ECC public key info: Elliptic Curve Cryptography Subject Public Key Information

Network Working Group                                          S. Turner
Request for Comments: 5480                                          IECA
Updates: 3279                                                   D. Brown
Category: Standards Track                                       Certicom
                                                                  K. Yiu
                                                               Microsoft
                                                              R. Housley
                                                          Vigil Security
                                                                 T. Polk
                                                                    NIST
                                                              March 2009


      Elliptic Curve Cryptography Subject Public Key Information

Status of This Memo

   This document specifies an Internet standards track protocol for the
   Internet community, and requests discussion and suggestions for
   improvements.  Please refer to the current edition of the "Internet
   Official Protocol Standards" (STD 1) for the standardization state
   and status of this protocol.  Distribution of this memo is unlimited.

Copyright Notice

   Copyright (c) 2009 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents in effect on the date of
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   Please review these documents carefully, as they describe your rights
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Abstract

   This document specifies the syntax and semantics for the Subject
   Public Key Information field in certificates that support Elliptic
   Curve Cryptography.  This document updates Sections 2.3.5 and 5, and
   the ASN.1 module of "Algorithms and Identifiers for the Internet
   X.509 Public Key Infrastructure Certificate and Certificate
   Revocation List (CRL) Profile", RFC 3279.

Table of Contents

   1. Introduction ....................................................2
      1.1. Terminology ................................................3
   2. Subject Public Key Information Fields ...........................3
      2.1. Elliptic Curve Cryptography Public Key Algorithm
           Identifiers ................................................3
      2.2. Subject Public Key .........................................7
   3. Key Usage Bits ..................................................7
   4. Security Considerations .........................................8
   5. ASN.1 Considerations ...........................................10
   6. IANA Considerations ............................................11
   7. Acknowledgments ................................................11
   8. References .....................................................11
      8.1. Normative References ......................................11
      8.2. Informative References ....................................12
   Appendix A. ASN.1 Module ..........................................13

1.  Introduction

   This document specifies the format of the subjectPublicKeyInfo field
   in X.509 certificates [PKI] that use Elliptic Curve Cryptography
   (ECC).  It updates RFC 3279 [PKI-ALG].  This document specifies the
   encoding formats for public keys used with the following ECC
   algorithms:

      o Elliptic Curve Digital Signature Algorithm (ECDSA);

      o Elliptic Curve Diffie-Hellman (ECDH) family schemes; and

      o Elliptic Curve Menezes-Qu-Vanstone (ECMQV) family schemes.

   Two methods for specifying the algorithms that can be used with the
   subjectPublicKey are defined.  One method allows the key to be used
   with any ECC algorithm, while the other method restricts the usage of
   the key to specific algorithms.  To promote interoperability, this
   document indicates which is required to implement for Certification
   Authorities (CAs) that implement ECC algorithms and relying parties
   that claim to process ECC algorithms.

   The ASN.1 [X.680] module in this document includes ASN.1 for ECC
   algorithms.  It also includes ASN.1 for non-ECC algorithms defined in
   [PKI-ALG] and [PKI-ADALG], even though the associated text is
   unaffected.  By updating all of the ASN.1 from [PKI-ALG] in this
   document, implementers only need to use the module found in this
   document.

1.1.  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 [MUSTSHOULD].

2.  Subject Public Key Information Fields

   In the X.509 certificate, the subjectPublicKeyInfo field has the
   SubjectPublicKeyInfo type, which has the following ASN.1 syntax:

     SubjectPublicKeyInfo  ::=  SEQUENCE  {
       algorithm         AlgorithmIdentifier,
       subjectPublicKey  BIT STRING
     }

   The fields in SubjectPublicKeyInfo have the following meanings:

      o algorithm is the algorithm identifier and parameters for the ECC
        public key.

      o subjectPublicKey is the ECC public key.  See Section 2.2.

   The AlgorithmIdentifier type, which is included for convenience
   [PKI], is defined as follows:

      AlgorithmIdentifier  ::=  SEQUENCE  {
        algorithm   OBJECT IDENTIFIER,
        parameters  ANY DEFINED BY algorithm OPTIONAL
      }

   The fields in AlgorithmIdentifier have the following meanings:

      o algorithm identifies the cryptographic algorithm with an object
        identifier.  See Section 2.1.

      o parameters, which are optional, are the associated parameters
        for the algorithm identifier in the algorithm field.  See
        Section 2.1.1.

