INTERNET-DRAFT                       Simon Blake-Wilson, Certicom Corp
draft-ietf-smime-ecc-02.txt          Daniel R. L. Brown
draft-ietf-smime-ecc-01.txt Brown, Certicom Corp
14 July,
7 September, 2000                    Expires:  14 January 7 March, 2001

                      Use of ECC Algorithms in S/MIME CMS

Status of this Memo

   This document is an Internet-Draft and is in full conformance with
   all provisions of Section 10 of RFC2026.  Internet-Drafts are
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Abstract

   This document is the second draft of a profile for the
   incorporation of describes how to use Elliptic Curve Cryptography
   (ECC) public key public-key algorithms in the Cryptographic Message Syntax
   (CMS).  The ECC algorithms support the creation of digital
   signatures and the exchange of keys to encrypt or authenticate message
   content.  The definition of the algorithm processing is based on
   the ANSI X9.62 standard and the ANSI X9.63 draft, developed by the
   ANSI X9F1 working group.

Table of Contents

   1  Introduction ........................................ 3
      1.1  Requirement terminology ........................ 3
   2  EnvelopedData  SignedData using ECC ............................. ................................ 3
      2.1  EnvelopedData  SignedData using X9.63 ECDH ................. ECDSA ......................... 3
           2.1.1  Fields of KeyAgreeRecipientInfo type .... 4 the SignedData ................ 3
           2.1.2  Actions of the sending agent ............ 5 4
           2.1.3  Actions of the receiving agent .......... 4
   3  EnvelopedData using ECC ............................. 5
      2.2
      3.1  EnvelopedData using X9.63 modified ECDH ........ ....................... 5
           2.2.1
           3.1.1  Fields of KeyAgreeRecipientInfo type .... 6
           2.2.2 ......... 5
           3.1.2  Actions of the sending agent ............ 6
           2.2.3 5
           3.1.3  Actions of the receiving agent .......... 6
      2.3
      3.2  EnvelopedData using X9.63 1-Pass MQV ........... 7
           2.3.1 ECMQV ............... 6
           3.2.1  Fields of KeyAgreeRecipientInfo type .... 7
           2.3.2 ......... 6
           3.2.2  Actions of the sending agent ............ 9
           2.3.3 7
           3.2.3  Actions of the receiving agent .......... 9
           2.3.4  Originator certificates ................. 9
   3 8
   4  AuthenticatedData using X9.63 1-Pass MQV ECC ............ 10
      3.1  AuthenticatedData using X9.63 1-pass MQV ....... 11
           3.1.1  Fields of KeyAgreeRecipientInfo type .... 11
           3.1.2  Actions of the sending agent ............ 11
           3.1.3  Actions of the receiving agent .......... 11
           3.1.4  Originator certificates ................. 11
           3.1.5  Re-using a KEK with 1-Pass MQV .......... 11
   4  SignedData using ECC ................................ 12 8
      4.1  SignedData  AuthenticatedData using X9.62 ECDSA ................... 12 1-pass ECMQV ........... 8
           4.1.1  Fields of the SignedData type ........... 13 KeyAgreeRecipientInfo ......... 8
           4.1.2  Actions of the sending agent ............ 14 8
           4.1.3  Actions of the receiving agent .......... 14 9
   5  Recommended Elliptic Curves ......................... 9
   6  Certificates using ECC .............................. 15
   6  SMIMECapabilites 9
   7  SMIMECapabilities Attribute and ECC .................. 15
   7 ................. 9
   8  ASN.1 Types and Identifiers ......................... 15
      7.1  Object Syntax ........................................ 9
      8.1  Algorithm identifiers ............................. 15
      7.2  Type definitions ............................... 17
   8 .......................... 9
      8.2  Other syntax ................................... 11
   9  Summary ............................................. 17 12
   References ............................................. 18 12
   Security Considerations ................................ 19 14
   Intellectual Property Rights ........................... 19 14
   Acknowledgments ........................................ 20
   Author's 14
   Authors' Address ....................................... 20 14
   Full Copyright Statement ............................... 20 15

1  Introduction

   The Cryptographic Message Syntax (CMS) is cryptographic algorithm
   independent.  This specification defines a standard profile for the
   use of Elliptic Curve Cryptography (ECC) public key algorithms in
   the CMS.  The ECC algorithms are incorporated into the following
   CMS content types:

      - 'SignedData' to support ECC-based digital signature methods
        (ECDSA) to sign content

      - 'EnvelopedData' to support ECC public key ECC-based public-key agreement
        methods (ECDH and MQV) ECMQV) to generate pairwise key-encryption
        keys to encrypt content-encryption keys used for content
        encryption

      - 'AuthenticatedData' to support ECC based public key ECC-based public-key agreement
        methods (MQV) (ECMQV) to generate pairwise key-encryption keys to
        encrypt MAC keys used for content authentication

      - 'SignedData'

   Certification of EC public keys is also described to provide
   public-key distribution in support ECC based digital signature methods
        (ECDSA) to sign content

   Certificates based on ECC digital signatures (ECDSA) are also
   supported. of the specified techniques.

1.1  Requirements terminology

   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 RFC 2119
   [MUST].

2  EnvelopedData  SignedData using X9.63 ECC methods

   Elliptic curve cryptography (ECC) methods for key agreement are
   specified in [X9.63].

   This specification refers section describes how to [X9.63] for the
   cryptographic operations.

   Note: all the key agreement methods here use ECC algorithms with the key derivation
   method specified in [X9.63, Section 5.6.3]. CMS
   SignedData format to sign data.

2.1  EnvelopedData  SignedData using X9.63 (standard) ephemeral-static ECDH

   Ephemeral-static ECDSA

   This section describes how to use the Elliptic Curve Diffie-Hellman (ECDH) key agreement
   algorithm Digital
   Signature Algorithm (ECDSA) with SignedData.  ECDSA is the elliptic curve analog of the Diffie-Hellman key
   agreement algorithm specified jointly in the documents [CMS,
   Section 12.3.1.1] and [DH-X9.42].
   [X9.62].  The key agreement method is
   adapted to use the elliptic curve methods from [X9.63, Section
   6.2], the "1-Pass Diffie-Hellman scheme" using analog of the standard
   Diffie-Hellman primitive [X9.63, Section 5.4.1].
   Digital Signature Algorithm (DSA) [FIPS 186-2].

