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Versions: 00 01 02 03 04 05 06 RFC 6954

Network Working Group                                          J. Merkle
Internet-Draft                                 secunet Security Networks
Intended status: Informational                                M. Lochter
Expires: August 11, 2013                Bundesamt fuer Sicherheit in der
                                               Informationstechnik (BSI)
                                                        February 7, 2013


         Using the ECC Brainpool Curves for IKEv2 Key Exchange
                   draft-merkle-ikev2-ke-brainpool-03

Abstract

   This document specifies the use of ECC Brainpool elliptic curve
   groups for key exchange in the Internet Key Exchange version 2
   (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
   Task Force (IETF).  Note that other groups may also distribute
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   Internet-Drafts are draft documents valid for a maximum of six months
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   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on August 11, 2013.

Copyright Notice

   Copyright (c) 2013 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
   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
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   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.



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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
     1.1.  Requirements Language  . . . . . . . . . . . . . . . . . .  3
   2.  IKEv2 Key Exchange using the ECC Brainpool Curves  . . . . . .  4
     2.1.  Diffie-Hellman Group Transform IDs . . . . . . . . . . . .  4
     2.2.  Using the Twisted Brainpool Curves Internally  . . . . . .  4
     2.3.  Key Exchange Payload and Shared Secret . . . . . . . . . .  4
   3.  Security Considerations  . . . . . . . . . . . . . . . . . . .  6
   4.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . .  7
   5.  Intellectual Property Rights . . . . . . . . . . . . . . . . .  8
   6.  References . . . . . . . . . . . . . . . . . . . . . . . . . .  9
     6.1.  Normative References . . . . . . . . . . . . . . . . . . .  9
     6.2.  Informative References . . . . . . . . . . . . . . . . . .  9
   Appendix A.  Test Vectors  . . . . . . . . . . . . . . . . . . . . 11
     A.1.  224 Bit Curve  . . . . . . . . . . . . . . . . . . . . . . 11
     A.2.  256 Bit Curve  . . . . . . . . . . . . . . . . . . . . . . 12
     A.3.  384 Bit Curve  . . . . . . . . . . . . . . . . . . . . . . 12
     A.4.  512 Bit Curve  . . . . . . . . . . . . . . . . . . . . . . 13
































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1.  Introduction

   In [RFC5639], a new set of elliptic curve groups over finite prime
   fields for use in cryptographic applications was specified.  These
   groups, denoted as ECC Brainpool curves, were generated in a
   verifiably pseudo-random way and comply with the security
   requirements of relevant standards from ISO [ISO1] [ISO2], ANSI
   [ANSI1], NIST [FIPS], and SecG [SEC2].

   While the ASN.1 object identifiers defined in RFC 5639 allow usage of
   the ECC Brainpool curves in certificates and certificate revocation
   lists, their utilization for key exchange in IKEv2 [RFC5996] requires
   the definition and assignment of additional Diffie-Hellman Group
   Transform IDs in the respective IANA registry.  This document
   specifies tranform IDs for four curves from RFC 5639 as well as the
   encoding of the key exchange payload and derivation of the shared
   secret when using one of these curves.

1.1.  Requirements Language

   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].




























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2.  IKEv2 Key Exchange using the ECC Brainpool Curves

2.1.  Diffie-Hellman Group Transform IDs

   In order to use the ECC Brainpool curves for key exchange within
   IKEv2, the Diffie-Hellman Group Transform IDs (Transform Type 4)
   listed in the following table are to be registered with IANA
   [IANA-IKE2].  The parameters associated with these curves are defined
   in RFC 5639 [RFC5639].

