Diffie-Hellman Proof-of-Possession Algorithms
draft-schaad-pkix-rfc2875-bis-01

The information below is for an old version of the document
Document Type Active Internet-Draft (individual)
Authors Jim Schaad , Hemma Prafullchandra 
Last updated 2012-04-29
Stream (None)
Formats pdf htmlized (tools) htmlized bibtex
Reviews
Stream Stream state (No stream defined)
Consensus Boilerplate Unknown
RFC Editor Note (None)
IESG IESG state I-D Exists
Telechat date
Responsible AD (None)
Send notices to (None)
PKIX                                                           J. Schaad
Internet-Draft                                   Soaring Hawk Consulting
Obsoletes: 2875 (if approved)                          H. Prafullchandra
Intended status: Standards Track                          April 29, 2012
Expires: October 31, 2012

             Diffie-Hellman Proof-of-Possession Algorithms
                    draft-schaad-pkix-rfc2875-bis-01

Abstract

   This document describes two methods for producing an integrity check
   value from a Diffie-Hellman key pair and one method for producing an
   integrity check value from an Elliptic Curve key pair.  This behavior
   is needed for such operations as creating the signature of a PKCS #10
   certification request.  These algorithms are designed to provide a
   proof-of-possession rather than general purpose signing.

Status of this Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on October 31, 2012.

Copyright Notice

   Copyright (c) 2012 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
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of

Schaad & Prafullchandra  Expires October 31, 2012               [Page 1]
Internet-Draft              DH POP Algorithms                 April 2012

   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

   This document may contain material from IETF Documents or IETF
   Contributions published or made publicly available before November
   10, 2008.  The person(s) controlling the copyright in some of this
   material may not have granted the IETF Trust the right to allow
   modifications of such material outside the IETF Standards Process.
   Without obtaining an adequate license from the person(s) controlling
   the copyright in such materials, this document may not be modified
   outside the IETF Standards Process, and derivative works of it may
   not be created outside the IETF Standards Process, except to format
   it for publication as an RFC or to translate it into languages other
   than English.

Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
     1.1.  Changes since RFC2875  . . . . . . . . . . . . . . . . . .  3
     1.2.  Requirements Terminology . . . . . . . . . . . . . . . . .  4
   2.  Terminology  . . . . . . . . . . . . . . . . . . . . . . . . .  4
   3.  Notation . . . . . . . . . . . . . . . . . . . . . . . . . . .  4
   4.  Static DH Proof-of-Possession Process  . . . . . . . . . . . .  5
     4.1.  ASN Encoding . . . . . . . . . . . . . . . . . . . . . . .  6
   5.  Discrete Logarithm Signature . . . . . . . . . . . . . . . . .  9
     5.1.  Expanding the Digest Value . . . . . . . . . . . . . . . . 10
     5.2.  Signature Computation Algorithm  . . . . . . . . . . . . . 11
     5.3.  Signature Verification Algorithm . . . . . . . . . . . . . 11
     5.4.  ASN.1 Encoding . . . . . . . . . . . . . . . . . . . . . . 12
   6.  Static ECDH Proof-of-Possession Process  . . . . . . . . . . . 14
     6.1.  ASN.1 Encoding . . . . . . . . . . . . . . . . . . . . . . 16
   7.  Security Considerations  . . . . . . . . . . . . . . . . . . . 18
   8.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 19
     8.1.  Normative References . . . . . . . . . . . . . . . . . . . 19
     8.2.  Informative References . . . . . . . . . . . . . . . . . . 19
   Appendix A.  Open Issues . . . . . . . . . . . . . . . . . . . . . 20
   Appendix B.  ASN.1 Modules . . . . . . . . . . . . . . . . . . . . 20
     B.1.  1988 ASN.1 Module  . . . . . . . . . . . . . . . . . . . . 20
     B.2.  2008 ASN.1 Module  . . . . . . . . . . . . . . . . . . . . 21
   Appendix C.  Example of Static DH Proof-of-Possession  . . . . . . 26
   Appendix D.  Example of Discrete Log Signature . . . . . . . . . . 34
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 39

Schaad & Prafullchandra  Expires October 31, 2012               [Page 2]
Internet-Draft              DH POP Algorithms                 April 2012

1.  Introduction

   PKCS #10 [RFC2314] and the Certificate Request Message Format (CRMF)
   [CRMF] define syntaxes for certification requests.  While CRMF
   supports an alternative method to support Proof-of-Possession (POP)
   for encryption only keys, PKCS #10 does not.  PKCS #10 assumes that
   the public key being requested for certification corresponds to an
   algorithm that is capable producing a POP by a signing/encrypting
   operation.  Diffie-Hellman (DH) and Elliptic Curve Diffie-Hellman
   (ECDH) are a key agreement algorithms and as such cannot be directly
   used for signing or encryption.

   This document describes new proof-of-possession algorithms.  Two
   methods use the Diffie-Hellman key agreement process to provide a
   shared secret as the basis of an integrity check value and one method
   uses the Elliptic-Curve key agreement process.  In the first and
   third algorithm, the value is constructed for a specific recipient/
   verifier by using a public key of that verifier.  In the second
   algorithm, the value is constructed for arbitrary verifiers.

   It should be noted that we did not create an algorithm that parallels
   ECDSA (Elliptical Curve Digital Signature Standard) like was done for
   DSA (Digital Signature Standard).  Given the current PKIX definitions
   for the public key parameters of Elliptical curve, the number of
   groups is both limited and pre-defined.  This means that the
   probability that the same set of parameters are going to be used by
   the key requester and the key validator would be high.  Also since
   the group verification has been done centrally and with lots of
   validation, the odds that a cryptographically weak group are used is
   much reduced.  Additionally, any system which could compute such a
   parallel algorithm would just be able to use the ECDSA algorithm in
   any event.

1.1.  Changes since RFC2875

   The following changes have been made:

   o  The Static DH Proof-of-Possession algorithm has been re-written
      for parameterization of the hash algorithm and the message
      authentication code (MAC) algorithm.

   o  A new instance of the static DH POP algorithm has been created
      using HMAC and SHA-256.

   o  The Discrete Logarithm Signature algorithm has been re-written for
      parameterization of the hash algorithm.

Schaad & Prafullchandra  Expires October 31, 2012               [Page 3]
Internet-Draft              DH POP Algorithms                 April 2012

   o  A new instances of the algorithm has been created for the SHA-224,
      SHA-256, SHA-384 and SHA-512 hash functions.

   o  A new Static ECDH Proof-of-Possession algorithm has been added.

   o  New instances of the Static ECDH POP algorithm has been created
      using HMAC paired with the SHA-224, SHA-256, SHA-384 and SHA-512
      hash functions.

1.2.  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 [RFC2119].

   When the words are in lower case they have their natural language
   meaning.

2.  Terminology

   The following definitions will be used in this document

   DH certificate = a certificate whose SubjectPublicKey is a DH public
   value and is signed with any signature algorithm (e.g.  RSA or DSA).

   ECDH certificate = a certificate whose SubjectPublicKey is a ECDH
   public value and is signed with any signature algorithm (i.e.  RSA or
   ECDSA).

   Proof-of-Possession (POP) is a method that provides a method for a
   second party to perform an algorithm to establish with some degree of
   assurance that the first party does possess and has the ability to
   use a private key.  The reasoning behind doing POP can be found in
   Appendix C in [CRMF].

3.  Notation

   This section describes mathematical notations, conventions and
   symbols used throughout this document.

Schaad & Prafullchandra  Expires October 31, 2012               [Page 4]
Internet-Draft              DH POP Algorithms                 April 2012

      a | b          : Concatenation of a and b
      a ^ b          : a raised to the power of b
      a mod b        : a modulo b
      a / b          : a divided by b using integer division

      KDF(a)         : Key Derivation function producing a value from a.
      MAC(a, b)      : Message Authentication Code function where
                       a is the text and b is the key
      LEFTMOST(a,b)  : Return the b left most bits of a

4.  Static DH Proof-of-Possession Process

   The Static DH POP algorithm is setup to use a key derivation function
   (KDF) and a message authentication code (MAC).  This algorithm
   requires that a common set of group parameters be used by both the
   creator and verifier of the POP value.

   The steps for creating a DH POP are:

   1.  An entity (E) chooses the group parameters for a DH key
       agreement.

       This is done simply by selecting the group parameters from a
       certificate for the recipient of the POP process.

       A certificate with the correct group parameters has to be
       available.  Let these common DH parameters be g and p; and let
       this DH key-pair be known as the Recipient key pair (Rpub and
       Rpriv).

