Network Working Group J. Merkle Internet-Draft secunet Security Networks Updates: 4492 (if approved) M. Lochter Intended status: Informational Bundesamt fuer Sicherheit in der Expires: May 9, 2013 Informationstechnik (BSI) November 5, 2012 ECC Brainpool Curves for Transport Layer Security (TLS) draft-merkle-tls-brainpool-00 Abstract This document specifies the use of several ECC Brainpool elliptic curves for authentication and key exchange in the Transport Layer Security (TLS) protocol. Status of This Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at http://datatracker.ietf.org/drafts/current/. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." This Internet-Draft will expire on May 9, 2013. Copyright Notice Copyright (c) 2012 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 Expires May 9, 2013 [Page 1]

Internet-Draft ECC Brainpool Curves for TLS November 2012 Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Values to be Used in the Supported Elliptic Curve Extension . 4 3. Security Considerations . . . . . . . . . . . . . . . . . . . 5 4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 6 5. Intellectual Property Rights . . . . . . . . . . . . . . . . . 7 6. References . . . . . . . . . . . . . . . . . . . . . . . . . . 8 6.1. Normative References . . . . . . . . . . . . . . . . . . . 8 6.2. Informative References . . . . . . . . . . . . . . . . . . 8 Appendix A. Test Vectors . . . . . . . . . . . . . . . . . . . . 10 A.1. 256 Bit Curve . . . . . . . . . . . . . . . . . . . . . . 10 A.2. 384 Bit Curve . . . . . . . . . . . . . . . . . . . . . . 11 A.3. 512 Bit Curve . . . . . . . . . . . . . . . . . . . . . . 11 Merkle & Lochter Expires May 9, 2013 [Page 2]

Internet-Draft ECC Brainpool Curves for TLS November 2012 1. Introduction In [RFC5639], a new set of elliptic curve groups over finite prime fields for use in cryptographic applications was specified. 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]. Usage of elliptic curves for authentication and key agreement in TLS 1.1 and TLS 2.0 is defined in [RFC4492]. 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], 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]. Merkle & Lochter Expires May 9, 2013 [Page 3]

Internet-Draft ECC Brainpool Curves for TLS November 2012 2. Values to be Used in the Supported Elliptic Curve Extension According to [RFC4492], the Supported Elliptic Curve Extension allows the negotiation of elliptic curve groups during a handshake starting a new TLS session. A client that proposes ECC cipher suites in its ClientHello message SHOULD include this extension to indicate the elliptic curves it supports through NamedCurve IDs, and a server that receives a ClientHello containing this extension MUST use the client's enumerated capabilities to guide its selection of an appropriate cipher suite. Furthermore, the server SHOULD use a NamedCurve ID, if applicable, to specify the elliptic curve corresponding to its ephemeral ECDH public key. The values of NamedCurve, by which the elliptic curves are identified, are governed by the EC Named Curve Registry of IANA [IANA-TLS]. In Table 1, new values for NamedCurve for three of the ECC Brainpool curves defined in [RFC5639] are specified. All three curves are suitable for usage in DTLS [RFC6347]. +-----------------+-------+ | Curve | Value | +-----------------+-------+ | brainpoolP256r1 | TBD1 | | | | | brainpoolP384r1 | TBD2 | | | | | brainpoolP512r1 | TBD3 | +-----------------+-------+ Table 1 Test vectors for a Diffie-Hellman key exchange using these ECC Brainpool curves are provided in Appendix A Merkle & Lochter Expires May 9, 2013 [Page 4]

Internet-Draft ECC Brainpool Curves for TLS November 2012 3. Security Considerations The security considerations of [RFC5246] apply accordingly. 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 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- channel attacks. General guidance on resistence of elliptic curve cryptography implementations against side-channel-attacks is given in [BSI1] and [HMV]. Merkle & Lochter Expires May 9, 2013 [Page 5]

Internet-Draft ECC Brainpool Curves for TLS November 2012 4. IANA Considerations Before this document can become an RFC, IANA is required to assign numbers for the elliptic curves specified in Table 1 to the NamedCurve name space in its Transport Layer Security (TLS) Parameters registry [IANA-TLS]. For all these elliptic curves, suitability with DTLS shall be indicated in the registry. Merkle & Lochter Expires May 9, 2013 [Page 6]

Internet-Draft ECC Brainpool Curves for TLS November 2012 5. Intellectual Property Rights Although, the authors have no knowledge about any intellectual property rights which cover the general usage of the ECP groups defined herein, implementations based on these domain parameters may require use of inventions covered by patent rights. In particular, techniques for an efficient arithmetic exploiting the special parameters of the twisted curves (see Section 3) may be covered by patents. Merkle & Lochter Expires May 9, 2013 [Page 7]

Internet-Draft ECC Brainpool Curves for TLS November 2012 6. References 6.1. Normative References [IANA-TLS] Internet Assigned Numbers Authority, "Transport Layer Security (TLS) Parameters", <http://www.iana.org/ assignments/tls-parameters/tls-parameters.xml>. [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997. [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. 6.2. 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. [ISO1] International Organization for Standardization, "Information Technology - Security Techniques - Digital Merkle & Lochter Expires May 9, 2013 [Page 8]

Internet-Draft ECC Brainpool Curves for TLS November 2012 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. [RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic Curve Cryptography Algorithms", RFC 6090, February 2011. [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 Expires May 9, 2013 [Page 9]

Internet-Draft ECC Brainpool Curves for TLS November 2012 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 . In all of the following sections the following notation is used: 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, y_Z are represented as hexadecimal values using the FieldElement-to-OctetString conversion method specified in [SEC1]. A.1. 256 Bit Curve Curve brainpoolP256r1 dA = 81DB1EE100150FF2EA338D708271BE38300CB54241D79950F77B063039804F1D x_qA = 44106E913F92BC02A1705D9953A8414DB95E1AAA49E81D9E85F929A8E3100BE5 y_qA = 8AB4846F11CACCB73CE49CBDD120F5A900A69FD32C272223F789EF10EB089BDC dB = 55E40BC41E37E3E2AD25C3C6654511FFA8474A91A0032087593852D3E7D76BD3 x_qB = 8D2D688C6CF93E1160AD04CC4429117DC2C41825E1E9FCA0ADDD34E6F1B39F7B Merkle & Lochter Expires May 9, 2013 [Page 10]

Internet-Draft ECC Brainpool Curves for TLS November 2012 y_qB = 990C57520812BE512641E47034832106BC7D3E8DD0E4C7F1136D7006547CEC6A x_Z = 89AFC39D41D3B327814B80940B042590F96556EC91E6AE7939BCE31F3A18BF2B y_Z = 49C27868F4ECA2179BFD7D59B1E3BF34C1DBDE61AE12931648F43E59632504DE 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 A.3. 512 Bit Curve Curve brainpoolP512r1 dA = 16302FF0DBBB5A8D733DAB7141C1B45ACBC8715939677F6A56850A38BD87B D59B09E80279609FF333EB9D4C061231FB26F92EEB04982A5F1D1764CAD5766542 2 x_qA = 0A420517E406AAC0ACDCE90FCD71487718D3B953EFD7FBEC5F7F27E28C6 149999397E91E029E06457DB2D3E640668B392C2A7E737A7F0BF04436D11640FD0 9FD Merkle & Lochter Expires May 9, 2013 [Page 11]

Internet-Draft ECC Brainpool Curves for TLS November 2012 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 Expires May 9, 2013 [Page 12]

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Internet-Draft ECC Brainpool Curves for TLS November 2012
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 Expires May 9, 2013 [Page 13]
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