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<pre>Internet Engineering Task Force (IETF) Y. Nir
Request for Comments: 8031 Check Point
Category: Standards Track S. Josefsson
ISSN: 2070-1721 SJD
December 2016
<span class="h1">Curve25519 and Curve448 for the</span>
<span class="h1">Internet Key Exchange Protocol Version 2 (IKEv2) Key Agreement</span>
Abstract
This document describes the use of Curve25519 and Curve448 for
ephemeral key exchange in the Internet Key Exchange Protocol Version
2 (IKEv2).
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/rfc8031">http://www.rfc-editor.org/info/rfc8031</a>.
Copyright Notice
Copyright (c) 2016 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">Nir & Josefsson Standards Track [Page 1]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-2" ></span>
<span class="grey"><a href="./rfc8031">RFC 8031</a> Curve25519 and Curve448 for IKEv2 December 2016</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>. Conventions Used in This Document . . . . . . . . . . . . <a href="#page-2">2</a>
<a href="#section-2">2</a>. Curve25519 and Curve448 . . . . . . . . . . . . . . . . . . . <a href="#page-3">3</a>
<a href="#section-3">3</a>. Use and Negotiation in IKEv2 . . . . . . . . . . . . . . . . <a href="#page-3">3</a>
<a href="#section-3.1">3.1</a>. Key Exchange Payload . . . . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-3.2">3.2</a>. Recipient Tests . . . . . . . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-4">4</a>. Security Considerations . . . . . . . . . . . . . . . . . . . <a href="#page-4">4</a>
<a href="#section-5">5</a>. IANA Considerations . . . . . . . . . . . . . . . . . . . . . <a href="#page-5">5</a>
<a href="#section-6">6</a>. References . . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-5">5</a>
<a href="#section-6.1">6.1</a>. Normative References . . . . . . . . . . . . . . . . . . <a href="#page-5">5</a>
<a href="#section-6.2">6.2</a>. Informative References . . . . . . . . . . . . . . . . . <a href="#page-6">6</a>
<a href="#appendix-A">Appendix A</a>. Numerical Example for Curve25519 . . . . . . . . . . <a href="#page-7">7</a>
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-8">8</a>
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . <a href="#page-8">8</a>
<span class="h2"><a class="selflink" id="section-1" href="#section-1">1</a>. Introduction</span>
The "Elliptic Curves for Security" document [<a href="./rfc7748" title=""Elliptic Curves for Security"">RFC7748</a>] describes two
elliptic curves, Curve25519 and Curve448, as well as the X25519 and
X448 functions for performing key agreement using Diffie-Hellman
operations with these curves. The curves and functions are designed
for both performance and security.
Elliptic curve Diffie-Hellman [<a href="./rfc5903" title=""Elliptic Curve Groups modulo a Prime (ECP Groups) for IKE and IKEv2"">RFC5903</a>] has been specified for the
Internet Key Exchange Protocol Version 2 (IKEv2) [<a href="./rfc7296" title=""Internet Key Exchange Protocol Version 2 (IKEv2)"">RFC7296</a>] for almost
ten years. <a href="./rfc5903">RFC 5903</a> and its predecessor specified the so-called NIST
curves. The state of the art has advanced since then. More modern
curves allow faster implementations while making it much easier to
write constant-time implementations that are resilient to time-based
side-channel attacks. This document defines two such curves for use
in IKEv2. See [<a href="#ref-Curve25519">Curve25519</a>] for details about the speed and security
of the Curve25519 function.
<span class="h3"><a class="selflink" id="section-1.1" href="#section-1.1">1.1</a>. Conventions Used in This Document</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>].