                    +-----------------+--------------+
                    |      Curve      | Transform ID |
                    +-----------------+--------------+
                    | brainpoolP224r1 |     TBD1     |
                    |                 |              |
                    | brainpoolP256r1 |     TBD2     |
                    |                 |              |
                    | brainpoolP384r1 |     TBD3     |
                    |                 |              |
                    | brainpoolP512r1 |     TBD4     |
                    +-----------------+--------------+

                                  Table 1

   Test vectors for the groups defined by the ECC Brainpool curves are
   provided in Appendix A

2.2.  Using the Twisted Brainpool Curves Internally

   In [RFC5639] for each random curve, a "twisted curve" (defined by a
   quadratic twist, see [HMV]) is defined offering the same level of
   security but potentially allowing more efficient arithmetic due to
   the curve parameter A = -3.  The transform IDs listed in Table 1 also
   allow using the twisted curve corresponding to the specified random
   curve: points (x,y) of any curve listed in can be efficiently
   transformed to the corresponding point (x',y') on the twisted curve
   of same bit length - and vice versa - by setting (x',y') = (x*Z^2,
   y*Z^3) with the coefficient Z specified for that curve in [RFC5639].

2.3.  Key Exchange Payload and Shared Secret

   For the encoding of the key exchange payload and the derivation of
   the shared secret, the methods specified in [RFC5903] are adopted.

   In an ECP key exchange in IKEv2, the Diffie-Hellman public value
   passed in a KE payload consists of two components, x and y,
   corresponding to the coordinates of an elliptic curve point.  Each
   component MUST be computed from the corresponding coordinate using



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   the FieldElement-to-OctetString conversion method specified in [SEC1]
   and MUST have bit length as indicated in Table 2.  This length is
   enforced by the FieldElement-to-OctetString conversion method, if
   necessary, by prepending the value with zeros.

   Note: The FieldElement-to-OctetString conversion method specified in
   [SEC1] is equivalent to applying the conversion between integers and
   octet strings of Section 6 of [RFC6090] after representing the field
   element as integer in the interval [0, p-1].

   +-----------------+------------------------+------------------------+
   |      Curves     |   Bit length of each   |    Bit length of key   |
   |                 |   component (x or y)   |    exchange payload    |
   +-----------------+------------------------+------------------------+
   | brainpoolP224r1 |           224          |           448          |
   |                 |                        |                        |
   | brainpoolP256r1 |           256          |           512          |
   |                 |                        |                        |
   | brainpoolP384r1 |           384          |           768          |
   |                 |                        |                        |
   | brainpoolP512r1 |           512          |          1024          |
   +-----------------+------------------------+------------------------+

                                  Table 2

   From these components, the key exchange payload MUST be computed as
   the concatenation of the x and y coordinates.  Hence, the key
   exchange payload has the bit length indicated in Table 2.

   The Diffie-Hellman shared secret value consists only of the x value.
   In particular, the shared secret value MUST be computed from the x
   coordinate of the Diffie-Hellman common value using the FieldElement-
   to-OctetString conversion method specified in [SEC1] and MUST have
   bit length as indicated in the Table 2.

















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3.  Security Considerations

   The security considerations of [RFC5996] apply accordingly.

   In order to thwart certain active attacks, the validity of the other
   peer's public Diffie-Hellmann key recovered from the received key
   exchange payload needs to be verified.  In particular, the
   recomendations and requirements of [IKE_DH_Req] MUST be observed.
   For the curves listed in Table 1, Section 2.3 of [IKE_DH_Req]
   applies.

   The confidentiality, authenticity and integrity of a secure
   communication based on IKEv2 is limited by the weakest cryptographic
   primitive applied.  In order to achieve a maximum security level when
   using one of the elliptic curves from Table 1 for key exchange, the
   key derivation function, the algorithms and key lengths of symmetric
   encryption and message authentication as well as the algorithm, bit
   length and hash function used for signature generation should be
   chosen according to the recommendations of [NIST800-57] and
   [RFC5639].  Furthermore, the private Diffie-Hellman keys should be
   selected with the same bit length as the order of the group generated
   by the base point G and with approximately maximum entropy.

