Diffie-Hellman Proof-of-Possession Algorithms
draft-schaad-pkix-rfc2875-bis-05

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Document Type Active Internet-Draft (individual in sec area)
Authors Jim Schaad , Hemma Prafullchandra 
Last updated 2013-01-02 (latest revision 2012-12-28)
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PKIX                                                           J. Schaad
Internet-Draft                                   Soaring Hawk Consulting
Obsoletes: 2875 (if approved)                          H. Prafullchandra
Intended status: Standards Track                                Hy-Trust
Expires: July 1, 2013                                  December 28, 2012

             Diffie-Hellman Proof-of-Possession Algorithms
                    draft-schaad-pkix-rfc2875-bis-05

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.

   This document obsoletes RFC 2875.

Status of this Memo

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   This Internet-Draft will expire on July 1, 2013.

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   Copyright (c) 2012 IETF Trust and the persons identified as the
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   carefully, as they describe your rights and restrictions with respect

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   to this document.  Code Components extracted from this document must
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   This document may contain material from IETF Documents or IETF
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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  4
     1.1.  Changes since RFC2875  . . . . . . . . . . . . . . . . . .  4
     1.2.  Requirements Terminology . . . . . . . . . . . . . . . . .  5
   2.  Terminology  . . . . . . . . . . . . . . . . . . . . . . . . .  5
   3.  Notation . . . . . . . . . . . . . . . . . . . . . . . . . . .  5
   4.  Static DH Proof-of-Possession Process  . . . . . . . . . . . .  6
     4.1.  ASN.1 Encoding . . . . . . . . . . . . . . . . . . . . . .  8
   5.  Discrete Logarithm Signature . . . . . . . . . . . . . . . . . 11
     5.1.  Expanding the Digest Value . . . . . . . . . . . . . . . . 11
     5.2.  Signature Computation Algorithm  . . . . . . . . . . . . . 12
     5.3.  Signature Verification Algorithm . . . . . . . . . . . . . 13
     5.4.  ASN.1 Encoding . . . . . . . . . . . . . . . . . . . . . . 13
   6.  Static ECDH Proof-of-Possession Process  . . . . . . . . . . . 16
     6.1.  ASN.1 Encoding . . . . . . . . . . . . . . . . . . . . . . 17
   7.  Security Considerations  . . . . . . . . . . . . . . . . . . . 19
   8.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 20
   9.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 20
     9.1.  Normative References . . . . . . . . . . . . . . . . . . . 20
     9.2.  Informative References . . . . . . . . . . . . . . . . . . 21
   Appendix A.  ASN.1 Modules . . . . . . . . . . . . . . . . . . . . 21
     A.1.  2008 ASN.1 Module  . . . . . . . . . . . . . . . . . . . . 21
     A.2.  1988 ASN.1 Module  . . . . . . . . . . . . . . . . . . . . 26
   Appendix B.  Example of Static DH Proof-of-Possession  . . . . . . 28
   Appendix C.  Example of Discrete Log Signature . . . . . . . . . . 36
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 41

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1.  Introduction

   PKCS #10 [RFC2986] 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 of producing a POP by a signing/encrypting
   operation.  Diffie-Hellman (DH) and Elliptic Curve Diffie-Hellman
   (ECDH) are 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 Algorithm) like was done
   for DSA (Digital Signature Algorithm).  Given the current PKIX
   definitions for the public key parameters of elliptic curve, the
   number of groups is both limited and predefined.  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 is used are
   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  New instances of the static DH POP algorithm have been created
      using HMAC paired with the SHA-224, SHA-256, SHA-384 and SHA-512
      hash algorithms.

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

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   o  New instances of the Discrete Logarithm Signature have 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 an ECDH
   public value and is signed with any signature algorithm (e.g., RSA or
   ECDSA).

   Proof-of-Possession (POP) is a means 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.

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      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
      a * b          : a times b
                       depending on context multiplication may be within
                       an Elliptic Curve or normal multiplication

      KDF(a)         : Key Derivation Function producing a value from a.
      MAC(a, b)      : Message Authentication Code function where
                       a is the key and b is the text
      LEFTMOST(a, b) : Return the b left most bits of a
      FLOOR(a, b)    : Return n where n is the largest integer such that
                       n*b <= a

   Details on how to implement the HMAC version of the MAC function used
   in this document can be found in RFC 2104 [RFC2104], RFC 6234
   [RFC6234] and RFC 4231 [RFC4231].