       Rpub = g^x mod p (where x=Rpriv, the private DH value and ^
       denotes exponentiation)

   2.  The entity generates a DH public/private key-pair using the
       parameters from step 1.

       For an entity E:

       Epriv = DH private value = y
       Epub = DH public value = g^y mod p

   3.  The POP computation process will then consist of:

Schaad & Prafullchandra  Expires October 31, 2012               [Page 5]
Internet-Draft              DH POP Algorithms                 April 2012

       a)  The value to be signed is obtained.  (For a PKCS #10 object,
           the value is the DER encoded certificationRequestInfo field
           represented as an octet string.)

       b)  A shared DH secret is computed, as follows,

           shared secret = ZZ = g^xy mod p

           [This is done by the entity E as Rpub^y and by the Recipient
           as Epub^x, where Rpub is retrieved from the Recipient's DH
           certificate (or is the one that was locally generated by the
           Entity) and Epub is retrieved from the actual certification
           request.]

       c)  A temporary key K is derived from the shared secret ZZ as
           follows:

              K = KDF(LeadingInfo | ZZ | TrailingInfo)

              LeadingInfo ::= Subject Distinguished Name from
              certificate

              TrailingInfo ::= Issuer Distinguished Name from
              certificate

       d)  Using the defined MAC function, compute MAC(K, text).

   The POP verification process requires the Recipient to carry out
   steps (a) through (d) and then simply compare the result of step (d)
   with what it received as the signature component.  If they match then
   the following can be concluded:

   a)  The Entity possesses the private key corresponding to the public
       key in the certification request because it needed the private
       key to calculate the shared secret; and

   b)  Only the Recipient that the entity sent the request to could
       actually verify the request because they would require their own
       private key to compute the same shared secret.  In the case where
       the recipient is a Certification Authority, this protects the
       Entity from rogue CAs.

4.1.  ASN Encoding

   The alogorithm outlined above allows for the use of an arbitrary hash
   function in computing the temporary key and the MAC value.  In this
   specfication we defined object identifiers for the SHA-1 and SHA-256
   hash values.  The ASN.1 structures associated with the static Diffie-

Schaad & Prafullchandra  Expires October 31, 2012               [Page 6]
Internet-Draft              DH POP Algorithms                 April 2012

   Hellman POP algorithm are:

      DhSigStatic ::= SEQUENCE {
          issuerAndSerial IssuerAndSerialNumber OPTIONAL,
          hashValue       MessageDigest
      }

      sa-dhPop-static-sha1-hmac-sha1 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-dhPop-static-HMAC-SHA1
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS {pk-dh}
      }

      id-dhPop-static-HMAC-SHA1 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 3
      }

      id-dhPop-static-SHA1-HMAC-SHA1 OBJECT IDENTIFIER ::=
           id-dhPop-static-HMAC-SHA1

      sa-dhPop-static-SHA224-HMAC-SHA224 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-alg-dhPop-static-SHA224-HMAC-SHA224
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS {pk-dh}
      }

      id-alg-dhPop-static-SHA224-HMAC-SHA224 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD1
      }

      sa-dhPop-static-SHA256-HMAC-SHA256 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-alg-dhPop-static-SHA256-HMAC-SHA256
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS {pk-dh}
      }

      id-alg-dhPop-static-SHA256-HMAC-SHA256 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD2
      }

      sa-dhPop-static-SHA384-HMAC-SHA384 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-alg-dhPop-static-SHA384-HMAC-SHA384
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS {pk-dh}

Schaad & Prafullchandra  Expires October 31, 2012               [Page 7]
Internet-Draft              DH POP Algorithms                 April 2012

      }

      id-alg-dhPop-static-SHA384-HMAC-SHA384 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD3
      }

      sa-dhPop-static-SHA512-HMAC-SHA512 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-alg-dhPop-static-SHA512-HMAC-SHA512
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS {pk-dh}
      }

      id-alg-dhPop-static-SHA512-HMAC-SHA512 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD4
      }

   In the above ASN.1 the following items are defined:

   DhSigStatic  is an ASN.1 type structure.  This structure holds the
      information describing the signature.  The structure has the
      following fields:

      issuerAndSerial  is the issuer name and serial number of the
         certificate from which the public key was obtained.  The
         issuerAndSerial field is omitted if the public key did not come
         from a certificate.

      hashValue  contains the result of the MAC operation in step 3d.

   sa-dh-static-SHA1-HMAC-SHA1  is an ASN.1 SIGNATURE-ALGORITHM object
      which associates together the information describing a signature
      algorithm.  The structure DhSigStatic represents the signature
      value and the parameters MUST be absent.

   id-dhPop-static-SHA1-HMAC-SHA1  identifies the Static DH POP
      algorithm that uses SHA1 as the KDF and HMAC-SHA1 as the MAC
      function.  The new OID was created for naming consistency with the
      other OIDs defined here.  The value of the OID is the same value
      as id-dhPop-static-HMAC-SHA1 which was defined in the previous
      version of this document [RFC2875].

   sa-dh-static-SHA224-HMAC-SHA224  is an ASN.1 SIGNATURE-ALGORITHM
      object that associates together the information describing this
      signature algorithm.  The structure DhSigStatic represents the
      signature value and the parameters MUST be absent.

Schaad & Prafullchandra  Expires October 31, 2012               [Page 8]
Internet-Draft              DH POP Algorithms                 April 2012

   id-dhPop-static-SHA224-HMAC-SHA224  identifies the Static DH POP
      algorithm that uses SHA224 as the KDF and HMAC-SHA224 as the MAC
      function.

   sa-dh-static-SHA256-HMAC-SHA256  is an ASN.1 SIGNATURE-ALGORITHM
      object that associates together the information describing this
      signature algorithm.  The structure DhSigStatic represents the
      signature value and the parameters MUST be absent.

   id-dhPop-static-SHA1-HMAC-SHA256  identifies the Static DH POP
      algorithm that uses SHA256 as the KDF and HMAC-SHA256 as the MAC
      function.

   sa-dh-static-SHA384-HMAC-SHA384  is an ASN.1 SIGNATURE-ALGORITHM
      object that associates together the information describing this
      signature algorithm.  The structure DhSigStatic represents the
      signature value and the parameters MUST be absent.

   id-dhPop-static-SHA1-HMAC-SHA384  identifies the Static DH POP
      algorithm that uses SHA384 as the KDF and HMAC-SHA384 as the MAC
      function.

   sa-dh-static-SHA512-HMAC-SHA512  is an ASN.1 SIGNATURE-ALGORITHM
      object that associates together the information describing this
      signature algorithm.  The structure DhSigStatic represents the
      signature value and the parameters MUST be absent.

   id-dhPop-static-SHA1-HMAC-SHA512  identifies the Static DH POP
      algorithm that uses SHA512 as the KDF and HMAC-SHA512 as the MAC
      function.

5.  Discrete Logarithm Signature

   The use of a single set of parameters for an entire public key
   infrastructure allows all keys in the group to be attacked together.

   For this reason we need to create a proof of possession for Diffie-
   Hellman keys that does not require the use of a common set of
   parameters.

   This POP is based on the Digital Signature Algorithm, but we have
   removed the restrictions imposed by the [FIPS-186] standard.  The use
   of this method does impose some additional restrictions on the set of
   keys that may be used, however if the key generation algorithm
   documented in [RFC2631] is used the required restrictions are met.
   The additional restrictions are the requirement for the existence of
   a q parameter.  Adding the q parameter is generally accepted as a

Schaad & Prafullchandra  Expires October 31, 2012               [Page 9]
Internet-Draft              DH POP Algorithms                 April 2012

   good practice as it allows for checking of small group attacks.

   The following definitions are used in the rest of this section:

   p is a large prime
   g = h(p-1)/q mod p ,
   where h is any integer 1 < h < p-1 such that h(p-1) mod q > 1
   (g has order q mod p)
   q is a large prime
   j is a large integer such that p = qj + 1
   x is a randomly or pseudo-randomly generated integer with 1 < x < q
   y = g^x mod p
   HASH is a hash function such that
   h = the output size of HASH in bits

   Note: These definitions match the ones in [RFC2631].

5.1.  Expanding the Digest Value

   Besides the addition of a q parameter, [FIPS-186] also imposes size
   restrictions on the parameters.  The length of q must be 160-bits
   (matching output of the SHA-1 digest algorithm) and length of p must
   be 1024-bits.  The size restriction on p is eliminated in this
   document, but the size restriction on q is replaced with the
   requirement that q must be at least h bits in length.  (If the hash
   function is SHA-1, then h=160 bits and the size restriction on q is
   identical with that in [RFC2631].)

   Given that there is not a random length-hashing algorithm, a hash
   value of the message will need to be derived such that the hash is in
   the range from 0 to q-1.  If the length of q is greater than h then a
   method must be provided to expand the hash length.

   The method for expanding the digest value used in this section does
   not add any additional security beyond the h bits provided by the
   hash algorithm.  The value being signed is increased mainly to
   enhance the difficulty of reversing the signature process.

   This algorithm produces m the value to be signed.

