Network Working Group L. Zhu
Request for Comments: 5349 K. Jaganathan
Category: Informational K. Lauter
Microsoft Corporation
September 2008
Elliptic Curve Cryptography (ECC) Support for Public Key Cryptography
for Initial Authentication in Kerberos (PKINIT)
Status of This Memo
This memo provides information for the Internet community. It does
not specify an Internet standard of any kind. Distribution of this
memo is unlimited.
Abstract
This document describes the use of Elliptic Curve certificates,
Elliptic Curve signature schemes and Elliptic Curve Diffie-Hellman
(ECDH) key agreement within the framework of PKINIT -- the Kerberos
Version 5 extension that provides for the use of public key
cryptography.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Conventions Used in This Document . . . . . . . . . . . . . . . 2
3. Using Elliptic Curve Certificates and Elliptic Curve
Signature Schemes . . . . . . . . . . . . . . . . . . . . . . . 2
4. Using the ECDH Key Exchange . . . . . . . . . . . . . . . . . . 3
5. Choosing the Domain Parameters and the Key Size . . . . . . . . 4
6. Interoperability Requirements . . . . . . . . . . . . . . . . . 6
7. Security Considerations . . . . . . . . . . . . . . . . . . . . 6
8. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 7
9. References . . . . . . . . . . . . . . . . . . . . . . . . . . 7
9.1. Normative References . . . . . . . . . . . . . . . . . . . 7
9.2. Informative References . . . . . . . . . . . . . . . . . . 8
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1. Introduction
Elliptic Curve Cryptography (ECC) is emerging as an attractive
public-key cryptosystem that provides security equivalent to
currently popular public-key mechanisms such as RSA and DSA with
smaller key sizes [LENSTRA] [NISTSP80057].
Currently, [RFC4556] permits the use of ECC algorithms but it does
not specify how ECC parameters are chosen or how to derive the shared
key for key delivery using Elliptic Curve Diffie-Hellman (ECDH)
[IEEE1363] [X9.63].
This document describes how to use Elliptic Curve certificates,
Elliptic Curve signature schemes, and ECDH with [RFC4556]. However,
it should be noted that there is no syntactic or semantic change to
the existing [RFC4556] messages. Both the client and the Key
Distribution Center (KDC) contribute one ECDH key pair using the key
agreement protocol described in this document.
2. Conventions Used in This Document
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].
3. Using Elliptic Curve Certificates and Elliptic Curve Signature
Schemes
ECC certificates and signature schemes can be used in the
Cryptographic Message Syntax (CMS) [RFC3852] [RFC3278] content type
'SignedData'.
X.509 certificates [RFC5280] that contain ECC public keys or are
signed using ECC signature schemes MUST comply with [RFC3279].
The signatureAlgorithm field of the CMS data type 'SignerInfo' can
contain one of the following ECC signature algorithm identifiers:
ecdsa-with-Sha1 [RFC3279]
ecdsa-with-Sha256 [X9.62]
ecdsa-with-Sha384 [X9.62]
ecdsa-with-Sha512 [X9.62]
The corresponding digestAlgorithm field contains one of the following
hash algorithm identifiers respectively:
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id-sha1 [RFC3279]
id-sha256 [X9.62]
id-sha384 [X9.62]
id-sha512 [X9.62]
Namely, id-sha1 MUST be used in conjunction with ecdsa-with-Sha1,
id-sha256 MUST be used in conjunction with ecdsa-with-Sha256,
id-sha384 MUST be used in conjunction with ecdsa-with-Sha384, and
id-sha512 MUST be used in conjunction with ecdsa-with-Sha512.
Implementations of this specification MUST support ecdsa-with-Sha256
and SHOULD support ecdsa-with-Sha1.
4. Using the ECDH Key Exchange
This section describes how ECDH can be used as the Authentication
Service (AS) reply key delivery method [RFC4556]. Note that the
protocol description here is similar to that of Modular Exponential
Diffie-Hellman (MODP DH), as described in [RFC4556].