2.1.  Elliptic Curve Cryptography Public Key Algorithm Identifiers

   The algorithm field in the SubjectPublicKeyInfo structure [PKI]
   indicates the algorithm and any associated parameters for the ECC
   public key (see Section 2.2).  Three algorithm identifiers are
   defined in this document:

      o id-ecPublicKey indicates that the algorithms that can be used
        with the subject public key are unrestricted.  The key is only
        restricted by the values indicated in the key usage certificate
        extension (see Section 3).  id-ecPublicKey MUST be supported.
        See Section 2.1.1.  This value is also included in certificates
        when a public key is used with ECDSA.

      o id-ecDH indicates that the algorithm that can be used with the
        subject public key is restricted to the Elliptic Curve Diffie-
        Hellman algorithm.  See Section 2.1.2.  id-ecDH MAY be
        supported.

      o id-ecMQV indicates that the algorithm that can be used with the
        subject public key is restricted to the Elliptic Curve Menezes-
        Qu-Vanstone key agreement algorithm.  See Section 2.1.2.
        id-ecMQV MAY be supported.

2.1.1.  Unrestricted Algorithm Identifier and Parameters

   The "unrestricted" algorithm identifier is:

     id-ecPublicKey OBJECT IDENTIFIER ::= {
       iso(1) member-body(2) us(840) ansi-X9-62(10045) keyType(2) 1 }

   The public key (ECPoint) syntax is described in Section 2.2.

   The parameter for id-ecPublicKey is as follows and MUST always be
   present:

     ECParameters ::= CHOICE {
       namedCurve         OBJECT IDENTIFIER
       -- implicitCurve   NULL
       -- specifiedCurve  SpecifiedECDomain
     }
       -- implicitCurve and specifiedCurve MUST NOT be used in PKIX.
       -- Details for SpecifiedECDomain can be found in [X9.62].
       -- Any future additions to this CHOICE should be coordinated
       -- with ANSI X9.

   The fields in ECParameters have the following meanings:

      o namedCurve identifies all the required values for a particular
        set of elliptic curve domain parameters to be represented by an
        object identifier.  This choice MUST be supported.  See Section
        2.1.1.1.

      o implicitCurve allows the elliptic curve domain parameters to be
        inherited.  This choice MUST NOT be used.

      o specifiedCurve, which is of type SpecifiedECDomain type (defined
        in [X9.62]), allows all of the elliptic curve domain parameters
        to be explicitly specified.  This choice MUST NOT be used.  See
        Section 5, "ASN.1 Considerations".

   The addition of any new choices in ECParameters needs to be
   coordinated with ANSI X9.

   The AlgorithmIdentifier within SubjectPublicKeyInfo is the only place
   within a certificate where the elliptic curve domain parameters may
   be located.  If the elliptic curve domain parameters are not present,
   then clients MUST reject the certificate.

2.1.1.1.  Named Curve

   The namedCurve field in ECParameters uses object identifiers to name
   well-known curves.  This document publishes curve identifiers for the
   fifteen NIST-recommended curves [FIPS186-3].  Other documents can
   publish other name curve identifiers.  The NIST-named curves are:

     -- Note that in [X9.62] the curves are referred to as 'ansiX9' as
     -- opposed to 'sec'.  For example, secp192r1 is the same curve as
     -- ansix9p192r1.

     -- Note that in [PKI-ALG] the secp192r1 curve was referred to as
     -- prime192v1 and the secp256r1 curve was referred to as
     -- prime256v1.