   Implementations of elliptic curve cryptography for IKEv2 may be
   susceptible to side-channel attacks.  Particular care should be taken
   for implementations that internally use the corresponding twisted
   curve to take advantage of an efficient arithmetic for the special
   parameters (A = -3): although the twisted curve itself offers the
   same level of security as the corresponding random curve (through
   mathematical equivalence), an arithmetic based on small curve
   parameters may be harder to protect against side-channel attacks.
   General guidance on resistence of elliptic curve cryptography
   implementations against side-channel-attacks is given in [BSI1] and
   [HMV].

















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4.  IANA Considerations

   Before this document can become an RFC, IANA is required to assign
   Transform Type 4 (Diffie-Hellman Group Transform) IDs to the groups
   specified in Table 1 for the Internet Key Exchange Version 2 (IKEv2)
   Parameters registry [IANA-IKE2].  For the new entries in the table of
   the Transform Type 4 repository, a reference to Section 2.3 of
   [IKE_DH_Req] shall be included in the column named "Recipient Tests"
   indicating the required checks for the other peer's Diffie-Hellman
   public keys.

   Another I-D is being submitted for publication as RFC [BP_IKE]
   requesting assignment for the same groups in the corresponding
   registry for IKEv1; in order to keep the registries for IKEv1 and
   IKEv2 in accordance, IANA is requested to assign the same values in
   both registries.



































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5.  Intellectual Property Rights

   Although, the authors have no knowledge about any intellectual
   property rights which cover the general usage of the ECP groups
   defined herein, implementations based on these domain parameters may
   require use of inventions covered by patent rights.  In particular,
   techniques for an efficient arithmetic based on the special
   parameters of the twisted curves as explained in Section 2.1 may be
   covered by patents.










































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6.  References

6.1.  Normative References

   [IANA-IKE2]   Internet Assigned Numbers Authority, "Internet Key
                 Exchange Version 2 (IKEv2) Parameters",
                 <http://www.iana.org/assignments/ikev2-parameters>.

   [RFC2119]     Bradner, S., "Key words for use in RFCs to Indicate
                 Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC5996]     Kaufman, C., Hoffman, P., Nir, Y., and P. Eronen,
                 "Internet Key Exchange Protocol Version 2 (IKEv2)",
                 RFC 5996, September 2010.

   [RFC5639]     Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
                 (ECC) Brainpool Standard Curves and Curve Generation",
                 RFC 5639, March 2010.

   [IKE_DH_Req]  Sheffer, Y. and S. Fluhrer, "Additional Diffie-Hellman
                 Tests for IKEv2 (work in progress)",
                 draft-ietf-ipsecme-dh-checks-00 (work in progress),
                 January 2013.

6.2.  Informative References

   [ANSI1]       American National Standards Institute, "Public Key
                 Cryptography For The Financial Services Industry: The
                 Elliptic Curve Digital Signature Algorithm (ECDSA)",
                 ANSI X9.62, 2005.

   [BSI1]        Bundesamt fuer Sicherheit in der Informationstechnik,
                 "Minimum Requirements for Evaluating Side-Channel
                 Attack Resistance of Elliptic Curve Implementations",
                 July 2011.

   [FIPS]        National Institute of Standards and Technology,
                 "Digital Signature Standard (DSS)", FIPS PUB 186-2,
                 December 1998.

   [BP_IKE]      Harkins, D., "Brainpool Elliptic Curves for the IKE
                 Group Description Registry (work in progress)",
                 draft-harkins-brainpool-ike-groups-04 (work in
                 progress), August 2012.

   [HMV]         Hankerson, D., Menezes, A., and S. Vanstone, "Guide to
                 Elliptic Curve Cryptography", Springer Verlag, 2004.




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   [ISO1]        International Organization for Standardization,
                 "Information Technology - Security Techniques - Digital
                 Signatures with Appendix - Part 3: Discrete Logarithm
                 Based Mechanisms", ISO/IEC 14888-3, 2006.