If the client wishes to use the ECDH key agreement method, it encodes
its ECDH public key value and the key's domain parameters [IEEE1363]
[X9.63] in clientPublicValue of the PA-PK-AS-REQ message [RFC4556].
As described in [RFC4556], the ECDH domain parameters for the
client's public key are specified in the algorithm field of the type
SubjectPublicKeyInfo [RFC3279] and the client's ECDH public key value
is mapped to a subjectPublicKey (a BIT STRING) according to
[RFC3279].
The following algorithm identifier is used to identify the client's
choice of the ECDH key agreement method for key delivery.
id-ecPublicKey (Elliptic Curve Diffie-Hellman [RFC3279])
If the domain parameters are not accepted by the KDC, the KDC sends
back an error message [RFC4120] with the code
KDC_ERR_DH_KEY_PARAMETERS_NOT_ACCEPTED [RFC4556]. This error message
contains the list of domain parameters acceptable to the KDC. This
list is encoded as TD-DH-PARAMETERS [RFC4556], and it is in the KDC's
decreasing preference order. The client can then pick a set of
domain parameters from the list and retry the authentication.
Both the client and the KDC MUST have local policy that specifies
which set of domain parameters are acceptable if they do not have a
priori knowledge of the chosen domain parameters. The need for such
local policy is explained in Section 7.
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If the ECDH domain parameters are accepted by the KDC, the KDC sends
back its ECDH public key value in the subjectPublicKey field of the
PA-PK-AS-REP message [RFC4556].
As described in [RFC4556], the KDC's ECDH public key value is encoded
as a BIT STRING according to [RFC3279].
Note that in the steps above, the client can indicate to the KDC that
it wishes to reuse ECDH keys or it can allow the KDC to do so, by
including the clientDHNonce field in the request [RFC4556]; the KDC
can then reuse the ECDH keys and include the serverDHNonce field in
the reply [RFC4556]. This logic is the same as that of the Modular
Exponential Diffie-Hellman key agreement method [RFC4556].
If ECDH is negotiated as the key delivery method, then the
PA-PK-AS-REP and AS reply key are generated as in Section 3.2.3.1 of
[RFC4556] with the following difference: The ECDH shared secret value
(an elliptic curve point) is calculated using operation ECSVDP-DH as
described in Section 7.2.1 of [IEEE1363]. The x-coordinate of this
point is converted to an octet string using operation FE2OSP as
described in Section 5.5.4 of [IEEE1363]. This octet string is the
DHSharedSecret.
Both the client and KDC then proceed as described in [RFC4556] and
[RFC4120].
Lastly, it should be noted that ECDH can be used with any
certificates and signature schemes. However, a significant advantage
of using ECDH together with ECC certificates and signature schemes is
that the ECC domain parameters in the client certificates or the KDC
certificates can be used. This obviates the need of locally
preconfigured domain parameters as described in Section 7.
5. Choosing the Domain Parameters and the Key Size
The domain parameters and the key size should be chosen so as to
provide sufficient cryptographic security [RFC3766]. The following
table, based on table 2 on page 63 of NIST SP800-57 part 1
[NISTSP80057], gives approximate comparable key sizes for symmetric-
and asymmetric-key cryptosystems based on the best-known algorithms
for attacking them.
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Symmetric | ECC | RSA
-------------+----------- +------------
80 | 160 - 223 | 1024
112 | 224 - 255 | 2048
128 | 256 - 383 | 3072
192 | 384 - 511 | 7680
256 | 512+ | 15360
Table 1: Comparable key sizes (in bits)
Thus, for example, when securing a 128-bit symmetric key, it is
prudent to use 256-bit Elliptic Curve Cryptography (ECC), e.g., group
P-256 (secp256r1) as described below.
A set of ECDH domain parameters is also known as a "curve". A curve
is a "named curve" if the domain parameters are well known and can be
identified by an Object Identifier; otherwise, it is called a "custom
curve". [RFC4556] supports both named curves and custom curves, see
Section 7 on the tradeoffs of choosing between named curves and
custom curves.
