2875
PROPOSED STANDARD
Diffie-Hellman Proof-of-Possession Algorithms (Obsoleted)
Authors: H. Prafullchandra, J. Schaad
Date: July 2000
Area: sec
Working Group: pkix
Stream: IETF
Obsoleted by:
RFC 6955
Abstract
This document describes two methods for producing an integrity check value from a Diffie-Hellman key pair. [STANDARDS-TRACK]
RFC 2875
Obsoleted by: 6955 PROPOSED STANDARD
Network Working Group H. Prafullchandra
Request for Comments: 2875 Critical Path Inc
Category: Standards Track J. Schaad
July 2000
<span class="h1">Diffie-Hellman Proof-of-Possession Algorithms</span>
Status of this Memo
This document specifies an Internet standards track protocol for the
Internet community, and requests discussion and suggestions for
improvements. Please refer to the current edition of the "Internet
Official Protocol Standards" (STD 1) for the standardization state
and status of this protocol. Distribution of this memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2000). All Rights Reserved.
Abstract
This document describes two methods for producing an integrity check
value from a Diffie-Hellman 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.
<span class="h2"><a class="selflink" id="section-1" href="#section-1">1</a>. Introduction</span>
PKCS #10 [<a href="./rfc2314" title=""PKCS #10: Certification Request Syntax v1.5"">RFC2314</a>] defines a syntax for certification requests. It
assumes that the public key being requested for certification
corresponds to an algorithm that is capable of signing/encrypting.
Diffie-Hellman (DH) is a key agreement algorithm and as such cannot
be directly used for signing or encryption.
This document describes two new proof-of-possession algorithms using
the Diffie-Hellman key agreement process to provide a shared secret
as the basis of an integrity check value. In the first 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.
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<span class="h2"><a class="selflink" id="section-2" href="#section-2">2</a>. Terminology</span>
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).
<span class="h2"><a class="selflink" id="section-3" href="#section-3">3</a>. Static DH Proof-of-Possession Process</span>
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:
a) The value to be signed is obtained. (For a <a href="./rfc2314">RFC2314</a> object, the
value is the DER encoded certificationRequestInfo field
represented as an octet string.) This will be the `text'
referred to in [<a href="./rfc2104" title=""HMAC: Keyed- Hashing for Message Authentication"">RFC2104</a>], the data to which HMAC-SHA1 is
applied.
b) A shared DH secret is computed, as follows,
shared secret = ZZ = g^xy mod p
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[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 = SHA1(LeadingInfo | ZZ | TrailingInfo),
where "|" means concatenation.
LeadingInfo ::= Subject Distinguished Name from certificate
TrailingInfo ::= Issuer Distinguished Name from certificate
d) Compute HMAC-SHA1 over the data `text' as per [<a href="./rfc2104" title=""HMAC: Keyed- Hashing for Message Authentication"">RFC2104</a>] as:
SHA1(K XOR opad, SHA1(K XOR ipad, text))
where,
opad (outer pad) = the byte 0x36 repeated 64 times and
ipad (inner pad) = the byte 0x5C repeated 64 times.
Namely,
(1) Append zeros to the end of K to create a 64 byte string
(e.g., if K is of length 16 bytes it will be appended
with 48 zero bytes 0x00).
(2) XOR (bitwise exclusive-OR) the 64 byte string computed
in step (1) with ipad.
(3) Append the data stream `text' to the 64 byte string
resulting from step (2).
(4) Apply SHA1 to the stream generated in step (3).
(5) XOR (bitwise exclusive-OR) the 64 byte string computed
in step (1) with opad.
(6) Append the SHA1 result from step (4) to the 64 byte
string resulting from step (5).
(7) Apply SHA1 to the stream generated in step (6) and
output the result.
Sample code is also provided in [<a href="./rfc2104" title=""HMAC: Keyed- Hashing for Message Authentication"">RFC2104</a>].
e) The output of (d) is encoded as a BIT STRING (the Signature
value).
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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.
ASN Encoding
The ASN.1 structures associated with the static Diffie-Hellman POP
algorithm are:
id-dhPop-static-HMAC-SHA1 OBJECT IDENTIFIER ::= { id-pkix
id-alg(6) 3}
DhPopStatic ::= SEQUENCE {
issuerAndSerial IssuerAndSerialNumber OPTIONAL,
hashValue MessageDigest
}
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 SHA-1 HMAC operation in step
3d.
