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Date: Tue, 02 Sep 2014 09:13:14 -0400
From: Bill Cox <waywardgeek@...hershed.org>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] A review per day - Schvrch

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Here is a devastating TMTO attack against Schvrch.  The idea is very
simple, and has been used against Scrypt.  Simply save the state of
some memory and associated state at various points in memory, and
recompute the following memory locations that we didn't store when
needed.  For Scrypt, this creates a runtime that is O(t^2), where t is
the ratio of memory the defender used vs the attacker.  This attack on
Scrypt is serious, but not devastating, because the time*memory cost
remains constant.  Actually, it drops by 4X as t rises, but no more,
which is good for the attacker, but not devastating.

The same attack against Schvrch does not cause runtime to increase
more than 2.5X.  At the same time, only 6KiB of memory is required!
This is a devastating attack, that dramatically reduces an attacker's
time*memory cost.

The attacker simply saves the initial 256 64-bit words of state, and
he needs two more buffers of equal size.  He does the t_cost loop, at
the same speed as the defender, and then has to call stir on a
large-ish memory that fits in L3 cache, such as 4MiB.  This memory has
locations 0 .. 255 initialized to the values from the state array, and
then stir is called with 4 rounds.

To compute the second 256 words of state of memory, the attacker
computes the carry from hashing the first 256 words.  He remembers the
carry value at the end of this.  Since the rest of memory is just 0,
he can compute the rest of memory, but he does not need to save *any*
of it.

On the second round, the first 256 words were correctly updated from
the prior pass, and we have computed the initial carry, so the
attacker can compute new values for the first 256 words.  Again, he
remembers the carry at this point.

Since he remembered the carry from the first pass, he can now
recompute the second block of 256 words.  Then he can compute the new
value, to compute the carry out for that block.  Each of the following
blocks is computed by first recomputing the old carry in, and the
recomputing the values from the first pass.

Similarly, the 3rd pass requires that we do 2 recomputations of each
block.  The 4rd pass requires 3.  The total recomputations is 3+2+1 =
6, so the attacker does 10 passes worth of computation.  The defender
did 4.  That is a 2.5X recomputation penalty, with only 6KiB of memory.

Last spring, when we starting bringing up serious attacks against
Schvrch, the author refused to respond with fixes, insisting that
these attacks don't matter.  That's why we stopped bothering to come
up with any further attacks.  We moved on.

I didn't know how to say that we should just move on properly, so I
just stated Schvrch is weak and moved onto RIG.  I don't know if the
author will hear what we are saying this time.  The evidence so far
says probably not.  It is not worth spending more time on Schvrch when
the author refuses to modify his algorithm when we have shown to be
dangerously weak.

So, I'll suggest again that we move on.

However, if you want to have some fun, I think there is an even more
serious attack that can be done which is worse than any of these that
I've pointed out today.  If you want a fun challenge, examine the stir
function carefully from the point of view of an attacker.  For
example, data only flows from low bits to high bits.  The value of the
low 8 bits out in no way depend on the upper 7 bytes of any word of
state.  There may be a devastating module 256 attack here.  This is
why people use ARX (add/rotate/xor) operations in secure hashes.
POMELO uses these, plus unpredictable memory reads, frustrating my
more serious attacks.  Schvrch has no rotate.  I suspect there is a
very cool attack that can be made that takes advantage of this.  Have
fun :-)

Bill
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