   [ISO2]        International Organization for Standardization,
                 "Information Technology - Security Techniques -
                 Cryptographic Techniques Based on Elliptic Curves -
                 Part 2: Digital signatures", ISO/IEC 15946-2, 2002.

   [NIST800-57]  National Institute of Standards and Technology,
                 "Recommendation for Key Management - Part 1: General
                 (Revised)", NIST Special Publication 800-57,
                 March 2007.

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

   [RFC6090]     McGrew, D., Igoe, K., and M. Salter, "Fundamental
                 Elliptic Curve Cryptography Algorithms", RFC 6090,
                 February 2011.

   [SEC1]        Certicom Research, "Elliptic Curve Cryptography",
                 Standards for Efficient Cryptography (SEC) 1,
                 September 2000.

   [SEC2]        Certicom Research, "Recommended Elliptic Curve Domain
                 Parameters", Standards for Efficient Cryptography
                 (SEC) 2, September 2000.





















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Appendix A.  Test Vectors

   This section provides some test vectors for example Diffie-Hellman
   key exchanges using each of the curves defined in Section 2 .  In all
   of the following sections the following notation is used:

      d_A: the secret key of party A

      x_qA: the x-coordinate of the public key of party A

      y_qA: the y-coordinate of the public key of party A

      d_B: the secret key of party B

      x_qB: the x-coordinate of the public key of party B

      y_qB: the y-coordinate of the public key of party B

      x_Z: the x-coordinate of the shared secret that results from
      completion of the Diffie-Hellman computation

      y_Z: the y-coordinate of the shared secret that results from
      completion of the Diffie-Hellman computation

   The field elements x_qA, y_qA, x_qB, y_qB, x_Z, y_Z are represented
   as hexadecimal values using the FieldElement-to-OctetString
   conversion method specified in [SEC1].

