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Date: Fri, 17 Apr 2015 22:16:05 +0300
From: Solar Designer <solar@...nwall.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] "Attack on the iterative compression function"

Dmitry,

On Fri, Apr 17, 2015 at 10:55:31AM +0200, Dmitry Khovratovich wrote:
> On Thu, Apr 16, 2015 at 3:01 AM, Solar Designer <solar@...nwall.com> wrote:
> >
> > Yes, now I can see how the shuffling may affect this.  Original scrypt's
> > sub-block shuffling appears to double the latency of your attack at each
> > level of the recomputation tree.  Correct?
> 
> Possibly. But there is always an option to store some extra subblocks
> so that latency decreases further...

Yes.

I think it would help this community if you try applying your attack to
scrypt proper.  Initially for storage of just the last sub-blocks (in
addition to some full blocks), and then (after publishing your initial
results) also for storage of arbitrary sub-blocks.  Try to identify
which ones and how many are optimal to store.  Perhaps the "how many"
will vary depending on the higher-level TMTO factor that you apply, so
perhaps the SMix-level and BlockMix-level TMTO factors would need to be
optimized together.

The scrypt paper is very careful when it talks about a "constant factor"
without specifying any upper bound on it, so it won't exactly be a break
of scrypt if you show that this constant factor is higher than is
possible with an SMix-level attack alone.  But it will be a significant
new result.

> > I guess original scrypt's sub-block shuffling is defined in the exact
> > way it is in order to ensure that two successive applications of the
> > shuffling don't cancel each other.  However, I don't immediately see a
> > specific reason to have this requirement, and from the point of view of
> > maximizing latency in your attack, simple reverse order of sub-blocks
> > (e.g., "B_15 xor B_14", "B_14 xor B_13", etc. written to new B_0, B_1,
> > etc. instead of the current "B_15 xor B_0", "B_0 xor B_1", etc.) feels
> > like it'd work best.  I haven't thought this through yet.  I'd
> > appreciate your thoughts on the reverse order of sub-blocks idea.
> 
> An attacker would just store every $q$-th subblock thus spliting the
> entire block into segments.

Yes, I've been thinking in this same direction after I sent the previous
message.

> Then the recomputation can be contained to segments and parallelized,
> like in our attack on Catena.
> 
> First I intended to write that playing with subblocks just complicates
> the security. However, I have realized,
> that it might be possible to devise a rigorous approach to that. To
> figure out how the latency is affected by tradeoffs,
> we consider a _stack_ of compression functions (BlockMixes, Argon2d
> permutation, etc.) and mount a tradeoff attack on it.
> The attacker's goal is to reduce the latency by careful storing of
> subblocks (or their parts). We could give extra power to the attacker
> by assuming he knows the recomputation tree structure in advance
> (always true for data-independent addressing), so he might want to
> store different subblocks in different blocks.

Right.

So maybe you can start with scrypt proper, as I suggested above?

> >> Our approach is to avoid this
> >> situation for all, requiring that there simply must not be any
> >> tradeoff attack on the compression function, or, in other words, the
> >> computational latency must be tradeoff-resistant. The Argon2
> >> parallelism that you have mentioned is somewhat unavoidable if we want
> >> this resistance.
> >
> > Yes, I figured this out yesterday.
> >
> > I think it's avoidable, but a possible reduction of parallelism just
> > does not occur with your approach naturally, and it'd cost a few extra
> > XORs or such to introduce it.  Looking at it from a different angle,
> > maybe this is your opportunity to easily introduce tunable
> > instruction-level parallelism (have a couple of flags dictate whether to
> > introduce or skip those extra data dependencies).
> 
> I think now it should be easy to add some chaining at 25% cost or so,
> which increases the normal latency and avoids parallelism. Still,
> this chaining will be subject to tradeoffs, so the tradeoff latency
> will be pretty much the same as now.

Right.  Yet I think this combination makes sense.

You currently have 8 parallel BLAKE2b's.  With a two-bit tunable
parallelism parameter, you can introduce optional data dependencies
between every BLAKE2b, between every other, between two groups of four,
or none (as it is currently).

I think the "between two groups of four" mode would result in a
negligible performance cost on current CPUs.

Maybe it's best to use 64-bit ADDs (maybe SIMD) rather than XORs for
those data dependencies.  Whatever maximum amount of defensive
processing you can do there in 1 clock cycle.

> > I confirm your analysis.
> >
> > I assume the C(q) and D(q) figures are currently inexact, for the reason
> > you mention ("have to plug yescrypt mode of operation (and its
> > addressing) into our ranking method"), but they look sane to me, and the
> > combination with your attack on BlockMix_pwxform looks correct to me.
> >
> > I hope that yescrypt's D(q) will turn out to be slightly higher than
> > what you included here once you consider yescrypt's Wrap().  I guess
> > your current C(q) and D(q) assume modulo division in place of Wrap()?
> 
> No, I used the real Wrap(). Without wrap the numbers would be smaller.
> But I did not exploit Wrap(), i.e. the storing algorithm does not know that
> you never refer to first blocks.

You mean when moving the last 1/2 sized window to higher offsets?

There's a swap-out and swap-in (for SMix2) possibility here, which is
why I claim a lower area-time: 1/3+1/3 rather than 1/2+1/3 (for
SMix1+SMix2), so 80% of what's theoretically possible for same running
time.  Is this what you mean you could have exploited, or do you have
additional ideas?

> I have posted the code that I used to generate the numbers online:
> https://github.com/khovratovich/Tradeoff
> The output .log file that is created contains the numbers. As
> explained in our earlier paper,
> the ranking method has parameter <q> (segment length). We run 100
> tests on each q from 2 to 80,
> and cluster tradeoffs that have the memory reduction around 1/D for
> all integer D.
> 
> It lacks comments and is quite a mess, but at least people will see
> where the numbers are coming from.
> 
> In order to get the numbers for other values of t, you just change the
> constant 1.33 in main() to the number of passes.

Thank you!  I haven't looked yet, but I intend to.

> > You make two observations: about late inter-lane diffusion, and about
> > recovering missing blocks subblockwise.  It appears that you currently
> > only make use of the latter observation.  Do you think the former is of
> > any use in an attack?
> 
> It is just an extra parallelism. As long as it is fully employed by
> the defender, I do not see an attack.

OK.

> > Thanks again,
> 
> You're welcome!

This is best tradeoff analysis of yescrypt so far.  Very helpful.

Alexander

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