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MSEC Working Group                                          A. Milne
Internet Draft                                              M. Blaser
Expires December 2005                                       D. Brown

                                                            L. Dondeti

                                                            June 2005

                         ECC Algorithms For MIKEY

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   This document proposes extensions to the authentication,
   encryption and digital signature methods described for use in
   MIKEY, employing elliptic-curve cryptography (ECC).  These
   extensions are defined to align MIKEY with other ECC
   implementations and standards.

   It should be noted that this document is not self-contained; it
   uses the notations and definitions of [MIKEY].


   Comments on this draft should be addressed to

   1.  Introduction

   This document describes additional algorithms for use in MIKEY.
   The document assumes that the reader is familiar with the MIKEY

   RFC 3830 [MIKEY] defines three methods of key exchange during
   establishment of a TGK.  The pre-shared key (MIKEY-PSA) and public
   key (MIKEY-RSA) methods are mandatory, while support for
   Diffie-Hellman (MIKEY-DHSIGN) is optional.  Elliptic curve
   Diffie-Hellman (ECDH) can be used in the MIKEY Diffie-Hellman
   method; we specify this mode in this document. In addition,
   the elliptic curve protocols MCMQV and ECIES can be
   used in MIKEY in exchanges similar to those of MIKEY-RSA; we
   specify these modes, and name them MIKEY-ECIES and
   MIKEY-ECMQV respectively.

   Implementations have shown that elliptic curve algorithms can
   significantly improve performance and security-per-bit over other
   recommended algorithms.  The purpose of this document is to expand
   the options available to implementers of MIKEY to take advantage of
   these benefits.

   In addition, elliptic curve algorithms are capable of providing
   security consistent with AES keys of 128, 192, and 256 bits without
   extensive growth in asymmetric key sizes. The following table, taken
   from [HOF] and [LEN], gives approximate comparable key sizes for

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   symmetric systems, ECC systems, and DH/DSA/RSA systems. The estimates
   are based on the running times of the best algorithms known today.

                 Symmetric   |  ECC    |  DH/DSA/RSA
                   80        |  163    |   1024
                  128        |  283    |   3072
                  192        |  409    |   7680
                  256        |  571    |  15360

                  Table 1: Comparable key sizes

   Thus, for example, when securing a 192-bit symmetric key, it is
   prudent to use either 409-bit ECC or 7680-bit DH/DSA/RSA. Of course
   it is possible to use shorter asymmetric keys, but it should be
   recognized in this case that the security of the system is likely
   dependent on the strength of the public-key algorithm and claims
   such as "this system is highly secure because it uses 192-bit
   encryption" are misleading.

   Section 2 below describes the use of elliptic curve methods for
   public-key authentication and encryption.  Section 3 describes
   the use of ECIES (The Elliptic Curve Integrated Encryption
   Scheme). Section 4 describes methods for Elliptic Curve Diffie-
   Hellman, including fifteen ECDH groups. Section 5 describes the
   MIKEY-MQV method.  Section 6 includes modifications to specific
   sections of [MIKEY].

   2. Use of EC methods with public-key encryption (MIKEY-RSA)

   MIKEY-RSA specifies the use of RSA PKCS#1, v1.5 as mandatory and RSA
   PSS as recommended.  This section describes how ECDSA signatures may
   be used for certificate signature and signature operations, enabling
   use of smaller signatures and certificates.  This section also
   describes the ECIES encryption/decryption scheme, for use with
   elliptic curve key pairs.

   2.1 ECDSA signature

   Section 6.5 of [MIKEY] describes the signature payload for the PK
   and DH exchange messages.  The ECDSA signature algorithm can be
   applied to allow shorter and more-efficient signatures.

   ECDSA signatures are detailed in ANSI X9.62 [X9.62].  Curve selection
   and other parameters will be defined by, and dependent on the
   certificate used.

   RFC3279 describes algorithms and identifiers for Internet X.509
   certificates and CRLs.  It includes ECC algorithms and identifiers.

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   MIKEY's public-key encryption method (MIKEY-RSA) uses public key
   methods securely to transmit keying material between communicating
   parties having previously acquired one another's public keys. The
   Elliptic Curve Integrated Encryption Scheme (ECIES) specifies how
   two communicating parties having previously acquired one another's
   public keys--assuming these are EC public keys--may use these keys
   to transmit encrypted and authenticated messages. This section
   therefore proposes how ECIES may be used in MIKEY. We call this
   scheme MIKEY-ECIES.

