PKIX H. Prafullchandra
Internet-Draft
Obsoletes: 2875 (if approved) J. Schaad
Intended status: Standards Track Soaring Hawk Consulting
Expires: September 3, 2012 March 2, 2012
Diffie-Hellman Proof-of-Possession Algorithms
draft-schaad-pkix-rfc2875-bis-00
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.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Changes since RFC2875 . . . . . . . . . . . . . . . . . . 3
2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Static DH Proof-of-Possession Process . . . . . . . . . . . . 4
3.1. ASN Encoding . . . . . . . . . . . . . . . . . . . . . . . 6
4. Discrete Logarithm Signature . . . . . . . . . . . . . . . . . 7
4.1. Expanding the Digest Value . . . . . . . . . . . . . . . . 7
4.2. Signature Computation Algorithm . . . . . . . . . . . . . 8
4.3. Signature Verification Algorithm . . . . . . . . . . . . . 9
4.4. ASN.1 Encoding . . . . . . . . . . . . . . . . . . . . . . 9
5. Static ECDH Proof-of-Possession Process . . . . . . . . . . . 10
5.1. ASN.1 Encoding . . . . . . . . . . . . . . . . . . . . . . 12
6. Security Considerations . . . . . . . . . . . . . . . . . . . 12
7. References . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7.1. Normative References . . . . . . . . . . . . . . . . . . . 13
7.2. Informative References . . . . . . . . . . . . . . . . . . 13
Appendix A. Open Issues . . . . . . . . . . . . . . . . . . . . . 14
Appendix B. ASN.1 Modules . . . . . . . . . . . . . . . . . . . . 15
B.1. 1988 ASN.1 Module . . . . . . . . . . . . . . . . . . . . 15
B.2. 2008 ASN.1 Module . . . . . . . . . . . . . . . . . . . . 16
Appendix C. Example of Static DH Proof-of-Possession . . . . . . 18
Appendix D. Example of Discrete Log Signature . . . . . . . . . . 26
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 31
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1. Introduction
PKCS #10 [RFC2314] 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) and Elliptic Curve Diffie-Hellman (ECDH) are a
key agreement algorithms and as such cannot be directly used for
signing or encryption.
This document describes new proof-of-possession algorithms. Two
methods use the Diffie-Hellman key agreement process to provide a
shared secret as the basis of an integrity check value and one method
uses the Elliptic-Curve key agreement process. In the first and
third algorithm, the value is constructed for a specific recipient/
verifier by using a public key of that verifier. In the second
algorithm, the value is constructed for arbitrary verifiers.
It should be noted that we did not create an algorithm that parallels
ECDSA like was done for DSA. Given the current PKIX definitions for
the public key parameters of Elliptical curve, the number of groups
is both limited and pre-defined. This means that the probability
that the same set of parameters are going to be used by the key
requester and the key validator would be high. Also since the group
verification has been done centrally and with lots of validation, the
odds that a cryptographically weak group are used is much reduced.
Additionally, any system which could compute such a parallel
algorithm would just be able to use the ECDSA algorithm in any event.
1.1. Changes since RFC2875
The following changes have been made:
o The Static DH Proof-of-Possession algorithm has been re-written to
parameterize for a hash algorithm and a message authentication
code (MAC) algorithm.
o A new instance of the static DH POP algorithm has been created
using HMAC and SHA-256.
o The Discrete Logarithm Signature algorithm has been re-written to
parameterize for a hash algorithm.
o A new instance of the algorithm has been created using SHA-256.
o A new Static ECDH Proof-of-Possession algorithm has been added.
o An instance of the Static ECHD POP algorithm has been created
using HMAC and SHA-256.
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2. Terminology
The following definitions will be used in this document
DH certificate = a certificate whose SubjectPublicKey is a DH public
value and is signed with any signature algorithm (e.g. RSA or DSA).
ECDH certificate = a certificate whose SubjectPublicKey is a ECDH
public value and is signed with any signature algorithm (i.e. RSA or
ECDSA).
Proof-of-Possession (POP) is a method that provides a method for a
second party to perform an algorithm to establish with some degree of
assurance that the first party does possess and has the ability to
use a private key. The reasoning behind doing POP can be found in
Appendix C in [CRMF].
3. Static DH Proof-of-Possession Process
The Static DH POP algorithm is setup to use a key derivation function
(KDF) and a message authentication code (MAC). This algorithm
requires that a common set of group parameters be used by both the
creator and verifier of the POP value.
The steps for creating a DH POP are:
1. An entity (E) chooses the group parameters for a DH key
agreement.
