| Network Working Group | J.M. Merkle |
| Internet-Draft | secunet Security Networks |
| Intended status: Informational | M.L. Lochter |
| Expires: October 25, 2013 | Bundesamt fuer Sicherheit in der Informationstechnik (BSI) |
| April 23, 2013 |
Using the ECC Brainpool Curves for IKEv2 Key Exchange
draft-merkle-ikev2-ke-brainpool-05
This document specifies the use of ECC Brainpool elliptic curve groups for key exchange in the Internet Key Exchange version 2 (IKEv2) protocol.
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In [RFC5639], a new set of elliptic curve groups over finite prime fields for use in cryptographic applications was specified. 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 SecG [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 tranform 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.
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].
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 are to be 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 |
Test vectors for the groups defined by the ECC Brainpool curves are provided in Appendix A
In [RFC5639] for each random curve, a "twisted curve" (defined by a quadratic twist, see [HMV]) is defined offering the same level of security but potentially allowing 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 curve listed in can be efficiently transformed to the corresponding point (x',y') on the twisted curve of same bit length - and vice versa - by setting (x',y') = (x*Z^2, y*Z^3) with the coefficient Z specified for that curve in [RFC5639].
For the encoding of the key exchange payload and the derivation of the shared secret, the methods specified in [RFC5903] are adopted.
In an ECP key exchange in IKEv2, the Diffie-Hellman public value passed in a 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 bit 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 of Section 6 of [RFC6090] after representing the field element as integer in the interval [0, p-1].
| Curves | Bit length of each component (x or y) | Bit length of key exchange payload |
|---|---|---|
| brainpoolP224r1 | 224 | 448 |
| brainpoolP256r1 | 256 | 512 |
| brainpoolP384r1 | 384 | 768 |
| brainpoolP512r1 | 512 | 1024 |
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 the Table 2.
The security considerations of [RFC5996] apply accordingly.
In order to thwart certain active attacks, the validity of the other peer's public Diffie-Hellmann value (x,y) recovered from the received key exchange payload needs to be verified. In particular, it must be verified that the coordinates x and y of the public value satisfy the curve equation.
The confidentiality, authenticity and integrity of a secure communication based on IKEv2 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, the key derivation function, the algorithms and key lengths of symmetric encryption and message authentication as well as the algorithm, bit length and hash function used for signature generation should be chosen according to the recommendations of [NIST800-57] and [RFC5639]. 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 resistence of elliptic curve cryptography implementations against side-channel-attacks is given in [BSI1] and [HMV].
IANA has updated its Transform Type 4 (Diffie-Hellman Group Transform) registry in [IANA-IKE2] to include the groups listed in Table 1.
| [IANA-IKE2] | Internet Assigned Numbers Authority, "Internet Key Exchange Version 2 (IKEv2) Parameters", . |
| [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. |
| [SEC1] | Certicom Research , "Elliptic Curve Cryptography ", Standards for Efficient Cryptography (SEC) 1, September 2000. |
This section provides some test vectors for example Diffie-Hellman key exchanges using each of the curves defined in Section 2 . In all of the following sections the following notation is used: [SEC1].
The field elements x_qA, y_qA, x_qB, y_qB, x_Z, y_Z are represented as hexadecimal values using the FieldElement-to-OctetString conversion method specified in
Curve brainpoolP224r1
Curve brainpoolP256r1
Curve brainpoolP384r1
Curve brainpoolP512r1