   We propose that ECIES be used as follows:

      1. The ephemeral public key transmitted by the initiator,
         is transmitted in an ECCPT payload (see section 5.1)
         preceding the KEMAC payload.
      2. The ciphertext and message digest required under ECIES
         are transmitted in the KEMAC payload, as in other forms
         of the MIKEY protocol.
      3. The encryption key and HMAC key in use in the KEMAC are those
         extracted from the shared key derived using ECIES.
      4. The PKE payload is not used.

   Note that this differs from the 'envelope key' method used in the
   MIKEY-RSA form of the protocol. ECIES, however, uses a symmetric
   encapsulation algorithm, so encrypting an envelope key (to be
   used with another symmetric method to decrypt the actual payload)
   would be redundant.

   Note also that the derived ECIES key can be used as an input for the
   key generation algorithm described in section 4.1.4 of RFC 3830, in
   identical fashion as is the envelope key used in the MIKEY-RSA

   A MIKEY-ECIES exchange

   Initiator                                           Responder
   ---------                                           ---------

   HDR, T, RAND, [IDi|CERTi], [IDr], {SP},
        ECCPT, KEMAC, [CHASH], SIGNi         --->

                                                      R_MESSAGE =

                                            [<---]    HDR, T, [IDr], V

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   Note also that the derived key generated may also be cached for the
   lifetime of a CSB, at the direction of the Initiator, and used as a
   preshared key, as described for the envelope key in RFC 3830, section 

   ECIES options

   IEEE 1363A describes a number of options for ECIES. We recommend that
   in MIKEY-ECIES, the following options be understood as given:

      -- the KDF in use for the generation of the ephemeral key pairs
           shall be ECSVDP-DHC, without compatibility for the
           corresponding -DH primitive

      -- DHAES mode shall not be used.

   4. Use of EC methods with Diffie-Hellman key exchange (MIKEY-DHSIGN)

   The MIKEY-DHSIGN key exchange method is described in Section 3.3 of
   [MIKEY].  Section 4.2.7 of [MIKEY] specifies the use of OAKLEY group
   5 as mandatory and groups 1 and 2 as optional.  However,
   implementations have shown that users of elliptic curve groups can
   significantly improve performance and security by using groups other
   than the Oakley Groups 1, 2, or 5.

   The DH data payload specified in Section 6.4 of [MIKEY] can be used
   without modification.  The data in the KEMAC payload when using
   these groups is the octet string representation specified in ANSI
   X9.62 [X9.62], ANSI X9.63 [X9.63], FIPS 186-2 [FIPS 186-2], and
   IEEE P1363 of the point on the curve chosen by taking the randomly
   chosen secret Ka and computing Ka*P, where * is the repetition of the
   group addition and double operations.

   An updated DH-Group table (as shown in Section 6.4 of [MIKEY]) will
   be specified upon assignment of IANA numbers for the groups described
   in section 8. See also the section "IANA considerations" in this

   5. Using ECMQV in MIKEY (MIKEY-MQV)

   MQV is a protocol primitive equivalent to simultaneous Diffie-Hellman
   key exchange and digital signature authentication, achievable in a
   single transmission.  The S_i and S_r values function as implicit
   signatures proving possession of the private key corresponding to the
   communicating party's known public key.

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   ECMQV (Elliptic Curve Menezes-Qu-Vanstone) is a three-pass or 1-pass
   protocol that has been standardized in ANSI X9.63. Both modes of
   ECMQV provide mutual authentication between the communicating parties
   and key establishment for the secure transport of data; the 1-pass
   version is thus particularly attractive for MIKEY, as an alternative
   method of establishing a secure channel for the transport of the TGK.
   In this draft, we propose a fourth mode in MIKEY, called MIKEY-MQV,
   in which ECMQV is used in this fashion.

   A MIKEY-MQV exchange proceeds in similar fashion to the MIKEY-RSA
   exchange; the PKE is absent, and an ECCPT payload (see section 5.1)
   MUST precede the KEMAC payload in the intiator's first message:

   Initiator                                    Responder
   ---------                                    ---------

   HDR, T, RAND, [IDi|CERTi], [IDr], {SP},
       ECCPT, KEMAC, [CHASH], SIGNi         --->

   ... the responder's acknowledgement, as in MIKEY-RSA, is optional,
   and the initiator indicates whether a response is required. If
   present, the acknowledgement is of the form:

                                                      R_MESSAGE =
                                            [<---]    HDR, T, [IDr], V

   The ECCPT payload carries Q_(e,I) as per the nomenclature of ANSI
   X9.63 -- the ephemeral public key contributed by the initiator.