2.1.1  Fields of KeyAgreeRecipientInfo type the SignedData

   When using ephemeral-static ECDH, ECDSA with SignedData the EnvelopedData RecipientInfos
   KeyAgreementInfo fields must be used as follows:

      version is 3, of SignerInfo are as in [CMS, section 12.3.1.1].

      originator is
   [CMS], but with the following restrictions:

      digestAlgorithm contains the alternative originatorKey, as in [CMS, Section
      12.3.1.1].  The originatorKey algorithm fields identifier sha-1 (see
      Section 8.1) which identifies the SHA-1 hash algorithm.

      signatureAlgorithm contains the
      id-ecPublicKey object identifer with absent parameters.  The
      id-ecPublicKey object algorithm identifier is:

         id-ecPublicKey OBJECT IDENTIFIER ::= { iso(1) member-body(2)
            ansi-x9-62(10045) keyType(2) 1 }

      The originatorKey publicKey field
      ecdsa-with-SHA1 (see Section 8.1) which identifies the ECDSA
      signature algorithm.

      signature contains the sender's
      ephemeral EC public key as determined below (by methods DER encoding (as an octet string) of a
      value of
      [X9.63]).

      ukm may be absent, as in [CMS, Section 12.3.1.1], and has the
      same meaning as in [CMS].

      keyEncryptionAlgorithm is ASN.1 type ECDSA-Sig-Value (see Section
      7.2).

   When using ECDSA, the dhSinglePass-stdDH-sha1kdf-scheme
      algorithm identifier, with parameter SignedData certificates field KeyWrapAlgorithm
      present, with may include the follow value and syntax:

         dhSinglePass-stdDH-sha1kdf-scheme OBJECT IDENTIFIER ::= {
            iso(1) identified-organization(3) tc68(133) country(16)
            x9(840) x9-63(63) schemes(0) 2}

         KeyWrapAlgorithm ::= AlgorithmIdentifier

      The KeyWrapAlgorithm indicates
   certificate(s) for the symmetric encryption
      algorithm EC public key(s) used to encrypt in the CEK with generation of
   the KEK.

      recipientEncryptedKeys contains an encrypted (wrapped)
      content-encryption key and an identifier for each recipient, as ECDSA signatures in [CMS, section 12.3.1.1].

   The next two sections specify actions of sending and receiving
   agents to handle ephemeral-static ECDH SignedData.  ECC certificates are discussed
   in keyAgreeRecipientInfo
   fields of EnvelopedData. Section 6.

2.1.2  Actions of the sending agent

   When using ephemeral-static ECDH to generate EnvelopedData
   KeyAgreeRecipientInfo fields, ECDSA with SignedData, the sending agent selects groups of
   recipients with common EC domain parameters.  For each group, uses the
   message digest calculation process and signature generation process
   for SignedData that are specified in [CMS]. To sign data, the
   sending agent selects an ephemeral EC public key pair, as per uses the
   1-Pass Diffie-Hellman scheme initiator transformation, signature method specified in
   [X9.63, [X9.62,
   Section 6.2.1].  The sending agent determines an 5.3] with the following exceptions:

      - In [X9.62, Section 5.3.1], the integer
   "keydatalen" from key-size of "e" shall instead be
        determined by converting the KeyWrapAlgorithm and a bit octet string
   "SharedData" resulting from [CMS,
        Section 5.4] to an integer using the ukm field if present.  For each recipient data conversion method in
   the group, the
        [X9.62, Section 4.3.2].

   The sending agent completes encodes the X9.63 1-Pass
   Diffie-Hellman initiator transformation resulting signature using the selected
   ephemeral EC public key
   ECDSA-sig-value syntax and places it in the recipient's static EC public key
   (i.e. from a certificate) to obtain a bit string "KeyData". The
   "KeyData" bit string becomes the pairwise key-encryption key for
   the recipient. SignerInfo signature
   field.

2.1.3  Actions of the receiving agent

   The

   When using ECDSA with SignedData, the receiving agent uses the following
   message digest calculation process on an EnvelopedData
   to detect if ephemeral-static Diffie-Hellman is used to transfer
   the CEK to the receiving agent, and if so to compute the
   key-encryption key used to unwrap signature verification
   process for SignedData that are specified in [CMS].  To verify
   SignedData, the CEK.

   The receiving agent determines uses the bit string "SharedData" from signature verification
   method specified in [X9.62, Section 5.4] with the
   ukm field if present, and following
   exceptions:

      - In [X9.62, Section 5.4.1] the integer "keydatalen" "e" shall instead be
        determined by converting the octet string resulting from [CMS,
        Section 5.4] to an integer using the
   key-size of data conversion method in
        [X9.62, Section 4.3.2].

   In order to verify the KeyWrapAlgorithm and completes signature, the X9.63 1-Pass
   Diffie-Hellman responder transformation [X9.63, Section 6.2.2],
   using receiving agent retrieves the ephemeral EC public key
   integers r and s from the identified receiving
   agent's static EC public key, to obtain a bit string "KeyData".
   The "KeyData" bit string becomes SignerInfo signature field of the pairwise key-encryption key
   for
   received message.

3  EnvelopedData using ECC Algorithms

   This section describes how to use ECC algorithms with the receiving agent.

2.2 CMS
   EnvelopedData format.

3.1  EnvelopedData using X9.63 modified ephemeral-static (ephemeral-static) ECDH

   Modified

   This section describes how to use ephemeral-static Elliptic Curve
   Diffie-Hellman (ECDH) key agreement algorithm with EnvelopedData.
   Ephemeral-static ECDH is identical to standard specified in [X9.63].  Ephemeral-static
   ECDH except that a
   modified version of the Diffie-Hellman primitive [X9.63, Section
   5.4.2] is used. The modification involves multiplication by a
   cofactor.  A purpose of the modification is to prevent the
   small-subgroup attack [SSG].  To indicate that elliptic curve analog of the modified ephemeral-static
   Diffie-Hellman primitive is used, a different algorithm identifider
   for this key agreement algorithm is provided, as specified below.

2.2.1 jointly in the
   documents [CMS, Section 12.3.1.1] and [CMS-DH].

