





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,
                  <http://csrc.nist.gov/publications/nistpubs/>.

   [RFC2119]      Bradner, S., "Key words for use in RFCs to Indicate
                  Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC3278]      Blake-Wilson, S., Brown, D., and P. Lambert, "Use of
                  Elliptic Curve Cryptography (ECC) Algorithms in
                  Cryptographic Message Syntax (CMS)", RFC 3278,
                  April 2002.

   [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", RFC 3279, April 2002.

   [RFC3766]      Orman, H. and P. Hoffman, "Determining Strengths For
                  Public Keys Used For Exchanging Symmetric Keys",
                  BCP 86, RFC 3766, April 2004.

   [RFC3852]      Housley, R., "Cryptographic Message Syntax (CMS)",
                  RFC 3852, July 2004.

   [RFC4120]      Neuman, C., Yu, T., Hartman, S., and K. Raeburn, "The
                  Kerberos Network Authentication Service (V5)",
                  RFC 4120, July 2005.

   [RFC4556]      Zhu, L. and B. Tung, "Public Key Cryptography for
                  Initial Authentication in Kerberos (PKINIT)",
                  RFC 4556, June 2006.





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   [RFC5280]      Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
                  Housley, R., and W. Polk, "Internet X.509 Public Key
                  Infrastructure Certificate and Certificate Revocation
                  List (CRL) Profile", RFC 5280, May 2008.

   [X9.62]        ANSI, "Public Key Cryptography For The Financial
                  Services Industry: The Elliptic Curve Digital
                  Signature Algorithm (ECDSA)", ANSI X9.62, 2005.

   [X9.63]        ANSI, "Public Key Cryptography for the Financial
                  Services Industry: Key Agreement and Key Transport
                  using Elliptic Curve Cryptography", ANSI X9.63, 2001.

9.2.  Informative References

   [LENSTRA]      Lenstra, A. and E. Verheul, "Selecting Cryptographic
                  Key Sizes", Journal of Cryptography 14, 255-293, 2001.

   [SEC2]         Standards for Efficient Cryptography Group, "SEC 2 -
                  Recommended Elliptic Curve Domain Parameters",
                  Ver. 1.0, 2000, <http://www.secg.org>.






























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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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