<span class="grey">Nir & Josefsson Standards Track [Page 2]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-3" ></span>
<span class="grey"><a href="./rfc8031">RFC 8031</a> Curve25519 and Curve448 for IKEv2 December 2016</span>
<span class="h2"><a class="selflink" id="section-2" href="#section-2">2</a>. Curve25519 and Curve448</span>
Implementations of Curve25519 and Curve448 in IKEv2 SHALL follow the
steps described in this section. All cryptographic computations are
done using the X25519 and X448 functions defined in [<a href="./rfc7748" title=""Elliptic Curves for Security"">RFC7748</a>]. All
related parameters (for example, the base point) and the encoding (in
particular, pruning the least/most significant bits and using little-
endian encoding) are compliant with [<a href="./rfc7748" title=""Elliptic Curves for Security"">RFC7748</a>].
An ephemeral Diffie-Hellman key exchange using Curve25519 or Curve448
is performed as follows: each party picks a secret key d uniformly at
random and computes the corresponding public key. "X" is used below
to denote either X25519 or X448, and "G" is used to denote the
corresponding base point:
pub_mine = X(d, G)
Parties exchange their public keys (see <a href="#section-3.1">Section 3.1</a>) and compute a
shared secret:
SHARED_SECRET = X(d, pub_peer)
This shared secret is used directly as the value denoted g^ir in
<a href="./rfc7296#section-2.14">Section 2.14 of RFC 7296</a>. It is 32 octets when Curve25519 is used
and 56 octets when Curve448 is used.
<span class="h2"><a class="selflink" id="section-3" href="#section-3">3</a>. Use and Negotiation in IKEv2</span>
The use of Curve25519 and Curve448 in IKEv2 is negotiated using a
Transform Type 4 (Diffie-Hellman group) in the Security Association
(SA) payload of either an IKE_SA_INIT or a CREATE_CHILD_SA exchange.
The value 31 is used for the group defined by Curve25519 and the
value 32 is used for the group defined by Curve448.
<span class="grey">Nir & Josefsson Standards Track [Page 3]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-4" ></span>
<span class="grey"><a href="./rfc8031">RFC 8031</a> Curve25519 and Curve448 for IKEv2 December 2016</span>
<span class="h3"><a class="selflink" id="section-3.1" href="#section-3.1">3.1</a>. Key Exchange Payload</span>
The diagram for the Key Exchange payload from <a href="./rfc7296#section-3.4">Section 3.4 of RFC 7296</a>
is copied below for convenience:
1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Next Payload |C| RESERVED | Payload Length |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Diffie-Hellman Group Num | RESERVED |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
~ Key Exchange Data ~
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
o Payload Length - For Curve25519, the public key is 32 octets, so
the Payload Length field will be 40. For Curve448, the public key
is 56 octets, so the Payload Length field will be 64.
o The Diffie-Hellman Group Num is 31 for Curve25519 or 32 for
Curve448.
o The Key Exchange Data is the 32 or 56 octets as described in
<a href="./rfc7748#section-6">Section 6 of [RFC7748]</a>.
<span class="h3"><a class="selflink" id="section-3.2" href="#section-3.2">3.2</a>. Recipient Tests</span>
Receiving and handling of incompatible point formats MUST follow the
considerations described in <a href="./rfc7748#section-5">Section 5 of [RFC7748]</a>. In particular,
receiving entities MUST mask the most-significant bit in the final
byte for X25519 (but not X448), and implementations MUST accept non-
canonical values.
<span class="h2"><a class="selflink" id="section-4" href="#section-4">4</a>. Security Considerations</span>
Curve25519 and Curve448 are designed to facilitate the production of
high-performance constant-time implementations. Implementors are
encouraged to use a constant-time implementation of the functions.
This point is of crucial importance, especially if the implementation
chooses to reuse its ephemeral key pair in many key exchanges for
performance reasons.
Curve25519 is intended for the ~128-bit security level, comparable to
the 256-bit random ECP Groups (group 19) defined in <a href="./rfc5903">RFC 5903</a>, also
known as NIST P-256 or secp256r1. Curve448 is intended for the
~224-bit security level.
<span class="grey">Nir & Josefsson Standards Track [Page 4]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-5" ></span>
<span class="grey"><a href="./rfc8031">RFC 8031</a> Curve25519 and Curve448 for IKEv2 December 2016</span>
While the NIST curves are advertised as being chosen verifiably at
random, there is no explanation for the seeds used to generate them.
