RFC 8734

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

📅 published February 2020, from ietf

RFC 8734 ✨ Elliptic Curve Cryptography (ECC) Brainpool Curves for Transport Layer Security (TLS) Version 1.3 🎀

okay bestie, let's get into this one 💖 it's an Informational RFC from February 2020, written by L. Bruckert (secunet Security Networks), J. Merkle (secunet Security Networks), and M. Lochter (BSI). It's published as an Independent Submission, it's ISSN 2070-1721, and it doesn't obsolete or update anything. The whole vibe is "here are the Brainpool curves, plugged into TLS 1.3 🦋"

Heads up, this is part 1 of 2 💅 more is coming, so stay tuned!

Abstract 🌸

okay so the Brainpool elliptic curves were a thing for authentication and key exchange in TLS 1.2, but the IETF deprecated them for TLS 1.3 because nobody was really using them 🥲 but like, they haven't been shown to have any big cryptographic weaknesses, and people are still interested in using a few of them in TLS 1.3. this doc gives the protocol bits you need to do that. and the IETF does not endorse this approach, just so we're clear 🙈

Status of This Memo 🧚

this is not an Internet Standards Track spec, it's just published for info purposes 💜

it's a contribution to the RFC Series, independent of any other RFC stream. the RFC Editor picked to publish it at their discretion and makes no statement about whether you should actually implement or deploy it. docs approved by the RFC Editor aren't candidates for any level of Internet Standard, see Section 2 of RFC 7841 ✨

for the current status, errata, or how to give feedback, check https://www.rfc-editor.org/info/rfc8734 🔗

Copyright Notice 🌈

this doc is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/license-info) as of the publication date. please actually read those, they explain your rights and restrictions 🫶

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 🦋

okay so [RFC5639] 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 pseudorandom way. they meet the security requirements of ISO [ISO1][ISO2], ANSI [ANSI1], NIST [FIPS], and SECG [SEC2] standards, so they're legit 👑

[RFC8422] covers using elliptic curves for authentication and key agreement in TLS 1.2 and earlier. [RFC7027] covers using Brainpool curves for auth and key exchange in TLS. the catch is that RFC 7027 only works for TLS 1.2 and earlier, not 1.3, because TLS 1.3 deprecates the Brainpool curve IDs from RFC 7027 since they never really got deployed widely 😭 people still want them in 1.3 though, so here we are ✨

so for key negotiation in TLS 1.3 under [RFC8446], you need to define and assign some new NamedGroup IDs. this doc does the NamedGroup IDs and the SignatureScheme IDs for three Brainpool curves from [RFC5639] 💅

once again: the IETF does not endorse this approach. implementers and deployers need to know the strengths and weaknesses of every security mechanism they use, no cap 🙈

2. Requirements Terminology 🎀

the key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be read as described in BCP 14 [RFC2119] [RFC8174], but only when they show up in ALL CAPS like that 💖

3. Brainpool NamedGroup Types 🌸

so according to [RFC8446], the "supported_groups" extension is how you negotiate Diffie-Hellman groups and elliptic curve groups for key exchange during a handshake that starts a new TLS session. this doc adds new named groups for three curves from [RFC5639] into that extension, like this 👑

        enum {
             brainpoolP256r1tls13(31),
             brainpoolP384r1tls13(32),
             brainpoolP512r1tls13(33)
        } NamedGroup;

the ECDHE parameter encoding for sec256r1, secp384r1, and secp521r1 from Section 4.2.8.2 of [RFC8446] also applies to this doc 🦋

test vectors for a Diffie-Hellman key exchange with these curves are in Appendix A ✨

4. Brainpool SignatureScheme Types 🧚

according to [RFC8446], the SignatureScheme name space is used to negotiate elliptic curve groups for authentication through the "signature_algorithms" extension. you also have to specify the hash function used to hash the message before signing. this doc adds new SignatureScheme types for three [RFC5639] curves, like so 💜

        enum {
             ecdsa_brainpoolP256r1tls13_sha256(0x081A),
             ecdsa_brainpoolP384r1tls13_sha384(0x081B),
             ecdsa_brainpoolP512r1tls13_sha512(0x081C)
        } SignatureScheme;

5. IANA Considerations 🌈

IANA updated the references for the ECC Brainpool curves in the "TLS Supported Groups" [IANA-TLS] subregistry of the "Transport Layer Security (TLS) Parameters" registry so they point at this doc 🍓