3.1.1  Fields of KeyAgreeRecipientInfo type

   When using modified ephemeral-static ECDH, ECDH with EnvelopedData, the EnvelopedData
   RecipientInfos KeyAgreementInfo fields of
   KeyAgreeRecipientInfo are the same as in those
   specified in Section 2.1.1 of this document, except:

      keyEncryptionAlgorithm [CMS], but with the following
   restrictions:

      originator is the
      dhSinglePass-cofactorDH-sha1kdf-scheme alternative originatorKey.  The originatorKey
      algorithm identifier, field contains the id-ecPublicKey object identifier
      (see Section 8.1) with parameter KeyWrapAlgorithm present, and NULL parameters.  The originatorKey
      publicKey field contains the following value
      and syntax:

         dhSinglePass-cofactorDH-sha1kdf-scheme OBJECT IDENTIFIER ::=
            { iso(1) identified-organization(3) tc68(133) country(16)
            x9(840) x9-63(63) schemes(0) 3}

         KeyWrapAlgorithm ::= AlgorithmIdentifier

2.2.2  Actions DER-encoding of the sending agent

   The actions a value of the sending agent are identical to
      ASN.1 type ECPoint (see Section 8.2).

      keyEncryptionAlgorithm contains the actions of
   sending agent using
      dhSinglePass-stdDH-sha1kdf-scheme object identifier (see Section
      7.1) if standard ephemeral-static ECDH specified above
   in Section 2.1.2, except that:

      - The sending agent uses the modified Diffie-Hellman primitive
        of [X9.63, Section 5.4.2] rather than is used, or the standard
        Diffie-Hellman primitive [X9.63,
      dhSinglePass-cofactorDH-sha1kdf-scheme object identifier (see
      Section 5.4.1].

   Note: modified and standard ephemeral-static ECDH can only be used
   within separate KeyAgreeRecipientInfo fields.

2.2.3  Actions of 8.1) if the receiving agent cofactor ECDH primitive is used.  The actions of
      parameter field contains KeyWrapAlgorithm.  The KeyWrapAlgorithm
      is the receiving agent are identical algorithm identifier that indicates the symmetric
      encryption algorithm used to encrypt the actions CEK with the KEK.

3.1.2  Actions of
   receiving the sending agent

   When using standard ephemeral-static ECDH specified
   above in Section 2.1.2, except that:

      - with EnvelopedData, the sending
   agent first obtains the recipient's EC public key and domain
   parameters (e.g. from the recipient's certificate).  The receiving sending
   agent uses then determines an integer "keydatalen" which is the modified Diffie-Hellman primitive
   key-size, in bits, of [X9.63, Section 5.4.2] rather than the standard
        Diffie-Hellman primitive [X9.63, Section 5.4.1].

2.3  EnvelopedData using X9.63 1-Pass MQV

   In [X9.63, Appendix H.4.5], 1-Pass MQV KeyWrapAlgorithm and a bit string
   "SharedData".  The "SharedData" bit string is suggested for
   store-and-forward applications such as e-mail. the DER encoding of
   ASN.1 type X9-63-CMS-SharedInfo (see Section 8.2).  The sending
   agent then performs the initiator transformation of the 1-Pass MQV key agreement method,
   Diffie-Hellman scheme specified in [X9.63, Section
   6.9], uses three EC public keys to generate keying data
   (i.e. pairwise key-encryption key).  The three keys are: a static
   recipient key, 6.2.1].  As a static originator key, and
   result the sending agent obtains:

      - an ephemeral originator
   key.

   The originator's static EC public key key, which is identified represented as a value of
        the type ECPoint (see Section 8.2), encapsulated in a bit
        string and placed in the KeyAgreeRecipientInfo originator
        field, usually by reference to and

      - a certificate.  The
   originator's ephemeral EC public shared secret bit string "KeyData" which is specified within used as the ukm field.
   The recipient's static EC public
        pairwise key-encryption key is identified according to
   [CMS], within a rid field.

2.3.1  Fields of for that recipient.

3.1.3  Actions of the receiving agent

   When using ephemeral-static ECDH with EnvelopedData, the receiving
   agent determines the bit string "SharedData" (see Section 8.2) and
   the integer "keydatalen" from the key-size, in bits, of the
   KeyWrapAlgorithm.  The receiving agent retrieves the ephemeral EC
   public key from the bit string KeyAgreeRecipientInfo originator,
   which an value of the type

   When ECPoint (see Section 8.2) encapsulated
   as a bit string.  The receiving agent completes the responder
   transformation of the 1-Pass Diffie-Hellman scheme [X9.63, Section
   6.2.2].  As a result the receiving agent obtains a shared secret
   bit string "KeyData" which is used as the pairwise key-encryption
   key to unwrap the CEK.

3.2  EnvelopedData using 1-Pass MQV, ECMQV

   This section describes how to use the 1-Pass elliptic curve MQV
   (ECMQV) key agreement algorithm with EnvelopedData.  1-Pass ECMQV
   is specified in [X9.63].  Like the KEA algorithm [CMS-KEA], 1-Pass
   ECMQV uses three key pairs: an ephemeral key pair, a static key
   pair of the sending agent, and a static key pair of the receiving
   agent.  An advantage of using 1-Pass ECMQV is that it may be used
   with both EnvelopedData and AuthenticatedData.

3.2.1  Fields of KeyAgreeRecipientInfo

   When using 1-Pass ECMQV with EnvelopedData RecipientInfos
   KeyAgreementInfo the fields are used as follows: of
   KeyAgreeRecipientInfo are:

      version is 3, as in [CMS, section 12.3.1.1]. 3

      originator identifies the static EC public key of the sender.
      It should be the one of the alternatives issuerAndSerialNumber
      or subjectKeyIdentifier and point to one of the sender's sending agent's
      certificates supplied in the EnvelopedData originatorInfo field.
      (If necessary, it may be the alternative originatorKey, as in
      [CMS, Section 12.3.1.1], and if so, the originatorKey algorithm
      field contains the id-ecPublicKey object identifer with absent
      parameters.  The id-ecPublicKey object identifier is:

         id-ecPublicKey OBJECT IDENTIFIER ::= { iso(1) member-body(2)
            ansi-x9-62(10045) keyType(2) 1 }

      The originatorKey publicKey field contains the sender's static
      EC public key.)

      ukm is present.  It identifies the ephemeral EC public key of
      the sender.  It may also identify some additional information
      for purposes similar to those specified in [CMS, Section
      12.3.1.1].  The ukm field contains an octet string which is
      the DER encoding of the following ASN.1 type MQVuserKeyingMaterial ::= SEQUENCE {
            ephemeralPublicKey OriginatorPublicKey,
            addedukm [0] EXPLICIT UserKeyingMaterial OPTIONAL }

