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Versions: (draft-nir-ipsecme-curve25519) 00 01 02 03 04 05 RFC 8031

Network Working Group                                             Y. Nir
Internet-Draft                                               Check Point
Intended status: Standards Track                            S. Josefsson
Expires: April 14, 2017                                              SJD
                                                        October 11, 2016


            Curve25519 and Curve448 for IKEv2 Key Agreement
                    draft-ietf-ipsecme-safecurves-05

Abstract

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

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
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   This Internet-Draft will expire on April 14, 2017.

Copyright Notice

   Copyright (c) 2016 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
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   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.





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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Conventions Used in This Document . . . . . . . . . . . .   2
   2.  Curve25519 & Curve448 . . . . . . . . . . . . . . . . . . . .   2
   3.  Use and Negotiation in IKEv2  . . . . . . . . . . . . . . . .   3
     3.1.  Key Exchange Payload  . . . . . . . . . . . . . . . . . .   3
     3.2.  Recipient Tests . . . . . . . . . . . . . . . . . . . . .   4
   4.  Security Considerations . . . . . . . . . . . . . . . . . . .   4
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   4
   6.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   5
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   5
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .   5
     7.2.  Informative References  . . . . . . . . . . . . . . . . .   5
   Appendix A.  Numerical Example for Curve25519 . . . . . . . . . .   6
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .   7

1.  Introduction

   The "Elliptic Curves for Security" document [RFC7748] 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 [RFC5903] has been specified for the
   Internet Key Exchange (IKEv2 - [RFC7296]) for almost ten years.  RFC
   5903 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 resilient to time-based side-channel attacks.
   This document defines two such curves 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

   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 [RFC7748].  All
   related parameters (for example, the base point) and the encoding (in




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   particular, pruning the least/most significant bits and use of
   little-endian encoding) are compliant with [RFC7748].

   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 Section 3.1) and compute a
   shared secret:

         SHARED_SECRET = X(d, pub_peer).

   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.  The value TBA1 is used
   for the group defined by Curve25519 and the value TBA2 is used for
   the group defined by Curve448.

3.1.  Key Exchange Payload

   The diagram for the Key Exchange Payload from section 3.4 of RFC 7296
   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, and for Curve448 the public
      key is 56 octets, so the Payload Length field will be 64.



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   o  The Diffie-Hellman Group Num is TBA1 for Curve25519, or TBA2 for
      Curve448.
   o  The Key Exchange Data is the 32 or 56 octets as described in
      section 6 of [RFC7748]

3.2.  Recipient Tests

   Receiving and handling of incompatible point formats MUST follow the
   considerations described in section 5 of [RFC7748].  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.

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 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 group (group 19) defined in RFC 5903, 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 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,
   since 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 [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:



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         +--------+------------+---------------------+-----------+
         | Number |    Name    |   Recipient Tests   | Reference |
         +--------+------------+---------------------+-----------+
         |  TBA1  | Curve25519 | RFCxxxx Section 3.2 |  RFCxxxx  |
         |  TBA2  |  Curve448  | RFCxxxx Section 3.2 |  RFCxxxx  |
         +--------+------------+---------------------+-----------+

                   Table 1: New Transform Type 4 Values

6.  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 RFC 7748 by Adam Langley, Mike Hamburg, and Sean
   Turner.

   The example in Appendix A was calculated using the master version of
   OpenSSL, retrieved on August 4th, 2016.

7.  References

7.1.  Normative References

   [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.

   [RFC7748]  Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
              for Security", RFC 7748, January 2016.

7.2.  Informative References

   [Curve25519]
              Bernstein, J., "Curve25519: New Diffie-Hellman Speed
              Records", LNCS 3958, February 2006,
              <http://dx.doi.org/10.1007/11745853_14>.

   [RFC5903]  Fu, D. and J. Solinas, "Elliptic Curve Groups modulo a
              Prime (ECP Groups) for IKE and IKEv2", RFC 5903, June
              2010.

   [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.



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Appendix A.  Numerical Example for Curve25519

   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
   section 5 of RFC 7748.  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
   Section 2:

   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 Section 3.1.  The shared value is
   calculated as in Section 2:

   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



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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




































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