RFC 8734

Independent Submission                                       L. Bruckert
Request for Comments: 8734                                     J. Merkle
Category: Informational                        secunet Security Networks
ISSN: 2070-1721                                               M. Lochter
                                                           February 2020

Elliptic Curve Cryptography (ECC) Brainpool Curves for Transport Layer
                       Security (TLS) Version 1.3


   Elliptic Curve Cryptography (ECC) Brainpool curves were an option for
   authentication and key exchange in the Transport Layer Security (TLS)
   protocol version 1.2 but were deprecated by the IETF for use with TLS
   version 1.3 because they had little usage.  However, these curves
   have not been shown to have significant cryptographical weaknesses,
   and there is some interest in using several of these curves in TLS

   This document provides the necessary protocol mechanisms for using
   ECC Brainpool curves in TLS 1.3.  This approach is not endorsed by
   the IETF.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This is a contribution to the RFC Series, independently of any other
   RFC stream.  The RFC Editor has chosen to publish this document at
   its discretion and makes no statement about its value for
   implementation or deployment.  Documents approved for publication by
   the RFC Editor are not candidates for any level of Internet Standard;
   see Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at

Copyright Notice

   Copyright (c) 2020 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
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   (https://trustee.ietf.org/license-info) in effect on the date of
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   to this document.

Table of Contents

   1.  Introduction
   2.  Requirements Terminology
   3.  Brainpool NamedGroup Types
   4.  Brainpool SignatureScheme Types
   5.  IANA Considerations
   6.  Security Considerations
   7.  References
     7.1.  Normative References
     7.2.  Informative References
   Appendix A.  Test Vectors
     A.1.  256-Bit Curve
     A.2.  384-Bit Curve
     A.3.  512-Bit Curve

   Authors' Addresses

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
   pseudorandom way and comply with the security requirements of
   relevant standards from ISO [ISO1][ISO2], ANSI [ANSI1], NIST [FIPS],
   and SECG [SEC2].

   [RFC8422] defines the usage of elliptic curves for authentication and
   key agreement in TLS 1.2 and earlier versions, and [RFC7027] defines
   the usage of the ECC Brainpool curves for authentication and key
   exchange in TLS.  The latter is applicable to TLS 1.2 and earlier
   versions but not to TLS 1.3, which deprecates the ECC Brainpool curve
   IDs defined in [RFC7027] due to the lack of widespread deployment.
   However, there is some interest in using these curves in TLS 1.3.

   The negotiation of ECC Brainpool curves for key exchange in TLS 1.3,
   according to [RFC8446], requires the definition and assignment of
   additional NamedGroup IDs.  This document provides the necessary
   definition and assignment of additional SignatureScheme IDs for using
   three ECC Brainpool curves from [RFC5639].

   This approach is not endorsed by the IETF.  Implementers and
   deployers need to be aware of the strengths and weaknesses of all
   security mechanisms that they use.

2.  Requirements Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "OPTIONAL" in this document are to be interpreted as described in
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

3.  Brainpool NamedGroup Types

   According to [RFC8446], the "supported_groups" extension is used for
   the negotiation of Diffie-Hellman groups and elliptic curve groups
   for key exchange during a handshake starting a new TLS session.  This
   document adds new named groups for three elliptic curves defined in
   [RFC5639] to the "supported_groups" extension, as follows.

           enum {
           } NamedGroup;

   The encoding of Ephemeral Elliptic Curve Diffie-Hellman (ECDHE)
   parameters for sec256r1, secp384r1, and secp521r1, as defined in
   Section of [RFC8446], also applies to this document.

   Test vectors for a Diffie-Hellman key exchange using these elliptic
   curves are provided in Appendix A.

4.  Brainpool SignatureScheme Types

   According to [RFC8446], the name space SignatureScheme is used for
   the negotiation of elliptic curve groups for authentication via the
   "signature_algorithms" extension.  Besides, it is required to specify
   the hash function that is used to hash the message before signing.
   This document adds new SignatureScheme types for three elliptic
   curves defined in [RFC5639], as follows.

           enum {
           } SignatureScheme;

5.  IANA Considerations

   IANA has updated the references for the ECC Brainpool curves listed
   in the "TLS Supported Groups" [IANA-TLS] subregistry of the
   "Transport Layer Security (TLS) Parameters" registry to refer to this

   | Value |     Description      | DTLS-OK | Recommended | Reference |
   |   31  | brainpoolP256r1tls13 |    Y    |      N      |  RFC 8734 |
   |   32  | brainpoolP384r1tls13 |    Y    |      N      |  RFC 8734 |
   |   33  | brainpoolP512r1tls13 |    Y    |      N      |  RFC 8734 |

                                 Table 1

   IANA has updated the references for the ECC Brainpool curves in the
   "TLS SignatureScheme" subregistry [IANA-TLS] of the "Transport Layer
   Security (TLS) Parameters" registry to refer to this document.

   |Value |            Description            | Recommended |Reference |
   |0x081A| ecdsa_brainpoolP256r1tls13_sha256 |      N      | RFC 8734 |
   |0x081B| ecdsa_brainpoolP384r1tls13_sha384 |      N      | RFC 8734 |
   |0x081C| ecdsa_brainpoolP512r1tls13_sha512 |      N      | RFC 8734 |

                                  Table 2

6.  Security Considerations

   The security considerations of [RFC8446] 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 key exchange and/or one of
   the signature algorithms from Table 2 for authentication in TLS,
   parameters of other deployed cryptographic schemes should be chosen
   at commensurate strengths, for example, according to the
   recommendations of [NIST800-57] and [RFC5639].  In particular, this
   applies to (a) the key derivation function, (b) the algorithms and
   key length of symmetric encryption and message authentication, and
   (c) the algorithm, bit length, and hash function for signature
   generation.  Furthermore, the private Diffie-Hellman keys should be
   generated from a random keystream with a length equal to the length
   of the order of the group E(GF(p)) defined in [RFC5639].  The value
   of the private Diffie-Hellman keys should be less than the order of
   the group E(GF(p)).