This is done simply by selecting the group parameters from a
certificate for the recipient of the POP process.
A certificate with the correct group parameters has to be
available. Let these common DH parameters be g and p; and let
this DH key-pair be known as the Recipient key pair (Rpub and
Rpriv).
Rpub = g^x mod p (where x=Rpriv, the private DH value and ^
denotes exponentiation)
2. The entity generates a DH public/private key-pair using the
parameters from step 1.
For an entity E:
Epriv = DH private value = y
Epub = DH public value = g^y mod p
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3. The POP computation process will then consist of:
a) The value to be signed is obtained. (For a PKCS #10 object,
the value is the DER encoded certificationRequestInfo field
represented as an octet string.) This will be the 'text'
referred to in [RFC2104], the data to which HMAC-SHA1 is
applied.
b) A shared DH secret is computed, as follows,
shared secret = ZZ = g^xy mod p
[This is done by the entity E as Rpub^y and by the Recipient
as Epub^x, where Rpub is retrieved from the Recipient's DH
certificate (or is the one that was locally generated by the
Entity) and Epub is retrieved from the actual certification
request.]
c) A temporary key K is derived from the shared secret ZZ as
follows:
K = KDF(LeadingInfo | ZZ | TrailingInfo), where "|" means
concatenation.
LeadingInfo ::= Subject Distinguished Name from
certificate
TrailingInfo ::= Issuer Distinguished Name from
certificate
d) Compute MAC(K, text).
e) The output of (d) is encoded as a BIT STRING (the Signature
value).
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
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Entity from rogue CAs.
3.1. ASN Encoding
The alogorithm outlined above allows for the use of an arbitrary hash
function in computing the temporary key and the MAC value. In this
specfication we defined object identifiers for the SHA-1 and SHA-256
hash values. The ASN.1 structures associated with the static Diffie-
Hellman POP algorithm are:
sa-dhPop-static-sha1-hmac-sha1 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-dhPop-static-HMAC-SHA1
VALUE DhSigStatic
PARAMS ARE absent
HASHES {mda-sha1}
PUBLIC-KEYS {pk-dh}
}
id-dhPop-static-HMAC-SHA1 OBJECT IDENTIFIER ::= {
id-pkix id-alg(6) 3
}
id-dhPop-static-sha1-hmac-sha1 OBJECT IDENTIFIER ::=
id-dhPop-static-HMAC-SHA1
DhSigStatic ::= SEQUENCE {
issuerAndSerial IssuerAndSerialNumber OPTIONAL,
hashValue MessageDigest
}
sa-dhPop-static-sha256-hmac-sha256 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-alg-dhPop-static-sha256-hmac-sha256
VALUE DhSigStatic
PARAMS ARE absent
HASHES {mda-sha256}
PUBLIC-KEYS {pk-dh}
}
id-alg-dhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= {
id-pkix id-alg(6) TBD1
}
issuerAndSerial is the issuer name and serial number of the
certificate from which the public key was obtained. The
issuerAndSerial field is omitted if the public key did not come from
a certificate.
hashValue contains the result of the MAC operation in step 3d.
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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).
4. Discrete Logarithm Signature
The use of a single set of parameters for an entire public key
infrastructure allows all keys in the group to be attacked together.
For this reason we need to create a proof of possession for Diffie-
Hellman keys that does not require the use of a common set of
parameters.
This POP is based on the Digital Signature Algorithm, but we have
removed the restrictions imposed by the [FIPS-186] standard. The use
of this method does impose some additional restrictions on the set of
keys that may be used, however if the key generation algorithm
documented in [RFC2631] is used the required restrictions are met.
The additional restrictions are the requirement for the existence of
a q parameter. Adding the q parameter is generally accepted as a
good practice as it allows for checking of small group attacks.
The following definitions are used in the rest of this section:
p is a large prime
g = h(p-1)/q mod p ,
where h is any integer 1 < h < p-1 such that h(p-1) mod q > 1
(g has order q mod p)
q is a large prime
j is a large integer such that p = qj + 1
x is a randomly or pseudo-randomly generated integer with 1 < x < q
y = g^x mod p
HASH is a hash function such that
h = the output size of HASH in bits
Note: These definitions match the ones in [RFC2631].
4.1. Expanding the Digest Value
Besides the addition of a q parameter, [FIPS-186] also imposes size
restrictions on the parameters. The length of q must be 160-bits
(matching output of the SHA-1 digest algorithm) and length of p must
be 1024-bits. The size restriction on p is eliminated in this
document, but the size restriction on q is replaced with the
requirement that q must be at least h bits in length. (If the hash
function is SHA-1, then h=160 bits and the size restriction on q is
identical with that in [RFC2631].)
