RFC 7027: Elliptic Curve Cryptography (ECC) Brainpool Curves for Transport Layer Security (TLS)

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.





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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

 [] 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].

 [] 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].



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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-




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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

 [] Internet Assigned Numbers Authority, "Transport Layer
 Security (TLS) Parameters",
 <http://www.iana.org/assignments/tls-parameters>.

 [] 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.

 [] Dierks, T. and E. Rescorla, "The Transport Layer
 Security (TLS) Protocol Version 1.2", RFC 5246,
 August 2008.

 [] Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
 (ECC) Brainpool Standard Curves and Curve Generation",
 RFC 5639, March 2010.

 [] Rescorla, E. and N. Modadugu, "Datagram Transport Layer
 Security Version 1.2", RFC 6347, January 2012.

5.2. Informative References

 [] American National Standards Institute, "Public Key
 Cryptography For The Financial Services Industry: The
 Elliptic Curve Digital Signature Algorithm (ECDSA)",
 ANSI X9.62, 2005.

 [] Bundesamt fuer Sicherheit in der Informationstechnik,
 "Minimum Requirements for Evaluating Side-Channel
 Attack Resistance of Elliptic Curve Implementations",
 July 2011.

 [] National Institute of Standards and Technology,
 "Digital Signature Standard (DSS)", FIPS PUB 186-2,
 December 1998.

 [] Hankerson, D., Menezes, A., and S. Vanstone, "Guide to
 Elliptic Curve Cryptography", Springer Verlag, 2004.





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 [] International Organization for Standardization,
 "Information Technology - Security Techniques - Digital
 Signatures with Appendix - Part 3: Discrete Logarithm
 Based Mechanisms", ISO/IEC 14888-3, 2006.

 [] International Organization for Standardization,
 "Information Technology - Security Techniques -
 Cryptographic Techniques Based on Elliptic Curves -
 Part 2: Digital signatures", ISO/IEC 15946-2, 2002.

 [] National Institute of Standards and Technology,
 "Recommendation for Key Management - Part 1: General
 (Revised)", NIST Special Publication 800-57,
 March 2007.

 [] 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.

 [] Turner, S., Brown, D., Yiu, K., Housley, R., and T.
 Polk, "Elliptic Curve Cryptography Subject Public Key
 Information", RFC 5480, March 2009.

 [] Certicom Research, "Elliptic Curve Cryptography",
 Standards for Efficient Cryptography (SEC) 1,
 September 2000.

 [] Certicom Research, "Recommended Elliptic Curve Domain
 Parameters", Standards for Efficient Cryptography
 (SEC) 2, September 2000.




















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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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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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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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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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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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RFC 7027: Elliptic Curve Cryptography (ECC) Brainpool Curves for Transport Layer Security (TLS)