Date: Fri, 8 Aug 2014 08:15:02 +0800
From: Ben Harris <ben@...rr.is>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Tradeoff cryptanalysis of password hashing schemes

I'll have to test your pebbling scheme for Catena - but an initial comment
on the time comparisons.

Catena with lambda=4 and n=20 takes 2^20 storage and 5x2^20 hashes.
Presentation takes Lx2^(n-k) storage. So at k=1 you are using more memory,
and k=2 you are using the same. Need k=3 to use 1/2 the memory.
At k=3 you need 3.5x2^6 to get 2^3 vertices, so 3.5*2^6*2^(20-3) to get all
the vertices for the final row. So 3.5x2^23 to get the last row.

Catena will take 2^20 to get the final row, so that is a slowdown of
3.5x2^3 = 28x. You only have 13.1x slowdown?


On 7 August 2014 17:15, Ben Harris <ben@...rr.is> wrote:

> Thanks Dimitry,
>
> Page 26 just needs to be updated then - it says "Consider vertices
> [AB0]... where each letter has k bits" suggesting that A and B are k bits
> each - not that C is k bits.
>
>
> On 7 August 2014 17:10, Dmitry Khovratovich <khovratovich@...il.com>
> wrote:
>
>> 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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