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Given that there is not a random length-hashing algorithm, a hash
value of the message will need to be derived such that the hash is in
the range from 0 to q-1. If the length of q is greater than h then a
method must be provided to expand the hash length.
The method for expanding the digest value used in this section does
not add any additional security beyond the h bits provided by the
hash algorithm. The value being signed is increased mainly to
enhance the difficulty of reversing the signature process.
This algorithm produces m the value to be signed.
Let L = the size of q (i.e. 2^L <= q < 2^(L+1)).
Let M be the original message to be signed.
Let h be the length of HASH output
1. Compute d = HASH(M), the digest of the original message.
2. If L == h then m = d.
3. If L > h then follow steps (a) through (d) below.
a) Set n = L / h, where / represents integer division,
consequently, if L = 200, h = 160 then n = 1.
b) Set m = d, the initial computed digest value.
c) For i = 0 to n - 1 m = m | HASH(m), 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.
4.2. 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.
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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.
4.3. Signature Verification Algorithm
The signature verification process is far more complicated than is
normal for the Digital Signature Algorithm, as some assumptions about
the validity of parameters cannot be taken for granted.
Given a message m to be validated, the signature value pair (r, s)
and the parameters for the key.
1. Perform a strong verification that p is a prime number.
2. Perform a strong verification that q is a prime number.
3. Verify that q is a factor of p-1, if any of the above checks fail
then the signature cannot be verified and must be considered a
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.
4.4. ASN.1 Encoding
The signature algorithm is parameterized by the hash algorithm. We
define two different object identifiers, one for SHA-1 and one for
SHA-256. The signature is encoded using
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sa-dh-pop-SHA1 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-alg-dh-pop
VALUE DSA-Sig-Value
PARAMS TYPE DomainParameters ARE optional
HASHES { mda-sha1}
PUBLIC-KEYS { pk-dh }
}
id-alg-dh-pop-SHA1 OBJECT IDENTIFIER ::= id-alg-dh-pop
id-alg-dh-pop OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 4}
sa-dh-pop-SHA256 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-alg-dh-pop-SHA256
VALUE DSA-Sig-Value
PARAMS TYPE DomainParameters ARE optional
HASHES { mda-sha256 }
PUBLIC-KEYS { pk-dh }
}
id-alg-dh-pop-SHA256 OBJECT IDENTIFIER ::= {
id-pkix id-alg(6) TBD2
}
The parameters for these algorithms are encoded as DomainParameters
(imported from [RFC5280]). 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 [RFC5280]).
5. Static ECDH Proof-of-Possession Process
The Static ECDH POP algorithm is setup to use a key derivation
function (KDF) and a message authentication code (MAC). This
algorithm requires that a common set of group parameters be used by
both the creator and verifier of the POP value.
The steps for creating a ECDH POP are:
1. An entity (E) chooses the group parameters for a ECDH key
agreement.
This is done simply by selecting the group parameters from a
certificate for the recipient of the POP process.
A certificate with the correct group parameters has to be
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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 PKCS #10 object,
the value is the DER encoded certificationRequestInfo field
represented as an octet string.) This will be the `text'
referred to in [RFC2104], the data to which HMAC-SHA1 is
applied.
b) A shared ECDH secret is computed, as follows,
shared secret = ZZ = g^xy mod p
[This is done by the entity E as Rpub^y and by the Recipient
as Epub^x, where Rpub is retrieved from the Recipient's DH
certificate (or is the one that was locally generated by the
Entity) and Epub is retrieved from the actual certification
request.]
c) A temporary key K is derived from the shared secret ZZ as
follows:
K = KDF(LeadingInfo | ZZ | TrailingInfo), where "|" means
concatenation.
LeadingInfo ::= Subject Distinguished Name from certificate
TrailingInfo ::= Issuer Distinguished Name from certificate
d) Compute MAC(K, text).
e) The output of (d) is encoded as a BIT STRING (the Signature
value).
The POP verification process requires the Recipient to carry out
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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.
5.1. ASN.1 Encoding
The alogorithm outlined above allows for the use of an arbitrary hash
function in computing the temporary key and the MAC value. In this
specfication we defined object identifiers for the SHA-1 and SHA-256
hash values. The ASN.1 structures associated with the static Diffie-
Hellman POP algorithm are:
id-alg-ecdhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= {
id-pkix id-alg(6) TBD3
}
sa-ecdh-pop-SHA256-HMAC-SHA256 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-alg-ecdhPop-static-sha256-hmac-sha256
VALUE DhSigStatic
PARAMS ARE absent
HASHES { mda-sha256 }
PUBLIC-KEYS { pk-ec }
}
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).
