Movatterモバイル変換

Internet Engineering Task Force (IETF)                            Y. NirRequest for Comments: 8031                                   Check PointCategory: Standards Track                                   S. JosefssonISSN: 2070-1721                                                      SJD                                                           December 2016Curve25519 and Curve448 for theInternet Key Exchange Protocol Version 2 (IKEv2) Key AgreementAbstract   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 inSection 2 of RFC 7841.   Information about the current status of this document, any errata,   and how to provide feedback on it may be obtained athttp://www.rfc-editor.org/info/rfc8031.Copyright Notice   Copyright (c) 2016 IETF Trust and the persons identified as the   document authors.  All rights reserved.   This document is subject toBCP 78 and the IETF Trust's Legal   Provisions Relating to IETF Documents   (http://trustee.ietf.org/license-info) 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.Nir & Josefsson              Standards Track                    [Page 1]

RFC 8031            Curve25519 and Curve448 for IKEv2      December 2016Table of Contents1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .21.1.  Conventions Used in This Document . . . . . . . . . . . .22.  Curve25519 and Curve448 . . . . . . . . . . . . . . . . . . .33.  Use and Negotiation in IKEv2  . . . . . . . . . . . . . . . .33.1.  Key Exchange Payload  . . . . . . . . . . . . . . . . . .43.2.  Recipient Tests . . . . . . . . . . . . . . . . . . . . .44.  Security Considerations . . . . . . . . . . . . . . . . . . .45.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .56.  References  . . . . . . . . . . . . . . . . . . . . . . . . .56.1.  Normative References  . . . . . . . . . . . . . . . . . .56.2.  Informative References  . . . . . . . . . . . . . . . . .6Appendix A.  Numerical Example for Curve25519 . . . . . . . . . .7   Acknowledgements  . . . . . . . . . . . . . . . . . . . . . . . .8   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .81.  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 Protocol Version 2 (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 that are resilient to time-based   side-channel attacks.  This document defines two such curves for use   in IKEv2.  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].Nir & Josefsson              Standards Track                    [Page 2]

RFC 8031            Curve25519 and Curve448 for IKEv2      December 20162.  Curve25519 and 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   particular, pruning the least/most significant bits and using 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 (seeSection 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 inSection 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 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.Nir & Josefsson              Standards Track                    [Page 3]

RFC 8031            Curve25519 and Curve448 for IKEv2      December 20163.1.  Key Exchange Payload   The diagram for the Key Exchange payload fromSection 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.  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 inSection 6 of [RFC7748].3.2.  Recipient Tests   Receiving and handling of incompatible point formats MUST follow the   considerations described inSection 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 Groups (group 19) defined inRFC 5903, also   known as NIST P-256 or secp256r1.  Curve448 is intended for the   ~224-bit security level.Nir & Josefsson              Standards Track                    [Page 4]

RFC 8031            Curve25519 and Curve448 for IKEv2      December 2016   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 [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   pseudorandom prime, it is significantly slower than NIST P-256, which   is itself slower than Curve25519.5.  IANA Considerations   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 |RFC 8031, Section 3.2 |RFC 8031 |        |   32   |  Curve448  |RFC 8031, Section 3.2 |RFC 8031 |        +--------+------------+-----------------------+-----------+                   Table 1: New Transform Type 4 Values6.  References6.1.  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>.   [RFC7296]  Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T.              Kivinen, "Internet Key Exchange Protocol Version 2              (IKEv2)", STD 79,RFC 7296, DOI 10.17487/RFC7296, October              2014, <http://www.rfc-editor.org/info/rfc7296>.   [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>.Nir & Josefsson              Standards Track                    [Page 5]

RFC 8031            Curve25519 and Curve448 for IKEv2      December 20166.2.  Informative References   [Curve25519]              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,              <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,              DOI 10.17487/RFC5903, June 2010,              <http://www.rfc-editor.org/info/rfc5903>.   [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,              DOI 10.17487/RFC6954, July 2013,              <http://www.rfc-editor.org/info/rfc6954>.Nir & Josefsson              Standards Track                    [Page 6]

RFC 8031            Curve25519 and Curve448 for IKEv2      December 2016Appendix 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 inSection 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 inSection 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 inSection 3.1.  The shared value is   calculated as inSection 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 50Nir & Josefsson              Standards Track                    [Page 7]

RFC 8031            Curve25519 and Curve448 for IKEv2      December 2016Acknowledgements   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 inRFC 7748 by Adam Langley, Mike Hamburg, and Sean   Turner.   The example inAppendix 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.orgNir & Josefsson              Standards Track                    [Page 8]