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rfc:rfc6954

Internet Engineering Task Force (IETF) J. Merkle Request for Comments: 6954 secunet Security Networks Category: Informational M. Lochter ISSN: 2070-1721 BSI

                                                             July 2013
    Using the Elliptic Curve Cryptography (ECC) Brainpool Curves
      for the Internet Key Exchange Protocol Version 2 (IKEv2)

Abstract

 This document specifies use of the Elliptic Curve Cryptography (ECC)
 Brainpool elliptic curve groups for key exchange in the Internet Key
 Exchange Protocol version 2 (IKEv2).

Status of This Memo

 This document is not an Internet Standards Track specification; it is
 published for informational purposes.
 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).  Not all documents
 approved by the IESG are a candidate for any level of Internet
 Standard; see Section 2 of RFC 5741.
 Information about the current status of this document, any errata,
 and how to provide feedback on it may be obtained at
 http://www.rfc-editor.org/info/rfc6954.

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
 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.

Merkle & Lochter Informational [Page 1] RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013

Table of Contents

 1. Introduction ....................................................2
    1.1. Requirements Language ......................................2
 2. IKEv2 Key Exchange Using the ECC Brainpool Curves ...............3
    2.1. Diffie-Hellman Group Transform IDs .........................3
    2.2. Using the Twisted Brainpool Curves Internally ..............3
    2.3. Key Exchange Payload and Shared Secret .....................3
 3. Security Considerations .........................................4
 4. IANA Considerations .............................................5
 5. References ......................................................5
    5.1. Normative References .......................................5
    5.2. Informative References .....................................6
 Appendix A. Test Vectors ...........................................8
   A.1. 224-Bit Curve ...............................................8
   A.2. 256-Bit Curve ...............................................9
   A.3. 384-Bit Curve ...............................................9
   A.4. 512-Bit Curve ..............................................10

1. Introduction

 [RFC5639] specified a new set of elliptic curve groups over finite
 prime fields for use in cryptographic applications.  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 the Standards for Efficient Cryptography Group [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 transform 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].

Merkle & Lochter Informational [Page 2] RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013

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 have been registered with IANA
 [IANA-IKE2].  The parameters associated with these curves are defined
 in RFC 5639 [RFC5639].
                    +-----------------+--------------+
                    |      Curve      | Transform ID |
                    +-----------------+--------------+
                    | brainpoolP224r1 |      27      |
                    | brainpoolP256r1 |      28      |
                    | brainpoolP384r1 |      29      |
                    | brainpoolP512r1 |      30      |
                    +-----------------+--------------+
                                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 that offers the same level of
 security but potentially allows 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 of the listed curves can be efficiently
 transformed to the corresponding point (x',y') on the twisted curve
 of the same bit length -- and vice versa -- by setting (x',y') =
 (x*Z^2, y*Z^3) with the coefficient Z specified for that curve
 [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 Elliptic Curve Group over GF[P] (ECP) key exchange in IKEv2,
 the Diffie-Hellman public value passed in a key establishment (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 the FieldElement-to-
 OctetString conversion method specified in [SEC1] and MUST have a bit

Merkle & Lochter Informational [Page 3] RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013

 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 (as described in Section 6 of [RFC6090]) after
 representing the field element as an 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 Table 2.

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-Hellman value (x,y) recovered from the received
 key exchange payload needs to be verified.  In particular, it MUST be
 verified that the x- and y-coordinates of the public value satisfy
 the curve equation.  For additional information, we refer the reader
 to [RFC6989].
 The confidentiality, authenticity, and integrity of a secure
 communication based on IKEv2 are limited by the weakest cryptographic
 primitive applied.  In order to achieve a maximum security level when

Merkle & Lochter Informational [Page 4] RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013

 using one of the elliptic curves from Table 1 for key exchange, the
 following should be chosen according to the recommendations of
 [NIST800-57] and [RFC5639]:
 o  key derivation function
 o  algorithms and key lengths of symmetric encryption and message
    authentication
 o  algorithm, bit length, and hash function used for signature
    generation
 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 could 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 could be harder to protect against side-channel attacks.
 General guidance on resistance of elliptic curve cryptography
 implementations against side-channel attacks is given in [BSI1] and
 [HMV].

4. IANA Considerations

 IANA has updated its "Transform Type 4 - Diffie-Hellman Group
 Transform IDs" registry in [IANA-IKE2] to include the groups listed
 in Table 1.

5. References

5.1. Normative References

 [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.

Merkle & Lochter Informational [Page 5] RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013

 [RFC6989]    Sheffer, Y. and S. Fluhrer, "Additional Diffie-Hellman
              Tests for the Internet Key Exchange Protocol Version 2
              (IKEv2)", RFC 6989, July 2013.
 [IANA-IKE2]  Internet Assigned Numbers Authority, "Internet Key
              Exchange Version 2 (IKEv2) Parameters",
              <http://www.iana.org/assignments/ikev2-parameters>.
 [SEC1]       Certicom Research, "Elliptic Curve Cryptography",
              Standards for Efficient Cryptography (SEC) 1,
              September 2000.

5.2. Informative References

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

Merkle & Lochter Informational [Page 6] RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013

 [NIST800-57] National Institute of Standards and Technology,
              "Recommendation for Key Management -- Part 1: General
              (Revised)", NIST Special Publication 800-57, March 2007.
 [SEC2]       Certicom Research, "Recommended Elliptic Curve Domain
              Parameters", Standards for Efficient Cryptography (SEC)
              2, September 2000.

Merkle & Lochter Informational [Page 7] RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013

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.  The
 following notation is used in the subsequent subsections:
    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, and 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

Merkle & Lochter Informational [Page 8] RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013

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

Merkle & Lochter Informational [Page 9] RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013

    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

Merkle & Lochter Informational [Page 10] RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013

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

Merkle & Lochter Informational [Page 11]

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