   When using ECDHE key agreement with the curves brainpoolP256r1tls13,
   brainpoolP384r1tls13, or brainpoolP512r1tls13, the peers MUST
   validate each other's public value Q by ensuring that the point is a
   valid point on the elliptic curve.  If this check is not conducted,
   an attacker can force the key exchange into a small subgroup, and the
   resulting shared secret can be guessed with significantly less

   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), arithmetic based on
   small curve parameters may be harder to protect against side-channel
   attacks.  General guidance on resistance of elliptic curve
   cryptography implementations against side-channel attacks is given in
   [BSI1] and [HMV].

7.  References

7.1.  Normative References

   [IANA-TLS] IANA, "Transport Layer Security (TLS) Parameters",

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,

   [RFC5639]  Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
              (ECC) Brainpool Standard Curves and Curve Generation",
              RFC 5639, DOI 10.17487/RFC5639, March 2010,

   [RFC7027]  Merkle, J. and M. Lochter, "Elliptic Curve Cryptography
              (ECC) Brainpool Curves for Transport Layer Security
              (TLS)", RFC 7027, DOI 10.17487/RFC7027, October 2013,

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

   [RFC8422]  Nir, Y., Josefsson, S., and M. Pegourie-Gonnard, "Elliptic
              Curve Cryptography (ECC) Cipher Suites for Transport Layer
              Security (TLS) Versions 1.2 and Earlier", RFC 8422,
              DOI 10.17487/RFC8422, August 2018,

   [RFC8446]  Rescorla, E., "The Transport Layer Security (TLS) Protocol
              Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,

7.2.  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, November 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 186-4,
              DOI 10.6028/NIST.FIPS.186-4, July 2013,

   [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
              Signatures with Appendix - Part 3: Discrete Logarithm
              Based Mechanisms", ISO/IEC 14888-3, November 2018.

   [ISO2]     International Organization for Standardization,
              "Information Technology - Security techniques -
              Cryptographic techniques based on elliptic curves - Part
              2: Digital signatures", ISO/IEC 15946-2:2002, December

              National Institute of Standards and Technology,
              "Recommendation for Key Management - Part 1: General
              (Revised)", NIST Special Publication 800-57,
              DOI 10.6028/NIST.SP.800-57ptlr4, January 2016,

   [SEC1]     Standards for Efficient Cryptography Group, "SEC1:
              Elliptic Curve Cryptography", May 2019.

   [SEC2]     Standards for Efficient Cryptography Group, "SEC 2:
              Recommended Elliptic Curve Domain Parameters", January

Appendix A.  Test Vectors

   This non-normative Appendix 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 all of the subsequent

   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 premaster 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].

A.1.  256-Bit Curve

   Curve brainpoolP256r1

   dA =

   x_qA =

   y_qA =

   dB =

   x_qB =

   y_qB =

   x_Z =

   y_Z =

A.2.  384-Bit Curve

   Curve brainpoolP384r1

   dA = 1E20F5E048A5886F1F157C74E91BDE2B98C8B52D58E5003D57053FC4B0BD6

   x_qA = 68B665DD91C195800650CDD363C625F4E742E8134667B767B1B47679358

   y_qA = 55BC91A39C9EC01DEE36017B7D673A931236D2F1F5C83942D049E3FA206

   dB = 032640BC6003C59260F7250C3DB58CE647F98E1260ACCE4ACDA3DD869F74E

   x_qB = 4D44326F269A597A5B58BBA565DA5556ED7FD9A8A9EB76C25F46DB69D19

   y_qB = 62D692136DE56CBE93BF5FA3188EF58BC8A3A0EC6C1E151A21038A42E91

   x_Z = 0BD9D3A7EA0B3D519D09D8E48D0785FB744A6B355E6304BC51C229FBBCE2

   y_Z = 0DF213417EBE4D8E40A5F76F66C56470C489A3478D146DECF6DF0D94BAE9

A.3.  512-Bit Curve

   Curve brainpoolP512r1

   dA = 16302FF0DBBB5A8D733DAB7141C1B45ACBC8715939677F6A56850A38BD87B

   x_qA = 0A420517E406AAC0ACDCE90FCD71487718D3B953EFD7FBEC5F7F27E28C6

   y_qA = 72E6882E8DB28AAD36237CD25D580DB23783961C8DC52DFA2EC138AD472

   dB = 230E18E1BCC88A362FA54E4EA3902009292F7F8033624FD471B5D8ACE49D1

   x_qB = 9D45F66DE5D67E2E6DB6E93A59CE0BB48106097FF78A081DE781CDB31FC

   y_qB = 2FDC313095BCDD5FB3A91636F07A959C8E86B5636A1E930E8396049CB48

   x_Z = A7927098655F1F9976FA50A9D566865DC530331846381C87256BAF322624

   y_Z = 7DB71C3DEF63212841C463E881BDCF055523BD368240E6C3143BD8DEF8B3

Authors' Addresses

   Leonie Bruckert
   secunet Security Networks
   Ammonstr. 74
   01067 Dresden

   Phone: +49 201 5454 3819
   Email: leonie.bruckert@secunet.com

   Johannes Merkle
   secunet Security Networks
   Mergenthaler Allee 77
   65760 Eschborn

   Phone: +49 201 5454 3091
   Email: johannes.merkle@secunet.com

   Manfred Lochter
   Postfach 200363
   53133 Bonn

   Phone: +49 228 9582 5643
   Email: manfred.lochter@bsi.bund.de