In contrast, the process used to pick Curve25519 and Curve448 is
fully documented and rigid enough so that independent verification
can and has been done. This is widely seen as a security advantage
because it prevents the generating party from maliciously
manipulating the parameters.
Another family of curves available in IKE that were generated in a
fully verifiable way is the Brainpool curves [<a href="./rfc6954" title=""Using the Elliptic Curve Cryptography (ECC) Brainpool Curves for the Internet Key Exchange Protocol Version 2 (IKEv2)"">RFC6954</a>]. For example,
brainpoolP256 (group 28) is expected to provide a level of security
comparable to Curve25519 and NIST P-256. However, due to the use of
pseudorandom prime, it is significantly slower than NIST P-256, which
is itself slower than Curve25519.
<span class="h2"><a class="selflink" id="section-5" href="#section-5">5</a>. IANA Considerations</span>
IANA has assigned two values for the names "Curve25519" and
"Curve448" in the IKEv2 "Transform Type 4 - Diffie-Hellman Group
Transform IDs" and has listed this document as the reference. The
Recipient Tests field should also point to this document:
+--------+------------+-----------------------+-----------+
| Number | Name | Recipient Tests | Reference |
+--------+------------+-----------------------+-----------+
| 31 | Curve25519 | <a href="./rfc8031#section-3.2">RFC 8031, Section 3.2</a> | <a href="./rfc8031">RFC 8031</a> |
| 32 | Curve448 | <a href="./rfc8031#section-3.2">RFC 8031, Section 3.2</a> | <a href="./rfc8031">RFC 8031</a> |
+--------+------------+-----------------------+-----------+
Table 1: New Transform Type 4 Values
<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-RFC7296">RFC7296</a>] Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T.
Kivinen, "Internet Key Exchange Protocol Version 2
(IKEv2)", STD 79, <a href="./rfc7296">RFC 7296</a>, DOI 10.17487/RFC7296, October
2014, <<a href="http://www.rfc-editor.org/info/rfc7296">http://www.rfc-editor.org/info/rfc7296</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>>.
<span class="grey">Nir & Josefsson Standards Track [Page 5]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-6" ></span>
<span class="grey"><a href="./rfc8031">RFC 8031</a> Curve25519 and Curve448 for IKEv2 December 2016</span>
<span class="h3"><a class="selflink" id="section-6.2" href="#section-6.2">6.2</a>. Informative References</span>
[<a id="ref-Curve25519">Curve25519</a>]
Bernstein, J., "Curve25519: New Diffie-Hellman Speed
Records", Public Key Cryptography - PKC 2006, Lecture
Notes in Computer Science (LNCS), Vol. 3958, pp. 207-228,
DOI 10.1007/11745853_14, February 2006,
<<a href="http://dx.doi.org/10.1007/11745853_14">http://dx.doi.org/10.1007/11745853_14</a>>.
[<a id="ref-RFC5903">RFC5903</a>] Fu, D. and J. Solinas, "Elliptic Curve Groups modulo a
Prime (ECP Groups) for IKE and IKEv2", <a href="./rfc5903">RFC 5903</a>,
DOI 10.17487/RFC5903, June 2010,
<<a href="http://www.rfc-editor.org/info/rfc5903">http://www.rfc-editor.org/info/rfc5903</a>>.
[<a id="ref-RFC6954">RFC6954</a>] Merkle, J. and M. Lochter, "Using the Elliptic Curve
Cryptography (ECC) Brainpool Curves for the Internet Key
Exchange Protocol Version 2 (IKEv2)", <a href="./rfc6954">RFC 6954</a>,
DOI 10.17487/RFC6954, July 2013,
<<a href="http://www.rfc-editor.org/info/rfc6954">http://www.rfc-editor.org/info/rfc6954</a>>.