   Let L = the size of q (i.e. 2^L <= q < 2^(L+1)).
   Let M be the original message to be signed.
   Let h be the length of HASH output

   1.  Compute d = HASH(M), the digest of the original message.

   2.  If L == h then m = d.

Schaad & Prafullchandra  Expires October 31, 2012              [Page 10]
Internet-Draft              DH POP Algorithms                 April 2012

   3.  If L > h then follow steps (a) through (d) below.

       a)  Set n = L / h, (if L = 200, h = 160 then n = 1)

       b)  Set m = d, the initial computed digest value.

       c)  For i = 0 to n - 1
           m = m | HASH(m)

       d)  m = LEFTMOST(m, L-1)

   Thus the final result of the process meets the criteria that 0 <= m <
   q.

5.2.  Signature Computation Algorithm

   The signature algorithm produces the pair of values (r, s), which is
   the signature.  The signature is computed as follows:

   Given m, the value to be signed, as well as the parameters defined
   earlier in section 5.

   1.  Generate a random or pseudorandom integer k, such that 0 < k^-1 <
       q.

   2.  Compute r = (g^k mod p) mod q.

   3.  If r is zero, repeat from step 1.

   4.  Compute s = (k^-1 (m + xr)) mod q.

   5.  If s is zero, repeat from step 1.

5.3.  Signature Verification Algorithm

   The signature verification process is far more complicated than is
   normal for the Digital Signature Algorithm, as some assumptions about
   the validity of parameters cannot be taken for granted.

   Given a message m to be validated, the signature value pair (r, s)
   and the parameters for the key.

   1.  Perform a strong verification that p is a prime number.

   2.  Perform a strong verification that q is a prime number.

   3.  Verify that q is a factor of p-1, if any of the above checks fail
       then the signature cannot be verified and must be considered a

Schaad & Prafullchandra  Expires October 31, 2012              [Page 11]
Internet-Draft              DH POP Algorithms                 April 2012

       failure.

   4.  Verify that r and s are in the range [1, q-1].

   5.  Compute w = (s^-1) mod q.

   6.  Compute u1 = m*w mod q.

   7.  Compute u2 = r*w mod q.

   8.  Compute v = ((g^u1 * y^u2) mod p) mod q.

   9.  Compare v and r, if they are the same then the signature verified
       correctly.

5.4.  ASN.1 Encoding

   The signature algorithm is parameterized by the hash algorithm.  The
   ASN.1 structures associated with the Discrete Logarithm Signature
   algorithm are:

      sa-dh-pop-SHA1 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent
         HASHES { mda-sha1}
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dh-pop-SHA1 OBJECT IDENTIFIER ::= id-alg-dh-pop

      id-alg-dh-pop OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 4}

      sa-dh-pop-SHA224 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop-SHA224
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent
         HASHES { mda-sha224 }
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dh-pop-SHA224 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD5
      }

      sa-dh-pop-SHA256 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop-SHA256
         VALUE DSA-Sig-Value

Schaad & Prafullchandra  Expires October 31, 2012              [Page 12]
Internet-Draft              DH POP Algorithms                 April 2012

         PARAMS TYPE DomainParameters ARE preferredAbsent
         HASHES { mda-sha256 }
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dh-pop-SHA256 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD6
      }

      sa-dh-pop-SHA384 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop-SHA384
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent
         HASHES { mda-sha384 }
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dh-pop-SHA384 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD7
      }

      sa-dh-pop-SHA512 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop-SHA512
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent
         HASHES { mda-sha512 }
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dh-pop-SHA512 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD8
      }

   In the above ASN.1 the following items are defined:

   sa-dh-pop-SHA1  is a SIGNATURE-ALGORITHM object that associates
      together the informaiton describing this signature algorithm.  The
      structure DSA-Sig-Value represents the signature value and the
      parameters DomainParameters SHOULD be omitted in the signature,
      but MUST be present in the associated key request.

   id-alg-dh-pop-SHA1  is the OID that identifies the discrete logarithm
      signature using SHA1 as the hash algorithm.  The new OID was
      created for naming consistency with the others defined here.  The
      value of the OID is the same as id-alg-dh-pop which was defined in
      the previous version of this document [RFC2875].

Schaad & Prafullchandra  Expires October 31, 2012              [Page 13]
Internet-Draft              DH POP Algorithms                 April 2012

   sa-dh-pop-SHA224  is a SIGNATURE-ALGORITHM object that associates
      together the informaiton describing this signature algorithm.  The
      structure DSA-Sig-Value represents the signature value and the
      parameters DomainParameters SHOULD be omitted in the signature,
      but MUST be present in the associated key request.

   id-alg-dh-pop-SHA224  is the OID that identifies the discrete
      logarithm signature using SHA224 as the hash algorithm.

   sa-dh-pop-SHA256  is a SIGNATURE-ALGORITHM object that associates
      together the informaiton describing this signature algorithm.  The
      structure DSA-Sig-Value represents the signature value and the
      parameters DomainParameters SHOULD be omitted in the signature,
      but MUST be present in the associated key request.

   id-alg-dh-pop-SHA256  is the OID that identifies the discrete
      logarithm signature using SHA256 as the hash algorithm.

   sa-dh-pop-SHA384  is a SIGNATURE-ALGORITHM object that associates
      together the informaiton describing this signature algorithm.  The
      structure DSA-Sig-Value represents the signature value and the
      parameters DomainParameters SHOULD be omitted in the signature,
      but MUST be present in the associated key request.

   id-alg-dh-pop-SHA384  is the OID that identifies the discrete
      logarithm signature using SHA384 as the hash algorithm.

   sa-dh-pop-SHA512  is a SIGNATURE-ALGORITHM object that associates
      together the informaiton describing this signature algorithm.  The
      structure DSA-Sig-Value represents the signature value and the
      parameters DomainParameters SHOULD be omitted in the signature,
      but MUST be present in the associated key request.

   id-alg-dh-pop-SHA512  is the OID that identifies the discrete
      logarithm signature using SHA512 as the hash algorithm.

6.  Static ECDH Proof-of-Possession Process

   The Static ECDH POP algorithm is setup to use a key derivation
   function (KDF) and a message authentication code (MAC).  This
   algorithm requires that a common set of group parameters be used by
   both the creator and verifier of the POP value.  Full details of how
   Elliptical Curve Cryptography work can be found in RFC 6090
   [RFC6090].

   The steps for creating a ECDH POP are:

Schaad & Prafullchandra  Expires October 31, 2012              [Page 14]
Internet-Draft              DH POP Algorithms                 April 2012

   1.  An entity (E) chooses the group parameters for a ECDH key
       agreement.

       This is done simply by selecting the group parameters from a
       certificate for the recipient of the POP process.

       A certificate with the correct group parameters has to be
       available.  Let these common DH parameters be g and p; and let
       this DH key-pair be known as the Recipient key pair (Rpub and
       Rpriv).

       Rpub = g^x mod p (where x=Rpriv, the private DH value)

   2.  The entity generates a DH public/private key-pair using the
       parameters from step 1.

       For an entity E:

       Epriv = DH private value = y
       Epub = DH public value = g^y mod p

   3.  The POP computation process will then consist of:

       a)  The value to be signed is obtained.  (For a PKCS #10 object,
           the value is the DER encoded certificationRequestInfo field
           represented as an octet string.)

       b)  A shared ECDH secret is computed, as follows,

           shared secret = ZZ = g^xy mod p

           [This is done by the entity E as Rpub^y and by the Recipient
           as Epub^x, where Rpub is retrieved from the Recipient's DH
           certificate (or is the one that was locally generated by the
           Entity) and Epub is retrieved from the actual certification
           request.]

       c)  A temporary key K is derived from the shared secret ZZ as
           follows:

           K = KDF(LeadingInfo | ZZ | TrailingInfo)

           LeadingInfo ::= Subject Distinguished Name from certificate
           TrailingInfo ::= Issuer Distinguished Name from certificate

Schaad & Prafullchandra  Expires October 31, 2012              [Page 15]
Internet-Draft              DH POP Algorithms                 April 2012

       d)  Compute MAC(K, text).

   The POP verification process requires the Recipient to carry out
   steps (a) through (d) and then simply compare the result of step (d)
   with what it received as the signature component.  If they match then
   the following can be concluded:

   a)  The Entity possesses the private key corresponding to the public
       key in the certification request because it needed the private
       key to calculate the shared secret; and

   b)  Only the Recipient that the entity sent the request to could
       actually verify the request because they would require their own
       private key to compute the same shared secret.  In the case where
       the recipient is a Certification Authority, this protects the
       Entity from rogue CAs.