   The encr_key and auth_key used in forming the KEMAC are the
   encryption and authentication keys extracted from the derived key
   arrived at via MQV.

   1-pass ECMQV algorithm steps

   1-pass ECMQV is described in detail in ANSI X9.63-2001; for a
   detailed specification for implementation purposes, see that
   document. The following discussion is provided here for information
   purposes only, to clarify the mechanism, and to ease mapping it to
   the protocol components in this draft proposal.

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   Note that 1-pass MQV differs from 3-pass MQV in that only three
   key pairs are used as inputs: the initiator's public, private key
   pair, the respondent's public, private key pair, and the ephemeral
   public, private key pair contributed by the initiator. The
   respondent's public, private key pair is used twice--effectively
   replacing the ephemeral key pair contributed by the respondent in
   the 3-pass method.

   Initiator transformation

      1. Initiator selects an ephemeral private key k_A from the
         set {1..n-1}, where n is the order of the base point P
         for the curve in use. Initiator computes the corresponding
         ephemeral public key R_A = (k_A)P, and sends R_A to the
         respondent. The ephemeral public key R_A derived is the
         value Q_(e,I) in the protocol described above. The
         selection of k_A and the generation of R_A from it are
         covered in detail in X9.63-2001 section 5.2.1--Key Pair
         Generation Primitive.
      2. Initiator calculates the shared secret value z as follows
         (see X9.63-2001 section 5.5)--
           2a. Initiator uses their own private and public key,
               and the ephemeral private and public key they
               generated in step 1 as inputs (d_1, Q_1) and
               (d_2, Q_2) respectively.
           2b. Initiator uses the respondent's public key for
               the values Q_3 and Q_4.
           2c. Using the associate value function avf (see
               X9.63-2001 section 5.6.1), and the values d_1,
               d_2 and Q_2 as above (their own private key, and
               the ephemeral key pair private and public values),
               the Initiator calculates the implicit signature
               S_i = d_2 + (avf(Q_2) x d_1) mod n.
           2d. Using the associate value function avf, the
               signature just calculated, the system cofactor h,
               and the respondent's public key, the Initiator
               finds the EC point
               P = h x S_i x (Q_4 + (avf(Q_4) x Q_3)).
           2e. Initiator verifies that P != 0.
           2f. Initiator sets z = x_P, where x_P is the
               x-coordinate of P.
      3. Initiator converts z to bit string Z, using the convention
         specified in X9.63-2001 section 4.3.3.
      4. Initiator uses the key derivation function described in
         X9.63-2001 section 5.6.3 with the hash function given in
         table MQV_PARAMS to derive the keying data; the length of
         the key to be generated is also given in MQV_PARAMS.

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   Respondent transformation

   The respondent transformation is parallel to the initiator
   transformation, except that the respondent does not generate an
   ephemeral key pair, and the inputs d_1, Q_1, d_2, Q_2, Q_3 and Q_4
   come from different sources. Again, see X9.63-2001 section 5.5 for
   a detailed description appropriate for implementation purposes.

      1. Respondent verifies that Q_(e, U) is a valid key for the
         domain parameters (see X9.63-2001 section 5.2.2).
      2. Respondent calculates the shared secret value z as follows
         (see X9.63-2001 section 5.5)--
           2a. Respondent uses their own private and public key in
               step 1 as inputs for both (d_1, Q_1) and (d_2, Q_2).
           2b. Respondent uses the initiator's public key for the
               value Q_3, and the initiator's ephemeral public key
               for the value Q_4.
           2c. Using the associate value function avf (see X9.63-2001
               section 5.6.1), and the values d_1, d_2 and Q_2 as
               above (their own private key is both d_1 and d_2,
               while Q_2 is their public key), the Respondent
               calculates the implicit signature
               S_r = d_2 + (avf(Q_2) x d_1) mod n.
           2d. Using the associate value function avf, the signature
               just calculated, the system cofactor h, the respondent's
               public key, and the respondent's ephemeral public key,
               the Respondent finds the EC point
               P = h x S_r x (Q_4 + (avf(Q_4) x Q_3)).
           2e. Respondent verifies that P != 0.
           2f. Respondent sets z = x_P, where x_P is the x-coordinate
               of P.
      3. Respondent converts z to bit string Z, using the convention
         specified in X9.63-2001 section 4.3.3.
      4. Respondent uses the key derivation function described in
         X9.63-2001 section 5.6.3 with the hash function given in table
         MQV_PARAMS to derive the keying data; the length of the key to
         be generated is also given in MQV_PARAMS.