DhPopStatic is encoded as a BIT STRING and is the signature value
(i.e. encodes the above sequence instead of the raw output from 3d).
<span class="h2"><a class="selflink" id="section-4" href="#section-4">4</a>. Discrete Logarithm Signature</span>
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.
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This POP is based on the Digital Signature Algorithm, but we have
removed the restrictions imposed by the [<a href="#ref-FIPS-186" title=""Digital Signature Standard"">FIPS-186</a>] 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 [<a href="#ref-DH-X9.42" title=""Diffie-Hellman Key Agreement Method"">DH-X9.42</a>] 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 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
Note: These definitions match the ones in [<a href="#ref-DH-X9.42" title=""Diffie-Hellman Key Agreement Method"">DH-X9.42</a>].
<span class="h3"><a class="selflink" id="section-4.1" href="#section-4.1">4.1</a> Expanding the Digest Value</span>
Besides the addition of a q parameter, [<a href="#ref-FIPS-186" title=""Digital Signature Standard"">FIPS-186</a>] 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 160-bits. (The size restriction
on q is identical with that in [<a href="#ref-DH-X9.42" title=""Diffie-Hellman Key Agreement Method"">DH-X9.42</a>].)
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 160-bits
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 160-bits provided by SHA-
1. The value being signed is increased mainly to enhance the
difficulty of reversing the signature process.
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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.
1. Compute d = SHA-1(M), the SHA-1 digest of the original message.
2. If L == 160 then m = d.
3. If L > 160 then follow steps (a) through (d) below.
a) Set n = L / 160, where / represents integer division,
consequently, if L = 200, n = 1.
b) Set m = d, the initial computed digest value.
c) For i = 0 to n - 1
m = m | SHA(m), where "|" means concatenation.
d) m = LEFTMOST(m, L-1), where LEFTMOST returns the L-1 left most
bits of m.
Thus the final result of the process meets the criteria that 0 <= m <
q.
<span class="h3"><a class="selflink" id="section-4.2" href="#section-4.2">4.2</a> Signature Computation Algorithm</span>
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 <a href="#section-5">section 5</a>.
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.
<span class="h3"><a class="selflink" id="section-4.3" href="#section-4.3">4.3</a> Signature Verification Algorithm</span>
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.
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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
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.
<span class="h3"><a class="selflink" id="section-4.4" href="#section-4.4">4.4</a> ASN Encoding</span>
The signature is encoded using
id-alg-dhPOP OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 4}
The parameters for id-alg-dhPOP are encoded as DomainParameters
(imported from [<a href="#ref-PROFILE" title=""Internet X.509 Public Key Infrastructure: Certificate and CRL Profile"">PROFILE</a>]). The parameters may be omitted in the
signature, as they must exist in the associated key request.
The signature value pair r and s are encoded using Dss-Sig-Value
(imported from [<a href="#ref-PROFILE" title=""Internet X.509 Public Key Infrastructure: Certificate and CRL Profile"">PROFILE</a>]).
<span class="h2"><a class="selflink" id="section-5" href="#section-5">5</a>. Security Considerations</span>
In the static DH POP algorithm, an appropriate value can be produced
by either party. Thus this algorithm 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. [<a href="#ref-FIPS-186" title=""Digital Signature Standard"">FIPS-186</a>] Appendixes 2 and 3 contain information on
the selection of parameters. The practices outlined in this document
will lead to better selection of parameters.
<span class="h2"><a class="selflink" id="section-6" href="#section-6">6</a>. References</span>
[<a id="ref-FIPS-186">FIPS-186</a>] Federal Information Processing Standards Publication
(FIPS PUB) 186, "Digital Signature Standard", 1994 May
19.
[<a id="ref-RFC2314">RFC2314</a>] Kaliski, B., "PKCS #10: Certification Request Syntax
v1.5", <a href="./rfc2314">RFC 2314</a>, October 1997.
[<a id="ref-RFC2104">RFC2104</a>] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", <a href="./rfc2104">RFC 2104</a>, February
1997.
[<a id="ref-PROFILE">PROFILE</a>] Housley, R., Ford, W., Polk, W., and D. Solo, "Internet
X.509 Public Key Infrastructure: Certificate and CRL
Profile", <a href="./rfc2459">RFC 2459</a>, January 1999.