     -- Note that [FIPS186-3] refers to secp192r1 as P-192, secp224r1 as
     -- P-224, secp256r1 as P-256, secp384r1 as P-384, and secp521r1 as
     -- P-521.

     secp192r1 OBJECT IDENTIFIER ::= {
       iso(1) member-body(2) us(840) ansi-X9-62(10045) curves(3)
       prime(1) 1 }

     sect163k1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 1 }

     sect163r2 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 15 }

     secp224r1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 33 }

     sect233k1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 26 }
     sect233r1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 27 }

     secp256r1 OBJECT IDENTIFIER ::= {
       iso(1) member-body(2) us(840) ansi-X9-62(10045) curves(3)
       prime(1) 7 }

     sect283k1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 16 }

     sect283r1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 17 }

     secp384r1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 34 }

     sect409k1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 36 }

     sect409r1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 37 }

     secp521r1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 35 }

     sect571k1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 38 }

     sect571r1 OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) curve(0) 39 }

2.1.2.  Restricted Algorithm Identifiers and Parameters

   Two "restricted" algorithms are defined for key agreement algorithms:
   the Elliptic Curve Diffie-Hellman (ECDH) key agreement family schemes
   and the Elliptic Curve Menezes-Qu-Vanstone (ECMQV) key agreement
   family schemes.  Both algorithms are identified by an object
   identifier and have parameters.  The object identifier varies based
   on the algorithm, but the parameters are always ECParameters and they
   MUST always be present (see Section 2.1.1).

   The ECDH algorithm uses the following object identifier:

     id-ecDH OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) schemes(1)
       ecdh(12) }

   The ECMQV algorithm uses the following object identifier:

     id-ecMQV OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) certicom(132) schemes(1)
       ecmqv(13) }

2.2.  Subject Public Key

   The subjectPublicKey from SubjectPublicKeyInfo is the ECC public key.
   ECC public keys have the following syntax:

     ECPoint ::= OCTET STRING

   Implementations of Elliptic Curve Cryptography according to this
   document MUST support the uncompressed form and MAY support the
   compressed form of the ECC public key.  The hybrid form of the ECC
   public key from [X9.62] MUST NOT be used.  As specified in [SEC1]:

      o The elliptic curve public key (a value of type ECPoint that is
        an OCTET STRING) is mapped to a subjectPublicKey (a value of
        type BIT STRING) as follows: the most significant bit of the
        OCTET STRING value becomes the most significant bit of the BIT
        STRING value, and so on; the least significant bit of the OCTET
        STRING becomes the least significant bit of the BIT STRING.
        Conversion routines are found in Sections 2.3.1 and 2.3.2 of
        [SEC1].

      o The first octet of the OCTET STRING indicates whether the key is
        compressed or uncompressed.  The uncompressed form is indicated
        by 0x04 and the compressed form is indicated by either 0x02 or
        0x03 (see 2.3.3 in [SEC1]).  The public key MUST be rejected if
        any other value is included in the first octet.

3.  Key Usage Bits

   If the keyUsage extension is present in a Certification Authority
   (CA) certificate that indicates id-ecPublicKey in
   SubjectPublicKeyInfo, then any combination of the following values
   MAY be present:

     digitalSignature;
     nonRepudiation;
     keyAgreement;
     keyCertSign; and
     cRLSign.

   If the CA certificate keyUsage extension asserts keyAgreement, then
   it MAY assert either encipherOnly or decipherOnly.  However, this
   specification RECOMMENDS that if keyCertSign or cRLSign is present,
   then keyAgreement, encipherOnly, and decipherOnly SHOULD NOT be
   present.

   If the keyUsage extension is present in an End Entity (EE)
   certificate that indicates id-ecPublicKey in SubjectPublicKeyInfo,
   then any combination of the following values MAY be present:

     digitalSignature;
     nonRepudiation; and
     keyAgreement.

   If the EE certificate keyUsage extension asserts keyAgreement, then
   it MAY assert either encipherOnly or decipherOnly.

   If the keyUsage extension is present in a certificate that indicates
   id-ecDH or id-ecMQV in SubjectPublicKeyInfo, then the following MUST
   be present:

     keyAgreement;

   one of the following MAY be present:

     encipherOnly; or
     decipherOnly.

   If the keyUsage extension is present in a certificate that indicates
   id-ecDH or id-ecMQV in SubjectPublicKeyInfo, then the following
   values MUST NOT be present:

     digitalSignature;
     nonRepudiation;
     keyTransport;
     keyCertSign; and
     cRLSign.

4.  Security Considerations

   The security considerations in [PKI-ALG] apply.