         The MQVuserKeyingMaterial (see Section
      8.2).  The MQVuserKeyingMaterial ephemeralPublicKey algorithm
      field contains the id-ecPublicKey object identifer with absent
         parameters.  The id-ecPublicKey object identifier is:

            id-ecPublicKey OBJECT IDENTIFIER ::= { iso(1)
               member-body(2) ansi-x9-62(10045) keyType(2) 1 } (see Section
      8.1) with NULL parameters field.  The MQVuserKeyingMaterial
      ephemeralPublicKey publicKey field contains the sender's DER-encoding of
      the ASN.1 type ECPoint representing sending agent's ephemeral EC
      public key as determined
         below (by methods of [X9.63]). key.  The MQVuserKeyingMaterial addedukm field, if
      present, contains an octet string, whose
         meaning is similar to meaning string of additional user keying
      material of the ukm field in [CMS,
         Section 12.3.1.1]. sending agent.

      keyEncryptionAlgorithm is the mqvSinglePass-sha1kdf-scheme
      algorithm identifier, identifier (see Section 8.1), with parameter field KeyWrapAlgorithm
      present, with the following values and syntax:

         mqvSinglePass-sha1kdf-scheme OBJECT IDENTIFIER ::= { iso(1)
            identified-organization(3) tc68(133) country(16) x9(840)
            x9-63(63) schemes(0) 16}

         KeyWrapAlgorithm ::= AlgorithmIdentifier
      KeyWrapAlgorithm. The KeyWrapAlgorithm indicates the symmetric
      encryption algorithm used to encrypt the CEK with the KEK
      generated using the 1-Pass MQV ECMQV algorithm.

      recipientEncryptedKeys contains an encrypted (wrapped)
      content-encryption key and an identifier for each recipient, as
      in [CMS, section 12.3.1.1].

2.3.2

3.2.2  Actions of the sending agent

   When using 1-Pass MQV to generate EnvelopedData
   KeyAgreeRecipientInfo fields, the sending agent selects groups of
   recipients ECMQV with common EC domain parameters.  For each group, the
   sending agent selects an ephemeral EC public key pair, as per EnvelopedData, the
   1-Pass MQV scheme initiator transformation, specified in [X9.63,
   Section 6.9.1].  The sending agent specifies first
   obtains the ephemeral recipient's EC public key in and domain parameters,
   (e.g. from the KeyAgreeRecipientInfo ukm field, ASN.1 encoded
   within in recipient's certificate) and checks that the MQVuserKeyingMaterial ephemeralPublickey publicKey
   field. domain
   parameters are the same.  The sending agent then determines an
   integer "keydatalen" from
   key-size which is the key-size, in bits, of the
   KeyWrapAlgorithm and a bit string "SharedData" from
   the MQVuserKeyingMaterial addedukm field (if present) ASN.1 encoded
   in the ukm field.  For each recipient in the group, the (see Section 8.2).
   The sending agent completes then performs the 1-Pass MQV initiator transformation using of the
   selected ephemeral EC public key pair,
   1-Pass ECMQV scheme specified in [X9.63, Section 6.9.1].  As a
   result the static EC sending agent obtains

      - an ephemeral public keys
   (i.e. from certificates) key, which is represented as a value of the originator and the recipient, and
   the bit string "SharedData" if present, to obtain
        type ECPoint (see Section 8.2), encapsulated in a bit string
   "KeyData".  The string,
        placed in an MQVuserKeyingMaterial ephemeralPublicKey
        publicKey field (see Section 8.2), and

      - a shared secret bit string "KeyData" becomes which is used as the
        pairwise key-encryption key (KEK) for the that recipient.

2.3.3  Actions of  Parity bits
        are adjust according to the receiving agent key wrap algorithm.

   The receiving agent uses the following process on ephemeral public key may be re-used with an EnvelopedData
   to detect if 1-Pass MQV is used to agree on the pairwise KEK AuthenticatedData
   for greater efficiency.

3.2.3  Actions of the receiving agent, and if so to compute agent

   When using 1-Pass ECMQV with EnvelopedData, the pairwise KEK.

   The receiving agent
   determines the bit string "SharedData" from the
   ukm field if present, (see Section 8.2) and the
   integer "keydatalen" from the
   key-size key-size, in bits, of the KeyWrapAlgorithm and completes the 1-Pass MQV
   responder transformation [X9.63, Section 6.9.2], using
   KeyWrapAlgorithm.  The receiving agent then retrieves the static
   and ephemeral EC public key, keys of the identified originator, from the originator
   and ukm fields as described in Section 3.2.1, and its static EC
   public keys of key identified in the recipient and originator, rid field and checks that the bit string "SharedData" if
   present, to obtain a bit string "KeyData". domain
   parameters are the same.  The receiving agent then performs the
   responder transformation of the 1-Pass ECMQV scheme [X9.63, Section
   6.9.2].  As a result the receiving agent obtains a shared secret
   bit string "KeyData" becomes the which is used as the pairwise key-encryption
   key (KEK) for to unwrap the
   receiving agent.

2.3.4  Originator's certificates

   If some recipients do not have other means CEK.

4  AuthenticatedData using ECC

   This section describes how to obtain use ECC algorithms with the
   originator's certificate for a static EC public key used CMS
   AuthenticatedData format.  AuthenticatedData lacks non-repudiation,
   and so in 1-Pass
   MQV, then some instances is preferrable SignedData.  (For example,
   the originator's certificate containing sending agent may not want the originator
   static EC public key should message to be included in the EnvelopedData
   originatorInfo field.

3 authenticated when
   forwarded.)

4.1  AuthenticatedData using ECC

   The 1-pass ECMQV

   This section describes how to use the 1-Pass elliptic curve MQV scheme of [X9.63] has been selected
   (ECMQV) key agreement algorithm with AuthenticatedData.  1-Pass
   ECMQV is specified in this document
   for AuthenticatedData [X9.63].  An advantage of using ECC because it has security attributes 1-Pass ECMQV
   is that are appropriate for the AuthenticatedData CMS type.

   Note: in general, pure 'ephemeral-static' key agreement methods are
   not suitable for AuthenticatedData because the originator's key is
   ephemeral and therefore not authenticated.

   Note: both SignedData and AuthenticatedData provide assurance to
   the receiving agent that the content data originated from the
   purported originator and the content was in no way modified.
   However, SignedData and AuthenticatedData differ in some important
   respects:

      1.  In AuthenticatedData the assurance of the content origin and
      integrity is only provided to the specific recipients of the
      AuthenticatedData.  In SignedData, the assurance of content
      origin and integrity is provided to potentially everyone.

