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+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]
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+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.
+
+
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+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
+
+
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+Merkle & Lochter Informational [Page 11]
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