Re: [Cfrg] Fwd: Hash-Based Key Derivation (fwd)

[Hugo Krawczyk <[e-mail]>]

I will not enter a too detailed technical discussion here (there is
enough material in this thread to write a full book). My only intent in
this note is to propose a change to the KDF described in the recent
NIST internet draft.  This is something I already pointed out in my
public comments to NIST SP 800-56 (where the KDF is originally described)
and is essentially the same as Dave Wagner (and possibly others)
pointed out earlier in this discussion.

The KDF function takes input SV in the form of some "shared value"
between two parties and it derives certain amount of keying material
KM using some hash function and some "context information"
(ID's, algorithm-id, shared-info, etc)

The current proposal (in very sketchy form) is:
      KM = H1||H2||...
where Hi = H(counter++ || SV || context-information)

Here, H is used as a random oracle without a well-defined cryptographic
key, instead H is used to repeatedly hash the SV.

The proposed change is to move to a more modular, two layer, scheme

 First  step:  K=H(SV || [context-information1])
 Second step:  Hi=PRF(K, counter++ || [context-information2]

The PRF can be instatiated with HMAC (or with CBC-MAC if using a
block cipher instead of a hash function).
The values context-information1 and 2 can be defined as needed (I
don't want to get into this level of detail here).

In this way the use of an "idealized primitive" (i.e. H as a random
oracle) is confined to its necessary minimum and with as little
inputs (or iterations) as possible. A further advantage is that this
modular construct allows (eventually or in some other applications)
to replace H with other non-ideal primitives. Depending on the
application such H may be simply the identity function (for example,
if the value SV is already a full cryptographic key), or a randomness
extractor as those discussed earlier in this thread.

Personally, I would also suggest changing the counter mode
currently used with H (and which I copied to the PRF setting) with a
feedback mode much alike the TLS and IKE KDFs.

Those interested may want to take a look at the design of the KDF function
in the IKE protocols (the description is cleaner in IKEv2) which has tried
to apply the existing randomness-extraction theory in an engineering-friendly
way, and which could be applicable to other KDF scenarios. I have
written briefly about this IKE's KDF design (in simple plain English) in
appendix C of my SIGMA paper http://www.ee.technion.ac.il/sigma.ps, and
have provided more theoretical backing in a paper with Gennaro and Rabin
from Eurocrypt 2004 (on the subject of computational entropy in DH values),
and in another paper with Dodis, Gennaro, Hastad and Rabin from Crypto04
(which tries to bridge between the theory of randomness extractors and
practical PRF schemes). These apers touch in many of the issues
raised during this discussion.

One final comment about random oracles. Take the example of NIST's KDF.
Note that the counter value comes before the the SV value. Why?
I do not really know. Of course, if H is a random oracle then the
order of counter and SV is immaterial (as long as it is kept fixed).
But with an actual function such as SHA-1 it may make a difference.
For example, Preneel and van Oorschot showed that if you are putting
a key as part of a hash message then it is best not to put it across
block boundaries. If this advise holds here then it might have been better
to put SV before counter. Now, I have not tried to really analyze this.
I am using this as an example showing that the idealization of H as a
random oracle may be too much of an abstraction driving us to bad
decisions.

To make this last (important) point even clearer, think of the
design of a MAC. If SHA-1 is to be treated as a random oracle then
MAC(K,msg)=SHA-1(K||msg) makes a "provably secure" MAC.  But as we
know it is *completely insecure* due to extension attacks.  One can
say: "well we know about extension attacks so we won't do that"
(note that this is already an important realization that SHA-1 is
NOT a random oracle -- even if the compresion function was purely random).
So we'll try another construct: MAC(K,msg)=SHA-1(msg||K).
How about this one?  Again, it is provable secure in the RO model.
How secure is it in practice? Until a couple of years ago very secure.
Now it is not secure anymore since it is vulnerable to collision attacks
on SHA-1!  Again, too much confidence (or reliance) on the random oracle
approach can easily lead us to bad (or at least sub-optimal) choices.

Going back to the KDF example: should counter come before or after SV?
I do not know and I do not care. If we move to the two-layer prf-based
scheme the question does not even come up (in a prf one does not
have to guess, or consult other cryptographers, about the "right
place" to put a key).

Hugo

PS: Well, I must say this for the record. The above is not trying to
say let's abandon the random oracle model. We do need it. In many
cases it is the best alternative when considering theoretical and
practical issues. But let's always be very careful about it and
let's minimize our reliance on it.

On Tue, 25 Oct 2005, David McGrew wrote:

> FYI
>
> Begin forwarded message:
>
> > From: Russ Housley <[e-mail]>
> > Date: October 25, 2005 9:44:42 AM PDT
> > To: [e-mail]
> > Subject: Hash-Based Key Derivation
> >
> >
> > I wanted call your attention to an individual draft on "Hash-Based
> > Key Derivation."
> >
> >     http://www.ietf.org/internet-drafts/draft-dang-nistkdf-00.txt
> >
> > This draft specifies a soon to be NIST-approved algorithm for
> > deriving secret key material from a shared secret using a hash
> > algorithm.This algorithm is in the NIST draft SP 800-56.
> >
> > I encourage review and comment.If you have concerns with this
> > document, then the concerns probably apply to he NIST draft SP
> > 800-56 document too.
> >
> > I am considering sponsoring this document asan Informational RFC.
> > Please let me know if you have any concerns with this proposed action.
> >
> > Thanks,
> > Russ
>
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