      2.  In AuthenticatedData, the sending agent and receiving agent
      are equally capable producing any given AuthenticatedData.  In
      SignedData, only the sending agent is capable of producing the
      SignedData.

   Careful consideration should it may be applied to the choice of using
   AuthenticatedData or SignedData because of the these differences.
   In particular, in AuthenticatedData the originator has less
   'commitment' to the content than SignedData because
   AuthenticatedData does not have the non-repudiative feature of
   SignedData.

3.1  AuthenticatedData using 1-pass MQV

   In general, using 1-Pass MQV in AuthenticatedData is similar to
   using 1-Pass MQV in used with both EnvelopedData (see Section 2.3 of this
   document).  Further details are provided in Sections 3.1.1 to
   3.1.4.

   However, 1-Pass MQV, AuthenticatedData and EnvelopedData can be use
   together more efficiently by the re-using pairwise key-encryption
   keys.  A method to do this is specified in Section 3.1.5.

3.1.1
   AuthenticatedData.

4.1.1  Fields of the KeyAgreementInfo type KeyAgreeRecipientInfo

   The AuthenticatedData KeyAgreeRecipientInfo fields are used in the
   same manner as the fields for the corresponding EnvelopedData
   KeyAgreeRecipeintInfo
   KeyAgreeRecipientInfo fields of Section 2.3.1 3.2.1 of this document.

   Note: the originator field should be one of the alternatives
   issuerAndSerialNumber or subjectKeyIdentifier.  If it is necessary
   to use the originatorKey alternative, the recipients should have
   other means (i.e. without certificates) to authenticate the
   originator's static key.

3.1.2

4.1.2  Actions of the sending agent

   The sending agent may use uses the same actions as for EnvelopedData
   with 1-Pass MQV, ECMQV, as specified in Section 2.3.2 3.2.2 of this document.

3.1.3  Actions of the receiving agent

   The receiving agent ephemeral public key may use the same actions as for EnvelopedData be re-used with 1-Pass MQV, as specified in Section 2.3.3 of this document.

3.1.4  Originator certificates

   If some recipients do not have other means to obtain the
   originator's certificate an EnvelopedData for a static EC public key used in 1-Pass
   MQV, then the originator's certificate certifying the originator
   static EC public key should be included in the AuthenticatedData
   originatorInfo field.

   For recipients that do not have other measn to obtain all the issue
   certificates necessary to authenticate the originator's static EC
   public key, then the necessary certificates (i.e. CA
   cross-certifcates) may be included in the AuthenticatedData
   originatorInfo field.

3.1.5  Re-using a KEK with 1-Pass MQV

   When using 1-Pass MQV for an AuthenticatedData whose content is an
   EnvelopedData, or for an AuthenticatedData which is the content is
   an EnvelopedData, the KEKRecipientInfo type of [CMS] is an
   efficient way to re-use a 1-Pass MQV generated pairwise KEK from
   the EnvelopedData.  Re-use of the EnvelopedData KEK helps to reduce
   the total length of the ASN.1 encoding of the AuthenticatedData and
   the total number of public key cryptographic operations performed
   by both sending agents and receiving agents.

   The KEKRecipientInfo encryptedKey field contains the wrapped "MAC"
   key, encrypted with the previously generated KEK using 1-Pass MQV.
   Generally, the pairwise KEK will have been generated within an
   EnvelopedData.  The KEKRecipientInfo KEKIdentifier keyIdentifier
   field may be used to identify the re-used secret pairwise KEK
   by providing an octet encoding of the originator's ephemeral EC
   public key used in a 1-Pass MQV to to generate the KEK.

   The KEKIdentifier other field may be absent, if it is certain that
   the KEK is unambiguously identified.  If the KEKIdentifier
   keyIdentifier field alone is insufficient to identify the KEK
   (perhaps because the receiving agent supports other methods that
   use KEKReicipientInfo) then the KEKIdentifier other keyAttrId
   field may be object identifier mqvSinglePass-sha1kdf-scheme (see
   Section 2.3.1 of this document).

   Note: if the content of the AuthenticatedData is an EnvelopedData,
   then the KeyAgreeRecipientInfo fields of the EnvelopedData are in
   plaintext and therefore, the KEK can be computed before the
   EnvelopedData is decrypted or encrypted.  If the content of an
   EnvelopedData is an AuthenticatedData the KEK will be computed
   before the AuthenticatedData is encrypted or decrypted.  In the
   either case, both the sending agent and receiving agent are able to
   determine the necessary KEK from the EnvelopedData.

4  SignedData using ECC

   An elliptic curve cryptography (ECC) method for signing is
   specified in [X9.62].  In a single SignedData type [CMS] many
   signing algorithms may be used but within each SignerInfo field
   only one signing algorithm can be used.

4.1  SignedData using X9.62 ECDSA

   The Elliptic Curve Digital Signature Algorithm (ECDSA) is specified
   in [X9.62].  The method is the elliptic curve analog of the [X9.30]
   Digital Signature Algorithm (DSA).  In [CMS] the meanings of the
   fields of SignedData are specified, the actions of the sending
   agent to generate SignedData are specified and the actions of the
   receiving agent to process SignedData are specified.  In [CMS], the
   specificiations are algorithm independent.  The following
   subsections provide additional details about the SignedData fields
   and actions of S/MIME agents when [X9.62] ECDSA is being used with
   SignedData.

4.1.1  Fields of the SignedData type

   When using [X9.62] ECDSA in an SignedData SignerInfo type the
   fields are as in [CMS], but with the following restrictions.

      digestAlgorithm is the following algorithm identifier for SHA-1:

         sha-1 OBJECT IDENTIFIER ::= { iso(1) identified-organization(3)
            oiw(14) secsig(3) algorithm(2) 26 }

      signatureAlgorithm is an algorithm identifer with parameters
      field absent that identifies the ECDSA signature algorithm with
      the object identifier:

         ecdsa-with-SHA1 OBJECT IDENTIFIER ::= { iso(1) member-body(2)
            us(840) 10045 signatures(4) 1 }

      signature is the DER encoding (as an octet string) of a value of
      the [X9.62] ASN.1 type:

         ECDSA-Sig-Value ::= SEQUENCE {
            r INTEGER,
            s INTEGER }

      where the integers r and s
   greater efficiency.