4.  Static DH Proof-of-Possession Process

   The Static DH POP algorithm is set up 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)

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

       For an entity E:

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       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 (text) 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^(x*y) 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 provided in the protocol) 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 it would require its 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.

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4.1.  ASN.1 Encoding

   The algorithm outlined above allows for the use of an arbitrary hash
   function in computing the temporary key and the MAC value.  In this
   specification we define object identifiers for the SHA-1, SHA-256,
   SHA-384 and SHA-512 hash values.  The ASN.1 structures associated
   with the static Diffie-Hellman POP algorithm are:

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

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

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

      id-dhPop-static-sha1-hmac-sha1 OBJECT IDENTIFIER ::=
           id-dh-sig-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) 15
      }

      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) 16
      }

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      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) 17
      }

      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) 18
      }

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

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

      issuerAndSerial
         This field contains 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
         This field contains the result of the MAC operation in step 3d.

   sa-dhPop-static-sha1-hmac-sha1
      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.

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   id-dhPop-static-sha1-hmac-sha1
      This OID identifies the Static DH POP algorithm that uses SHA-1 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-dh-sig-hmac-sha1
      which was defined in the previous version of this document
      [RFC2875].

   sa-dhPop-static-sha224-hmac-sha224
      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-sha224-hmac-sha224
      This OID identifies the Static DH POP algorithm that uses SHA-224
      as the KDF and HMAC-SHA224 as the MAC function.

   sa-dhPop-static-sha256-hmac-sha256
      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-sha256-hmac-sha256
      This OID identifies the Static DH POP algorithm that uses SHA-256
      as the KDF and HMAC-SHA256 as the MAC function.

   sa-dhPop-static-sha384-hmac-sha384
      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-sha384-hmac-sha384
      This OID identifies the Static DH POP algorithm that uses SHA-384
      as the KDF and HMAC-SHA384 as the MAC function.

   sa-dhPop-static-sha512-hmac-sha512
      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-sha512-hmac-sha512
      This OID identifies the Static DH POP algorithm that uses SHA-512
      as the KDF and HMAC-SHA512 as the MAC function.

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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 dealing with the hash and key sizes 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 good practice as it allows for
   checking of small subgroup 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)/q) mod q > 1
   (g has order q mod p)
   q is a large prime
   j is a large integer such that p = q*j + 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
   b = 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 the output length of the SHA-1 digest algorithm) and the
   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 b bits in
   length.  (If the hash function is SHA-1, then b=160 bits and the size
   restriction on b is identical with that in [FIPS-186].)

   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 b then a

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   method must be provided to expand the hash.

   The method for expanding the digest value used in this section does
   not add any additional security beyond the b 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 b be the length of HASH output

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

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

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

       a)  Set n = FLOOR(L, b)

       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 + x*r)) mod q.

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   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 value 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
       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-dhPop-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-dhPop-sha1 OBJECT IDENTIFIER ::= id-alg-dh-pop

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

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

      id-alg-dhPop-sha224 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 5
      }

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

      id-alg-dhPop-sha256 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 6
      }

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

      id-alg-dhPop-sha384 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 7
      }

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

      id-alg-dhPop-sha512 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 8

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      }

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

   sa-dhPop-sha1
      A SIGNATURE-ALGORITHM object that associates together the
      information 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-dhPop-sha1
      This OID identifies the discrete logarithm signature using SHA-1
      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].

   sa-dhPop-sha224
      A SIGNATURE-ALGORITHM object that associates together the
      information 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-dhPop-sha224
      This OID identifies the discrete logarithm signature using SHA-224
      as the hash algorithm.

   sa-dhPop-sha256
      A SIGNATURE-ALGORITHM object that associates together the
      information 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-dhPop-sha256
      This OID identifies the discrete logarithm signature using SHA-256
      as the hash algorithm.

   sa-dhPop-sha384
      A SIGNATURE-ALGORITHM object that associates together the
      information 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.

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   id-alg-dhPop-sha384
      This OID identifies the discrete logarithm signature using SHA-384
      as the hash algorithm.

   sa-dhPop-sha512
      A SIGNATURE-ALGORITHM object that associates together the
      information 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-dhPop-sha512
      This OID identifies the discrete logarithm signature using SHA-512
      as the hash algorithm.