+-------+----------------------+---------+-------------+-----------+
| 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 also updated the references for the ECC Brainpool curves in the "TLS SignatureScheme" subregistry [IANA-TLS] of the "Transport Layer Security (TLS) Parameters" registry so they point at this doc 💖

+------+-----------------------------------+-------------+----------+
|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 💀

okay this part is important, so pay attention 🫶 the security considerations of [RFC8446] apply here too, accordingly.

the confidentiality, authenticity, and integrity of TLS communication is only as strong as the weakest crypto primitive being used. so to get max security when you use one of the curves from Table 1 for key exchange and/or one of the signature algorithms from Table 2 for auth in TLS, the other crypto parameters you deploy SHOULD be picked at commensurate strengths, for example following the recommendations of [NIST800-57] and [RFC5639] 🔥 this specifically covers (a) the key derivation function, (b) the algorithms and key length for symmetric encryption and message authentication, and (c) the algorithm, bit length, and hash function for signature generation.

also, the private Diffie-Hellman keys SHOULD be generated from a random keystream whose length equals the length of the order of the group E(GF(p)) defined in [RFC5639]. and the value of the private Diffie-Hellman keys SHOULD be less than the order of the group E(GF(p)) 🌸

now the big one 🚨 when you use ECDHE key agreement with brainpoolP256r1tls13, brainpoolP384r1tls13, or brainpoolP512r1tls13, the peers MUST validate each other's public value Q by checking that the point is a valid point on the elliptic curve. if you skip this check, an attacker can force the key exchange into a small subgroup, and the resulting shared secret can be guessed with way less effort 😱 that's a whole disaster, so don't skip it, bestie 💀

and implementations of elliptic curve crypto for TLS MAY be susceptible to side-channel attacks. take extra care with implementations that internally transform curve points onto the matching "twisted curve", using the map (x',y') = (x*Z^2, y*Z^3) with the coefficient Z specified for that curve in [RFC5639], so they can use efficient arithmetic based on the twisted curve's special parameters (A = -3). the twisted curve gives the same level of security as the corresponding random curve (through mathematical equivalence), but arithmetic based on small curve parameters may be harder to protect against side-channel attacks 👀 general guidance on resisting side-channel attacks against ECC implementations is in [BSI1] and [HMV] 🦋

7. References 🍓

7.1. Normative References ✨

[IANA-TLS] IANA, "Transport Layer Security (TLS) Parameters",
           <https://www.iana.org/assignments/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,
           <https://www.rfc-editor.org/info/rfc2119>.

[RFC5639]  Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
           (ECC) Brainpool Standard Curves and Curve Generation",
           RFC 5639, DOI 10.17487/RFC5639, March 2010,
           <https://www.rfc-editor.org/info/rfc5639>.

[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,
           <https://www.rfc-editor.org/info/rfc7027>.

[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,
           <https://www.rfc-editor.org/info/rfc8422>.

[RFC8446]  Rescorla, E., "The Transport Layer Security (TLS) Protocol
           Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
           <https://www.rfc-editor.org/info/rfc8446>.

That's the end of part 1! 🌈 More of RFC 8734 is coming in part 2, bestie 🦋✨

7.2. Informative References ✨

Okay so bestie, here's the reading list for the nerds who want the deep background 📚🤓 Every single one of these is a source the RFC leans on, so I'm keeping all the details exactly as they are 🫶

[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, <https://doi.org/10.6028/NIST.FIPS.186-4>.

[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 2002.

[NIST800-57] 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, <https://doi.org/10.6028/NIST.SP.800-57ptlr4>.

[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 2010.

Appendix A. Test Vectors 🧪

This non-normative Appendix is pure vibes and practice data, so nobody's required to use it 💜 It gives you some test vectors (for example, Diffie-Hellman key exchanges using each of the curves defined in Table 1). Here's the notation used in every section after this 🎀

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 =
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 💖

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

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 🎀

Leonie Bruckert secunet Security Networks Ammonstr. 74 01067 Dresden Germany

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

Johannes Merkle secunet Security Networks Mergenthaler Allee 77 65760 Eschborn Germany

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

Manfred Lochter BSI Postfach 200363 53133 Bonn Germany

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

That's the whole RFC, bestie, we made it 🌈💜🦋

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