[<a id="ref-DH-X9.42">DH-X9.42</a>] Rescorla, E., "Diffie-Hellman Key Agreement Method", <a href="./rfc2631">RFC</a>
<a href="./rfc2631">2631</a>, June 1999.
<span class="h2"><a class="selflink" id="section-7" href="#section-7">7</a>. Authors' Addresses</span>
Hemma Prafullchandra
Critical Path Inc.
5150 El Camino Real, #A-32
Los Altos, CA 94022
Phone: (640) 694-6812
EMail: [email protected]
Jim Schaad
EMail: [email protected]
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<span class="h2"><a class="selflink" id="appendix-A" href="#appendix-A">Appendix A</a>. ASN.1 Module</span>
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 CryptographicMessageSyntax { iso(1) member-body(2)
us(840) rsadsi(113549) pkcs(1) pkcs-9(9) smime(16)
modules(0) cms(1) }
Dss-Sig-Value, DomainParameters
FROM PKIX1Explicit88 {iso(1) identified-organization(3) dod(6)
internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
id-pkix1-explicit-88(1)};
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}
END
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<span class="h2"><a class="selflink" id="appendix-B" href="#appendix-B">Appendix B</a>. Example of Static DH Proof-of-Possession</span>
The following example follows the steps described earlier in <a href="#section-3">section</a>
<a href="#section-3">3</a>.
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'
: }
: }
: }
<span class="h2"><a class="selflink" id="section-108" href="#section-108">108</a> 30 </span>30: SEQUENCE {
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<span class="h2"><a class="selflink" id="section-110" href="#section-110">110</a> 17 </span>13: UTCTime '990914010557Z'
<span class="h2"><a class="selflink" id="section-125" href="#section-125">125</a> 17 </span>13: UTCTime '991113010557Z'
: }
<span class="h2"><a class="selflink" id="section-140" href="#section-140">140</a> 30 </span>70: SEQUENCE {
<span class="h2"><a class="selflink" id="section-142" href="#section-142">142</a> 31 </span>11: SET {
<span class="h2"><a class="selflink" id="section-144" href="#section-144">144</a> 30 </span> 9: SEQUENCE {
<span class="h2"><a class="selflink" id="section-146" href="#section-146">146</a> 06 </span> 3: OBJECT IDENTIFIER countryName (2 5 4 6)
<span class="h2"><a class="selflink" id="section-151" href="#section-151">151</a> 13 </span> 2: PrintableString 'US'
: }
: }
<span class="h2"><a class="selflink" id="section-155" href="#section-155">155</a> 31 </span>17: SET {
<span class="h2"><a class="selflink" id="section-157" href="#section-157">157</a> 30 </span>15: SEQUENCE {
<span class="h2"><a class="selflink" id="section-159" href="#section-159">159</a> 06 </span> 3: OBJECT IDENTIFIER organizationName (2 5 4 10)
<span class="h2"><a class="selflink" id="section-164" href="#section-164">164</a> 13 </span> 8: PrintableString 'XETI Inc'
: }
: }
<span class="h2"><a class="selflink" id="section-174" href="#section-174">174</a> 31 </span>16: SET {
<span class="h2"><a class="selflink" id="section-176" href="#section-176">176</a> 30 </span>14: SEQUENCE {
<span class="h2"><a class="selflink" id="section-178" href="#section-178">178</a> 06 </span> 3: OBJECT IDENTIFIER organizationalUnitName (2 5 4
11)
<span class="h2"><a class="selflink" id="section-183" href="#section-183">183</a> 13 </span> 7: PrintableString 'Testing'
: }
: }
<span class="h2"><a class="selflink" id="section-192" href="#section-192">192</a> 31 </span>18: SET {
<span class="h2"><a class="selflink" id="section-194" href="#section-194">194</a> 30 </span>16: SEQUENCE {
<span class="h2"><a class="selflink" id="section-196" href="#section-196">196</a> 06 </span> 3: OBJECT IDENTIFIER commonName (2 5 4 3)
<span class="h2"><a class="selflink" id="section-201" href="#section-201">201</a> 13 </span> 9: PrintableString 'DH TestCA'
: }
: }
: }
<span class="h2"><a class="selflink" id="section-212" href="#section-212">212</a> 30 577: </span> SEQUENCE {
<span class="h2"><a class="selflink" id="section-216" href="#section-216">216</a> 30 438: </span> SEQUENCE {
