ECC Support for PKINIT
draft-zhu-pkinit-ecc-04

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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.  Conventions Used in This Document
3.  Using Elliptic Curve Certificates and Elliptic Curve Signature Schemes
4.  Using ECDH Key Exchange
5.  Choosing the Domain Parameters and the Key Size
6.  Interoperability Requirements
7.  Security Considerations
8.  IANA Considerations
9.  Acknowledgements
10.  References
    10.1.  Normative References
    10.2.  Informative References
§  Authors' Addresses
§  Intellectual Property and Copyright Statements

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] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.) [NISTSP80057] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.).

Currently [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.) permits the use of ECC algorithms but it does not specify how ECC parameters are chosen and how to derive the shared key for key delivery using Elliptic Curve Diffie-Hellman (ECDH) [IEEE1363] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.) [X9.63] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.).

This document describes how to use Elliptic Curve certificates, Elliptic Curve signature schemes, and ECDH with [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.). However, it should be noted that there is no syntactic or semantic change to the existing [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.) messages. Both the client and the KDC contribute one ECDH key pair using the key agrement 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] (Bradner, S., “Key words for use in RFCs to Indicate Requirement Levels,” March 1997.).

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] (Housley, R., “Cryptographic Message Syntax (CMS),” July 2004.) [RFC3278] (Blake-Wilson, S., Brown, D., and P. Lambert, “Use of Elliptic Curve Cryptography (ECC) Algorithms in Cryptographic Message Syntax (CMS),” April 2002.) content type 'SignedData'.

X.509 certificates [RFC3280] (Housley, R., Polk, W., Ford, W., and D. Solo, “Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile,” April 2002.) containing ECC public keys or signed using ECC signature schemes MUST comply with [RFC3279] (Bassham, L., Polk, W., and R. Housley, “Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile,” April 2002.).

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:

   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 specfication MUST support ecdsa-with-Sha256 and SHOULD support ecdsa-with-Sha1.

4.  Using ECDH Key Exchange

This section describes how ECDH can be used as the AS reply key delivery method [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.). Note that the protocol description here is similar to that of Modular Exponential Diffie-Hellman (MODP DH), as described in [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.).

If the client wishes to use ECDH key agreement method, it encodes its ECDH public key value and the domain parameters [IEEE1363] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.) [X9.63] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.) for its ECDH public key in clientPublicValue of the PA-PK-AS-REQ message [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.).

As described in [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.), the ECDH domain parameters for the client's public key are specified in the algorithm field of the type SubjectPublicKeyInfo [RFC3279] (Bassham, L., Polk, W., and R. Housley, “Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile,” April 2002.) and the client's ECDH public key value is mapped to a subjectPublicKey (a BIT STRING) according to [RFC3279] (Bassham, L., Polk, W., and R. Housley, “Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile,” April 2002.).

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] (Neuman, C., Yu, T., Hartman, S., and K. Raeburn, “The Kerberos Network Authentication Service (V5),” July 2005.) with the code KDC_ERR_DH_KEY_PARAMETERS_NOT_ACCEPTED [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.). This error message contains the list of domain parameters acceptable to the KDC. This list is encoded as TD-DH-PARAMETERS [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.), 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 (Security Considerations).

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] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.).

As described in [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.), the KDC's ECDH public key value is encoded as a BIT STRING according to [RFC3279] (Bassham, L., Polk, W., and R. Housley, “Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile,” April 2002.).

Note that in the steps above, the client can indicate to the KDC that it wishes to reuse ECDH keys or to allow the KDC to do so, by including the clientDHNonce field in the request [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.), and the KDC can then reuse the ECDH keys and include serverDHNonce field in the reply [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.). This logic is the same as that of the Modular Exponential Diffie-Hellman key agreement method [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.).

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] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.) with the following difference: The DHSharedSecret is the x-coordinate of the shared secret value (an elliptic curve point); DHSharedSecret is the output of operation ECSVDP-DH as described in Section 7.2.1 of [IEEE1363] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.).

Both the client and KDC then proceed as described in [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.) and [RFC4120] (Neuman, C., Yu, T., Hartman, S., and K. Raeburn, “The Kerberos Network Authentication Service (V5),” July 2005.).

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 or KDC certificates can be used. This obviates the need of locally preconfigured domain parameters as described in Section 7 (Security Considerations).

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] (Orman, H. and P. Hoffman, “Determining Strengths For Public Keys Used For Exchanging Symmetric Keys,” April 2004.). The following table, based on table 2 on page 63 of NIST SP800-57 part 1 [NISTSP80057] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.), gives approximate comparable key sizes for symmetric- and asymmetric-key cryptosystems based on the best-known algorithms for attacking them.

              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 paratmeters are well known and can be identified by an Object Identifier, otherwise it is called a custom curve. [RFC4556] (Zhu, L. and B. Tung, “Public Key Cryptography for Initial Authentication in Kerberos (PKINIT),” June 2006.) supports both named curves and custom curves, see Section 7 (Security Considerations) on the tradeoff of choosing between named curves and custom curves.

The named curves recommended in this document are also recommended by NIST [FIPS186‑2] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.). These fifteen ECC curves are given in the following table [FIPS186‑2] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.) [SEC2] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.).

           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

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 certain checks to avoid the attacks described in [ECC‑Validation] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.). 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 acceptable locally, or 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 (and 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] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.) and [X9.62] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.).

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] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.), [X9.62] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.) and [FIPS186‑2] (Tung, B., Neuman, B., and S. Medvinsky, “Public Key Cryptography for Initial Authentication in Kerberos,” August 2004.).

8.  IANA Considerations

No IANA actions are required for this document.

9.  Acknowledgements

The following people have made significant contributions to this draft: Paul Leach, Dan Simon, Kelvin Yiu, David Cross, Sam Hartman, Tolga Acar, and Stefan Santesson.

10.  References

10.1. Normative References

10.2. Informative References

Authors' Addresses

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