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+Internet Engineering Task Force (IETF)                         J. Merkle
+Request for Comments: 7027                     secunet Security Networks
+Updates: 4492                                                 M. Lochter
+Category: Informational                                              BSI
+ISSN: 2070-1721                                             October 2013
+
+
+           Elliptic Curve Cryptography (ECC) Brainpool Curves
+                   for Transport Layer Security (TLS)
+
+Abstract
+
+   This document specifies the use of several Elliptic Curve
+   Cryptography (ECC) Brainpool curves for authentication and key
+   exchange in the Transport Layer Security (TLS) protocol.
+
+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/rfc7027.
+
+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 7027              ECC Brainpool Curves for TLS          October 2013
+
+
+Table of Contents
+
+   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . 2
+   2.  Brainpool NamedCurve Types  . . . . . . . . . . . . . . . . . . 2
+   3.  IANA Considerations . . . . . . . . . . . . . . . . . . . . . . 3
+   4.  Security Considerations . . . . . . . . . . . . . . . . . . . . 3
+   5.  References  . . . . . . . . . . . . . . . . . . . . . . . . . . 4
+     5.1.  Normative References  . . . . . . . . . . . . . . . . . . . 4
+     5.2.  Informative References  . . . . . . . . . . . . . . . . . . 4
+   Appendix A.  Test Vectors . . . . . . . . . . . . . . . . . . . . . 6
+     A.1.  256-Bit Curve . . . . . . . . . . . . . . . . . . . . . . . 7
+     A.2.  384-Bit Curve . . . . . . . . . . . . . . . . . . . . . . . 8
+     A.3.  512-Bit Curve . . . . . . . . . . . . . . . . . . . . . . . 9
+
+1.  Introduction
+
+   [RFC5639] specifies 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 SecG [SEC2].
+
+   [RFC4492] defines the usage of elliptic curves for authentication and
+   key agreement in TLS 1.0 and TLS 1.1; these mechanisms may also be
+   used with TLS 1.2 [RFC5246].  While the ASN.1 object identifiers
+   defined in [RFC5639] already allow usage of the ECC Brainpool curves
+   for TLS (client or server) authentication through reference in X.509
+   certificates according to [RFC3279] and [RFC5480], their negotiation
+   for key exchange according to [RFC4492] requires the definition and
+   assignment of additional NamedCurve IDs.  This document specifies
+   such values for three curves from [RFC5639].
+
+2.  Brainpool NamedCurve Types
+
+   According to [RFC4492], the name space NamedCurve is used for the
+   negotiation of elliptic curve groups for key exchange during a
+   handshake starting a new TLS session.  This document adds new
+   NamedCurve types to three elliptic curves defined in [RFC5639] as
+   follows:
+
+           enum {
+                brainpoolP256r1(26),
+                brainpoolP384r1(27),
+                brainpoolP512r1(28)
+           } NamedCurve;
+
+   These curves are suitable for use with Datagram TLS [RFC6347].
+
+
+
+Merkle & Lochter              Informational                     [Page 2]
+
+RFC 7027              ECC Brainpool Curves for TLS          October 2013
+
+
+   Test vectors for a Diffie-Hellman key exchange using these elliptic
+   curves are provided in Appendix A.
+
+3.  IANA Considerations
+
+   IANA has assigned numbers for the ECC Brainpool curves listed in
+   Section 2 in the "EC Named Curve" [IANA-TLS] registry of the
+   "Transport Layer Security (TLS) Parameters" registry as follows:
+
+             +-------+-----------------+---------+-----------+
+             | Value |   Description   | DTLS-OK | Reference |
+             +-------+-----------------+---------+-----------+
+             |   26  | brainpoolP256r1 |    Y    |  RFC 7027 |
+             |   27  | brainpoolP384r1 |    Y    |  RFC 7027 |
+             |   28  | brainpoolP512r1 |    Y    |  RFC 7027 |
+             +-------+-----------------+---------+-----------+
+
+                                  Table 1
+
+4.  Security Considerations
+
+   The security considerations of [RFC5246] apply to the ECC Brainpool
+   curves described in this document.
+
+   The confidentiality, authenticity, and integrity of the TLS
+   communication 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 authentication and/or key
+   exchange in TLS, 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 TLS may be
+   susceptible to side-channel attacks.  Particular care should be taken
+   for implementations that internally transform curve points to points
+   on the corresponding "twisted curve", using the map (x',y') = (x*Z^2,
+   y*Z^3) with the coefficient Z specified for that curve in [RFC5639],
+   in order to take advantage of an efficient arithmetic based on the
+   twisted curve's 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-
+
+
+
+
+Merkle & Lochter              Informational                     [Page 3]
+
+RFC 7027              ECC Brainpool Curves for TLS          October 2013
+
+
+   channel attacks.  General guidance on resistance of elliptic curve
+   cryptography implementations against side-channel-attacks is given in
+   [BSI1] and [HMV].