   Note: if there are caculated according to [X9.62,
      Section 5.3] using the signer's private key except that the
      integer "e" is the result of the SignedData message digest
      specified in [CMS] converted from an octet string to an intger
      (i.e. not the result of [X9.63, Section 5.3.1]).

   When using [X9.62] ECDSA the SignedData certificates field may
   include the certificates for the EC public keys used in generation
   of ECDSA signatures in the SignedData.  If it is expected that multiple recipients have alternative means of obtaining the certain
   certificates necessary to authenticate the EC public keys used for
   signing, then such certificates may be omitted from the SignedData
   certificates field.  All certificates necessary for the
   authentication of the EC public keys using for signing for which it
   is not expected that the recipients have alternative means of
   obtaining should be included in the SignedData certificates field.

4.1.2  Actions of the sending agent

   The sending agent uses the message digest calculation process and
   signature generation process for SignedData that are specified in
   [CMS].  The sending agent follows the actions for ECDSA signature
   generation specified in [X9.62, Section 5.3] with the following
   exceptions:

      - In [X9.62, Section 5.3.1], the integer "e" shall instead
        be determined by converting the octet string resulting from
        [CMS, Section 5.4] to an integer using the data conversion
        method in [X9.62, Section 4.3.2].

   The sending agent uses the encoding process specified [X9.62,
   Section 6.5] to convert (encode) the ECDSA signature as an octet
   string.  This octet string is the value of attack is possible
   where one recipient modifies the SignerInfo
   SignatureValue field.  The content without other recipients
   noticing [BON].  A sending agent uses DER encoding rules
   and includes the entire encoding of the ASN.1 type ECDSA-Sig-Value
   (see above and [X9.62]) including the tag and length octets in the
   octet string SignerInfo SignatureValue. who is concerned with such an
   attack should use a separate AuthenticatedData for each recipient.

4.1.3  Actions of the receiving agent

   The receiving agent uses the message digest calculation process
   and signature verification process for SignedData that are
   specified in [CMS].  The receiving agent follows the same actions as for ECDSA signature verification EnvelopedData
   with 1-Pass ECMQV, as specified in [X9.62, Section 5.4]
   with the following exceptions:

      - In [X9.62, Section 5.4.1] the integer "e" shall instead be
        determined by converting the octet string resulting from [CMS, Section 5.4] to an integer using the data conversion method 3.2.3 of this document.

   Note: see Note in
        [X9.62, Section 4.3.2].

   The receiving agent uses 4.1.2.

5  Recommended Elliptic Curves

   It is strongly recommended that agents use the encoding process specified in elliptic curve
   domain parameters recommended by ANSI [X9.62,
   Section 6.5] to convert (decode) the octet string value of the
   SignerInfo SignatureValue field to the [X9.62] signature.  The
   receiving agent uses DER decoding rules.

5 X9.63], NIST [REC-EC]
   and SECG [SEC3].

6  Certificates using ECC

   Internet X.509 certificates [PKI] may be used in conjunction with
   this specification to distribute agents' public keys.  The use of a certificates with
   ECC algorithms and keys within X.509 certificates is specified in [EPKIX].
   Further information on the use ECC with certificates is given
   [PKI-ALG].  More details can be found in
   [SECG-WG-EC].

6 [SEC3].

7  SMIMECapabilities Attribute and ECC

   A sending agent may choose to announce to receiving agents that it
   supports one or more of the ECC algorithms in this document by
   using the SMIMECapabilities signed attribute as specified in [MSG, Section 2.5.2].

   The SMIMECapability value to indicate support for the ECDSA
   signature algorithm is the SEQUENCE with the capabilityID field
   containing the object identifier ecdsa-with-SHA1 with NULL
   parameters.

   The SMIMECapability capabilityID object identifiers for the
   supported key agreement algorithms in this document are
   dhSinglePass-stdDH-sha1kdf-scheme,
   dhSinglePass-cofactorDH-sha1kdf-scheme, and
   mqvSinglePass-sha1kdf-scheme.  For each of these SMIMECapability
   SEQUENCEs the parameters field is present and indicates the
   supported key-encryption algorithm with the KeyWrapAlgorithm
   algorithm identifier.

   The SMIMECapability value to indicate support for the ECDSA
   signature algorithm is the SEQUENCE with the capabilityID field
   containing the object identifier ecdsa-with-SHA1 and the parameters
   field absent.

7 identifier.

8  ASN.1 Types and Identifiers Syntax

   The ASN.1 types and object identifiers syntax that are is used in this document are is gathered together
   in this section for reference purposes.

7.1  Object

8.1  Algorithm identifiers

   The object algorithm identifiers used in this document are taken from [CMS],
   [X9.63]
   [X9.62] and [X9.62]. [X9.63].

   The following object identifiers indicate identifier indicates the key agreement
   algorithms hash algorithm used
   in this document:

      dhSinglePass-stdDH-sha1kdf-scheme

      sha-1 OBJECT IDENTIFIER ::= { iso(1) identified-organization(3) tc68(133) country(16) x9(840)
         x9-63(63) schemes(0) 2}

      dhSinglePass-cofactorDH-sha1kdf-scheme
         oiw(14) secsig(3) algorithm(2) 26 }

   The following object identifier is used in this document to
   indicate an elliptic curve public key:

      id-ecPublicKey OBJECT IDENTIFIER ::= {
         iso(1) identified-organization(3) tc68(133) country(16)
         x9(840) x9-63(63) schemes(0) 3}

      mqvSinglePass-sha1kdf-scheme ansi-x9-62 keyType(2) 1 }

   where

      ansi-x9-62 OBJECT IDENTIFIER ::= { iso(1)
         identified-organization(3) tc68(133) country(16) x9(840)
         x9-63(63) schemes(0) 16} member-body(2) us(840)
         10045 }

   When the object identifier id-ecPublicKey is used here with an
   algorithm identifier, the associated parameters contain NULL.

   The following object identifier indicates the digital signature
   algorithm used in this document:

      ecdsa-with-SHA1 OBJECT IDENTIFIER ::= { iso(1) member-body(2)
         us(840) 10045 ansi-x9-62 signatures(4)
         1 }

   When the object identifier ecdsa-with-SHA1 is used within an
   algorithm identifier, the associated parameters field contains
   NULL.