<span class="h2"><a class="selflink" id="section-220" href="#section-220">220</a> 06 </span> 7: OBJECT IDENTIFIER dhPublicKey (1 2 840 10046 2 1)
<span class="h2"><a class="selflink" id="section-229" href="#section-229">229</a> 30 425: </span> SEQUENCE {
<span class="h2"><a class="selflink" id="section-233" href="#section-233">233</a> 02 129: </span> 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
<span class="h2"><a class="selflink" id="section-365" href="#section-365">365</a> 02 128: </span> 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
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: 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
<span class="h2"><a class="selflink" id="section-496" href="#section-496">496</a> 02 </span>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
<span class="h2"><a class="selflink" id="section-531" href="#section-531">531</a> 02 </span>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
<span class="h2"><a class="selflink" id="section-630" href="#section-630">630</a> 30 </span>26: SEQUENCE {
<span class="h2"><a class="selflink" id="section-632" href="#section-632">632</a> 03 </span>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
<span class="h2"><a class="selflink" id="section-655" href="#section-655">655</a> 02 </span> 1: INTEGER 55
: }
: }
: }
<span class="h2"><a class="selflink" id="section-658" href="#section-658">658</a> 03 132: </span> 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
: }
<span class="h2"><a class="selflink" id="section-793" href="#section-793">793</a> A3 </span>85: [3] {
<span class="h2"><a class="selflink" id="section-795" href="#section-795">795</a> 30 </span>83: SEQUENCE {
<span class="h2"><a class="selflink" id="section-797" href="#section-797">797</a> 30 </span>29: SEQUENCE {
<span class="h2"><a class="selflink" id="section-799" href="#section-799">799</a> 06 </span> 3: OBJECT IDENTIFIER subjectKeyIdentifier (2 5 29
14)
<span class="h2"><a class="selflink" id="section-804" href="#section-804">804</a> 04 </span>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
: }
<span class="h2"><a class="selflink" id="section-828" href="#section-828">828</a> 30 </span>34: SEQUENCE {
<span class="h2"><a class="selflink" id="section-830" href="#section-830">830</a> 06 </span> 3: OBJECT IDENTIFIER authorityKeyIdentifier (2 5 29
35)
<span class="grey">Prafullchandra & Schaad Standards Track [Page 12]</span><span id="page-13" ></span>
<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
<span class="h2"><a class="selflink" id="section-835" href="#section-835">835</a> 01 </span> 1: BOOLEAN TRUE
<span class="h2"><a class="selflink" id="section-838" href="#section-838">838</a> 04 </span>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
: }
<span class="h2"><a class="selflink" id="section-864" href="#section-864">864</a> 30 </span>14: SEQUENCE {
<span class="h2"><a class="selflink" id="section-866" href="#section-866">866</a> 06 </span> 3: OBJECT IDENTIFIER keyUsage (2 5 29 15)
<span class="h2"><a class="selflink" id="section-871" href="#section-871">871</a> 01 </span> 1: BOOLEAN TRUE
<span class="h2"><a class="selflink" id="section-874" href="#section-874">874</a> 04 </span> 4: OCTET STRING
: 03 02 03 08
: }
: }
: }
: }
<span class="h2"><a class="selflink" id="section-880" href="#section-880">880</a> 30 </span>11: SEQUENCE {
<span class="h2"><a class="selflink" id="section-882" href="#section-882">882</a> 06 </span> 7: OBJECT IDENTIFIER dsaWithSha1 (1 2 840 10040 4 3)
<span class="h2"><a class="selflink" id="section-891" href="#section-891">891</a> 05 </span> 0: NULL
: }
<span class="h2"><a class="selflink" id="section-893" href="#section-893">893</a> 03 </span>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:
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)
<span class="grey">Prafullchandra & Schaad Standards Track [Page 13]</span><span id="page-14" ></span>
<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
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.