   When implementing ECC in X.509 Certificates and Certificate
   Revocation Lists (CRLs), there are three algorithm-related choices
   that need to be made for the signatureAlgorithm field in a
   Certificate or CertificateList:

   1) What is the public key size?

   2) What is the hash algorithm [FIPS180-3]?

   3) What is the curve?

   Consideration must be given by the CA to the strength of the security
   provided by each of these choices.  Security is measured in bits,
   where a strong symmetric cipher with a key of X bits is said to
   provide X bits of security.  It is recommended that the bits of
   security provided by each choice are roughly equivalent.  The
   following table provides comparable minimum bits of security
   [SP800-57] for the ECDSA key sizes and message digest algorithms.  It
   also lists curves (see Section 2.1.1.1) for the key sizes.

   Minimum  | ECDSA    | Message    | Curves
   Bits of  | Key Size | Digest     |
   Security |          | Algorithms |
   ---------+----------+------------+-----------
   80       | 160-223  | SHA-1      | sect163k1
            |          | SHA-224    | secp163r2
            |          | SHA-256    | secp192r1
            |          | SHA-384    |
            |          | SHA-512    |
   ---------+----------+------------+-----------
   112      | 224-255  | SHA-224    | secp224r1
            |          | SHA-256    | sect233k1
            |          | SHA-384    | sect233r1
            |          | SHA-512    |
   ---------+----------+------------+-----------
   128      | 256-383  | SHA-256    | secp256r1
            |          | SHA-384    | sect283k1
            |          | SHA-512    | sect283r1
   ---------+----------+------------+-----------
   192      | 384-511  | SHA-384    | secp384r1
            |          | SHA-512    | sect409k1
            |          |            | sect409r1
   ---------+----------+------------+-----------
   256      | 512+     | SHA-512    | secp521r1
            |          |            | sect571k1
            |          |            | sect571r1
   ---------+----------+------------+-----------
   To promote interoperability, the following choices are RECOMMENDED:

   Minimum  | ECDSA    | Message    | Curves
   Bits of  | Key Size | Digest     |
   Security |          | Algorithms |
   ---------+----------+------------+-----------
   80       | 192      | SHA-256    | secp192r1
   ---------+----------+------------+-----------
   112      | 224      | SHA-256    | secp224r1
   ---------+----------+------------+-----------
   128      | 256      | SHA-256    | secp256r1
   ---------+----------+------------+-----------
   192      | 384      | SHA-384    | secp384r1
   ---------+----------+------------+-----------
   256      | 512      | SHA-512    | secp521r1
   ---------+----------+------------+-----------

   Using a larger hash value and then truncating it consumes more
   processing power than is necessary.  This is more important on
   constrained devices.  Since the signer does not know the environment
   that the recipient will use to validate the signature, it is better
   to use a hash function that provides the desired hash value output
   size, and no more.

   There are security risks with using keys not associated with well-
   known and widely reviewed curves.  For example, the curve may not
   satisfy the Menezes-Okamoto-Vanstone (MOV) condition [X9.62] or the
   curve may be vulnerable to the Anomalous attack [X9.62].
   Additionally, either a) all of the arithmetic properties of a
   candidate ECC public key must be validated to ensure that it has the
   unique correct representation in the correct (additive) subgroup (and
   therefore is also in the correct EC group) specified by the
   associated ECC domain parameters, or b) some of the arithmetic
   properties of a candidate ECC public key must be validated to ensure
   that it is in the correct group (but not necessarily the correct
   subgroup) specified by the associated ECC domain parameters
   [SP800-56A].

   As noted in [PKI-ALG], the use of MD2 and MD5 for new applications is
   discouraged.  It is still reasonable to use MD2 and MD5 to verify
   existing signatures.

5.  ASN.1 Considerations

   [X9.62] defines additional options for ECParameters and ECDSA-Sig-
   Value [PKI-ALG].  If an implementation needs to use these options,
   then use the [X9.62] ASN.1 module.  This RFC contains a conformant
   subset of the ASN.1 module defined in [X9.62].

   If an implementation generates a PER [X.691] encoding using the ASN.1
   module found in this specification, it might not achieve the same
   encoded output as one that uses the [X9.62] module.  PER is not
   required by either the PKIX or S/MIME environments.  If an
   implementation environment requires PER, then implementation concerns
   are less likely with the use of the [X9.62] module.