A.1.  224 Bit Curve

   Curve brainpoolP224r1

      dA = 39F155483CEE191FBECFE9C81D8AB1A03CDA6790E7184ACE44BCA161

      x_qA = A9C21A569759DA95E0387041184261440327AFE33141CA04B82DC92E

      y_qA = 98A0F75FBBF61D8E58AE5511B2BCDBE8E549B31E37069A2825F590C1

      dB = 6060552303899E2140715816C45B57D9B42204FB6A5BF5BEAC10DB00

      x_qB = 034A56C550FF88056144E6DD56070F54B0135976B5BF77827313F36B

      y_qB = 75165AD99347DC86CAAB1CBB579E198EAF88DC35F927B358AA683681

      x_Z = 1A4BFE705445120C8E3E026699054104510D119757B74D5FE2462C66

      y_Z = BB6802AC01F8B7E91B1A1ACFB9830A95C079CEC48E52805DFD7D2AFE




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A.2.  256 Bit Curve

   Curve brainpoolP256r1

      dA =
      81DB1EE100150FF2EA338D708271BE38300CB54241D79950F77B063039804F1D

      x_qA =
      44106E913F92BC02A1705D9953A8414DB95E1AAA49E81D9E85F929A8E3100BE5

      y_qA =
      8AB4846F11CACCB73CE49CBDD120F5A900A69FD32C272223F789EF10EB089BDC

      dB =
      55E40BC41E37E3E2AD25C3C6654511FFA8474A91A0032087593852D3E7D76BD3

      x_qB =
      8D2D688C6CF93E1160AD04CC4429117DC2C41825E1E9FCA0ADDD34E6F1B39F7B

      y_qB =
      990C57520812BE512641E47034832106BC7D3E8DD0E4C7F1136D7006547CEC6A

      x_Z =
      89AFC39D41D3B327814B80940B042590F96556EC91E6AE7939BCE31F3A18BF2B

      y_Z =
      49C27868F4ECA2179BFD7D59B1E3BF34C1DBDE61AE12931648F43E59632504DE

A.3.  384 Bit Curve

   Curve brainpoolP384r1

      dA = 1E20F5E048A5886F1F157C74E91BDE2B98C8B52D58E5003D57053FC4B0BD6
      5D6F15EB5D1EE1610DF870795143627D042

      x_qA = 68B665DD91C195800650CDD363C625F4E742E8134667B767B1B47679358
      8F885AB698C852D4A6E77A252D6380FCAF068

      y_qA = 55BC91A39C9EC01DEE36017B7D673A931236D2F1F5C83942D049E3FA206
      07493E0D038FF2FD30C2AB67D15C85F7FAA59

      dB = 032640BC6003C59260F7250C3DB58CE647F98E1260ACCE4ACDA3DD869F74E
      01F8BA5E0324309DB6A9831497ABAC96670

      x_qB = 4D44326F269A597A5B58BBA565DA5556ED7FD9A8A9EB76C25F46DB69D19
      DC8CE6AD18E404B15738B2086DF37E71D1EB4





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      y_qB = 62D692136DE56CBE93BF5FA3188EF58BC8A3A0EC6C1E151A21038A42E91
      85329B5B275903D192F8D4E1F32FE9CC78C48

      x_Z = 0BD9D3A7EA0B3D519D09D8E48D0785FB744A6B355E6304BC51C229FBBCE2
      39BBADF6403715C35D4FB2A5444F575D4F42

      y_Z = 0DF213417EBE4D8E40A5F76F66C56470C489A3478D146DECF6DF0D94BAE9
      E598157290F8756066975F1DB34B2324B7BD

A.4.  512 Bit Curve

   Curve brainpoolP512r1

      dA = 16302FF0DBBB5A8D733DAB7141C1B45ACBC8715939677F6A56850A38BD87B
      D59B09E80279609FF333EB9D4C061231FB26F92EEB04982A5F1D1764CAD5766542
      2

      x_qA = 0A420517E406AAC0ACDCE90FCD71487718D3B953EFD7FBEC5F7F27E28C6
      149999397E91E029E06457DB2D3E640668B392C2A7E737A7F0BF04436D11640FD0
      9FD

      y_qA = 72E6882E8DB28AAD36237CD25D580DB23783961C8DC52DFA2EC138AD472
      A0FCEF3887CF62B623B2A87DE5C588301EA3E5FC269B373B60724F5E82A6AD147F
      DE7

      dB = 230E18E1BCC88A362FA54E4EA3902009292F7F8033624FD471B5D8ACE49D1
      2CFABBC19963DAB8E2F1EBA00BFFB29E4D72D13F2224562F405CB80503666B2542
      9

      x_qB = 9D45F66DE5D67E2E6DB6E93A59CE0BB48106097FF78A081DE781CDB31FC
      E8CCBAAEA8DD4320C4119F1E9CD437A2EAB3731FA9668AB268D871DEDA55A54731
      99F

      y_qB = 2FDC313095BCDD5FB3A91636F07A959C8E86B5636A1E930E8396049CB48
      1961D365CC11453A06C719835475B12CB52FC3C383BCE35E27EF194512B7187628
      5FA

      x_Z = A7927098655F1F9976FA50A9D566865DC530331846381C87256BAF322624
      4B76D36403C024D7BBF0AA0803EAFF405D3D24F11A9B5C0BEF679FE1454B21C4CD
      1F

      y_Z = 7DB71C3DEF63212841C463E881BDCF055523BD368240E6C3143BD8DEF8B3
      B3223B95E0F53082FF5E412F4222537A43DF1C6D25729DDB51620A832BE6A26680
      A2







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Authors' Addresses

   Johannes Merkle
   secunet Security Networks
   Mergenthaler Allee 77
   65760 Eschborn
   Germany

   Phone: +49 201 5454 3091
   EMail: johannes.merkle@secunet.com


   Manfred Lochter
   Bundesamt fuer Sicherheit in der Informationstechnik (BSI)
   Postfach 200363
   53133 Bonn
   Germany

   Phone: +49 228 9582 5643
   EMail: manfred.lochter@bsi.bund.de































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