6. Security Considerations
In the static DH POP algorithm, an appropriate value can be produced
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by either party. Thus this algorithm only provides integrity and not
origination service. The Discrete Logarithm algorithm provides both
integrity checking and origination checking.
All the security in this system is provided by the secrecy of the
private keying material. If either sender or recipient private keys
are disclosed, all messages sent or received using that key are
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. The practices outlined in this document
will lead to better selection of parameters.
7. References
7.1. Normative References
[RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", RFC 2104,
February 1997.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC2314] Kaliski, B., "PKCS #10: Certification Request Syntax
Version 1.5", RFC 2314, March 1998.
[RFC2631] Rescorla, E., "Diffie-Hellman Key Agreement Method",
RFC 2631, June 1999.
7.2. Informative References
[CRMF] Schaad, J., "Internet X.509 Public Key Infrastructure
Certificate Request Message Format (CRMF)", RFC 4211,
September 2005.
[RFC5280] Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
Housley, R., and W. Polk, "Internet X.509 Public Key
Infrastructure Certificate and Certificate Revocation List
(CRL) Profile", RFC 5280, May 2008.
[RFC5912] Hoffman, P. and J. Schaad, "New ASN.1 Modules for the
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Public Key Infrastructure Using X.509 (PKIX)", RFC 5912,
June 2010.
Appendix A. Open Issues
The following is a partial list of issues to be addressed:
What are the correct KDF and MAC functions in Section 3 to be
created?
Should we move the definition of the mathematic and text
operations to a single location so that we can talk about ^ and |
without further definition?
What formatting needs to be done with the move from word to
xml2rfc?
Need additional text dealing with the ASN.1 inserted. Change to
use a hanging text list for all elements defined in the ASN.1 text
inserted.
Validate the conclusions - esp for b) at the end of Section 3 as I
am not sure it is really true as stated.
What are the correct hash functions for Section 4?
Section 5 was cut and past with a simple pass for edits. The math
needs to be corrected for ECDH from DH - or maybe just
generalized.
What are the KDF and MAC fucntions for Section 5 to be created?
Is the introduction correct that an ECDSA equivalent algorithm is
not needed?
Review security considerations section. Probably lacking based on
both increased understanding and the fact that ECDH was added.
What examples should be added?
Update references both for missing references and ones that have
since be updated.
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Appendix B. ASN.1 Modules
B.1. 1988 ASN.1 Module
This appendix represents the normative version of the ASN.1 module
for this document. In the event of a discrepancy between this module
and the 2008 version of the module, this module wins.
DH-Sign DEFINITIONS IMPLICIT TAGS ::=
BEGIN
--EXPORTS ALL
-- The types and values defined in this module are exported for use
-- in the other ASN.1 modules. Other applications may use them
-- for their own purposes.
IMPORTS
IssuerAndSerialNumber, MessageDigest
FROM CryptographicMessageSyntax2004 { iso(1) member-body(2)
us(840) rsadsi(113549) pkcs(1) pkcs-9(9) smime(16)
modules(0) cms-2004(24) }
id-pkix
FROM PKIX1Explicit88 { iso(1) identified-organization(3)
dod(6) internet(1) security(5) mechanisms(5) pkix(7)
id-mod(0) id-pkix1-explicit(18) }
Dss-Sig-Value, DomainParameters
FROM PKIX1Algorithms88 {iso(1) identified-organization(3) dod(6)
internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-pkix1-algorithms(17)};
id-dh-sig-hmac-sha1 OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 3}
DhSigStatic ::= SEQUENCE {
issuerAndSerial IssuerAndSerialNumber OPTIONAL,
hashValue MessageDigest
}
id-alg-dh-pop OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 4}
id-alg-dh-pop-sha256-hmac-sha256 OBJECT IDENTIFIER ::= {
id-pkix id-alg(6) TBD1
}
END
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B.2. 2008 ASN.1 Module
This appendix represents an informative version of the ASN.1 module
for this document. This module references the object classes defined
by [RFC5912] to more completely describe all of the associations
between the elements defined in this document. It also represents a
module that will compile using the most current definition of ASN.1
DH-Sign DEFINITIONS IMPLICIT TAGS ::=
BEGIN
--EXPORTS ALL
-- The types and values defined in this module are exported for use
-- in the other ASN.1 modules. Other applications may use them
-- for their own purposes.