The named curves recommended in this document are also recommended by
the National Institute of Standards and Technology (NIST)[FIPS186-2].
These fifteen ECC curves are given in the following table [FIPS186-2]
[SEC2].
Description SEC 2 OID
----------------- ---------
ECPRGF192Random group P-192 secp192r1
EC2NGF163Random group B-163 sect163r2
EC2NGF163Koblitz group K-163 sect163k1
ECPRGF224Random group P-224 secp224r1
EC2NGF233Random group B-233 sect233r1
EC2NGF233Koblitz group K-233 sect233k1
ECPRGF256Random group P-256 secp256r1
EC2NGF283Random group B-283 sect283r1
EC2NGF283Koblitz group K-283 sect283k1
ECPRGF384Random group P-384 secp384r1
EC2NGF409Random group B-409 sect409r1
EC2NGF409Koblitz group K-409 sect409k1
ECPRGF521Random group P-521 secp521r1
EC2NGF571Random group B-571 sect571r1
EC2NGF571Koblitz group K-571 sect571k1
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6. Interoperability Requirements
Implementations conforming to this specification MUST support curve
P-256 and P-384.
7. Security Considerations
When using ECDH key agreement, the recipient of an elliptic curve
public key should perform the checks described in IEEE P1363, Section
A16.10 [IEEE1363]. It is especially important, if the recipient is
using a long-term ECDH private key, to check that the sender's public
key is a valid point on the correct elliptic curve; otherwise,
information may be leaked about the recipient's private key, and
iterating the attack will eventually completely expose the
recipient's private key.
Kerberos error messages are not integrity protected; as a result, the
domain parameters sent by the KDC as TD-DH-PARAMETERS can be tampered
with by an attacker so that the set of domain parameters selected
could be either weaker or not mutually preferred. Local policy can
configure sets of domain parameters that are acceptable locally or
can disallow the negotiation of ECDH domain parameters.
Beyond elliptic curve size, the main issue is elliptic curve
structure. As a general principle, it is more conservative to use
elliptic curves with as little algebraic structure as possible.
Thus, random curves are more conservative than special curves (such
as Koblitz curves), and curves over F_p with p random are more
conservative than curves over F_p with p of a special form. (Also,
curves over F_p with p random might be considered more conservative
than curves over F_2^m, as there is no choice between multiple fields
of similar size for characteristic 2.) Note, however, that algebraic
structure can also lead to implementation efficiencies, and
implementors and users may, therefore, need to balance conservatism
against a need for efficiency. Concrete attacks are known against
only very few special classes of curves, such as supersingular
curves, and these classes are excluded from the ECC standards such as
[IEEE1363] and [X9.62].
Another issue is the potential for catastrophic failures when a
single elliptic curve is widely used. In this case, an attack on the
elliptic curve might result in the compromise of a large number of
keys. Again, this concern may need to be balanced against efficiency
and interoperability improvements associated with widely used curves.
Substantial additional information on elliptic curve choice can be
found in [IEEE1363], [X9.62], and [FIPS186-2].
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8. Acknowledgements
The following people have made significant contributions to this
document: Paul Leach, Dan Simon, Kelvin Yiu, David Cross, Sam
Hartman, Tolga Acar, and Stefan Santesson.
9. References
9.1. Normative References
[FIPS186-2] NIST, "Digital Signature Standard", FIPS 186-2, 2000.
[IEEE1363] IEEE, "Standard Specifications for Public Key
Cryptography", IEEE 1363, 2000.
[NISTSP80057] NIST, "Recommendation on Key Management", SP 800-57,
August 2005,
.
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Authors' Addresses
Larry Zhu
Microsoft Corporation
One Microsoft Way
Redmond, WA 98052
US
EMail: lzhu@microsoft.com
Karthik Jaganathan
Microsoft Corporation
One Microsoft Way
Redmond, WA 98052
US
EMail: karthikj@microsoft.com
Kristin Lauter
Microsoft Corporation
One Microsoft Way
Redmond, WA 98052
US
EMail: klauter@microsoft.com
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