   The following object identifier indicates identifiers indicate the hash algorithm key agreement
   algorithms used in this document:

      sha-1

      dhSinglePass-stdDH-sha1kdf-scheme OBJECT IDENTIFIER ::= { iso(1) identified-organization(3)
         oiw(14) secsig(3) algorithm(2) 26 }

   The following object identifier is used in this document to
   indicate an elliptic curve public key:

      id-ecPublicKey
         x9-63-scheme 2}

      dhSinglePass-cofactorDH-sha1kdf-scheme OBJECT IDENTIFIER ::= {
         x9-63-scheme 3}

      mqvSinglePass-sha1kdf-scheme OBJECT IDENTIFIER ::= {
         x9-63-scheme 16}

   where

      x9-63-scheme OBJECT IDENTIFIER ::= { iso(1) member-body(2)
         ansi-x9-62(10045) keyType(2) 1
         identified-organization(3) tc68(133) country(16) x9(840)
         x9-63(63) schemes(0) }

7.2  Type definitions

   When the object identifiers are used here within an algorithm
   identifier, the associated parameters field contains the CMS
   KeyWrapAlgorithm algorithm identifier.

8.2  Other syntax

   The following ASN.1 type defintions additional syntax is used here.

   When using ECDSA with SignedData, ECDSA signatures are used. encoded
   using the type:

      ECDSA-Sig-Value ::= SEQUENCE {
         r INTEGER,
         s INTEGER }

   ECDSA-Sig-Value is specified in [X9.62].  Within CMS,
   ECDSA-Sig-Value is DER-encoded and placed within a signature field
   of SignedData.

   When using ECDH and ECMQV with EnvelopedData and AuthenticatedData,
   ephemeral and static public keys are encoded using the type
   ECPoint.

      ECPoint ::= OCTET STRING

   When using ECQMV with EnvelopedData and AuthenticatedData, the
   sending agent's ephemeral public key and additional keying material
   are encoded using the type:

      MQVuserKeyingMaterial ::= SEQUENCE {
         ephemeralPublicKey OriginatorPublicKey,
         addedukm [0] EXPLICIT UserKeyingMaterial OPTIONAL  }

   The former is taken from [X9.62].  In this document, DER encodings
   as octet strings of values of ECPoint syntax in used to represent the two above ASN.1 types
   ECDSA-Sig-Value ephemeral public key
   and placed in the ephemeralPublicKey field.  The additional user
   keying material is place in the addedukm field.  Then the
   MQVuserKeyingMaterial value is DER-encoded and placed within in a
   ukm field of EnvelopedData or AuthenticatedData.

   When using ECDH or ECMQV with EnvelopedData or AuthenticatedData,
   the key-encryption keys are derived by using the type:

      ECC-CMS-SharedInfo ::= SEQUENCE {
         keyInfo AlgorithmIdentifier,
         entityUInfo [0] EXPLICIT OCTET STRING OPTIONAL,
         suppPubInfo [2] EXPLICIT OCTET STRING   }

   The fields of ECC-63-CMS-SharedInfo are used as values follows:

      keyInfo contains the object identifier of the key-encryption
      algorithm (used to wrap the CEK) and NULL parameters.

      entityUInfo optionally contains additional keying material
      supplied by the sending agent.  When used with ECDH and CMS, the
      entityUInfo field contains the octet string ASN.1 types from [CMS].  An encoding of
   ECDSA-Sig-Value is ukm.  When used as with
      ECMQV and CMS, the value entityUInfo contains the octet string
      addedukm (encoded in MQVuserKeyingMaterial).

      suppPubInfo contains the length of the generated KEK, in bits,
      represented as a SignedData SignerInfo
   SignatureValue and an encoding of MQVuserKeyingMaterial 32 bit number, as in [CMS-DH].  (E.g. for 3DES
      it would be 00 00 00 c0.)

   Within CMS, ECC-CMS-SharedInfo is DER-encoded and used as input to
   the key derivation function, as specified in [X9.63].  Note that
   ECC-CMS-SharedInfo differs from the OtherInfo specified in
   [CMS-DH].  Here a counter value of EnvelopedData KeyAgreeRecipeintInfo UserKeyingMaterial
   or AuthenticatedData KeyAgreeRecipeintInfo UserKeyingMaterial.

8 is not included in the keyInfo
   field because the key derivation function specified in [X9.63]
   ensures that sufficient keying data is provided.

9  Summary

   This document specifies how to use ECC methods algorithms with the S/MIME CMS
   type.  The most notable advantage
   CMS.  Use of ECC methods over integer
   arithmetic based methods (Diffie-Hellman, DSA and RSA) is the
   shorter length of cryptographic overhead algorithm within CMS can result in signatures,
   certificates, encrypted reduced
   processing requirements for S/MIME agents, and authenticated messages..

   This document specifies a cryptographic method to be used with the
   [CMS] content type AuthenticatedData. reduced bandwidth
   for CMS messages.

References

   [X9.42]      ANSI X9.42-xxxx, "Agreement Of Symmetric Keys Using
                Diffie-Hellman and MQV Algorithms", American National
                Standards Institute, 2000, Working draft.

   [X9.62]      ANSI X9.62-1999, "Public Key Cryptography For The cryptographic method is
   X9.63 1-Pass MQV scheme.
                Financial Services Industry: The AuthenticateData type achieves
   authentication without 'non-repudiation'.  For certain kinds of
   data, AuthenticatedData may be preferrable to SignedData.

References

   [CMS]       R. Housley, "Cryptographic Message Syntax", RFC 2630,
               June Elliptic Curve
                Digital Signature Algorithm (ECDSA)", Americal
                National Standards Institute, 1999.

   [DH-X9.42]  E. Rescorla, "Diffie-Hellman

   [X9.63]      ANSI X9.63-xzxx, "Public Key Cryptography For The
                Financial Services Industry: Key Agreement Method", RFC
               2631, June 1999.

   [EPKIX] and Key
                Transport Using Elliptic Curve Cryptography", American
                National Standards Institute, 1999, Working draft.

   [PKI-ALG]    L. Bassham Bassham, R. Housley and D. Johnson, W. Polk, "Internet X.509
                Public Key Infrastructure Representation of Elliptic Curve Digital
               Signature Algorithm (ECDSA) Public
                Keys and Digital Signatures in Internet X.509 Public
                Key Infrastructure Certificates", PKIX Working Group
                Internet-Draft, October, 1999. July 2000.

   [BON]        D. Boneh, "The Security of Multicast MAC",
                Presentation at Selected Areas of Cryptography 2000,
                Center for Applied Cryptographic Research, University
                of Waterloo, 2000

   [MUST]       S. Bradner, "Key Words for Use in RFCs to Indicate
                Requirement Levels", RFC 2119, March 1997.