6.1.  ASN.1 Encoding

   The alogorithm outlined above allows for the use of an arbitrary hash
   function in computing the temporary key and the MAC value.  In this
   specfication we defined object identifiers for the SHA-1 and SHA-256
   hash values.  The ASN.1 structures associated with the static EC-DH
   POP algorithm are:

Schaad & Prafullchandra  Expires October 31, 2012              [Page 16]
Internet-Draft              DH POP Algorithms                 April 2012

      id-alg-ecdhPop-static-SHA224-HMAC-SHA224 OBJECT IDENTIFIER ::= {
         id-pkix id-alg(6) TBD11
      }

      sa-ecdh-pop-SHA224-HMAC-SHA224 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-ecdhPop-static-SHA224-HMAC-SHA224
         VALUE DhSigStatic
         PARAMS ARE absent
         PUBLIC-KEYS { pk-ec }
      }

      id-alg-ecdhPop-static-SHA256-HMAC-SHA256 OBJECT IDENTIFIER ::= {
         id-pkix id-alg(6) TBD912
      }

      sa-ecdh-pop-SHA256-HMAC-SHA256 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-ecdhPop-static-SHA256-HMAC-SHA256
         VALUE DhSigStatic
         PARAMS ARE absent
         PUBLIC-KEYS { pk-ec }
      }

      id-alg-ecdhPop-static-SHA384-HMAC-SHA384 OBJECT IDENTIFIER ::= {
         id-pkix id-alg(6) TBD13
      }

      sa-ecdh-pop-SHA384-HMAC-SHA384 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-ecdhPop-static-SHA384-HMAC-SHA384
         VALUE DhSigStatic
         PARAMS ARE absent
         PUBLIC-KEYS { pk-ec }
      }

      id-alg-ecdhPop-static-SHA512-HMAC-SHA512 OBJECT IDENTIFIER ::= {
         id-pkix id-alg(6) TBD14
      }

      sa-ecdh-pop-SHA512-HMAC-SHA512 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-ecdhPop-static-SHA512-HMAC-SHA512
         VALUE DhSigStatic
         PARAMS ARE absent
         PUBLIC-KEYS { pk-ec }
      }

   In the above ASN.1 the following items are defined:

Schaad & Prafullchandra  Expires October 31, 2012              [Page 17]
Internet-Draft              DH POP Algorithms                 April 2012

   sa-ecdh-static-SHA224-HMAC-SHA224  is an ASN.1 SIGNATURE-ALGORITHM
      object that associates together the information describing this
      signature algorithm.  The structure DhSigStatic represents the
      signature value and the parameters MUST be absent.

   id-ecdhPop-static-SHA224-HMAC-SHA224  identifies the Static ECDH POP
      algorithm that uses SHA224 as the KDF and HMAC-SHA224 as the MAC
      function.

   sa-ecdh-static-SHA256-HMAC-SHA256  is an ASN.1 SIGNATURE-ALGORITHM
      object that associates together the information describing this
      signature algorithm.  The structure DhSigStatic represents the
      signature value and the parameters MUST be absent.

   id-ecdhPop-static-SHA256-HMAC-SHA256  identifies the Static ECDH POP
      algorithm that uses SHA256 as the KDF and HMAC-SHA256 as the MAC
      function.

   sa-ecdh-static-SHA384-HMAC-SHA384  is an ASN.1 SIGNATURE-ALGORITHM
      object that associates together the information describing this
      signature algorithm.  The structure DhSigStatic represents the
      signature value and the parameters MUST be absent.

   id-ecdhPop-static-SHA384-HMAC-SHA384  identifies the Static ECDH POP
      algorithm that uses SHA384 as the KDF and HMAC-SHA384 as the MAC
      function.

   sa-ecdh-static-SHA512-HMAC-SHA512  is an ASN.1 SIGNATURE-ALGORITHM
      object that associates together the information describing this
      signature algorithm.  The structure DhSigStatic represents the
      signature value and the parameters MUST be absent.

   id-ecdhPop-static-SHA512-HMAC-SHA512  identifies the Static ECDH POP
      algorithm that uses SHA512 as the KDF and HMAC-SHA512 as the MAC
      function.

7.  Security Considerations

   In the static DH POP and static ECDH POP algorithms, an appropriate
   value can be produced by either party.  Thus these algorithms only
   provides integrity and not origination service.  The Discrete
   Logarithm algorithm provides both integrity checking and origination
   checking.

   All the security in this system is provided by the secrecy of the
   private keying material.  If either sender or recipient private keys
   are disclosed, all messages sent or received using that key are

Schaad & Prafullchandra  Expires October 31, 2012              [Page 18]
Internet-Draft              DH POP Algorithms                 April 2012

   compromised.  Similarly, loss of the private key results in an
   inability to read messages sent using that key.

   Selection of parameters can be of paramount importance.  In the
   selection of parameters one must take into account the community/
   group of entities that one wishes to be able to communicate with.  In
   choosing a set of parameters one must also be sure to avoid small
   groups.  [FIPS-186] Appendixes 2 and 3 contain information on the
   selection of parameters for DH.  [RFC6090] Section 10 contains
   information on the selection of parameter for ECC.  The practices
   outlined in these document will lead to better selection of
   parameters.

8.  References

8.1.  Normative References

   [RFC2104]  Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
              Hashing for Message Authentication", RFC 2104,
              February 1997.

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

   [RFC2314]  Kaliski, B., "PKCS #10: Certification Request Syntax
              Version 1.5", RFC 2314, March 1998.

   [RFC2631]  Rescorla, E., "Diffie-Hellman Key Agreement Method",
              RFC 2631, June 1999.

8.2.  Informative References

   [CRMF]     Schaad, J., "Internet X.509 Public Key Infrastructure
              Certificate Request Message Format (CRMF)", RFC 4211,
              September 2005.

   [RFC2875]  Prafullchandra, H. and J. Schaad, "Diffie-Hellman Proof-
              of-Possession Algorithms", RFC 2875, July 2000.

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

   [RFC5912]  Hoffman, P. and J. Schaad, "New ASN.1 Modules for the
              Public Key Infrastructure Using X.509 (PKIX)", RFC 5912,
              June 2010.

Schaad & Prafullchandra  Expires October 31, 2012              [Page 19]
Internet-Draft              DH POP Algorithms                 April 2012

   [RFC6090]  McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic
              Curve Cryptography Algorithms", RFC 6090, February 2011.

Appendix A.  Open Issues

   The following is a partial list of issues to be addressed:

      What examples should be added?

Appendix B.  ASN.1 Modules

B.1.  1988 ASN.1 Module

   This appendix represents the normative version of the ASN.1 module
   for this document.  In the event of a discrepancy between this module
   and the 2008 version of the module, this module wins.

Schaad & Prafullchandra  Expires October 31, 2012              [Page 20]
Internet-Draft              DH POP Algorithms                 April 2012

   DH-Sign DEFINITIONS IMPLICIT TAGS ::=

   BEGIN
   --EXPORTS ALL
   -- The types and values defined in this module are exported for use
   -- in the other ASN.1 modules. Other applications may use them
   -- for their own purposes.

   IMPORTS
      IssuerAndSerialNumber, MessageDigest
      FROM CryptographicMessageSyntax2004 { iso(1) member-body(2)
           us(840) rsadsi(113549) pkcs(1) pkcs-9(9) smime(16)
           modules(0) cms-2004(24) }

      id-pkix
      FROM PKIX1Explicit88 { iso(1) identified-organization(3)
           dod(6) internet(1) security(5) mechanisms(5) pkix(7)
           id-mod(0) id-pkix1-explicit(18) }

      Dss-Sig-Value, DomainParameters
      FROM PKIX1Algorithms88 {iso(1) identified-organization(3) dod(6)
           internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
           id-mod-pkix1-algorithms(17)};

      id-dh-sig-hmac-sha1 OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 3}

      DhSigStatic ::= SEQUENCE {
          issuerAndSerial IssuerAndSerialNumber OPTIONAL,
          hashValue       MessageDigest
      }

      id-alg-dh-pop OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 4}

      id-alg-dh-pop-sha256-hmac-sha256 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD1
      }

   END

B.2.  2008 ASN.1 Module

   This appendix represents an informative version of the ASN.1 module
   for this document.  This module references the object classes defined
   by [RFC5912] to more completely describe all of the associations
   between the elements defined in this document.  It also represents a
   module that will compile using the most current definition of ASN.1

   DH-Sign

Schaad & Prafullchandra  Expires October 31, 2012              [Page 21]
Internet-Draft              DH POP Algorithms                 April 2012

      { iso(1) identified-organization(3) dod(6) internet(1)
        security(5) mechanisms(5) pkix(7) id-mod(0)
        TBD9 }
   DEFINITIONS IMPLICIT TAGS ::=

   BEGIN
   --EXPORTS ALL
   -- The types and values defined in this module are exported for use
   -- in the other ASN.1 modules. Other applications may use them
   -- for their own purposes.

