYkwp1R0i33ctD73Wg2_Og0mOBr066SpjqqbTmo"}
So the protected header could, for example, be:
{"alg":"ECDH-ES+A128KW","epk":{"kty":"OKP","crv":"X25519",
"x":"hSDwCYkwp1R0i33ctD73Wg2_Og0mOBr066SpjqqbTmo"},
"enc":"A128GCM","kid":"Bob"}
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:
{"kty":"OKP","crv":"X448","kid":"Dave",
"x":"PreoKbDNIPW8_AtZm2_sz22kYnEHvbDU80W0MCfYuXL8PjT7QjKhPKcG3LV67D2
uB73BxnvzNgk"}
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
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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):
{"kty":"OKP","crv":"X448",
"x":"mwj3zDG34-Z9ItWuoSEHSic70rg94Jxj-qc9LCLF2bvINmRyQdlT1AxbEtqIEg1
TF3-A5TLEH6A"}
So the protected header could for example be (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 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).
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Author's Address
Ilari Liusvaara
Independent
Email: ilariliusvaara@welho.com
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