Internet Draft Hemma Prafullchandra (XETI)
Expires in 6 months Jim Schaad (Microsoft)
February 25, 1999
Diffie-Hellman Proof-of-Possession Algorithms
Status of this Memo
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Abstract
This document describes two methods for producing a signature from a
Diffie-Hellman key pair. This behavior is needed for such operations
as creating a signature of a PKCS #10 certification request. These
algorithms are designed to provide a proof-of-possession rather than
general purpose signing.
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) is a key agreement algorithm and as such cannot be
directly used for signing or encryption.
This document describes two new signing algorithms using the Diffie-
Hellman key agreement process to provide a shared secret as the basis
of the signature. In the first signature algorithm, the signature is
constructed for a specific recipient/verifier by using a public key of
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that verifier. In the second signature algorithm, the signature is
constructed for arbitrary verifiers. This is done by creating an
appropriate D-H key pair and encoding them as part of the signature
value.
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).
3. DH Signature Process
The steps for creating a DH signature are:
1. An entity (E) chooses the group parameters for a DH key agreement.
In many cases this is done simply by selecting the group parameters
from a certificate for the recipient of the signature process
(static DH signatures) but they may be computed for other methods
(ephemeral DH signatures).
In the ephemeral DH signature scheme, a temporary DH key-pair is
generated using the group parameters, which may be computed or
acquired by some out-of-band means. In the static DH signature
scheme, 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 signature computation process will then consist of:
a) The value to be signed is obtained. (For a RFC2314 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,
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shared secret = ZZ = g^xy mod p
[This is done by the entity E as g^(y.Rpub) and by the Recipient
as g^(x.Epub), 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.
d) Compute HMAC-SHA1 over the data `text' as per [RFC2104] 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 [RFC2104].
e) The output of (d) is encoded as a BIT STRING (the Signature
value).
The signature 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:
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1) 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
2) For the static signature scheme, that only the Recipient that
the entity sent the request to could actually verify the request
because they would require their own private key to compute the same
shared secret. In the case where the recipient is a Certification
Authority, this protects the Entity from rogue CAs.
4. Static DH Signature
In the static DH Signature scheme, the public key used in the key
agreement process of step 2 is obtained from the entity that will be
verifying the signature (i.e. the recipient). In the case of a
certification request, the public key would normally be extracted from
a certificate issued to the CA with the appropriate key parameters.
The values used in step 3c for "LeadingInfo" and the "TrailingInfo"
are:
LeadingInfo ::= Subject Distinguished Name from certificate
TrailingInfo ::= Issuer Distinguished Name from certificate
The ASN.1 structures associated with the static Diffie-Hellman
signature algorithms are:
id-dhPop-static-HMAC-SHA1 OBJECT IDENTIFIER ::= { id-pkix id-alg(6)
}
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).
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.
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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.
The method outlined in this document is the same as used by 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 [DH-X9.42]
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 [DH-X9.42].
5.1 Expanding the Digest Value
Besides the addition of a q parameter, [FIPS-186] also imposes size
restrictions on the parameters. The length of q must be 160-bits
(matching output of the SHA-1 digest algorithm) and length of p must
be 1024-bits. The size restriction on p is eliminated in this
document, but the size restriction on q is replaced with the
requirement that q must be at least 160-bits. (The size restriction
on q is identical with that in [DH-X9.42].)
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.
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.
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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(d), 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.
5.2 Signature Computation Algorithm
The signature algorithm produces the pair of values (r, s), which is
the signature. The signature is computed as follows:
Given m, the value to be signed, as well as the parameters defined
earlier in section 5.
1. Generate a random or pseudorandom integer k, such that 0 < k^-1 <
q.
2. Compute r = (g^k mod p) mod q.
3. If r is zero, repeat from step 1.
4. Compute s = (k^-1 (m + xr)) mod q.
5. If s is zero, repeat from step 1.
5.3 Signature Verification Algorithm
The signature verification process is far more complicated than is
normal for the Digital Signature Algorithm, as some assumptions about
the validity of parameters cannot be taken for granted.
Given a message m to be validated, the signature value pair (r, s) and
the parameters for the key.
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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 Encoding
The signature is encoded using
id-alg-dhPOP OBJECT IDENTIFIER ::= {id-pkix id-alg(6) }
The parameters for id-alg-dhPOP are encoded as DomainParameters
(imported from [PROFILE]). 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 [PROFILE]).
5. Security Considerations
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
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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.
6. Open Issues
There are no known open issues.
7. References
[FIPS-186] Federal Information Processing Standards Publication (FIPS
PUB) 186, "Digital Signature Standard", 1994 May 19.
[RFC2314] B. Kaliski, "PKCS #10: Certification Request Syntax v1.5",
RFC 2314, October 1997
[RFC2104] H. Krawczyk, M. Bellare, R. Canetti, "HMAC: Keyed-Hashing
for Message Authentication", RFC 2104, February 1997.
[PROFILE] R. Housley, W. Ford, W. Polk, D. Solo, "Internet
X.509 Public Key Infrastructure: Certificate and CRL
Profile", RFC 2459, January 1999.
[DH-X9.42] E. Rescorla, "Diffie-Hellman Key Agreement Method".
(currently draft-ietf-smime-x942-*.txt)
8. Author's Addresses
Hemma Prafullchandra
XETI Inc.
5150 El Camino Real, #A-32
Los Altos, CA 94022
(640) 694-6812
hemma@xeti.com
Jim Schaad
Microsoft Corporation
One Microsoft Way
Redmond, WA 98052-6399
(425) 936-3101
jimsch@microsoft.com
Appendix A. ASN.1 Module
DH-Sign DEFINITIONS IMPLICIT TAGS ::=
BEGIN
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--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-dhSig-static-HMAC-SHA1 OBJECT IDENTIFIER ::= {id-pkix id-alg(6)
}
DhSigStatic ::= SEQUENCE {
IssuerAndSerial IssuerAndSerialNumber OPTIONAL,
hashValue MessageDigest
}
id-alg-dhPOP OBJECT IDENTIFIER ::= {id-pkix id-alg(6) }
END
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