6.  IANA Considerations

   This document makes extensive use of object identifiers to register
   public key types, elliptic curves, and algorithms.  Most are
   registered in the ANSI X9.62 arc, with the exception of the hash
   algorithms (which are in the NIST arc) and many of the curves (which
   are in the Certicom Inc. arc; these curves have been adopted by ANSI
   and NIST).  Additionally, an object identifier is used to identify
   the ASN.1 module found in Appendix A.  It is defined in an arc
   delegated by IANA to the PKIX Working Group.  No further action by
   IANA is necessary for this document or any anticipated updates.

7.  Acknowledgments

   The authors wish to thank Stephen Farrell, Alfred Hoenes, Johannes
   Merkle, Jim Schaad, and Carl Wallace for their valued input.

8.  References

8.1.  Normative References

   [FIPS180-3]  National Institute of Standards and Technology (NIST),
                FIPS Publication 180-3: Secure Hash Standard, October
                2008.

   [FIPS186-3]  National Institute of Standards and Technology (NIST),
                FIPS Publication 186-3: Digital Signature Standard,
                (draft) November 2008.

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

   [PKI]        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.

   [PKI-ALG]    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.

   [RSAOAEP]    Schaad, J., Kaliski, B., and R. Housley, "Additional
                Algorithms and Identifiers for RSA Cryptography for use
                in the Internet X.509 Public Key Infrastructure
                Certificate and Certificate Revocation List (CRL)
                Profile", RFC 4055, June 2005.

   [SEC1]       Standards for Efficient Cryptography Group (SECG), "SEC
                1: Elliptic Curve Cryptography", Version 1.0, September
                2000.

   [X9.62]      American National Standards Institute (ANSI), ANS
                X9.62-2005: The Elliptic Curve Digital Signature
                Algorithm (ECDSA), 2005.

   [X.680]      ITU-T Recommendation X.680 (2002) | ISO/IEC 8824-1:2002.
                Information Technology - Abstract Syntax Notation One.

8.2.  Informative References

   [PKI-ADALG]  Dang, Q., Santesson, S., Moriarty, K., Brown, D., and T.
                Polk, "Internet X.509 Public Key Infrastructure:
                Additional Algorithms and Identifiers for DSA and
                ECDSA", Work in Progress, October 2008.

   [SP800-56A]  National Institute of Standards and Technology (NIST),
                Special Publication 800-56A: Recommendation for Pair-
                Wise Key Establishment Schemes Using Discrete Logarithm
                Cryptography (Revised), March 2007.

   [SP800-57]   National Institute of Standards and Technology (NIST),
                Special Publication 800-57: Recommendation for Key
                Management - Part 1 (Revised), March 2007.

   [X.691]      ITU-T Recommendation X.691 (2002) | ISO/IEC 8825-2:2002.
                Information Technology - ASN.1 Encoding Rules:
                Specification of Packed Encoding Rules.

Appendix A.  ASN.1 Module

   PKIX1Algorithms2008 { iso(1) identified-organization(3) dod(6)
     internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) 45 }

   DEFINITIONS EXPLICIT TAGS ::=

   BEGIN

   -- EXPORTS ALL;

   IMPORTS

   -- From RFC 4055 [RSAOAEP]

   id-sha224, id-sha256, id-sha384, id-sha512
     FROM PKIX1-PSS-OAEP-Algorithms
       { iso(1) identified-organization(3) dod(6) internet(1)
         security(5) mechanisms(5) pkix(7) id-mod(0)
         id-mod-pkix1-rsa-pkalgs(33) }

   ;

   --
   -- Message Digest Algorithms
   --

   -- MD-2
   -- Parameters are NULL

   id-md2  OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) rsadsi(113549) digestAlgorithm(2) 2 }

   -- MD-5
   -- Parameters are NULL

   id-md5  OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) rsadsi(113549)digestAlgorithm(2) 5 }

   -- SHA-1
   -- Parameters are preferred absent

   id-sha1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) oiw(14) secsig(3)
     algorithm(2) 26 }

