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Date: Thu, 7 Aug 2014 02:10:45 -0700
From: Dmitry Khovratovich <khovratovich@...il.com>
To: "discussions@...sword-hashing.net" <discussions@...sword-hashing.net>
Subject: Re: [PHC] Tradeoff cryptanalysis of password hashing schemes

Hi Ben,

the following points are important:
 - A, C, *, 0 are all k-bit values. k<n/3, and for the attack being
efficient k>2.
 - [**0] takes 2^(n-k) storage per level as you store everything that ends
with k zeros.

The example in presentation has |A| = |C| = 1, and |B|=2. Such small values
are for the ease of understanding, but not for the efficiency. I attach the
picture in the higher resolution. The red indices are those precomputed for
the next level.

Best regards,
Dmitry


On Thu, Aug 7, 2014 at 1:19 AM, Ben Harris <ben@...rr.is> wrote:

> Just getting my head around the Catena one.
>
> Storing [**0] takes 2^2k storage per level? (presentation says 2^(n-k))
> And the [*B*] takes 2^(n-k) storage
> So L*2^2k + 2^(n-k) storage all up.
>
> Computing each [*B*] at level 0 takes 2^(n-2k) operations from each 2^k
> [*B0]. total 2^(n-k) operations? (presentation says 2^2k)
> Computing each [*^B*] at level 1 is more complicated because we don't
> always have what we need.
>
> At level 1, for the A = 1, B = 1, and len(C) = 2 (the example in the
> presentation). For the 2^(n-k) = 2^(4-1) = 8 [*^B*] we have
> [00 1 0] - h( h([00 0 0] + [1 0 00]) + [0 1 00]) = 2 hashes
> [00 1 1] - h([00 1 0] + [1 1 00]) - 1 hash
> [01 1 0] - h([01 0 1] + [0 1 10]) - but [01 0 1] is h([01 0 0] + [1 0 10])
> and I don't have [1 0 10] it takes 2 hashes from [1 0 00]
> [01 1 1] - 1 hash from previous
> [10 1 0] - h([10 0 1] + [0 1 10]) -  again, I don't have [10 0 1]?
> [10 1 1] - 1 hash from previous
> [11 1 0] - again, we are missing something
> [11 1 1] - 1 hash from previous
>
> These missing dependencies become exponential at level 2+.
>
> So there are three bits I'm getting a bit stuck on:
>   - Storage per level
>   - Operations for level 0
>   - Missing dependencies at level 1
>
> Maybe I'm just misreading the slides and needed to see the talk?
>
>
> On 7 August 2014 05:10, Marcos Simplicio <mjunior@...c.usp.br> wrote:
>
>> Hi, all.
>>
>> Very interesting analysis! We noticed the same attack venue described in
>> slide 47 for Lyra2 some time ago, so we provided and evaluated a simple
>> fix in the version provided in our website (http://lyra-kdf.net/, see
>> section 5.1.2.3 of the specification). I'm not sure how the tradeoffs
>> table is affected by this fix, but the costs are likely to grow (at
>> least that was my impression by crossing your results with our
>> preliminary analysis).
>>
>> BTW, the document in our website is being continuously updated as new
>> tests are performed, so we expect to introduce this and possibly other
>> tweaks in the corresponding phase of the PHC. We are still evaluating
>> the "possible extensions" mentioned in the original submission, for
>> example.
>>
>> BR,
>>
>> Marcos.
>>
>> On 06-Aug-14 14:31, Dmitry Khovratovich wrote:
>> > Hi all,
>> >
>> > here is the link to the slides of the talk I have just given at
>> > PasswordsCon'14. It investigates time-memory tradeoffs for PHC
>> candidates
>> > Catena, Lyra2, and Argon, and estimates the energy cost per password on
>> an
>> > optimal ASIC implementation with full or reduced memory.
>> >
>> > https://www.cryptolux.org/images/5/57/Tradeoffs.pdf
>> >
>> > Additional comment: It is a standard practice in the crypto community to
>> > give explicit security claims for the recommended parameter sets so that
>> > cryptanalysts could easily identify the primary targets. Many PHC
>> > candidates do not follow this rule by not only missing these claims but
>> > also concealing the recommended parameters. As a result, cryptanalysts
>> like
>> > me spend valuable time attacking wrong sets or spreading the attention
>> over
>> > multiple targets.
>> >
>> > Remember: third-party cryptanalysis increases the confidence in your
>> > design, not decreases it (unless it is badly broken). Analysis of a
>> 5%-part
>> > of your submission (one of 20 possible parameter sets) is little better
>> > than no analysis at all. It is also worth mentioning that to make fair
>> > comparison of candidates, benchmarks and performance discussion in
>> general
>> > should cover recommended parameter sets only.
>> >
>>
>
>


-- 
Best regards,
Dmitry Khovratovich

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