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   6. Additional MIKEY payloads

   6.1 ECCPT payload format

   The ECCPT payload provides for the transport of an EC point in the
   MIKEY-MQV and in the MIKEY-RSA exchange when ECIES is in use. It is
   of the form:

                        1                   2                   3
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
   ! Next payload  ! Point length                  !  Pt data ...  !
   ~                        Point data                             ~

   Point length is the length of the point data in *bits*.

   The point_data field is padded to end on a 32-bit boundary, and is
   encoded as per ANSI X9.63-2001 4.3.6. Uncompressed format MUST be
   supported. Hybrid and compressed formats MAY be supported.

   7. Multicast applications of MQV and ECIES

   Both MQV and ECDSA/ECIES may be used in multicast environments to
   establish a group TEK, in the same fashion as MIKEY-RSA.

   8. Recommended and optional domain parameter sets

   8.1 Available domain parameter sets

   Elliptic curve domain parameter sets available for use in this
   protocol for all methods employing EC primitives--and given here--
   are the fifteen groups that NIST recommends in FIPS 186-2
   [FIPS-186-2]. Detailed descriptions of the ECC groups recommended
   here for MIKEY are not given in this document but can be found
   elsewhere: All fifteen groups are detailed in each of FIPS 186-2
   [FIPS-186-2] and SEC 2 [SEC-2]. The elliptic curve domain parameters
   are uniquely identified in this document using the ASN.1 object
   identifiers provided in ANSI X9.63 [X9.63], which are also given in
   SEC2 [SEC-2].

   The fifteen groups proposed in this document use elliptic curves over
   GF[2^N] with N prime or over GF[P] with P prime.  Six of the groups
   proposed here have been assigned identifiers by IANA [IANA] and the
   remaining nine curves recommended by NIST might later be assigned
   identifiers by IANA. See also the 'IANA considerations' section.

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   IANA  Group Descriptions                X9.63 (and SEC 2) OID
   ----  -----------------------------     ---------------------

    NA   ECPRGF192Random   group P-192     secp192r1
    NA   EC2NGF163Random   group B-163     sect163r2
    7    EC2NGF163Koblitz  group K-163     sect163k1

    NA   ECPRGF224Random   group P-224     secp224r1
    NA   EC2NGF233Random   group B-233     sect233r1
    NA   EC2NGF233Koblitz  group K-233     sect233k1

    NA   ECPRGF256Random   group P-256     secp256r1
    8    EC2NGF283Random   group B-283     sect283r1
    9    EC2NGF283Koblitz  group K-283     sect283k1

    NA   ECPRGF384Random   group P-384     secp384r1
    10   EC2NGF409Random   group B-409     sect409r1
    11   EC2NGF409Koblitz  group K-409     sect409k1

    NA   ECPRGF521Random   group P-521     secp521r1
    12   EC2NGF571Random   group B-571     sect571r1
    13   EC2NGF571Koblitz  group K-571     sect571k1

   Three curves are defined at each strength - two curves chosen
   verifiably at random (as defined in ANSI [X9.62]), one over a
   binary field and another over a prime field, and a Koblitz curve
   over a binary field that, which enables especially efficient
   implementations due to the special structure of the curve [Kob, NSA].

   Note that the large number of proposed curves is for two reasons:
   Flexibility in implementation in using groups over prime fields
   (GF[p]) or binary fields (GF[2^N]), which have different
   characteristics; and to provide higher security strength capabilities
   for military-grade or future uses.  In ECDH, The 163-bit and 192-bit
   curves provide equivalent security strength to Oakley group 2; all
   other proposed curves offer significantly higher security strength
   equivalents than the three Diffie-Hellman groups included in [MIKEY].

   8.1 Recommended domain parameter sets

   It is RECOMMENDED that, for minimum interoperability, all
   implementations except those in highly constrained environments
   support use of the P-256 curve.