IMPORTS
SIGNATURE-ALGORITHM
FROM AlgorithmInformation-2009
{iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-algorithmInformation-02(58)}
IssuerAndSerialNumber, MessageDigest
FROM CryptographicMessageSyntax-2010 { iso(1) member-body(2)
us(840) rsadsi(113549) pkcs(1) pkcs-9(9) smime(16)
modules(0) id-mod-cms-2009(58) }
DSA-Sig-Value, DomainParameters, ECDSA-Sig-Value,
mda-sha1, mda-sha256,
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)};
sa-dhPop-static-sha1-hmac-sha1 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-dhPop-static-HMAC-SHA1
VALUE DhSigStatic
PARAMS ARE absent
HASHES {mda-sha1}
PUBLIC-KEYS {pk-dh}
}
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id-dhPop-static-HMAC-SHA1 OBJECT IDENTIFIER ::= {
id-pkix id-alg(6) 3
}
id-dhPop-static-sha1-hmac-sha1 OBJECT IDENTIFIER ::=
id-dhPop-static-HMAC-SHA1
DhSigStatic ::= SEQUENCE {
issuerAndSerial IssuerAndSerialNumber OPTIONAL,
hashValue MessageDigest
}
sa-dhPop-static-sha256-hmac-sha256 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-alg-dhPop-static-sha256-hmac-sha256
VALUE DhSigStatic
PARAMS ARE absent
HASHES {mda-sha256}
PUBLIC-KEYS {pk-dh}
}
id-alg-dhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= {
id-pkix id-alg(6) TBD1
}
sa-dh-pop-SHA1 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-alg-dh-pop
VALUE DSA-Sig-Value
PARAMS TYPE DomainParameters ARE optional
HASHES { mda-sha1}
PUBLIC-KEYS { pk-dh }
}
id-alg-dh-pop-SHA1 OBJECT IDENTIFIER ::= id-alg-dh-pop
id-alg-dh-pop OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 4}
sa-dh-pop-SHA256 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-alg-dh-pop-SHA256
VALUE DSA-Sig-Value
PARAMS TYPE DomainParameters ARE optional
HASHES { mda-sha256 }
PUBLIC-KEYS { pk-dh }
}
id-alg-dh-pop-SHA256 OBJECT IDENTIFIER ::= {
id-pkix id-alg(6) TBD2
}
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id-alg-ecdhPop-static-sha256-hmac-sha256 OBJECT IDENTIFIER ::= {
id-pkix id-alg(6) TBD3
}
sa-ecdh-pop-SHA256-HMAC-SHA256 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-alg-ecdhPop-static-sha256-hmac-sha256
VALUE DhSigStatic
PARAMS ARE absent
HASHES { mda-sha256 }
PUBLIC-KEYS { pk-ec }
}
END
Appendix C. Example of Static DH Proof-of-Possession
The following example follows the steps described earlier in section
3.
Step 1: Establishing common Diffie-Hellman parameters. Assume the
parameters are as in the DER encoded certificate. The certificate
contains a DH public key signed by a CA with a DSA signing key.
