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Date: Thu, 30 Apr 2015 14:43:45 +0200 (CEST)
From: Stefan.Lucks@...-weimar.de
To: discussions@...sword-hashing.net
Subject: Maximising Pseudo-Entropy versus resistance to Side-Channel
 Attacks

Dear all,

In this ideal world, the adversary (say, Mallory) will have to try out 
different passwords online, by trying to logging onto the defender's 
system. In this ideal world, cleartext passwords would be fine. 
Furthermore, passwords with x bit of entropy would be secure from Mallory, 
if 2^x log-in attempts would be infeasible/impossible on the defender's 
system.

(Informally, a password has x bit of entropy if Mallory's chance to guess 
it is at most 1/2^x.)

Password hashing is about offline attacks, where Mallory knows the 
password file. In this (partly real) world, cleartext passwords would 
allow Mallory to succeed immediately. Good password hashing functions are 
about adding y bit of "pseudo-entropy" to all passwords. I.e., trying out 
2^x passwords would raise Mallory's costs

 	from 	2^x 	to 	2^x * 2^y = 2^(x+y).

The sum x+y of password-entropy and pseudo-entropy defines the security of 
the password.

(Note that for different adversaries, using different tools, such as GPUs 
or ASICs or FPGAs or Bot-Nets for the attack, the pseudo-entropy may be 
different.)

Obviously, good password hashing functions are about maximising y for the 
adversaries we anticipate, given a limited "budget" for password hashing 
on the defender's side. Thus, it is reasonable to focus on performance, to 
answer the question "How far can we push y?"

Except that there is no law that requires defenders to publish their 
password files. Given past experience, it would be unwise for the defender 
to assume the password file will never be compromised. For this reason, the 
defender must use a good password hash function. On the other hand, is 
would be just as unwise to assume that the password file will actually be 
compromised. Without knowing the password file, Mallory would be back to 
on-line attacking the defender's system. The point I am trying to make is 
that in such a situation, a password hashing function being vulnerable to 
side-channel attacks would be a terrible choice.

As an example, let the password hashing function H1 be ten times faster 
than H2, i.e., if Mallory's costs for H1 are be ten times higher than his 
costs for H2 (for the same budget on the defender's side). Ten times 
faster sounds like a big deal, doesn't it?

Well, the H1 would provide log_2(10)=3.32 bit more pseudo-entropy than H2. 
To compensate for using H2, the defender could choose passwords, with 3.32 
bit of additional entropy. Just appending one single random digit to the 
password would suffice.

Even if the defender does not really understand how Mallory might mount a 
side-channel attack against H1, choosing H1 for the marginal gain of a ten 
times better performance could be a fatal move, if H2 is resistant to 
side-channel attacks. The most serious issue are cache-timing attacks, 
but one should also consider garbage collector attacks, and possibly other 
attacks as well.

(Note that the situation for password-based key derivation, is different. 
There, can hardly exclude Mallory from performing off-line attacks. Except 
when Mallory doesn't have the ciphertext -- but then, why should Mallory 
care for the key or the password at all?)


The consequence for PHC?

If PHC selects a single winner from one of the finalists, it should either 
be Argon2i or Catena. If PHC selects more than one winner, the set of 
winners should include at least one of Argon2i and Catena. (Or, if we 
don't care about forcing Mallory to allocate a large amount of memory, 
Makwa and Parallel would be alternatives.)


So long

Stefan


Remark: This is my personal view. Being one of the authors of Catena, I am 
biased. Nevertheless, I didn't write this to promote Catena.  Quite the 
contrary, I did write this, because I consider this a vital issue for PHC 
-- and this is one of the reasons, why Catena is, as it is.



------  I  love  the  taste  of  Cryptanalysis  in  the morning!  ------
uni-weimar.de/de/medien/professuren/mediensicherheit/people/stefan-lucks
--Stefan.Lucks (at) uni-weimar.de, Bauhaus-Universit├Ąt Weimar, Germany--

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