6.  Static ECDH Proof-of-Possession Process

   The Static ECDH POP algorithm is set up 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
   Elliptic Curve Cryptography works can be found in RFC 6090 [RFC6090].

   The steps for creating an ECDH POP are:

   1.  An entity (E) chooses the group parameters for an 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.  The ECDH parameters can be identified either by a
       named group or by a set of curve parameters.  Section 2.3.5 of
       RFC 3279 [RFC3279] documents how the parameters are encoded for
       PKIX certificates.  For PKIX-based applications, the parameters
       will almost always be defined by a named group.  Designate G as
       the group from the ECDH parameters.  Let the ECDH key-pair
       associated with the certificate be known as the Recipient key
       pair (Rpub and Rpriv).

       Rpub = Rpriv * G

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

       For an entity E:

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       Epriv = Entity private value
       Epub = ECDH public point = Epriv * G

   3.  The POP computation process will then consist of:

       a)  The value to be signed (text) 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 point (x, y) = Epriv * Rpub = Rpriv * Epub

           shared secret value ZZ is the x coordinate of the computed
           point

       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)  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 it would require its 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 algorithm outlined above allows for the use of an arbitrary hash
   function in computing the temporary key and the MAC value.  In this
   specification we defined object identifiers for the SHA-1 and SHA-256
   hash values.  The ASN.1 structures associated with the static ECDH
   POP algorithm are:

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      id-alg-ecdhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= {
         id-pkix id-alg(6) 25
      }

      sa-ecdhPop-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) 26
      }

      sa-ecdhPop-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) 27
      }

      sa-ecdhPop-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) 28
      }

      sa-ecdhPop-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:

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   sa-ecdhPop-static-sha224-hmac-sha224
      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
      This OID identifies the Static ECDH POP algorithm that uses SHA-
      224 as the KDF and HMAC-SHA224 as the MAC function.

   sa-ecdhPop-static-sha256-hmac-sha256
      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
      This OID identifies the Static ECDH POP algorithm that uses SHA-
      256 as the KDF and HMAC-SHA256 as the MAC function.

   sa-ecdhPop-static-sha384-hmac-sha384
      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
      This OID identifies the Static ECDH POP algorithm that uses SHA-
      384 as the KDF and HMAC-SHA384 as the MAC function.

   sa-ecdhPop-static-sha512-hmac-sha512
      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
      This OID identifies the Static ECDH POP algorithm that uses SHA-
      512 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.

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   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
   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.  IANA Considerations

   This document contains no IANA considerations.  The required OID
   assignments will be obtained from the PKIX Working Group ARC as part
   of any IETF last call comments.

9.  References

9.1.  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.

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

   [RFC2986]  Nystrom, M. and B. Kaliski, "PKCS #10: Certification
              Request Syntax Specification Version 1.7", RFC 2986,
              November 2000.

   [RFC4231]  Nystrom, M., "Identifiers and Test Vectors for HMAC-SHA-
              224, HMAC-SHA-256, HMAC-SHA-384, and HMAC-SHA-512",
              RFC 4231, December 2005.

   [RFC6234]  Eastlake, D. and T. Hansen, "US Secure Hash Algorithms
              (SHA and SHA-based HMAC and HKDF)", RFC 6234, May 2011.

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9.2.  Informative References

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

   [FIPS-186]
              "Digital Signature Standard", Federal Information
              Processing Standards Publication 186, May 1994.

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

   [RFC3279]  Bassham, L., Polk, W., and R. Housley, "Algorithms and
              Identifiers for the Internet X.509 Public Key
              Infrastructure Certificate and Certificate Revocation List
              (CRL) Profile", RFC 3279, April 2002.

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

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

Appendix A.  ASN.1 Modules

A.1.  2008 ASN.1 Module

   This appendix contains an ASN.1 module which is conformant with the
   2008 version of ASN.1.  This module references the object classes
   defined by [RFC5912] to more completely describe all of the
   associations between the elements defined in this document.  Where a
   difference exists between the module in this section and the 1988
   module, the 2008 module is the definitive module.

   DH-Sign
      { iso(1) identified-organization(3) dod(6) internet(1)
        security(5) mechanisms(5) pkix(7) id-mod(0)
        id-mod-dhSign-2012-08(80) }
   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.