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
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<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
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
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'
: }
: }
<span class="grey">Prafullchandra & Schaad Standards Track [Page 15]</span><span id="page-16" ></span>
<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
: }
91 30 577: SEQUENCE {
95 30 438: SEQUENCE {
99 06 7: OBJECT IDENTIFIER dhPublicKey (1 2 840 10046 2 1)
<span class="h2"><a class="selflink" id="section-108" href="#section-108">108</a> 30 425: </span> SEQUENCE {
<span class="h2"><a class="selflink" id="section-112" href="#section-112">112</a> 02 129: </span> 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
<span class="h2"><a class="selflink" id="section-244" href="#section-244">244</a> 02 128: </span> 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
<span class="h2"><a class="selflink" id="section-375" href="#section-375">375</a> 02 </span>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
<span class="h2"><a class="selflink" id="section-410" href="#section-410">410</a> 02 </span>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
<span class="h2"><a class="selflink" id="section-509" href="#section-509">509</a> 30 </span>26: SEQUENCE {
<span class="h2"><a class="selflink" id="section-511" href="#section-511">511</a> 03 </span>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
<span class="h2"><a class="selflink" id="section-534" href="#section-534">534</a> 02 </span> 1: INTEGER 55
: }
: }
: }
<span class="h2"><a class="selflink" id="section-537" href="#section-537">537</a> 03 132: </span> 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
<span class="grey">Prafullchandra & Schaad Standards Track [Page 16]</span><span id="page-17" ></span>
<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
: 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
: }
: }
<span class="h2"><a class="selflink" id="section-672" href="#section-672">672</a> 30 </span>12: SEQUENCE {
<span class="h2"><a class="selflink" id="section-674" href="#section-674">674</a> 06 </span> 8: OBJECT IDENTIFIER dh-sig-hmac-sha1 (1 3 6 1 5 5 7 6 3)
<span class="h2"><a class="selflink" id="section-684" href="#section-684">684</a> 05 </span> 0: NULL
: }
<span class="h2"><a class="selflink" id="section-686" href="#section-686">686</a> 03 109: </span> 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
: }
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
<span class="grey">Prafullchandra & Schaad Standards Track [Page 17]</span><span id="page-18" ></span>
<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
<span class="h2"><a class="selflink" id="appendix-C" href="#appendix-C">Appendix C</a>. Example of Discrete Log Signature</span>
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
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:
<span class="grey">Prafullchandra & Schaad Standards Track [Page 18]</span><span id="page-19" ></span>
<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
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
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
<span class="grey">Prafullchandra & Schaad Standards Track [Page 19]</span><span id="page-20" ></span>
<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
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
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
<span class="grey">Prafullchandra & Schaad Standards Track [Page 20]</span><span id="page-21" ></span>
<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
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
<span class="h2"><a class="selflink" id="section-193" href="#section-193">193</a> 02 </span>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
<span class="h2"><a class="selflink" id="section-324" href="#section-324">324</a> 02 </span> 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
<span class="h2"><a class="selflink" id="section-359" href="#section-359">359</a> 02 </span> 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
<span class="grey">Prafullchandra & Schaad Standards Track [Page 21]</span><span id="page-22" ></span>
<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
: 92
<span class="h2"><a class="selflink" id="section-458" href="#section-458">458</a> 30 </span> 26: SEQUENCE {
<span class="h2"><a class="selflink" id="section-460" href="#section-460">460</a> 03 </span> 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
<span class="h2"><a class="selflink" id="section-483" href="#section-483">483</a> 02 </span> 1: INTEGER 55
: }
: }
: }
<span class="h2"><a class="selflink" id="section-486" href="#section-486">486</a> 03 </span>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
: }
<span class="h2"><a class="selflink" id="section-621" href="#section-621">621</a> A0 </span> 0: [0]
: }
<span class="h2"><a class="selflink" id="section-623" href="#section-623">623</a> 30 </span> 12: SEQUENCE {
<span class="h2"><a class="selflink" id="section-625" href="#section-625">625</a> 06 </span> 8: OBJECT IDENTIFIER '1 3 6 1 5 5 7 6 4'
<span class="h2"><a class="selflink" id="section-635" href="#section-635">635</a> 05 </span> 0: NULL
: }
<span class="h2"><a class="selflink" id="section-637" href="#section-637">637</a> 03 </span> 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
: }
<span class="grey">Prafullchandra & Schaad Standards Track [Page 22]</span><span id="page-23" ></span>
<span class="grey"><a href="./rfc2875">RFC 2875</a> Diffie-Hellman Proof-of-Possession Algorithms July 2000</span>
Full Copyright Statement
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This document and translations of it may be copied and furnished to
others, and derivative works that comment on or otherwise explain it
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Prafullchandra & Schaad Standards Track [Page 23]
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