+
+5.  References
+
+5.1.  Normative References
+
+   [IANA-TLS]    Internet Assigned Numbers Authority, "Transport Layer
+                 Security (TLS) Parameters",
+                 <http://www.iana.org/assignments/tls-parameters>.
+
+   [RFC4492]     Blake-Wilson, S., Bolyard, N., Gupta, V., Hawk, C., and
+                 B. Moeller, "Elliptic Curve Cryptography (ECC) Cipher
+                 Suites for Transport Layer Security (TLS)", RFC 4492,
+                 May 2006.
+
+   [RFC5246]     Dierks, T. and E. Rescorla, "The Transport Layer
+                 Security (TLS) Protocol Version 1.2", RFC 5246,
+                 August 2008.
+
+   [RFC5639]     Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
+                 (ECC) Brainpool Standard Curves and Curve Generation",
+                 RFC 5639, March 2010.
+
+   [RFC6347]     Rescorla, E. and N. Modadugu, "Datagram Transport Layer
+                 Security Version 1.2", RFC 6347, January 2012.
+
+5.2.  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.
+
+   [HMV]         Hankerson, D., Menezes, A., and S. Vanstone, "Guide to
+                 Elliptic Curve Cryptography", Springer Verlag, 2004.
+
+
+
+
+
+Merkle & Lochter              Informational                     [Page 4]
+
+RFC 7027              ECC Brainpool Curves for TLS          October 2013
+
+
+   [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.
+
+   [RFC3279]     Bassham, L., Polk, W., and R. Housley, "Algorithms and
+                 Identifiers for the Internet X.509 Public Key
+                 Infrastructure Certificate and Certificate Revocation
+                 List (CRL) Profile", RFC 3279, April 2002.
+
+   [RFC5480]     Turner, S., Brown, D., Yiu, K., Housley, R., and T.
+                 Polk, "Elliptic Curve Cryptography Subject Public Key
+                 Information", RFC 5480, March 2009.
+
+   [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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+Merkle & Lochter              Informational                     [Page 5]
+
+RFC 7027              ECC Brainpool Curves for TLS          October 2013
+
+
+Appendix A.  Test Vectors
+
+   This section provides some test vectors for example Diffie-Hellman
+   key exchanges using each of the curves defined in Table 1.  The
+   following notation is used in the subsequent sections:
+
+      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, i.e., the hex
+      representation of the pre-master secret
+
+      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].
+
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+Merkle & Lochter              Informational                     [Page 6]
+
+RFC 7027              ECC Brainpool Curves for TLS          October 2013
+
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+A.1.  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
+
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+Merkle & Lochter              Informational                     [Page 7]
+
+RFC 7027              ECC Brainpool Curves for TLS          October 2013
+
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+A.2.  384-Bit Curve
+
+   Curve brainpoolP384r1
+
+      dA = 1E20F5E048A5886F1F157C74E91BDE2B98C8B52D58E5003D57053FC4B0BD6
+      5D6F15EB5D1EE1610DF870795143627D042
+
+      x_qA = 68B665DD91C195800650CDD363C625F4E742E8134667B767B1B47679358
+      8F885AB698C852D4A6E77A252D6380FCAF068
+
+      y_qA = 55BC91A39C9EC01DEE36017B7D673A931236D2F1F5C83942D049E3FA206
+      07493E0D038FF2FD30C2AB67D15C85F7FAA59
+
+      dB = 032640BC6003C59260F7250C3DB58CE647F98E1260ACCE4ACDA3DD869F74E
+      01F8BA5E0324309DB6A9831497ABAC96670
+
+      x_qB = 4D44326F269A597A5B58BBA565DA5556ED7FD9A8A9EB76C25F46DB69D19
+      DC8CE6AD18E404B15738B2086DF37E71D1EB4
+
+      y_qB = 62D692136DE56CBE93BF5FA3188EF58BC8A3A0EC6C1E151A21038A42E91
+      85329B5B275903D192F8D4E1F32FE9CC78C48
+
+      x_Z = 0BD9D3A7EA0B3D519D09D8E48D0785FB744A6B355E6304BC51C229FBBCE2
+      39BBADF6403715C35D4FB2A5444F575D4F42
+
+      y_Z = 0DF213417EBE4D8E40A5F76F66C56470C489A3478D146DECF6DF0D94BAE9
+      E598157290F8756066975F1DB34B2324B7BD
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+Merkle & Lochter              Informational                     [Page 8]
+
+RFC 7027              ECC Brainpool Curves for TLS          October 2013
+
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+A.3.  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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+Merkle & Lochter              Informational                     [Page 9]
+
+RFC 7027              ECC Brainpool Curves for TLS          October 2013
+
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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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