   IMPORTS
      SIGNATURE-ALGORITHM
      FROM AlgorithmInformation-2009
         {iso(1) identified-organization(3) dod(6) internet(1)
         security(5) mechanisms(5) pkix(7) id-mod(0)
          id-mod-algorithmInformation-02(58)}

      IssuerAndSerialNumber, MessageDigest
      FROM CryptographicMessageSyntax-2010 { iso(1) member-body(2)
           us(840) rsadsi(113549) pkcs(1) pkcs-9(9) smime(16)
           modules(0) id-mod-cms-2009(58) }

      DSA-Sig-Value, DomainParameters, ECDSA-Sig-Value,
      mda-sha1, mda-sha224, mda-sha256, mda-sha384, mda-sha512,
      pk-dh, pk-ec
      FROM PKIXAlgs-2009 { iso(1) identified-organization(3) dod(6)
        internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
        id-mod-pkix1-algorithms2008-02(56) }

      id-pkix
      FROM PKIX1Explicit-2009 {iso(1) identified-organization(3) dod(6)
           internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
           id-mod-pkix1-explicit-02(51)};

      DhSigStatic ::= SEQUENCE {
          issuerAndSerial IssuerAndSerialNumber OPTIONAL,
          hashValue       MessageDigest
      }

      sa-dhPop-static-sha1-hmac-sha1 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-dhPop-static-HMAC-SHA1
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS {pk-dh}
      }

      id-dhPop-static-HMAC-SHA1 OBJECT IDENTIFIER ::= {

Schaad & Prafullchandra  Expires October 31, 2012              [Page 22]
Internet-Draft              DH POP Algorithms                 April 2012

           id-pkix id-alg(6) 3
      }

      id-dhPop-static-SHA1-HMAC-SHA1 OBJECT IDENTIFIER ::=
           id-dhPop-static-HMAC-SHA1

      sa-dhPop-static-SHA224-HMAC-SHA224 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-alg-dhPop-static-SHA224-HMAC-SHA224
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS {pk-dh}
      }

      id-alg-dhPop-static-SHA224-HMAC-SHA224 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD1
      }

      sa-dhPop-static-SHA256-HMAC-SHA256 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-alg-dhPop-static-SHA256-HMAC-SHA256
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS {pk-dh}
      }

      id-alg-dhPop-static-SHA256-HMAC-SHA256 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD2
      }

      sa-dhPop-static-SHA384-HMAC-SHA384 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-alg-dhPop-static-SHA384-HMAC-SHA384
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS {pk-dh}
      }

      id-alg-dhPop-static-SHA384-HMAC-SHA384 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD3
      }

      sa-dhPop-static-SHA512-HMAC-SHA512 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-alg-dhPop-static-SHA512-HMAC-SHA512
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS {pk-dh}
      }

      id-alg-dhPop-static-SHA512-HMAC-SHA512 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD4

Schaad & Prafullchandra  Expires October 31, 2012              [Page 23]
Internet-Draft              DH POP Algorithms                 April 2012

      }

      sa-dh-pop-SHA1 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent
         HASHES { mda-sha1}
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dh-pop-SHA1 OBJECT IDENTIFIER ::= id-alg-dh-pop

      id-alg-dh-pop OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 4}

      sa-dh-pop-SHA224 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop-SHA224
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent
         HASHES { mda-sha224 }
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dh-pop-SHA224 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD5
      }

      sa-dh-pop-SHA256 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop-SHA256
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent
         HASHES { mda-sha256 }
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dh-pop-SHA256 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD6
      }

      sa-dh-pop-SHA384 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop-SHA384
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent
         HASHES { mda-sha384 }
         PUBLIC-KEYS { pk-dh }
      }

Schaad & Prafullchandra  Expires October 31, 2012              [Page 24]
Internet-Draft              DH POP Algorithms                 April 2012

      id-alg-dh-pop-SHA384 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD7
      }

      sa-dh-pop-SHA512 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop-SHA512
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent
         HASHES { mda-sha512 }
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dh-pop-SHA512 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) TBD8
      }

      id-alg-ecdhPop-static-SHA224-HMAC-SHA224 OBJECT IDENTIFIER ::= {
         id-pkix id-alg(6) TBD11
      }

      sa-ecdh-pop-SHA224-HMAC-SHA224 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-ecdhPop-static-SHA224-HMAC-SHA224
         VALUE DhSigStatic
         PARAMS ARE absent
         PUBLIC-KEYS { pk-ec }
      }

      id-alg-ecdhPop-static-SHA256-HMAC-SHA256 OBJECT IDENTIFIER ::= {
         id-pkix id-alg(6) TBD912
      }

      sa-ecdh-pop-SHA256-HMAC-SHA256 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-ecdhPop-static-SHA256-HMAC-SHA256
         VALUE DhSigStatic
         PARAMS ARE absent
         PUBLIC-KEYS { pk-ec }
      }

      id-alg-ecdhPop-static-SHA384-HMAC-SHA384 OBJECT IDENTIFIER ::= {
         id-pkix id-alg(6) TBD13
      }

      sa-ecdh-pop-SHA384-HMAC-SHA384 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-ecdhPop-static-SHA384-HMAC-SHA384
         VALUE DhSigStatic
         PARAMS ARE absent
         PUBLIC-KEYS { pk-ec }
      }

Schaad & Prafullchandra  Expires October 31, 2012              [Page 25]
Internet-Draft              DH POP Algorithms                 April 2012

      id-alg-ecdhPop-static-SHA512-HMAC-SHA512 OBJECT IDENTIFIER ::= {
         id-pkix id-alg(6) TBD14
      }

      sa-ecdh-pop-SHA512-HMAC-SHA512 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-ecdhPop-static-SHA512-HMAC-SHA512
         VALUE DhSigStatic
         PARAMS ARE absent
         PUBLIC-KEYS { pk-ec }
      }

   END

Appendix C.  Example of Static DH Proof-of-Possession

   The following example follows the steps described earlier in section
   3.

   Step 1: Establishing common Diffie-Hellman parameters.  Assume the
   parameters are as in the DER encoded certificate.  The certificate
   contains a DH public key signed by a CA with a DSA signing key.

  0 30 939: SEQUENCE {
  4 30 872:   SEQUENCE {
  8 A0   3:     [0] {
 10 02   1:       INTEGER 2
          :       }
 13 02   6:     INTEGER
          :       00 DA 39 B6 E2 CB
 21 30  11:     SEQUENCE {
 23 06   7:       OBJECT IDENTIFIER dsaWithSha1 (1 2 840 10040 4 3)
 32 05   0:       NULL
          :       }
 34 30  72:     SEQUENCE {
 36 31  11:       SET {
 38 30   9:         SEQUENCE {
 40 06   3:           OBJECT IDENTIFIER countryName (2 5 4 6)
 45 13   2:           PrintableString 'US'
          :           }
          :         }
 49 31  17:       SET {
 51 30  15:         SEQUENCE {
 53 06   3:           OBJECT IDENTIFIER organizationName (2 5 4 10)
 58 13   8:           PrintableString 'XETI Inc'
          :           }
          :         }

Schaad & Prafullchandra  Expires October 31, 2012              [Page 26]
Internet-Draft              DH POP Algorithms                 April 2012

 68 31  16:       SET {
 70 30  14:         SEQUENCE {
 72 06   3:           OBJECT IDENTIFIER organizationalUnitName (2 5 4
                                11)
 77 13   7:           PrintableString 'Testing'
          :           }
          :         }
 86 31  20:       SET {
 88 30  18:         SEQUENCE {
 90 06   3:           OBJECT IDENTIFIER commonName (2 5 4 3)
 95 13  11:           PrintableString 'Root DSA CA'
          :           }
          :         }
          :       }
108 30  30:     SEQUENCE {
110 17  13:       UTCTime '990914010557Z'
125 17  13:       UTCTime '991113010557Z'
          :       }
140 30  70:     SEQUENCE {
142 31  11:       SET {
144 30   9:         SEQUENCE {
146 06   3:           OBJECT IDENTIFIER countryName (2 5 4 6)
151 13   2:           PrintableString 'US'
          :           }
          :         }
155 31  17:       SET {
157 30  15:         SEQUENCE {
159 06   3:           OBJECT IDENTIFIER organizationName (2 5 4 10)
164 13   8:           PrintableString 'XETI Inc'
          :           }
          :         }
174 31  16:       SET {
176 30  14:         SEQUENCE {
178 06   3:           OBJECT IDENTIFIER organizationalUnitName (2 5 4
                                11)
183 13   7:           PrintableString 'Testing'
          :           }
          :         }
192 31  18:       SET {
194 30  16:         SEQUENCE {
196 06   3:           OBJECT IDENTIFIER commonName (2 5 4 3)
201 13   9:           PrintableString 'DH TestCA'
          :           }
          :         }
          :       }
212 30 577:     SEQUENCE {
216 30 438:       SEQUENCE {
220 06   7:         OBJECT IDENTIFIER dhPublicKey (1 2 840 10046 2 1)