0 30 939: SEQUENCE {
4 30 872: SEQUENCE {
8 A0 3: [0] {
10 02 1: INTEGER 2
: }
13 02 6: INTEGER
: 00 DA 39 B6 E2 CB
21 30 11: SEQUENCE {
23 06 7: OBJECT IDENTIFIER dsaWithSha1 (1 2 840 10040 4 3)
32 05 0: NULL
: }
34 30 72: SEQUENCE {
36 31 11: SET {
38 30 9: SEQUENCE {
40 06 3: OBJECT IDENTIFIER countryName (2 5 4 6)
45 13 2: PrintableString 'US'
: }
: }
49 31 17: SET {
51 30 15: SEQUENCE {
53 06 3: OBJECT IDENTIFIER organizationName (2 5 4 10)
58 13 8: PrintableString 'XETI Inc'
: }
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: }
68 31 16: SET {
70 30 14: SEQUENCE {
72 06 3: OBJECT IDENTIFIER organizationalUnitName (2 5 4
11)
77 13 7: PrintableString 'Testing'
: }
: }
86 31 20: SET {
88 30 18: SEQUENCE {
90 06 3: OBJECT IDENTIFIER commonName (2 5 4 3)
95 13 11: PrintableString 'Root DSA CA'
: }
: }
: }
108 30 30: SEQUENCE {
110 17 13: UTCTime '990914010557Z'
125 17 13: UTCTime '991113010557Z'
: }
140 30 70: SEQUENCE {
142 31 11: SET {
144 30 9: SEQUENCE {
146 06 3: OBJECT IDENTIFIER countryName (2 5 4 6)
151 13 2: PrintableString 'US'
: }
: }
155 31 17: SET {
157 30 15: SEQUENCE {
159 06 3: OBJECT IDENTIFIER organizationName (2 5 4 10)
164 13 8: PrintableString 'XETI Inc'
: }
: }
174 31 16: SET {
176 30 14: SEQUENCE {
178 06 3: OBJECT IDENTIFIER organizationalUnitName (2 5 4
11)
183 13 7: PrintableString 'Testing'
: }
: }
192 31 18: SET {
194 30 16: SEQUENCE {
196 06 3: OBJECT IDENTIFIER commonName (2 5 4 3)
201 13 9: PrintableString 'DH TestCA'
: }
: }
: }
212 30 577: SEQUENCE {
216 30 438: SEQUENCE {
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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
: 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
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: 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 {
830 06 3: OBJECT IDENTIFIER authorityKeyIdentifier (2 5 29
35)
835 01 1: BOOLEAN TRUE
838 04 24: OCTET STRING
: 30 16 80 14 6A 23 37 55 B9 FD 81 EA E8 4E D3 C9
: B7 09 E5 7B 06 E3 68 AA
: }
864 30 14: SEQUENCE {
866 06 3: OBJECT IDENTIFIER keyUsage (2 5 29 15)
871 01 1: BOOLEAN TRUE
874 04 4: OCTET STRING
: 03 02 03 08
: }
: }
: }
: }
880 30 11: SEQUENCE {
882 06 7: OBJECT IDENTIFIER dsaWithSha1 (1 2 840 10040 4 3)
891 05 0: NULL
: }
893 03 48: BIT STRING 0 unused bits
: 30 2D 02 14 7C 6D D2 CA 1E 32 D1 30 2E 29 66 BC
: 06 8B 60 C7 61 16 3B CA 02 15 00 8A 18 DD C1 83
: 58 29 A2 8A 67 64 03 92 AB 02 CE 00 B5 94 6A
: }
Step 2. End Entity/User generates a Diffie-Hellman key-pair using
the parameters from the CA certificate.
EE DH public key: SunJCE Diffie-Hellman Public Key:
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Y: 13 63 A1 85 04 8C 46 A8 88 EB F4 5E A8 93 74 AE
FD AE 9E 96 27 12 65 C4 4C 07 06 3E 18 FE 94 B8
A8 79 48 BD 2E 34 B6 47 CA 04 30 A1 EC 33 FD 1A
0B 2D 9E 50 C9 78 0F AE 6A EC B5 6B 6A BE B2 5C
DA B2 9F 78 2C B9 77 E2 79 2B 25 BF 2E 0B 59 4A
93 4B F8 B3 EC 81 34 AE 97 47 52 E0 A8 29 98 EC
D1 B0 CA 2B 6F 7A 8B DB 4E 8D A5 15 7E 7E AF 33
62 09 9E 0F 11 44 8C C1 8D A2 11 9E 53 EF B2 E8
EE DH private key:
X: 32 CC BD B4 B7 7C 44 26 BB 3C 83 42 6E 7D 1B 00
86 35 09 71 07 A0 A4 76 B8 DB 5F EC 00 CE 6F C3
Step 3. Compute K and the signature.
LeadingInfo: DER encoded Subject/Requestor DN (as in the generated
Certificate Signing Request)
30 4E 31 0B 30 09 06 03 55 04 06 13 02 55 53 31
11 30 0F 06 03 55 04 0A 13 08 58 45 54 49 20 49
6E 63 31 10 30 0E 06 03 55 04 0B 13 07 54 65 73
74 69 6E 67 31 1A 30 18 06 03 55 04 03 13 11 50
4B 49 58 20 45 78 61 6D 70 6C 65 20 55 73 65 72
TrailingInfo: DER encoded Issuer/Recipient DN (from the certificate
described in step 1)
30 46 31 0B 30 09 06 03 55 04 06 13 02 55 53 31
11 30 0F 06 03 55 04 0A 13 08 58 45 54 49 20 49
6E 63 31 10 30 0E 06 03 55 04 0B 13 07 54 65 73
74 69 6E 67 31 12 30 10 06 03 55 04 03 13 09 44
48 20 54 65 73 74 43 41
K:
F4 D7 BB 6C C7 2D 21 7F 1C 38 F7 DA 74 2D 51 AD
14 40 66 75
TBS: the "text" for computing the SHA-1 HMAC.
