phc-discussions - Re: [PHC] Deriving multiple keys (was RE: Mechanical tests)

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Date: Wed, 09 Apr 2014 11:48:07 +0200
From: Christian Forler <christian.forler@...-weimar.de>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Deriving multiple keys (was RE: Mechanical tests)

On 09.04.2014 00:10, Greg Zaverucha wrote:
> Christian, can you clarify/justify your recommendation?  

Let H be a KDF and let K1||K2 = H(PWD || salt).  Are K1 and K2 be
considered to be independent?

Personally, I would feel better when using the following key derivation
algorithm.

y= H(PWD || salt)
K1' =   F(y, 1)
K2' =   F(y, 2)

where F is a cryptographic hash function. Here you have only two
additional hash function calls and since (y, 1) != (y,2) one can argue
that K1' and K2' are pairwise independent. But is hard to argue that K1
and K2 are pairwise independent.

> Its common  practice to call a KDF with an input parameter for the required
> number of output bytes then divide the output into two or more keys.
> For instance, you might derive separate encryption authentication
> keys from a DH secret with one call to the KDF.

> One example standard that does this is in Section 7.3 of: 
> http://csrc.nist.gov/publications/nistpubs/800-108/sp800-108.pdf

Using KDF (modeled as PRF) in Counter or Feedback mode is fine.

Note that these modes do not work for password based key derivation. The
PRF model assumes a secret key K which is chosen uniformly at random
from a key space. A password is not chosen uniformly at random.

> Another example is the scrypt encryption utility
> (http://www.tarsnap.com/scrypt.html) Quoting the FORMAT file: 
> "AES256-CTR is computed with a 256-bit AES key key_enc, and
> HMAC-SHA256 is computed with a 256-bit key key_hmac, where 
> scrypt(password, salt, N, r, p, 64) == [key_enc][key_hmac]"
> 
> The reference code for all PHC submissions to accept an output
> length.  It should be a requirement that any subset of the output
> bytes be suitable for use as keying material.  Is this not the case?

Assume that the output of our KDF is larger than the internal
state of the underlying cryptographic primitive. Where should the
additional security come from?

An output transformation does not protect you against an adversary which
can reconstruct the internal state.

Best regards,
Christian

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