Schaad & Prafullchandra  Expires October 31, 2012              [Page 27]
Internet-Draft              DH POP Algorithms                 April 2012

229 30 425:         SEQUENCE {
233 02 129:           INTEGER
          :             00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7
          :             C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82
          :             F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21
          :             51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68
          :             5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72
          :             8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2
          :             32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02
          :             D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85
          :             27
365 02 128:           INTEGER
          :             26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90
          :             06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4
          :             64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57
          :             86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6
          :             4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE
          :             47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1
          :             39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48
          :             95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD
496 02  33:           INTEGER
          :             00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94
          :             B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30
          :             FB
531 02  97:           INTEGER
          :             00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7
          :             B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D
          :             AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39
          :             40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76
          :             B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56
          :             68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2
          :             92
630 30  26:           SEQUENCE {
632 03  21:             BIT STRING 0 unused bits
          :             1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB
          :             09 E4 98 34
655 02   1:             INTEGER 55
          :             }
          :           }
          :         }
658 03 132:       BIT STRING 0 unused bits
          :         02 81 80 5F CF 39 AD 62 CF 49 8E D1 CE 66 E2 B1
          :         E6 A7 01 4D 05 C2 77 C8 92 52 42 A9 05 A4 DB E0
          :         46 79 50 A3 FC 99 3D 3D A6 9B A9 AD BC 62 1C 69
          :         B7 11 A1 C0 2A F1 85 28 F7 68 FE D6 8F 31 56 22
          :         4D 0A 11 6E 72 3A 02 AF 0E 27 AA F9 ED CE 05 EF
          :         D8 59 92 C0 18 D7 69 6E BD 70 B6 21 D1 77 39 21
          :         E1 AF 7A 3A CF 20 0A B4 2C 69 5F CF 79 67 20 31

Schaad & Prafullchandra  Expires October 31, 2012              [Page 28]
Internet-Draft              DH POP Algorithms                 April 2012

          :         4D F2 C6 ED 23 BF C4 BB 1E D1 71 40 2C 07 D6 F0
          :         8F C5 1A
          :       }
793 A3  85:     [3] {
795 30  83:       SEQUENCE {
797 30  29:         SEQUENCE {
799 06   3:           OBJECT IDENTIFIER subjectKeyIdentifier (2 5 29 14)
804 04  22:           OCTET STRING
          :             04 14 80 DF 59 88 BF EB 17 E1 AD 5E C6 40 A3 42
          :             E5 AC D3 B4 88 78
          :           }
828 30  34:         SEQUENCE {
830 06   3:           OBJECT IDENTIFIER authorityKeyIdentifier (2 5 29
35)
835 01   1:           BOOLEAN TRUE
838 04  24:           OCTET STRING
          :             30 16 80 14 6A 23 37 55 B9 FD 81 EA E8 4E D3 C9
          :             B7 09 E5 7B 06 E3 68 AA
          :           }
864 30  14:         SEQUENCE {
866 06   3:           OBJECT IDENTIFIER keyUsage (2 5 29 15)
871 01   1:           BOOLEAN TRUE
874 04   4:           OCTET STRING
          :             03 02 03 08
          :           }
          :         }
          :       }
          :     }
880 30  11:   SEQUENCE {
882 06   7:     OBJECT IDENTIFIER dsaWithSha1 (1 2 840 10040 4 3)
891 05   0:     NULL
          :     }
893 03  48:   BIT STRING 0 unused bits
          :     30 2D 02 14 7C 6D D2 CA 1E 32 D1 30 2E 29 66 BC
          :     06 8B 60 C7 61 16 3B CA 02 15 00 8A 18 DD C1 83
          :     58 29 A2 8A 67 64 03 92 AB 02 CE 00 B5 94 6A
          :   }

   Step 2.  End Entity/User generates a Diffie-Hellman key-pair using
   the parameters from the CA certificate.

   EE DH public key: SunJCE Diffie-Hellman Public Key:

Schaad & Prafullchandra  Expires October 31, 2012              [Page 29]
Internet-Draft              DH POP Algorithms                 April 2012

      Y: 13 63 A1 85 04 8C 46 A8 88 EB F4 5E A8 93 74 AE
         FD AE 9E 96 27 12 65 C4 4C 07 06 3E 18 FE 94 B8
         A8 79 48 BD 2E 34 B6 47 CA 04 30 A1 EC 33 FD 1A
         0B 2D 9E 50 C9 78 0F AE 6A EC B5 6B 6A BE B2 5C
         DA B2 9F 78 2C B9 77 E2 79 2B 25 BF 2E 0B 59 4A
         93 4B F8 B3 EC 81 34 AE 97 47 52 E0 A8 29 98 EC
         D1 B0 CA 2B 6F 7A 8B DB 4E 8D A5 15 7E 7E AF 33
         62 09 9E 0F 11 44 8C C1 8D A2 11 9E 53 EF B2 E8

   EE DH private key:

      X: 32 CC BD B4 B7 7C 44 26 BB 3C 83 42 6E 7D 1B 00
         86 35 09 71 07 A0 A4 76 B8 DB 5F EC 00 CE 6F C3

   Step 3.  Compute K and the signature.

   LeadingInfo: DER encoded Subject/Requestor DN (as in the generated
   Certificate Signing Request)

        30 4E 31 0B 30 09 06 03 55 04 06 13 02 55 53 31
        11 30 0F 06 03 55 04 0A 13 08 58 45 54 49 20 49
        6E 63 31 10 30 0E 06 03 55 04 0B 13 07 54 65 73
        74 69 6E 67 31 1A 30 18 06 03 55 04 03 13 11 50
        4B 49 58 20 45 78 61 6D 70 6C 65 20 55 73 65 72

   TrailingInfo: DER encoded Issuer/Recipient DN (from the certificate
   described in step 1)

        30 46 31 0B 30 09 06 03 55 04 06 13 02 55 53 31
        11 30 0F 06 03 55 04 0A 13 08 58 45 54 49 20 49
        6E 63 31 10 30 0E 06 03 55 04 0B 13 07 54 65 73
        74 69 6E 67 31 12 30 10 06 03 55 04 03 13 09 44
        48 20 54 65 73 74 43 41

      K:
        F4 D7 BB 6C C7 2D 21 7F 1C 38 F7 DA 74 2D 51 AD
        14 40 66 75

   TBS: the "text" for computing the SHA-1 HMAC.

Schaad & Prafullchandra  Expires October 31, 2012              [Page 30]
Internet-Draft              DH POP Algorithms                 April 2012

      30 82 02 98 02 01 00 30 4E 31 0B 30 09 06 03 55
      04 06 13 02 55 53 31 11 30 0F 06 03 55 04 0A 13
      08 58 45 54 49 20 49 6E 63 31 10 30 0E 06 03 55
      04 0B 13 07 54 65 73 74 69 6E 67 31 1A 30 18 06
      03 55 04 03 13 11 50 4B 49 58 20 45 78 61 6D 70
      6C 65 20 55 73 65 72 30 82 02 41 30 82 01 B6 06
      07 2A 86 48 CE 3E 02 01 30 82 01 A9 02 81 81 00
      94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 C5
      A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 F5
      D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 51
      63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 5B
      79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 8A
      F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 32
      E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 D7
      B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 27
      02 81 80 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87
      53 3F 90 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5
      0C 53 D4 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6
      1B 7F 57 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31
      7A 48 B6 4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69
      D9 9B DE 47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33
      51 C8 F1 39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31
      15 26 48 95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E
      DA D1 CD 02 21 00 E8 72 FA 96 F0 11 40 F5 F2 DC
      FD 3B 5D 78 94 B1 85 01 E5 69 37 21 F7 25 B9 BA
      71 4A FC 60 30 FB 02 61 00 A3 91 01 C0 A8 6E A4
      4D A0 56 FC 6C FE 1F A7 B0 CD 0F 94 87 0C 25 BE
      97 76 8D EB E5 A4 09 5D AB 83 CD 80 0B 35 67 7F
      0C 8E A7 31 98 32 85 39 40 9D 11 98 D8 DE B8 7F
      86 9B AF 8D 67 3D B6 76 B4 61 2F 21 E1 4B 0E 68
      FF 53 3E 87 DD D8 71 56 68 47 DC F7 20 63 4B 3C
      5F 78 71 83 E6 70 9E E2 92 30 1A 03 15 00 1C D5
      3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB 09 E4
      98 34 02 01 37 03 81 84 00 02 81 80 13 63 A1 85
      04 8C 46 A8 88 EB F4 5E A8 93 74 AE FD AE 9E 96
      27 12 65 C4 4C 07 06 3E 18 FE 94 B8 A8 79 48 BD
      2E 34 B6 47 CA 04 30 A1 EC 33 FD 1A 0B 2D 9E 50
      C9 78 0F AE 6A EC B5 6B 6A BE B2 5C DA B2 9F 78
      2C B9 77 E2 79 2B 25 BF 2E 0B 59 4A 93 4B F8 B3
      EC 81 34 AE 97 47 52 E0 A8 29 98 EC D1 B0 CA 2B
      6F 7A 8B DB 4E 8D A5 15 7E 7E AF 33 62 09 9E 0F
      11 44 8C C1 8D A2 11 9E 53 EF B2 E8