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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 CAAEs private key, the CA certificate
and the generated Certification Request.
CA DH private key:
x: 3E 5D AD FD E5 F4 6B 1B 61 5E 18 F9 0B 84 74 a7
52 1E D6 92 BC 34 94 56 F3 0C BE DA 67 7A DD 7D
Appendix D. Example of Discrete Log Signature
Step 1. Generate a Diffie-Hellman Key with length of q being 256-
bits.
p:
94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7 C5
A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82 F5
D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21 51
63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68 5B
79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72 8A
F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2 32
E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02 D7
B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85 27
q:
E8 72 FA 96 F0 11 40 F5 F2 DC FD 3B 5D 78 94 B1
85 01 E5 69 37 21 F7 25 B9 BA 71 4A FC 60 30 FB
g:
26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90
06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4
64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57
86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6
4E 18 6E DD 1F 22 06 EB 3F EA D4 41 69 D9 9B DE
47 95 7A 72 91 D2 09 7F 49 5C 3B 03 33 51 C8 F1
39 9A FF 04 D5 6E 7E 94 3D 03 B8 F6 31 15 26 48
95 A8 5C DE 47 88 B4 69 3A 00 A7 86 9E DA D1 CD
j:
A3 91 01 C0 A8 6E A4 4D A0 56 FC 6C FE 1F A7 B0
CD 0F 94 87 0C 25 BE 97 76 8D EB E5 A4 09 5D AB
83 CD 80 0B 35 67 7F 0C 8E A7 31 98 32 85 39 40
9D 11 98 D8 DE B8 7F 86 9B AF 8D 67 3D B6 76 B4
61 2F 21 E1 4B 0E 68 FF 53 3E 87 DD D8 71 56 68
47 DC F7 20 63 4B 3C 5F 78 71 83 E6 70 9E E2 92
y:
5F CF 39 AD 62 CF 49 8E D1 CE 66 E2 B1 E6 A7 01
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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 values is then:
30 45 02 21 00 A1 B5 B4 90 01 34 6B A0 31 6A 73
F5 7D F6 5C 14 43 52 D2 10 BF 86 58 87 F7 BC 6E
5A 77 FF C3 4B 02 20 59 40 45 BC 6F 0D DC FF 9D
55 40 1E C4 9E 51 3D 66 EF B2 FF 06 40 9A 39 68
75 81 F7 EC 9E BE A1
Result:
30 82 02 c2 30 82 02 67 02 01 00 30 1b 31 19 30
17 06 03 55 04 03 13 10 49 45 54 46 20 50 4b 49
58 20 53 41 4d 50 4c 45 30 82 02 41 30 82 01 b6
06 07 2a 86 48 ce 3e 02 01 30 82 01 a9 02 81 81
00 94 84 e0 45 6c 7f 69 51 62 3e 56 80 7c 68 e7
c5 a9 9e 9e 74 74 94 ed 90 8c 1d c4 e1 4a 14 82
f5 d2 94 0c 19 e3 b9 10 bb 11 b9 e5 a5 fb 8e 21
51 63 02 86 aa 06 b8 21 36 b6 7f 36 df d1 d6 68
5b 79 7c 1d 5a 14 75 1f 6a 93 75 93 ce bb 97 72
8a f0 0f 23 9d 47 f6 d4 b3 c7 f0 f4 e6 f6 2b c2
32 e1 89 67 be 7e 06 ae f8 d0 01 6b 8b 2a f5 02
d7 b6 a8 63 94 83 b0 1b 31 7d 52 1a de e5 03 85
27 02 81 80 26 a6 32 2c 5a 2b d4 33 2b 5c dc 06
87 53 3f 90 06 61 50 38 3e d2 b9 7d 81 1c 12 10
c5 0c 53 d4 64 d1 8e 30 07 08 8c dd 3f 0a 2f 2c
d6 1b 7f 57 86 d0 da bb 6e 36 2a 18 e8 d3 bc 70