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   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-sha1-hmac-sha1
           VALUE DhSigStatic
           PARAMS ARE absent
           PUBLIC-KEYS { pk-dh }
      }

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

      id-dhPop-static-sha1-hmac-sha1 OBJECT IDENTIFIER ::=
           id-dh-sig-hmac-sha1

      sa-dhPop-static-sha224-hmac-sha224 SIGNATURE-ALGORITHM ::= {
           IDENTIFIER id-alg-dhPop-static-sha224-hmac-sha224
           VALUE DhSigStatic

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           PARAMS ARE absent
           PUBLIC-KEYS { pk-dh }
      }

      id-alg-dhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 15
      }

      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) 16
      }

      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) 17
      }

      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) 18
      }

      sa-dhPop-SHA1 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dh-pop
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent

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         HASHES { mda-sha1 }
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dhPop-sha1 OBJECT IDENTIFIER ::= id-alg-dh-pop

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

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

      id-alg-dhPop-sha224 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 5
      }

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

      id-alg-dhPop-sha256 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 6
      }

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

      id-alg-dhPop-sha384 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 7
      }

      sa-dhPop-sha512 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-dhPop-sha512
         VALUE DSA-Sig-Value
         PARAMS TYPE DomainParameters ARE preferredAbsent

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         HASHES { mda-sha512 }
         PUBLIC-KEYS { pk-dh }
      }

      id-alg-dhPop-sha512 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 8
      }

      id-alg-ecdhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= {
         id-pkix id-alg(6) 25
      }

      sa-ecdhPop-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) 26
      }

      sa-ecdhPop-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) 27
      }

      sa-ecdhPop-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) 28
      }

      sa-ecdhPop-sha512-hmac-sha512 SIGNATURE-ALGORITHM ::= {
         IDENTIFIER id-alg-ecdhPop-static-sha512-hmac-sha512
         VALUE DhSigStatic

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         PARAMS ARE absent
         PUBLIC-KEYS { pk-ec }
      }

   END

A.2.  1988 ASN.1 Module

   This appendix contains an ASN.1 module which is conformant with the
   1988 version of ASN.1 represents an informational version of the
   ASN.1 module for this document.  Where a difference exists between
   the module in this section and the 2008 module, the 2008 module is
   the definitive module.

   DH-Sign
      { iso(1) identified-organization(3) dod(6) internet(1)
        security(5) mechanisms(5) pkix(7) id-mod(0)
        id-mod-dhSign-2012-88(79) }
   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 {

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          issuerAndSerial IssuerAndSerialNumber OPTIONAL,
          hashValue       MessageDigest
      }

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

      id-dhPop-static-sha1-hmac-sha1 OBJECT IDENTIFIER ::=
           id-dh-sig-hmac-sha1

      id-alg-dhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 15 }

      id-alg-dhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 16 }

      id-alg-dhPop-static-sha384-hmac-sha384 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 17 }

      id-alg-dhPop-static-sha512-hmac-sha512 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 18 }

      id-alg-dhPop-sha1 OBJECT IDENTIFIER ::= id-alg-dh-pop

      id-alg-dhPop-sha224 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 5 }

      id-alg-dhPop-sha256 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 6 }

      id-alg-dhPop-sha384 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 7 }

      id-alg-dhPop-sha512 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 8 }

      id-alg-ecdhPop-static-sha224-hmac-sha224 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 25 }

      id-alg-ecdhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 26 }

      id-alg-ecdhPop-static-sha384-hmac-sha384 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 27 }

      id-alg-ecdhPop-static-sha512-hmac-sha512 OBJECT IDENTIFIER ::= {
           id-pkix id-alg(6) 28 }

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   END

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

   The following example follows the steps described earlier in section
   4.

   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'
          :           }
          :         }
 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'
          :           }

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          :         }
          :       }
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)
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

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          :             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
          :         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 {

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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:

      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

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   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.

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      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

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  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

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           :             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
           :   }

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   Signature verification requires CA's 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 C.  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

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        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

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      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 value 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

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        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

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            :            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
            :   }

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Authors' Addresses

   Jim Schaad
   Soaring Hawk Consulting

   Email: ietf@augustcellars.com

   Hemma Prafullchandra
   Hy-Trust

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