   -- SHA-224
   -- Parameters are preferred absent
   -- id-sha224 OBJECT IDENTIFIER ::= {
   --   joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101)
   --   csor(3) nistalgorithm(4) hashalgs(2) 4 }
   -- SHA-256
   -- Parameters are preferred absent

   -- id-sha256 OBJECT IDENTIFIER ::= {
   --   joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101)
   --   csor(3) nistalgorithm(4) hashalgs(2) 1 }

   -- SHA-384
   -- Parameters are preferred absent

   -- id-sha384 OBJECT IDENTIFIER ::= {
   --   joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101)
   --   csor(3) nistalgorithm(4) hashalgs(2) 2 }

   -- SHA-512
   -- Parameters are preferred absent

   -- id-sha512 OBJECT IDENTIFIER ::= {
   --   joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101)
   --   csor(3) nistalgorithm(4) hashalgs(2) 3 }

   --
   -- Public Key (PK) Algorithms
   --

   -- RSA PK Algorithm and Key

   rsaEncryption OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1) 1 }

   RSAPublicKey ::= SEQUENCE {
     modulus         INTEGER, -- n
     publicExponent  INTEGER  -- e
   }

   -- DSA PK Algorithm, Key, and Parameters

   id-dsa OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) x9-57(10040) x9algorithm(4) 1 }

   DSAPublicKey ::= INTEGER --  public key, y
   DSS-Parms ::= SEQUENCE {
     p  INTEGER,
     q  INTEGER,
     g  INTEGER
   }

   -- Diffie-Hellman PK Algorithm, Key, and Parameters

   dhpublicnumber OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) ansi-x942(10046) number-type(2) 1 }

   DHPublicKey ::= INTEGER  -- public key, y = g^x mod p

   DomainParameters ::= SEQUENCE {
     p                INTEGER,           -- odd prime, p=jq +1
     g                INTEGER,           -- generator, g
     q                INTEGER,           -- factor of p-1
     j                INTEGER OPTIONAL,  -- subgroup factor, j>= 2
     validationParms  ValidationParms OPTIONAL
   }

   ValidationParms ::= SEQUENCE {
     seed         BIT STRING,
     pgenCounter  INTEGER
   }

   -- KEA PK Algorithm and Parameters

   id-keyExchangeAlgorithm OBJECT IDENTIFIER ::= {
     joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101)
     dod(2) infosec(1) algorithms(1) 22 }


   KEA-Parms-Id ::= OCTET STRING

   -- Sec 2.1.1 Unrestricted Algorithm ID, Key, and Parameters
   -- (ECDSA keys use id-ecPublicKey)

   id-ecPublicKey OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) ansi-X9-62(10045) keyType(2) 1 }

   ECPoint ::= OCTET STRING

   -- Parameters for both Restricted and Unrestricted

   ECParameters ::= CHOICE {
     namedCurve         OBJECT IDENTIFIER
     -- implicitCurve   NULL
     -- specifiedCurve  SpecifiedECDomain
   }
     -- implicitCurve and specifiedCurve MUST NOT be used in PKIX.
     -- Details for SpecifiedECDomain can be found in [X9.62].
     -- Any future additions to this CHOICE should be coordinated
     -- with ANSI X9.

   -- Sec 2.1.2 Restricted Algorithm IDs, Key, and Parameters: ECDH

   id-ecDH OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) schemes(1)
     ecdh(12) }

   -- ECPoint ::= OCTET STRING

   -- Parameters are ECParameters.

   -- Sec 2.1.2 Restricted Algorithm IDs, Key, and Parameters: ECMQV

   id-ecMQV OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) schemes(1)
     ecmqv(13) }

   -- ECPoint ::= OCTET STRING

   -- Parameters are ECParameters.

