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Date: Mon, 30 Mar 2015 23:15:01 +0300
From: Solar Designer <solar@...nwall.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Another PHC candidates "mechanical" tests (ROUND2)

On Tue, Mar 31, 2015 at 02:08:34AM +0800, Hongjun Wu wrote:
> 3)  A strong hash function is not needed for POMELO.
>      I believe that POMELO  is much stronger than any existing hash
> function for the KDF/PH applications.

Most likely it is, but the confidence in it is currently lower than e.g.
in SHA-2 family functions.

> (For performance reason, a strong
> hash function has to be sufficiently fast and small.  So even in a very
> strong hash function, not many operations can be used for processing a
> message block.)
>      In the POMELO report, I did not talk much about POMELO against
> preimage and collision attack. I can explain more in the updated report.
>      When I was designing POMELO v2,  only the memory hardening security
> worth my analysis.   The preimage and collision security are trivial.

Of course, it's much easier (in fact, trivial as you say) to achieve
preimage and collision resistance in PHC candidates than in fast
cryptographic hashes.  The problem, though, is that "much easier" and
even "trivial" do not necessarily imply "has been achieved".

If you tried to, I think you would be able to deliberately construct a
PHC candidate that would appear OK at first glance, but would not be
preimage or/and collision resistant.  Right?  And this might happen
unintentionally, too.

> Simply speaking, the state size of POMELO is too large comparing to a hash
> function, and the operations used in a cryptographic hash function
> (compression function) is much less than that used in POMELO.
>      Some example: considering SHA-512, there are only 64+64 = 128 simple
> steps to compress a 128-byte message (if we consider message expansion as
> 64 steps); while in POMELO v2, there are about 3*256 = 768 steps when
> m_cost = 0, t_cost = 0.     In POMELO v2, in order to prevent password
> hashing being too fast, it is required that m_cost + t_cost >= 5.  It means
> that POMELO v2 consists of at least 32*256+512 = 8704 steps, far more than
> that in a compression function of SHA-512.

Simply comparing the number of operations is not convincing enough.
For example, what if most of those cancel out, or are reversible, or if
there are tiny biases that add up to something significant after so many
steps?  This is almost certainly not the case, but until shown otherwise
the possibilities are there.

A more realistic risk is issues with how the password and salt inputs
are processed early on.  Things like the original bcrypt $2$'s trivial
collisions for "ab" vs. "abab", etc.

I think it's reasonable that people want an analysis of POMELO's basic
security.

Alexander

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