Keywords: TLS, Elliptic Curve Cryptography
Independent Submission L. Bruckert
Request for Comments: 8734 J. Merkle
Category: Informational secunet Security Networks
ISSN: 2070-1721 M. Lochter
BSI
February 2020
Elliptic Curve Cryptography (ECC) Brainpool Curves for Transport Layer
Security (TLS) Version 1.3
Abstract
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
1.3.
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
https://www.rfc-editor.org/info/rfc8734.
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
Provisions Relating to IETF Documents
(https://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.
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",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"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 {
brainpoolP256r1tls13(31),
brainpoolP384r1tls13(32),
brainpoolP512r1tls13(33)
} NamedGroup;
The encoding of Ephemeral Elliptic Curve Diffie-Hellman (ECDHE)
parameters for sec256r1, secp384r1, and secp521r1, as defined in
Section 4.2.8.2 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 {
ecdsa_brainpoolP256r1tls13_sha256(0x081A),
ecdsa_brainpoolP384r1tls13_sha384(0x081B),
ecdsa_brainpoolP512r1tls13_sha512(0x081C)
} 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
document.
+-------+----------------------+---------+-------------+-----------+
| 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
effort.
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",
<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>.
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,
<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 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
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 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