Internet Engineering Task Force (IETF) J. Merkle
Request for Comments: 6954 secunet Security Networks
Category: Informational M. Lochter
ISSN: 2070-1721 BSI
July 2013
Using the Elliptic Curve Cryptography (ECC) Brainpool Curvesfor the Internet Key Exchange Protocol Version 2 (IKEv2)
Abstract
This document specifies use of the Elliptic Curve Cryptography (ECC)
Brainpool elliptic curve groups for key exchange in the Internet Key
Exchange Protocol version 2 (IKEv2).
Status of This Memo
This document is not an Internet Standards Track specification; it is
published for informational purposes.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Not all documents
approved by the IESG are a candidate for any level of Internet
Standard; see Section 2 of RFC 5741.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
http://www.rfc-editor.org/info/rfc6954.
Copyright Notice
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document authors. All rights reserved.
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RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013
Table of Contents
1. Introduction ....................................................21.1. Requirements Language ......................................22. IKEv2 Key Exchange Using the ECC Brainpool Curves ...............32.1. Diffie-Hellman Group Transform IDs .........................32.2. Using the Twisted Brainpool Curves Internally ..............32.3. Key Exchange Payload and Shared Secret .....................33. Security Considerations .........................................44. IANA Considerations .............................................55. References ......................................................55.1. Normative References .......................................55.2. Informative References .....................................6Appendix A. Test Vectors ...........................................8A.1. 224-Bit Curve ...............................................8A.2. 256-Bit Curve ...............................................9A.3. 384-Bit Curve ...............................................9A.4. 512-Bit Curve ..............................................101. Introduction
[RFC5639] specified 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
pseudo-random way and comply with the security requirements of
relevant standards from ISO [ISO1] [ISO2], ANSI [ANSI1], NIST [FIPS],
and the Standards for Efficient Cryptography Group [SEC2].
While the ASN.1 object identifiers defined in RFC 5639 allow usage of
the ECC Brainpool curves in certificates and certificate revocation
lists, their utilization for key exchange in IKEv2 [RFC5996] requires
the definition and assignment of additional Diffie-Hellman Group
Transform IDs in the respective IANA registry. This document
specifies transform IDs for four curves from RFC 5639, as well as the
encoding of the key exchange payload and derivation of the shared
secret when using one of these curves.
1.1. Requirements Language
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].
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RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 20132. IKEv2 Key Exchange Using the ECC Brainpool Curves2.1. Diffie-Hellman Group Transform IDs
In order to use the ECC Brainpool curves for key exchange within
IKEv2, the Diffie-Hellman Group Transform IDs (Transform Type 4)
listed in the following table have been registered with IANA
[IANA-IKE2]. The parameters associated with 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
provided in Appendix A.
2.2. Using the Twisted Brainpool Curves Internally
In [RFC5639], for each random curve, a "twisted curve" (defined by a
quadratic twist; see [HMV]) is defined that offers the same level of
security but potentially allows more efficient arithmetic due to the
curve parameter A = -3. The transform IDs listed in Table 1 also
allow using the twisted curve corresponding to the specified random
curve: points (x,y) of any of the listed curves can be efficiently
transformed to the corresponding 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 the encoding of the key exchange payload and the derivation of
the shared secret, the methods specified in [RFC5903] are adopted.
In an Elliptic Curve Group over GF[P] (ECP) key exchange in IKEv2,
the Diffie-Hellman public value passed in a key establishment (KE)
payload consists of two components, x and y, corresponding to the
coordinates of an elliptic curve point. Each component MUST be
computed from the corresponding coordinate using the FieldElement-to-
OctetString conversion method specified in [SEC1] and MUST have a bit
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RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013
length as indicated in Table 2. This length is enforced by the
FieldElement-to-OctetString conversion method, if necessary, by
prepending the value with zeros.
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 these components, the key exchange payload MUST be computed as
the concatenation of the x- and y-coordinates. Hence, the key
exchange payload has the bit length indicated in Table 2.
The Diffie-Hellman shared secret value consists only of the x value.
In particular, 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
MUST have bit length as indicated in Table 2.
3. Security Considerations
The security considerations of [RFC5996] apply accordingly.
In order to thwart certain active attacks, the validity of the other
peer's public Diffie-Hellman value (x,y) recovered from the received
key exchange payload needs to be verified. In particular, it MUST be
verified that the x- and y-coordinates of the public value satisfy
the curve equation. For additional information, we refer the reader
to [RFC6989].
The confidentiality, authenticity, and integrity of a secure
communication based on IKEv2 are limited by the weakest cryptographic
primitive applied. In order to achieve a maximum security level when
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RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013
using one of the elliptic curves from Table 1 for key exchange, the
following should be chosen according to the recommendations of
[NIST800-57] and [RFC5639]:
o key derivation function
o algorithms and key lengths of symmetric encryption and message
authentication
o algorithm, bit length, and hash function used for signature
generation
Furthermore, 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.
Implementations of elliptic curve cryptography for IKEv2 could be
susceptible to side-channel attacks. Particular care should be taken
for implementations that internally use the corresponding twisted
curve to take advantage of an efficient arithmetic for the special
parameters (A = -3): although the twisted curve itself offers the
same level of security as the corresponding random curve (through
mathematical equivalence), an arithmetic based on small curve
parameters could 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].
4. IANA Considerations
IANA has updated its "Transform Type 4 - Diffie-Hellman Group
Transform IDs" registry in [IANA-IKE2] to include the groups listed
in Table 1.
5. References5.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC5996] Kaufman, C., Hoffman, P., Nir, Y., and P. Eronen,
"Internet Key Exchange Protocol Version 2 (IKEv2)",
RFC 5996, September 2010.
[RFC5639] Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
(ECC) Brainpool Standard Curves and Curve Generation",
RFC 5639, March 2010.
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RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013
[RFC6989] Sheffer, Y. and S. Fluhrer, "Additional Diffie-Hellman
Tests for the Internet Key Exchange Protocol Version 2
(IKEv2)", RFC 6989, July 2013.
[IANA-IKE2] Internet Assigned Numbers Authority, "Internet Key
Exchange Version 2 (IKEv2) Parameters",
<http://www.iana.org/assignments/ikev2-parameters>.
[SEC1] Certicom Research, "Elliptic Curve Cryptography",
Standards for Efficient Cryptography (SEC) 1,
September 2000.
5.2. Informative References
[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.
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RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013
[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.
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RFC 6954 Brainpool Curves for IKEv2 Key Exchange July 2013Appendix A. Test Vectors
This section provides some test vectors, for example, Diffie-Hellman
key exchanges using each of the curves defined in Section 2. The
following notation is used in the subsequent subsections:
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
represented as hexadecimal values using the FieldElement-to-
OctetString conversion method specified in [SEC1].
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
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