<span class="grey">Nir & Josefsson Standards Track [Page 6]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-7" ></span>
<span class="grey"><a href="./rfc8031">RFC 8031</a> Curve25519 and Curve448 for IKEv2 December 2016</span>
<span class="h2"><a class="selflink" id="appendix-A" href="#appendix-A">Appendix A</a>. Numerical Example for Curve25519</span>
Suppose we have both the initiator and the responder generating
private keys by generating 32 random octets. As usual in IKEv2 and
its extension, we will denote Initiator values with the suffix _i and
responder values with the suffix _r:
random_i = 75 1f b4 30 86 55 b4 76 b6 78 9b 73 25 f9 ea 8c
dd d1 6a 58 53 3f f6 d9 e6 00 09 46 4a 5f 9d 94
random_r = 0a 54 64 52 53 29 0d 60 dd ad d0 e0 30 ba cd 9e
55 01 ef dc 22 07 55 a1 e9 78 f1 b8 39 a0 56 88
These numbers need to be fixed by unsetting some bits as described in
<a href="./rfc7748#section-5">Section 5 of RFC 7748</a>. This affects only the first and last octets
of each value:
fixed_i = 70 1f b4 30 86 55 b4 76 b6 78 9b 73 25 f9 ea 8c
dd d1 6a 58 53 3f f6 d9 e6 00 09 46 4a 5f 9d 54
fixed_r = 08 54 64 52 53 29 0d 60 dd ad d0 e0 30 ba cd 9e
55 01 ef dc 22 07 55 a1 e9 78 f1 b8 39 a0 56 48
The actual private keys are considered to be encoded in little-endian
format:
d_i = 549D5F4A460900E6D9F63F53586AD1DD8CEAF925739B78B676B4558630B41F70
d_r = 4856A039B8F178E9A1550722DCEF01559ECDBA30E0D0ADDD600D295352645408
The public keys are generated from this using the formula in
<a href="#section-2">Section 2</a>:
pub_i = X25519(d_i, G) =
48 d5 dd d4 06 12 57 ba 16 6f a3 f9 bb db 74 f1
a4 e8 1c 08 93 84 fa 77 f7 90 70 9f 0d fb c7 66
pub_r = X25519(d_r, G) =
0b e7 c1 f5 aa d8 7d 7e 44 86 62 67 32 98 a4 43
47 8b 85 97 45 17 9e af 56 4c 79 c0 ef 6e ee 25
And this is the value of the Key Exchange Data field in the Key
Exchange payload described in <a href="#section-3.1">Section 3.1</a>. The shared value is
calculated as in <a href="#section-2">Section 2</a>:
SHARED_SECRET = X25519(d_i, pub_r) = X25519(d_r, pub_i) =
c7 49 50 60 7a 12 32 7f-32 04 d9 4b 68 25 bf b0
68 b7 f8 31 9a 9e 37 08-ed 3d 43 ce 81 30 c9 50
<span class="grey">Nir & Josefsson Standards Track [Page 7]</span></pre>
<hr class='noprint'/><!--NewPage--><pre class='newpage'><span id="page-8" ></span>
<span class="grey"><a href="./rfc8031">RFC 8031</a> Curve25519 and Curve448 for IKEv2 December 2016</span>
Acknowledgements
Curve25519 was designed by D. J. Bernstein and the parameters for
Curve448 ("Goldilocks") were defined by Mike Hamburg. The
specification of algorithms, wire format, and other considerations
are documented in <a href="./rfc7748">RFC 7748</a> by Adam Langley, Mike Hamburg, and Sean
Turner.
The example in <a href="#appendix-A">Appendix A</a> was calculated using the master version of
OpenSSL, retrieved on August 4th, 2016.
Authors' Addresses
Yoav Nir
Check Point Software Technologies Ltd.
5 Hasolelim st.
Tel Aviv 6789735
Israel
Email: ynir.ietf@gmail.com
Simon Josefsson
SJD AB
Email: simon@josefsson.org
Nir & Josefsson Standards Track [Page 8]
</pre>
|