31 7a 48 b6 4e 18 6e dd 1f 22 06 eb 3f ea d4 41
69 d9 9b de 47 95 7a 72 91 d2 09 7f 49 5c 3b 03
33 51 c8 f1 39 9a ff 04 d5 6e 7e 94 3d 03 b8 f6
31 15 26 48 95 a8 5c de 47 88 b4 69 3a 00 a7 86
9e da d1 cd 02 21 00 e8 72 fa 96 f0 11 40 f5 f2
dc fd 3b 5d 78 94 b1 85 01 e5 69 37 21 f7 25 b9
ba 71 4a fc 60 30 fb 02 61 00 a3 91 01 c0 a8 6e
a4 4d a0 56 fc 6c fe 1f a7 b0 cd 0f 94 87 0c 25
be 97 76 8d eb e5 a4 09 5d ab 83 cd 80 0b 35 67
7f 0c 8e a7 31 98 32 85 39 40 9d 11 98 d8 de b8
7f 86 9b af 8d 67 3d b6 76 b4 61 2f 21 e1 4b 0e
68 ff 53 3e 87 dd d8 71 56 68 47 dc f7 20 63 4b
3c 5f 78 71 83 e6 70 9e e2 92 30 1a 03 15 00 1c
d5 3a 0d 17 82 6d 0a 81 75 81 46 10 8e 3e db 09
e4 98 34 02 01 37 03 81 84 00 02 81 80 5f cf 39
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Internet-Draft DH POP Algorithms March 2012
ad 62 cf 49 8e d1 ce 66 e2 b1 e6 a7 01 4d 05 c2
77 c8 92 52 42 a9 05 a4 db e0 46 79 50 a3 fc 99
3d 3d a6 9b a9 ad bc 62 1c 69 b7 11 a1 c0 2a f1
85 28 f7 68 fe d6 8f 31 56 22 4d 0a 11 6e 72 3a
02 af 0e 27 aa f9 ed ce 05 ef d8 59 92 c0 18 d7
69 6e bd 70 b6 21 d1 77 39 21 e1 af 7a 3a cf 20
0a b4 2c 69 5f cf 79 67 20 31 4d f2 c6 ed 23 bf
c4 bb 1e d1 71 40 2c 07 d6 f0 8f c5 1a a0 00 30
0c 06 08 2b 06 01 05 05 07 06 04 05 00 03 47 00
30 44 02 20 54 d9 43 8d 0f 9d 42 03 d6 09 aa a1
9a 3c 17 09 ae bd ee b3 d1 a0 00 db 7d 8c b8 e4
56 e6 57 7b 02 20 44 89 b1 04 f5 40 2b 5f e7 9c
f9 a4 97 50 0d ad c3 7a a4 2b b2 2d 5d 79 fb 38
8a b4 df bb 88 bc
Decoded Version of result:
0 30 707: SEQUENCE {
4 30 615: SEQUENCE {
8 02 1: INTEGER 0
11 30 27: SEQUENCE {
13 31 25: SET {
15 30 23: SEQUENCE {
17 06 3: OBJECT IDENTIFIER commonName (2 5 4 3)
22 13 16: PrintableString 'IETF PKIX SAMPLE'
: }
: }
: }
40 30 577: SEQUENCE {
44 30 438: SEQUENCE {
48 06 7: OBJECT IDENTIFIER dhPublicNumber (1 2 840 10046 2
1)
57 30 425: SEQUENCE {
61 02 129: INTEGER
: 00 94 84 E0 45 6C 7F 69 51 62 3E 56 80 7C 68 E7
: C5 A9 9E 9E 74 74 94 ED 90 8C 1D C4 E1 4A 14 82
: F5 D2 94 0C 19 E3 B9 10 BB 11 B9 E5 A5 FB 8E 21
: 51 63 02 86 AA 06 B8 21 36 B6 7F 36 DF D1 D6 68
: 5B 79 7C 1D 5A 14 75 1F 6A 93 75 93 CE BB 97 72
: 8A F0 0F 23 9D 47 F6 D4 B3 C7 F0 F4 E6 F6 2B C2
: 32 E1 89 67 BE 7E 06 AE F8 D0 01 6B 8B 2A F5 02
: D7 B6 A8 63 94 83 B0 1B 31 7D 52 1A DE E5 03 85
: 27
193 02 128: INTEGER
: 26 A6 32 2C 5A 2B D4 33 2B 5C DC 06 87 53 3F 90
: 06 61 50 38 3E D2 B9 7D 81 1C 12 10 C5 0C 53 D4
: 64 D1 8E 30 07 08 8C DD 3F 0A 2F 2C D6 1B 7F 57
: 86 D0 DA BB 6E 36 2A 18 E8 D3 BC 70 31 7A 48 B6
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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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Internet-Draft DH POP Algorithms March 2012
Authors' Addresses
Hemma Prafullchandra
Jim Schaad
Soaring Hawk Consulting
Email: ietf@augustcellars.com
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