Network Working Group Y. Nir
Internet-Draft Check Point
Intended status: Standards Track S. Josefsson
Expires: March 11, 2016 SJD
September 8, 2015

Curve25519 and Curve448 for IKEv2 Key Agreement


This document describes the use of Curve25519 and Curve448 for ephemeral key exchange in the Internet Key Exchange (IKEv2) protocol.

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Table of Contents

1. Introduction

[CFRG-Curves] describes the two elliptic curves Curve25519 and Curve448 and the X25519 and X448 functions for performing Diffie-Hellman operations on the curves. The curves and functions are designed with performance and security in mind.

Almost ten years ago [RFC4753] specified the first elliptic curve Diffie-Hellman groups for the Internet Key Exchange protocol (IKEv2 - [RFC7296]). These were 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 free from side-channel attacks. This document defines such a curve for use in IKE. See [Curve25519] for details about the speed and security of the Curve25519 function.

1.1. Conventions Used in This Document

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. Curve25519 & Curve448

All cryptographic computations are done using the X25519 and X448 functions defined in [CFRG-Curves]. All related parameters (for example, the base point) and the encoding (in particular, pruning the least/most significant bits and use of little-endian encoding) are inherited from [CFRG-Curves].

   x_mine = X(d, G)

An ephemeral Diffie-Hellman key exchange using Curve25519 or Curve448 goes 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:

	  SHARED_SECRET = X(d, x_peer).

Parties exchange their public keys (see Section 3.1) and compute a shared secret:

This shared secret is used directly as the value denoted g^ir in section 2.14 of RFC 7296. It is 32 octets when Curve25519 is used, and 56 octets when Curve448 is used.

3. Use and Negotiation in IKEv2

The use of Curve25519 and Curve448 in IKEv2 is negotiated using a Transform Type 4 (Diffie-Hellman group) in the SA payload of either an IKE_SA_INIT or a CREATE_CHILD_SA exchange.

3.1. Key Exchange Payload

                        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                       ~
   |                                                               |

The diagram for the Key Exchange Payload from section 3.4 of RFC 7296 is copied below for convenience:

3.2. Recipient Tests

This document match the discussion in [CFRG-Curves] related to receiving and accepting incompatible point formats. 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. See section 5 of [CFRG-Curves] for further discussion.

4. Security Considerations

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 if the implementation chooses to reuse its supposedly ephemeral key pair for many key exchanges, which some implementations do in order to improve performance.

Curve25519 is intended for the ~128-bit security level, comparable to the 256-bit random ECP group (group 19) defined in RFC 4753, also known as NIST P-256 or secp256r1. Curve448 is intended for the ~224-bit security level.

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 these curves is fully documented and rigid enough so that independent verification has been done. This is widely seen as a security advantage, since it prevents the generating party from maliciously manipulating the parameters.

Another family of curves available in IKE, generated in a fully verifiable way, is the Brainpool curves [RFC6954]. 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 pseudo-random prime, it is significantly slower than NIST P-256, which is itself slower than Curve25519.

5. IANA Considerations

IANA is requested to assign two values from the IKEv2 "Transform Type 4 - Diffie-Hellman Group Transform IDs" registry, with names "Curve25519" and "Curve448" and this document as reference. The Recipient Tests field should also point to this document.

6. Acknowledgements

Curve25519 was designed by D. J. Bernstein and Curve448 ("Goldilocks") is by Mike Hamburg. The specification of algorithms, wire format and other considerations are due to the CFRG document.

7. References

7.1. Normative References

[CFRG-Curves] Langley, A., Hamburg, M. and S. Turner, "Elliptic Curves for Security", Internet-Draft draft-irtf-cfrg-curves-06, August 2015.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC7296] Kivinen, T., Kaufman, C., Hoffman, P., Nir, Y. and P. Eronen, "Internet Key Exchange Protocol Version 2 (IKEv2)", RFC 7296, October 2014.

7.2. Informative References

[Curve25519] Bernstein, J., "Curve25519: New Diffie-Hellman Speed Records", LNCS 3958, February 2006.
[RFC4753] Fu, D. and J. Solinas, "ECP Groups For IKE and IKEv2", RFC 4753, January 2007.
[RFC6954] Merkle, J. and M. Lochter, "Using the Elliptic Curve Cryptography (ECC) Brainpool Curves for the Internet Key Exchange Protocol Version 2 (IKEv2)", RFC 6954, July 2013.

Authors' Addresses

Yoav Nir Check Point Software Technologies Ltd. 5 Hasolelim st. Tel Aviv, 6789735 Israel EMail:
Simon Josefsson SJD AB EMail: