RFC 6954

Using the Elliptic Curve Cryptography (ECC) Brainpool Curves for the Internet Key Exchange Protocol Version 2 (IKEv2)

📅 published July 2013, from ietf

RFC 6954 (Part 1 of 2) 🎀

okay bestie, the title block is giving main character energy 💅 Here's who we've got:

Series: Internet Engineering Task Force (IETF)
RFC: 6954
Title: Using the Elliptic Curve Cryptography (ECC) Brainpool Curves for the Internet Key Exchange Protocol Version 2 (IKEv2)
Authors: J. Merkle (secunet Security Networks) and M. Lochter (BSI)
Category: Informational
ISSN: 2070-1721
Date: July 2013
Obsoletes/Updates: none listed in its header 🌸

Abstract ✨

This doc is all about using the ECC Brainpool elliptic curve groups for key exchange in IKEv2 🔥

Status of This Memo 🦋

This one is NOT an Internet Standards Track spec, it's just published for info purposes 💜

It's an IETF product, so it represents the consensus of the IETF community. It 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 for the full story 🧚

For the current status, any errata, and how to send feedback, head to http://www.rfc-editor.org/info/rfc6954 🍓

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're in effect on the date of publication. Please actually read those, because they describe your rights and restrictions for this doc 🫶

Code Components pulled out of this document must include Simplified BSD License text, as described in Section 4.e of the Trust Legal Provisions. They come without warranty, as described in the Simplified BSD License ⭐

Table of Contents 🧚

1. Introduction ....................................................2
   1.1. Requirements Language ......................................2
2. IKEv2 Key Exchange Using the ECC Brainpool Curves ...............3
   2.1. Diffie-Hellman Group Transform IDs .........................3
   2.2. Using the Twisted Brainpool Curves Internally ..............3
   2.3. Key Exchange Payload and Shared Secret .....................3
3. Security Considerations .........................................4
4. IANA Considerations .............................................5
5. References ......................................................5
   5.1. Normative References .......................................5
   5.2. Informative References .....................................6
Appendix A. Test Vectors ...........................................8
  A.1. 224-Bit Curve ...............................................8
  A.2. 256-Bit Curve ...............................................9
  A.3. 384-Bit Curve ...............................................9
  A.4. 512-Bit Curve ..............................................10

1. Introduction 💖

Okay so [RFC5639] came along and specified a brand new set of elliptic curve groups over finite prime fields for crypto applications. These are called 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 the Standards for Efficient Cryptography Group [SEC2] 👑

Now, the ASN.1 object identifiers from RFC 5639 let you use the Brainpool curves in certificates and certificate revocation lists, which is great. But using them for key exchange in IKEv2 [RFC5996] means you need to define and assign extra Diffie-Hellman Group Transform IDs in the matching IANA registry 😭 This doc does exactly that: it specifies transform IDs for four curves from RFC 5639. It also covers how the key exchange payload gets encoded and how the shared secret gets derived when you use one of those curves 🦋

1.1. Requirements Language 🎀

Quick word on the caps-lock words 💅 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119].

2. IKEv2 Key Exchange Using the ECC Brainpool Curves 🧚

2.1. Diffie-Hellman Group Transform IDs 🌸

So to use the ECC Brainpool curves for key exchange within IKEv2, the Diffie-Hellman Group Transform IDs (Transform Type 4) in the table below have been registered with IANA [IANA-IKE2]. The parameters for these curves are defined in RFC 5639 [RFC5639] ✨

                      +-----------------+--------------+
                      |      Curve      | Transform ID |
                      +-----------------+--------------+
                      | brainpoolP224r1 |      27      |
                      | brainpoolP256r1 |      28      |
                      | brainpoolP384r1 |      29      |
                      | brainpoolP512r1 |      30      |
                      +-----------------+--------------+

                                  Table 1

Test vectors for the groups defined by the ECC Brainpool curves are in Appendix A, so go peek 🍓

2.2. Using the Twisted Brainpool Curves Internally 🌈

Here's the tea 🫖 In [RFC5639], every random curve gets a "twisted curve" (defined by a quadratic twist; see [HMV]). The twisted curve offers the same level of security, but it can potentially be more efficient arithmetic-wise because of the curve parameter A = -3. The transform IDs in Table 1 also let you use the twisted curve that goes with the random curve you picked. Points (x,y) on any of the listed curves can be efficiently transformed to the matching point (x',y') on the twisted curve of the same bit length, and vice versa, by setting (x',y') = (x*Z^2, y*Z^3) with the coefficient Z specified for that curve [RFC5639] 💜

2.3. Key Exchange Payload and Shared Secret ⭐

For encoding the key exchange payload and deriving the shared secret, the methods specified in [RFC5903] are adopted 🫶

So in an Elliptic Curve Group over GF[P] (ECP) key exchange in IKEv2, the Diffie-Hellman public value inside a key establishment (KE) payload is made of two components, x and y. Those are the coordinates of an elliptic curve point 🔥 Each component is computed from its matching coordinate using the FieldElement-to-OctetString conversion method specified in [SEC1], and each component MUST have the bit length shown in Table 2. If needed, that length gets enforced by the FieldElement-to-OctetString conversion method, which prepends zeros to the value 🙈

Note: The FieldElement-to-OctetString conversion method specified in [SEC1] is equivalent to applying the conversion between integers and octet strings (as described in Section 6 of [RFC6090]) after representing the field element as an integer in the interval [0, p-1].

   +---------------------+-----------------------+---------------------+
   |        Curves       |   Bit length of each  |  Bit length of key  |
   |                     |   component (x or y)  |   exchange payload  |
   +---------------------+-----------------------+---------------------+
   |   brainpoolP224r1   |          224          |         448         |
   |   brainpoolP256r1   |          256          |         512         |
   |   brainpoolP384r1   |          384          |         768         |
   |   brainpoolP512r1   |          512          |         1024        |
   +---------------------+-----------------------+---------------------+

                                  Table 2

From those components, the key exchange payload MUST be computed as the concatenation of the x- and y-coordinates. So the key exchange payload ends up with the bit length shown in Table 2 🎀

The Diffie-Hellman shared secret value is just the x value, nothing else 💅 To be specific, the shared secret value MUST be computed from the x-coordinate of the Diffie-Hellman common value using the FieldElement-to-OctetString conversion method specified in [SEC1], and it MUST have the bit length shown in Table 2 ✨

5.2. Informative References 📚

okay so these are the extra-credit reads 🤓 not required to get the core spec, but super helpful background bestie 💅

[RFC5903] Fu, D. and J. Solinas, "Elliptic Curve Groups modulo a Prime (ECP Groups) for IKE and IKEv2", RFC 5903, June 2010. 🌸
[RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic Curve Cryptography Algorithms", RFC 6090, February 2011. 🦋
[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 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. 🎀
[SEC2] Certicom Research, "Recommended Elliptic Curve Domain Parameters", Standards for Efficient Cryptography (SEC) 2, September 2000. 🌈

Appendix A. Test Vectors 🧪

okay the test vectors are the fun part 🫶 they're Diffie-Hellman key exchanges using each of the curves from Section 2, so you can check your work against real numbers. here's the notation we're using:

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
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 written as hexadecimal values, using the FieldElement-to-OctetString conversion method from [SEC1]. slay 🔥

A.1. 224-Bit Curve 🌸

Curve brainpoolP224r1

   dA = 39F155483CEE191FBECFE9C81D8AB1A03CDA6790E7184ACE44BCA161

   x_qA = A9C21A569759DA95E0387041184261440327AFE33141CA04B82DC92E

   y_qA = 98A0F75FBBF61D8E58AE5511B2BCDBE8E549B31E37069A2825F590C1

   dB = 6060552303899E2140715816C45B57D9B42204FB6A5BF5BEAC10DB00

   x_qB = 034A56C550FF88056144E6DD56070F54B0135976B5BF77827313F36B

   y_qB = 75165AD99347DC86CAAB1CBB579E198EAF88DC35F927B358AA683681

   x_Z = 1A4BFE705445120C8E3E026699054104510D119757B74D5FE2462C66

   y_Z = BB6802AC01F8B7E91B1A1ACFB9830A95C079CEC48E52805DFD7D2AFE

A.2. 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.3. 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.4. 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 💌

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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