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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]
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+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]
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+RFC 7027 ECC Brainpool Curves for TLS October 2013
+
+
+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]
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+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]
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+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]
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+RFC 7027 ECC Brainpool Curves for TLS October 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 10]
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