   It is RECOMMENDED that implementations in constrained environments
   support the K163 curve.

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   9. Security Considerations

   Since this document proposes new methods for use within MIKEY, many
   of the security considerations contained within RFC 3830 apply here
   as well.

   Some of the methods proposed in this document offer higher
   cryptographic strength than those proposed in RFC 3830. In
   particular, there are elliptic curves corresponding to each of
   the symmetric key  sizes 80 bits, 128 bits, 192 bits, and 256 bits.
   This allows the MIKEY  key exchange to offer security comparable
   with higher-strength AES  algorithms and SHA implementations.

   The methods proposed in this document are among those standardized
   by NIST in FIPS 186-2 [DSS], by the SECG in SEC2 [SEC2], and by ANSI
   in ANSI X9.62 [X9.62] and X9.63 [X9.63].

   Proper validation of elliptic curve public keys can help prevent the
   attacks described in [BMM].

   10. IANA Considerations

   This specification requires additional parameter sets be defined for
   use in MIKEY when elliptic curve cryptographic methods are used.
   These are listed in section 8.1.

   It is requested that these be added to the namespace for the
   DH-Group field in table 6.4 of RFC 3830, which that document requests
   shall be managed by the IANA.

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   12. References

   [IANA] Internet Assigned Numbers Authority. Attribute Assigned

   [IEEE 1363A-2004] Institute of Electrical and Electronics Engineers,
     IEEE P1363a, Draft Standard Specifications for Public Key
     Cryptography - Amendment 1: Additional Techniques.

   [KOB] N. Koblitz, CM curves with good cryptographic properties.
     Proceedings of Crypto '91. Pages 279-287. Springer-Verlag, 1992.

   [FIPS-186-2] U.S. Department of Commerce/National Institute of
     Standards and Technology. Digital Signature Standard (DSS), FIPS
     PUB 186-2, January 2000.

   [HOF] P. Hoffman and H. Orman, Determining strengths for public keys
     used for exchanging symmetric keys, Internet-draft. August 2000.

   [LEN] A. Lenstra and E. Verhuel, Selecting cryptographic key sizes.
     Available at: www.cryptosavvy.com.

   [MIKEY] [RFC-3830] J. Arkko, E. Carrara, F. Lindholm, M. Naslund,
     K. Norrman, MIKEY: Multimedia Internet KEYing, RFC 3830, August

   [NSA] J. Solinas, An improved algorithm for arithmetic on a family
     of elliptic curves, Proceedings of Crypto '97, Pages 357-371,
     Springer-Verlag, 1997.

   [RFC-3278] S. Blake-Wilson, D. Brown and P. Lambert, The Use of
     Elliptic Curve Cryptography (ECC) Algorithms in the Cryptographic
     Message Syntax (CMS), RFC 3279, April 2002.

   [RFC-3279] W. Polk, R. Housley, and L. Bassham, Algorithms and
     Identifiers for the Internet X.509 Public Key Infrastructure
     Certificate and Certificate Revocation List (CRL) Profile, RFC
     3279, April 2002.

   [SEC2] Standards for Efficient Cryptography Group. SEC 2 -
     Recommended Elliptic Curve Domain Parameters. Working Draft
     Ver. 1.0., 2000.  (http://www.secg.org)

   [X9.62] American National Standards Institute, ANSI X9.62-1998:
     Public Key Cryptography for the Financial Services Industry: The
     Elliptic Curve Digital Signature Algorithm.  January 1999.

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   [X9.63] American National Standards Institute. ANSI X9.63-2001,
     Public Key Cryptography for the Financial Services Industry: Key
     Agreement and Key Transport using Elliptic Curve Cryptography.
     November 2001.

   [HANKERSON] Hankerson, Darrel et al. "Guide to Elliptic Curve
     Cryptography". Springer-Verlag, 2004.

   Authors' Addresses

      Andrew Milne
      Certicom Corp.

      Mitch Blaser
      Certicom Corp.

      Daniel R. L. Brown
      Certicom Corp.

      Lakshminath Dondeti
      Qualcomm, Inc.

                              Expiry reminder

   This draft expires December 1, 2005.

   Copyright (C) The Internet Society (2005).  This document is subject
   to the rights, licenses and restrictions contained in BCP 78, and
   except as set forth therein, the authors retain all their rights.

   This document and the information contained herein are provided on an

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