   [FIPS-180]  Federal Information Processing Standards Publication
               (FIPS PUB)   FIPS 180-1, "Secure Hash Standard", 1995 April
               17.

   [FIPS-186]  Federal Information Processing National Institute
                of Standards Publication
               (FIPS PUB) 186, and Technology, April 17, 1995.

   [FIPS-186-2] FIPS 186-2, "Digital Signature Standard", 1994 May
               19.

   [GEC1]      Certicom Research, "Guidelines for Efficinet
               Cryptography", GEC1, February, 1999.

   [KEA]       J. Pawling, "CMS KEA National
                Institute of Standards and SKIPJACK Conventions", S/MIME Technology, 15 February
                2000.

   [PKI]        W. Ford, R. Housley, W. Polk and D. Solo, "Internet X.509
                Public Key Infrastructure Certificate and CRL
                Profile", PKIX Working Group Internet-Draft, December, July
                2000.

   [CMS]        R. Housley, "Cryptographic Message Syntax", RFC 2630,
                June 1999.

   [LAW98]

   [IEEE1363]   IEEE P1363, "Standard Specifications for Public Key
                Cryptography", Institute of Electrical and Electronics
                Engineers, 2000.

   [LMQSV]      L. Law, A. Menezes, M. Qu, J. Solinas and S. Vanstone,
                "An efficient protocol for authenticated key agreement",
                Technical report CORR 98-05, University of Waterloo,
                1998.

   [LL97]      C.H. Lim and P.J. Lee, "A key recovery attack on
               discrete log-based schemes using a prime order
               subgroup", B.S.  Kaliski, Jr., editor, Advances in
               Cryptology - Crypto '97, Lecture Notes in Computer
               Science, vol. 1295, 1997, Springer-Verlag, pp. 249-263.

   [MSG]       B. Ramsdell, "S/MIME Version 3 Message Specification",
               RFC 2633, June 1999.

   [MUST]      S. Bradner, "Key Words for Use in RFCs to Indicate
               Requirement Levels", RFC 2119, March 1997.

   [NIST-ECC]

   [REC-EC]     National Institute for of Standards and Technology,
                "Recommended Elliptic Curves for Federal Government
                Use", July 1999,
               <http://csrc.nist.gov/encryption/NISTReCur.pdf>

   [IEEE1363]  IEEE, "Standard Specifications for Public Key
               Cryptography", IEEE 1363-2000 Specification, 2000,
               Annex D.

   [SEC1]      Certicom Research, "Elliptic Curve Cryptography", SEC1,
               February, July, 1999.

   [SEC-WG-EC] Certicom Research, "ECC in X.509", SEC X.509  Available from:
                <http://csrc.nist.gov/encryption/>.

   [CMS-KEA]    J. Pawling, "CMS KEA and SKIPJACK Conventions", S/MIME
                Working Group Draft, August, Internet-Draft, December, 1999.

   [MSG]        B. Ramsdell, "S/MIME Version 3 Message Specification",
                RFC 2633, June 1999.

   [SSG]       R. Zuccherato, "Methods for Avoiding the Small-Subgroup
               Attacks on the Diffie-Hellman

   [CMS-DH]     E. Rescorla, "Diffie-Hellman Key Agreement Method for
               S/MIME", Method",
                RFC 2785, March 2000.

   [X9.30]     ANSI X9.30-1995, Part 1, "Public key cryptography using
               irreversible algorithms for the financial services
               industry: The Digital Signature Algorithm (Revised)",
               1995.

   [X9.42]     "Agreement Of Symmetric Keys Using Diffie-Hellman and
               MQV Algorithms", ANSI draft, May 2631, June 1999.

   [X9.62]     ANSI X9.62-1999, "Public Key Cryptography For The
               Financial Services Industry: The Elliptic

   [SEC1]       SECG, "Elliptic Curve Digital
               Signature Algorithm (ECDSA)", 1999.

   [X9.63]     "Public Key Cryptography", Standards for
                Efficient Cryptography For The Financial Services
               Industry: Key Agreement and Key Transport Using Group, 2000.

   [SEC2]       SECG, "Recommended Elliptic Curve Cryptography", Draft ANSI X9F1, October
               1999. Domain Parameters",
                Standards for Efficient Cryptography Group, 2000.

   [SEC3]       SECG, "ECC in X.509", Standards for Efficient
                Cryptography Group, 2000.

Security Considerations

   This specification is based on [CMS], [X9.62] and [X9.63] and the
   appropriate security considerations of those documents apply.

Intellectual Property Rights

   This

   The IETF has been notified of intellectual property rights claimed
   in regard to the specification is based contained in this document.  For
   more information, consult the online list of claimed rights
   (http://www.ietf.org/ipr.html).

   The IETF takes no position regarding the validity or scope of any
   intellectual property or other rights that might be claimed to
   pertain to the implementation or use of the technology described in
   this document or the extent to which any license under such rights
   might or might not be available; neither does it represent that it
   has made any effort to identify any such rights. Information on ANSI specification X9.62 the
   IETF's procedures with respect to rights in standards-track and X9.63.
   A variety of patent statements
   standards-related documentation can be found in these working may apply BCP-11. Copies of
   claims of rights made available for publication and any assurances
   of licenses to this
   specification.  A later draft will be made available, or the result of an attempt made
   to identify obtain a reference general license or permission for the ANSI X9F1 related claims. use of such
   proprietary rights by implementors or users of this specification
   can be obtained from the IETF Secretariat.

Acknowledgments

   The key agreement methods described in this document is are based on work done by
   the ANSI X9F1 working group.  The author wishes authors wish to extend his their
   thanks to ANSI X9F1 for their assistance.

   The author authors also wishes wish to thank Paul Lambert, Simon Blake-Wilson, Lambert and Peter de Rooij for
   their patient assistance.  The basis of this
   work is derived from the ANSI X9F1 working group and their
   specifications for ECDSA and EC key agreement techniques.

Author's

Authors' Address

   Simon Blake-Wilson
   Certicom Corp
   5520 Explorer Drive #400
   Mississauga, ON L4W 5L1

   EMail: sblakewi@certicom.com
   Daniel R. L. Brown
   Certicom Corp
   5520 Explorer Drive #400
   Mississauga, ON L4W 5L1

   EMail: dbrown@certicom.com

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