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Internet Engineering Task Force (IETF)                         J. MerkleRequest for Comments: 7027                     secunet Security NetworksUpdates:4492                                                 M. LochterCategory: Informational                                              BSIISSN: 2070-1721                                             October 2013Elliptic Curve Cryptography (ECC) Brainpool Curvesfor 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; seeSection 2 of RFC 5741.   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/rfc7027.Copyright Notice   Copyright (c) 2013 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.Merkle & Lochter              Informational                     [Page 1]

RFC 7027              ECC Brainpool Curves for TLS          October 2013Table of Contents1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . . .22.  Brainpool NamedCurve Types  . . . . . . . . . . . . . . . . . .23.  IANA Considerations . . . . . . . . . . . . . . . . . . . . . .34.  Security Considerations . . . . . . . . . . . . . . . . . . . .35.  References  . . . . . . . . . . . . . . . . . . . . . . . . . .45.1.  Normative References  . . . . . . . . . . . . . . . . . . .45.2.  Informative References  . . . . . . . . . . . . . . . . . .4Appendix A.  Test Vectors . . . . . . . . . . . . . . . . . . . . .6A.1.  256-Bit Curve . . . . . . . . . . . . . . . . . . . . . . .7A.2.  384-Bit Curve . . . . . . . . . . . . . . . . . . . . . . .8A.3.  512-Bit Curve . . . . . . . . . . . . . . . . . . . . . . .91.  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 inAppendix A.3.  IANA Considerations   IANA has assigned numbers for the ECC Brainpool curves listed inSection 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 14.  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.  References5.1.  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.Merkle & Lochter              Informational                     [Page 5]

RFC 7027              ECC Brainpool Curves for TLS          October 2013Appendix 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].Merkle & Lochter              Informational                     [Page 6]

RFC 7027              ECC Brainpool Curves for TLS          October 2013A.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 =      49C27868F4ECA2179BFD7D59B1E3BF34C1DBDE61AE12931648F43E59632504DEMerkle & Lochter              Informational                     [Page 7]

RFC 7027              ECC Brainpool Curves for TLS          October 2013A.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      E598157290F8756066975F1DB34B2324B7BDMerkle & Lochter              Informational                     [Page 8]

RFC 7027              ECC Brainpool Curves for TLS          October 2013A.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      A2Merkle & Lochter              Informational                     [Page 9]

RFC 7027              ECC Brainpool Curves for TLS          October 2013Authors' 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.deMerkle & Lochter              Informational                    [Page 10]