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Date: Wed, 09 Apr 2014 19:30:09 +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 13:32, Dmitry Khovratovich wrote:
> Hi Christian,
> 
>>Let H be a KDF and let K1||K2 = H(PWD || salt).  Are K1 and K2 be
> considered to be independent?
> 
> The independency is a not a well-defined notion here. Consider, for
> instance, distinct bytes of K1. Are they independent?
> 
> If we think about it for a while, it becomes clear that a single key can
> be splitted into as many keys as its length without any security loss.
> 
>>y= H(PWD || salt)
> K1' =   F(y, 1)
> K2' =   F(y, 2)
> 
> This method is clearly equivalent to the first one. Indeed, consider
> H'(x) = F(H(x)||1)||F(H(x)||2). Then the second method turns into the
> first one with H = H'.


Your observations are fine if H is a secure KDF. But it is easy to
construct an insecure KDF out of a (preimage) secure password scrambler.

Let G be a slow and memory-consuming cryptographic hash function and let
F be a cryptographic hash function. Suppose H is a password scrambler
and we have

y = H(x) := G(x) || F(G(x)).

H can be considered to be s secure password scrambler  since it is hard
to recover x from y. Nevertheless, it is a bad idea to use
y = y1||y2 directly as a key since you can derive y2 from y1
by just computing F(y1).

Therefore, it might be a good idea to output

F(y, 1) || F(y, 2) instead of y.

Best regards,
Christian













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