   --
   -- Signature Algorithms
   --

   -- RSA with MD-2
   -- Parameters are NULL

   md2WithRSAEncryption OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1) 2 }

   -- RSA with MD-5
   -- Parameters are NULL

   md5WithRSAEncryption OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1) 4 }

   -- RSA with SHA-1
   -- Parameters are NULL

   sha1WithRSAEncryption OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1) 5 }
   -- DSA with SHA-1
   -- Parameters are ABSENT

   id-dsa-with-sha1 OBJECT IDENTIFIER ::=  {
     iso(1) member-body(2) us(840) x9-57(10040) x9algorithm(4) 3 }

   -- DSA with SHA-224
   -- Parameters are ABSENT

   id-dsa-with-sha224 OBJECT IDENTIFIER  ::=  {
     joint-iso-ccitt(2) country(16) us(840) organization(1) gov(101)
     csor(3) algorithms(4) id-dsa-with-sha2(3) 1 }

   -- DSA with SHA-256
   -- Parameters are ABSENT

   id-dsa-with-sha256 OBJECT IDENTIFIER  ::=  {
     joint-iso-ccitt(2) country(16) us(840) organization(1) gov(101)
     csor(3) algorithms(4) id-dsa-with-sha2(3) 2 }

   -- ECDSA with SHA-1
   -- Parameters are ABSENT

   ecdsa-with-SHA1 OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) ansi-X9-62(10045) signatures(4) 1 }

   -- ECDSA with SHA-224
   -- Parameters are ABSENT

   ecdsa-with-SHA224 OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) ansi-X9-62(10045) signatures(4)
     ecdsa-with-SHA2(3) 1 }

   -- ECDSA with SHA-256
   -- Parameters are ABSENT

   ecdsa-with-SHA256 OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) ansi-X9-62(10045) signatures(4)
     ecdsa-with-SHA2(3) 2 }

   -- ECDSA with SHA-384
   -- Parameters are ABSENT

   ecdsa-with-SHA384 OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) ansi-X9-62(10045) signatures(4)
     ecdsa-with-SHA2(3) 3 }
   -- ECDSA with SHA-512
   -- Parameters are ABSENT

   ecdsa-with-SHA512 OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) ansi-X9-62(10045) signatures(4)
     ecdsa-with-SHA2(3) 4 }

   --
   -- Signature Values
   --

   -- DSA

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

   -- ECDSA

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

   --
   -- Named Elliptic Curves
   --

   -- Note that in [X9.62] the curves are referred to as 'ansiX9' as
   -- opposed to 'sec'.  For example secp192r1 is the same curve as
   -- ansix9p192r1.

   -- Note that in [PKI-ALG] the secp192r1 curve was referred to as
   -- prime192v1 and the secp256r1 curve was referred to as prime256v1.

   -- Note that [FIPS186-3] refers to secp192r1 as P-192, secp224r1 as
   -- P-224, secp256r1 as P-256, secp384r1 as P-384, and secp521r1 as
   -- P-521.

   secp192r1 OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) ansi-X9-62(10045) curves(3)
     prime(1) 1 }

   sect163k1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 1 }
   sect163r2 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 15 }

   secp224r1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 33 }

   sect233k1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 26 }

   sect233r1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 27 }

   secp256r1 OBJECT IDENTIFIER ::= {
     iso(1) member-body(2) us(840) ansi-X9-62(10045) curves(3)
     prime(1) 7 }

   sect283k1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 16 }

   sect283r1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 17 }

   secp384r1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 34 }

   sect409k1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 36 }

   sect409r1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 37 }

   secp521r1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 35 }

   sect571k1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 38 }

   sect571r1 OBJECT IDENTIFIER ::= {
     iso(1) identified-organization(3) certicom(132) curve(0) 39 }

   END

Authors' Addresses

   Sean Turner
   IECA, Inc.
   3057 Nutley Street, Suite 106
   Fairfax, VA 22031
   USA

   EMail: turners@ieca.com


   Kelvin Yiu
   Microsoft
   One Microsoft Way
   Redmond, WA 98052-6399
   USA

   EMail: kelviny@microsoft.com


   Daniel R. L. Brown
   Certicom Corp
   5520 Explorer Drive #400
   Mississauga, ON L4W 5L1
   CANADA

   EMail: dbrown@certicom.com


   Russ Housley
   Vigil Security, LLC
   918 Spring Knoll Drive
   Herndon, VA 20170
   USA

   EMail: housley@vigilsec.com


   Tim Polk
   NIST
   Building 820, Room 426
   Gaithersburg, MD 20899

   EMail: wpolk@nist.gov