   Certification Request:

   0 30 793: SEQUENCE {
   4 30 664:   SEQUENCE {
   8 02   1:     INTEGER 0

Schaad & Prafullchandra  Expires October 31, 2012              [Page 31]
Internet-Draft              DH POP Algorithms                 April 2012

  11 30  78:     SEQUENCE {
  13 31  11:       SET {
  15 30   9:         SEQUENCE {
  17 06   3:           OBJECT IDENTIFIER countryName (2 5 4 6)
  22 13   2:           PrintableString 'US'
           :           }
           :         }
  26 31  17:       SET {
  28 30  15:         SEQUENCE {
  30 06   3:           OBJECT IDENTIFIER organizationName (2 5 4 10)
  35 13   8:           PrintableString 'XETI Inc'
           :           }
           :         }
  45 31  16:       SET {
  47 30  14:         SEQUENCE {
  49 06   3:           OBJECT IDENTIFIER organizationalUnitName (2 5 4
                                 11)
  54 13   7:           PrintableString 'Testing'
           :           }
           :         }
  63 31  26:       SET {
  65 30  24:         SEQUENCE {
  67 06   3:           OBJECT IDENTIFIER commonName (2 5 4 3)
  72 13  17:           PrintableString 'PKIX Example User'
           :           }
           :         }
           :       }
  91 30 577:     SEQUENCE {
  95 30 438:       SEQUENCE {
  99 06   7:         OBJECT IDENTIFIER dhPublicKey (1 2 840 10046 2 1)
 108 30 425:         SEQUENCE {
 112 02 129:           INTEGER
           :             00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7
           :             C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82
           :             F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21
           :             51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68
           :             5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72
           :             8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2
           :             32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02
           :             D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85
           :             27
 244 02 128:           INTEGER
           :             26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90
           :             06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4
           :             64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57
           :             86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6
           :             4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE
           :             47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1

Schaad & Prafullchandra  Expires October 31, 2012              [Page 32]
Internet-Draft              DH POP Algorithms                 April 2012

           :             39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48
           :             95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD
 375 02  33:           INTEGER
           :             00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94
           :             B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30
           :             FB
 410 02  97:           INTEGER
           :             00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7
           :             B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D
           :             AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39
           :             40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76
           :             B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56
           :             68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2
           :             92
 509 30  26:           SEQUENCE {
 511 03  21:             BIT STRING 0 unused bits
           :               1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E
           :               DB 09 E4 98 34
 534 02   1:             INTEGER 55
           :             }
           :           }
           :         }
 537 03 132:       BIT STRING 0 unused bits
           :         02 81 80 13 63 A1 85 04 8C 46 A8 88 EB F4 5E A8
           :         93 74 AE FD AE 9E 96 27 12 65 C4 4C 07 06 3E 18
           :         FE 94 B8 A8 79 48 BD 2E 34 B6 47 CA 04 30 A1 EC
           :         33 FD 1A 0B 2D 9E 50 C9 78 0F AE 6A EC B5 6B 6A
           :         BE B2 5C DA B2 9F 78 2C B9 77 E2 79 2B 25 BF 2E
           :         0B 59 4A 93 4B F8 B3 EC 81 34 AE 97 47 52 E0 A8
           :         29 98 EC D1 B0 CA 2B 6F 7A 8B DB 4E 8D A5 15 7E
           :         7E AF 33 62 09 9E 0F 11 44 8C C1 8D A2 11 9E 53
           :         EF B2 E8
           :       }
           :     }
 672 30  12:   SEQUENCE {
 674 06   8:     OBJECT IDENTIFIER dh-sig-hmac-sha1 (1 3 6 1 5 5 7 6 3)
 684 05   0:     NULL
           :     }
 686 03 109:   BIT STRING 0 unused bits
           :     30 6A 30 52 30 48 31 0B 30 09 06 03 55 04 06 13
           :     02 55 53 31 11 30 0F 06 03 55 04 0A 13 08 58 45
           :     54 49 20 49 6E 63 31 10 30 0E 06 03 55 04 0B 13
           :     07 54 65 73 74 69 6E 67 31 14 30 12 06 03 55 04
           :     03 13 0B 52 6F 6F 74 20 44 53 41 20 43 41 02 06
           :     00 DA 39 B6 E2 CB 04 14 1B 17 AD 4E 65 86 1A 6C
           :     7C 85 FA F7 95 DE 48 93 C5 9D C5 24
           :   }

Schaad & Prafullchandra  Expires October 31, 2012              [Page 33]
Internet-Draft              DH POP Algorithms                 April 2012

   Signature verification requires CAAEs private key, the CA certificate
   and the generated Certification Request.

   CA DH private key:

       x:  3E 5D AD FD E5 F4 6B 1B 61 5E 18 F9 0B 84 74 a7
           52 1E D6 92 BC 34 94 56 F3 0C BE DA 67 7A DD 7D

Appendix D.  Example of Discrete Log Signature

   Step 1.  Generate a Diffie-Hellman Key with length of q being 256-
   bits.

      p:
        94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 C5
        A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 F5
        D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 51
        63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 5B
        79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 8A
        F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 32
        E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 D7
        B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 27

      q:
        E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 B1
        85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 FB

      g:
        26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90
        06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4
        64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57
        86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6
        4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE
        47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1
        39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48
        95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD

      j:
        A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 B0
        CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D AB
        83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 40
        9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 B4
        61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 68
        47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 92

      y:
        5F CF 39 AD 62 CF 49 8E D1 CE 66 E2 B1 E6 A7 01

Schaad & Prafullchandra  Expires October 31, 2012              [Page 34]
Internet-Draft              DH POP Algorithms                 April 2012

        4D 05 C2 77 C8 92 52 42 A9 05 A4 DB E0 46 79 50
        A3 FC 99 3D 3D A6 9B A9 AD BC 62 1C 69 B7 11 A1
        C0 2A F1 85 28 F7 68 FE D6 8F 31 56 22 4D 0A 11
        6E 72 3A 02 AF 0E 27 AA F9 ED CE 05 EF D8 59 92
        C0 18 D7 69 6E BD 70 B6 21 D1 77 39 21 E1 AF 7A
        3A CF 20 0A B4 2C 69 5F CF 79 67 20 31 4D F2 C6
        ED 23 BF C4 BB 1E D1 71 40 2C 07 D6 F0 8F C5 1A

      seed:
        1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB
        09 E4 98 34

      C:
        00000037

      x:
        3E 5D AD FD E5 F4 6B 1B 61 5E 18 F9 0B 84 74 a7
        52 1E D6 92 BC 34 94 56 F3 0C BE DA 67 7A DD 7D

   Step 2.  Form the value to be signed and hash with SHA1.  The result
   of the hash for this example is:

        5f a2 69 b6 4b 22 91 22 6f 4c fe 68 ec 2b d1 c6
        d4 21 e5 2c

   Step 3.  The hash value needs to be expanded since |q| = 256.  This
   is done by hashing the hash with SHA1 and appending it to the
   original hash.  The value after this step is:

        5f a2 69 b6 4b 22 91 22 6f 4c fe 68 ec 2b d1 c6
        d4 21 e5 2c 64 92 8b c9 5e 34 59 70 bd 62 40 ad
        6f 26 3b f7 1c a3 b2 cb

   Next the first 255 bits of this value are taken to be the resulting
   "hash" value.  Note in this case a shift of one bit right is done
   since the result is to be treated as an integer:

        2f d1 34 db 25 91 48 91 37 a6 7f 34 76 15 e8 e3
        6a 10 f2 96 32 49 45 e4 af 1a 2c b8 5e b1 20 56

   Step 4.  The signature value is computed.  In this case you get the
   values

Schaad & Prafullchandra  Expires October 31, 2012              [Page 35]
Internet-Draft              DH POP Algorithms                 April 2012

      R:
        A1 B5 B4 90 01 34 6B A0 31 6A 73 F5 7D F6 5C 14
        43 52 D2 10 BF 86 58 87 F7 BC 6E 5A 77 FF C3 4B

      S:
        59 40 45 BC 6F 0D DC FF 9D 55 40 1E C4 9E 51 3D
        66 EF B2 FF 06 40 9A 39 68 75 81 F7 EC 9E BE A1

   The encoded signature values is then:

      30 45 02 21 00 A1 B5 B4 90 01 34 6B A0 31 6A 73
      F5 7D F6 5C 14 43 52 D2 10 BF 86 58 87 F7 BC 6E
      5A 77 FF C3 4B 02 20 59 40 45 BC 6F 0D DC FF 9D
      55 40 1E C4 9E 51 3D 66 EF B2 FF 06 40 9A 39 68
      75 81 F7 EC 9E BE A1

      Result:
        30 82 02 c2 30 82 02 67 02 01 00 30 1b 31 19 30
        17 06 03 55 04 03 13 10 49 45 54 46 20 50 4b 49
        58 20 53 41 4d 50 4c 45 30 82 02 41 30 82 01 b6
        06 07 2a 86 48 ce 3e 02 01 30 82 01 a9 02 81 81
        00 94 84 e0 45 6c 7f 69 51 62 3e 56 80 7c 68 e7
        c5 a9 9e 9e 74 74 94 ed 90 8c 1d c4 e1 4a 14 82
        f5 d2 94 0c 19 e3 b9 10 bb 11 b9 e5 a5 fb 8e 21
        51 63 02 86 aa 06 b8 21 36 b6 7f 36 df d1 d6 68
        5b 79 7c 1d 5a 14 75 1f 6a 93 75 93 ce bb 97 72
        8a f0 0f 23 9d 47 f6 d4 b3 c7 f0 f4 e6 f6 2b c2
        32 e1 89 67 be 7e 06 ae f8 d0 01 6b 8b 2a f5 02
        d7 b6 a8 63 94 83 b0 1b 31 7d 52 1a de e5 03 85
        27 02 81 80 26 a6 32 2c 5a 2b d4 33 2b 5c dc 06
        87 53 3f 90 06 61 50 38 3e d2 b9 7d 81 1c 12 10
        c5 0c 53 d4 64 d1 8e 30 07 08 8c dd 3f 0a 2f 2c
        d6 1b 7f 57 86 d0 da bb 6e 36 2a 18 e8 d3 bc 70
        31 7a 48 b6 4e 18 6e dd 1f 22 06 eb 3f ea d4 41
        69 d9 9b de 47 95 7a 72 91 d2 09 7f 49 5c 3b 03
        33 51 c8 f1 39 9a ff 04 d5 6e 7e 94 3d 03 b8 f6
        31 15 26 48 95 a8 5c de 47 88 b4 69 3a 00 a7 86
        9e da d1 cd 02 21 00 e8 72 fa 96 f0 11 40 f5 f2
        dc fd 3b 5d 78 94 b1 85 01 e5 69 37 21 f7 25 b9
        ba 71 4a fc 60 30 fb 02 61 00 a3 91 01 c0 a8 6e
        a4 4d a0 56 fc 6c fe 1f a7 b0 cd 0f 94 87 0c 25
        be 97 76 8d eb e5 a4 09 5d ab 83 cd 80 0b 35 67
        7f 0c 8e a7 31 98 32 85 39 40 9d 11 98 d8 de b8
        7f 86 9b af 8d 67 3d b6 76 b4 61 2f 21 e1 4b 0e
        68 ff 53 3e 87 dd d8 71 56 68 47 dc f7 20 63 4b
        3c 5f 78 71 83 e6 70 9e e2 92 30 1a 03 15 00 1c
        d5 3a 0d 17 82 6d 0a 81 75 81 46 10 8e 3e db 09
        e4 98 34 02 01 37 03 81 84 00 02 81 80 5f cf 39

Schaad & Prafullchandra  Expires October 31, 2012              [Page 36]
Internet-Draft              DH POP Algorithms                 April 2012

        ad 62 cf 49 8e d1 ce 66 e2 b1 e6 a7 01 4d 05 c2
        77 c8 92 52 42 a9 05 a4 db e0 46 79 50 a3 fc 99
        3d 3d a6 9b a9 ad bc 62 1c 69 b7 11 a1 c0 2a f1
        85 28 f7 68 fe d6 8f 31 56 22 4d 0a 11 6e 72 3a
        02 af 0e 27 aa f9 ed ce 05 ef d8 59 92 c0 18 d7
        69 6e bd 70 b6 21 d1 77 39 21 e1 af 7a 3a cf 20
        0a b4 2c 69 5f cf 79 67 20 31 4d f2 c6 ed 23 bf
        c4 bb 1e d1 71 40 2c 07 d6 f0 8f c5 1a a0 00 30
        0c 06 08 2b 06 01 05 05 07 06 04 05 00 03 47 00
        30 44 02 20 54 d9 43 8d 0f 9d 42 03 d6 09 aa a1
        9a 3c 17 09 ae bd ee b3 d1 a0 00 db 7d 8c b8 e4
        56 e6 57 7b 02 20 44 89 b1 04 f5 40 2b 5f e7 9c
        f9 a4 97 50 0d ad c3 7a a4 2b b2 2d 5d 79 fb 38
        8a b4 df bb 88 bc

   Decoded Version of result:

   0 30  707: SEQUENCE {
   4 30  615:   SEQUENCE {
   8 02    1:     INTEGER 0
  11 30   27:     SEQUENCE {
  13 31   25:       SET {
  15 30   23:         SEQUENCE {
  17 06    3:           OBJECT IDENTIFIER commonName (2 5 4 3)
  22 13   16:           PrintableString 'IETF PKIX SAMPLE'
            :           }
            :         }
            :       }
  40 30  577:     SEQUENCE {
  44 30  438:       SEQUENCE {
  48 06    7:         OBJECT IDENTIFIER dhPublicNumber (1 2 840 10046 2
                                  1)
  57 30  425:         SEQUENCE {
  61 02  129:           INTEGER
            :            00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7
            :            C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82
            :            F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21
            :            51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68
            :            5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72
            :            8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2
            :            32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02
            :            D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85
            :            27
 193 02  128:           INTEGER
            :            26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90
            :            06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4
            :            64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57
            :            86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6

Schaad & Prafullchandra  Expires October 31, 2012              [Page 37]
Internet-Draft              DH POP Algorithms                 April 2012

            :            4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE
            :            47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1
            :            39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48
            :            95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD
 324 02   33:           INTEGER
            :            00 E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94
            :            B1 85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30
            :            FB
 359 02   97:           INTEGER
            :            00 A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7
            :            B0 CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D
            :            AB 83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39
            :            40 9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76
            :            B4 61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56
            :            68 47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2
            :            92
 458 30   26:           SEQUENCE {
 460 03   21:             BIT STRING 0 unused bits
            :            1C D5 3A 0D 17 82 6D 0A 81 75 81 46 10 8E 3E DB
            :            09 E4 98 34
 483 02    1:             INTEGER 55
            :             }
            :           }
            :         }
 486 03  132:       BIT STRING 0 unused bits
            :         02 81 80 5F CF 39 AD 62 CF 49 8E D1 CE 66 E2 B1
            :         E6 A7 01 4D 05 C2 77 C8 92 52 42 A9 05 A4 DB E0
            :         46 79 50 A3 FC 99 3D 3D A6 9B A9 AD BC 62 1C 69
            :         B7 11 A1 C0 2A F1 85 28 F7 68 FE D6 8F 31 56 22
            :         4D 0A 11 6E 72 3A 02 AF 0E 27 AA F9 ED CE 05 EF
            :         D8 59 92 C0 18 D7 69 6E BD 70 B6 21 D1 77 39 21
            :         E1 AF 7A 3A CF 20 0A B4 2C 69 5F CF 79 67 20 31
            :         4D F2 C6 ED 23 BF C4 BB 1E D1 71 40 2C 07 D6 F0
            :         8F C5 1A
            :       }
 621 A0    0:     [0]
            :     }
 623 30   12:   SEQUENCE {
 625 06    8:     OBJECT IDENTIFIER '1 3 6 1 5 5 7 6 4'
 635 05    0:     NULL
            :     }
 637 03   72:   BIT STRING 0 unused bits
            :     30 45 02 21 00 A1 B5 B4 90 01 34 6B A0 31 6A 73
            :     F5 7D F6 5C 14 43 52 D2 10 BF 86 58 87 F7 BC 6E
            :     5A 77 FF C3 4B 02 20 59 40 45 BC 6F 0D DC FF 9D
            :     55 40 1E C4 9E 51 3D 66 EF B2 FF 06 40 9A 39 68
            :     75 81 F7 EC 9E BE A1
            :   }

Schaad & Prafullchandra  Expires October 31, 2012              [Page 38]
Internet-Draft              DH POP Algorithms                 April 2012

Authors' Addresses

   Jim Schaad
   Soaring Hawk Consulting

   Email: ietf@augustcellars.com

   Hemma Prafullchandra

Schaad & Prafullchandra  Expires October 31, 2012              [Page 39]