RFC 7027

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

📅 published October 2013, from ietf

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

Okay bestie, let's start with the vibe check ✨ This doc is by J. Merkle (secunet Security Networks) and M. Lochter (BSI). It's dated October 2013, its ISSN is 2070-1721, and it's Informational, so it's published for information and isn't a Standards Track thing. It updates RFC 4492, and the title block doesn't list anything it obsoletes. 💅

Abstract 🌸

Here's the tea: this doc says how to use a few ECC Brainpool curves for authentication and key exchange in Transport Layer Security (TLS) 🔐

Status of This Memo 📜

Not a Standards Track spec, babe. It's just published for info 🙈

It's still an IETF product, though. It represents the IETF community's consensus, got public review, and was approved for publication by the Internet Engineering Steering Group (IESG). Not every IESG-approved doc is a candidate for any level of Internet Standard, so check out Section 2 of RFC 5741 if you want the details 🤓

For the current status, errata, and where to send feedback, go to http://www.rfc-editor.org/info/rfc7027 🦋

Copyright Notice 💜

This doc is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) as they stood on the publication date. Please read them carefully, because they spell out your rights and restrictions 📚 Any Code Components pulled out of this doc must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions, and they come without warranty, as the Simplified BSD License describes 🔥

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 ✨

Okay so [RFC5639] is the one that defines a new set of elliptic curve groups over finite prime fields for crypto stuff. These are the ECC Brainpool curves, and they were generated in a verifiably pseudo-random way. They also comply with the security requirements of relevant standards from ISO [ISO1] [ISO2], ANSI [ANSI1], NIST [FIPS], and SecG [SEC2]. Iconic behaviour 👑

[RFC4492] is the one that defines how elliptic curves get used for authentication and key agreement in TLS 1.0 and TLS 1.1. Those mechanisms can also be used with TLS 1.2 [RFC5246] 🌈

Here's the lowkey tricky part 🙈 The ASN.1 object identifiers defined in [RFC5639] already let you use the ECC Brainpool curves for TLS (client or server) authentication, through reference in X.509 certificates per [RFC3279] and [RFC5480]. But negotiating them for key exchange under [RFC4492] needs extra NamedCurve IDs to be defined and assigned. So this doc specifies those values for three curves from [RFC5639] 💖

2. Brainpool NamedCurve Types 🎀

Next up, the NamedCurve name space. According to [RFC4492], it's what gets used to negotiate elliptic curve groups for key exchange during a handshake that starts a new TLS session. This doc adds new NamedCurve types for three elliptic curves from [RFC5639], like so:

        enum {
             brainpoolP256r1(26),
             brainpoolP384r1(27),
             brainpoolP512r1(28)
        } NamedCurve;

These curves are suitable for use with Datagram TLS [RFC6347] 🦋

And test vectors for a Diffie-Hellman key exchange using these curves are in Appendix A 🧚

3. IANA Considerations 📋

IANA has assigned numbers for the ECC Brainpool curves listed in Section 2. They live in the "EC Named Curve" [IANA-TLS] registry, which is part of the "Transport Layer Security (TLS) Parameters" registry 🗂️ Here's the full set:

          +-------+-----------------+---------+-----------+
          | 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 🔥

Serious moment, bestie 😭 The security considerations of [RFC5246] apply to the ECC Brainpool curves described in this doc. Read that one too!!

Here's the big idea: the confidentiality, authenticity, and integrity of TLS communication is only as strong as the weakest cryptographic primitive applied. So if you're using one of the elliptic curves from Table 1 for authentication and/or key exchange in TLS, you want max security. That means the key derivation function, the algorithms and key lengths of symmetric encryption, and message authentication (plus the algorithm, bit length, and hash function used for signature generation) should be chosen according to the recommendations of [NIST800-57] and [RFC5639]. Also, 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 🧠🔐

Next, side-channel attacks. Implementations of elliptic curve cryptography for TLS may be susceptible to them 👀 Extra care is needed for implementations that internally transform curve points to points on the corresponding "twisted curve". They do this with the map (x',y') = (x*Z^2, y*Z^3), using the coefficient Z specified for that curve in [RFC5639]. The reason is to get efficient arithmetic from the twisted curve's special parameters (A = -3). The twisted curve itself offers the same level of security as the corresponding random curve, because of mathematical equivalence. But arithmetic based on small curve parameters may be harder to protect against side-channel attacks, so watch out 💅

General guidance on resisting side-channel attacks against elliptic curve cryptography implementations is in [BSI1] and [HMV] 📚

Part 1 of 2 is done, bestie. Part 2 is coming with the References and Appendix A test vectors 🫶

A.1. 256-Bit Curve ✨

okay bestie, we're in the test vectors now and these are the numbers you check your code against 💖 Here's the first one, for the brainpoolP256r1 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

A.2. 384-Bit Curve ✨

next up is the bigger one, brainpoolP384r1 🌸 the values are longer, so they wrap onto extra lines, and that's totally fine 🫶

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 ✨

and the biggest one, brainpoolP512r1 👑 these ones wrap a lot, so copy them exactly as they're shown, line breaks and all 💅

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

Authors' Addresses 💖

and that's the whole doc, bestie 🎀 here's who wrote it 🧚

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

📦 where this page comes from

ietf: rfc7027 2013-10
💖 girlified by claude-haiku-5-5 on 2026-10-17: a language model's rewrite of the original, under its terms