gmaxwell just made me aware of this mail thread [0]. Some days ago I had
independently and naively started implementing "something similar" [1].

My version totally ignored the commitment and signing part but I'm pretty sure
that 12GB is overkill. My code is currently broken and I have no time to work on
it much but I thought it might be helpful to chime in.

At this point in time the difference between 80GB and 3GB (as my current 1.5GB
of only outputs would suggest if I had covered the inputs) or even 12GB makes
the difference of being able to store it on a phone, vs. not being able to. 80GB
"compressed" to 3GB is not that bad at all. Unfortunately, with segWit this will
be worse, with the higher transaction count per MB.

Regards,

Leo

[0]
https://www.reddit.com/r/Bitcoin/comments/4v28jl/how_have_fungiblity_problems_affected_you_in/d5ux6aq
[1] https://github.com/Giszmo/TransactionFinder

On 05/11/2016 10:29 PM, Bob McElrath via bitcoin-dev wrote:
> Eerrrr....let me revise that last paragraph.  That's 12 *GB* of filters at
> today's block height (at fixed false-positive rate 1e-6.  Compared to block
> headers only which are about 33 MB today.  So this proposal is not really
> compatible with such a wallet being "light"...
>
> Damn units...
>
> Bob McElrath via bitcoin-dev [bitcoin-dev@lists.linuxfoundation.org] wrote:
>> I like this idea, but let's run some numbers...
>>
>> bfd--- via bitcoin-dev [bitcoin-dev@lists.linuxfoundation.org] wrote:
>>> A Bloom Filter Digest is deterministically created of every block
>> Bloom filters completely obfuscate the required size of the filter for a desired
>> false-positive rate.  But, an optimal filter is linear in the number of elements
>> it contains for fixed false-positive rate, and logarithmic in the false-positive
>> rate.  (This comment applies to a RLL encoded Bloom filter Greg mentioned, but
>> that's not the only way)  That is for N elements and false positive rate
>> \epsilon:
>>
>>     filter size = - N \log_2 \epsilon
>>
>> Given that the data that would be put into this particular filter is *already*
>> hashed, it makes more sense and is faster to use a Cuckoo[1] filter, choosing a
>> fixed false-positive rate, given expected wallet sizes.  For Bloom filters,
>> multiply the above formula by 1.44.
>>
>> To prevent light clients from downloading more blocks than necessary, the
>> false-positive rate should be roughly less than 1/(block height).  If we take
>> the false positive rate to be 1e-6 for today's block height ~ 410000, this is
>> about 20 bits per element.  So for todays block's, this is a 30kb filter, for a
>> 3% increase in block size, if blocks commit to the filter.  Thus the required
>> size of the filter commitment is roughly:
>>
>>     filter size = N \log_2 H
>>
>> where H is the block height.  If bitcoin had these filters from the beginning, a
>> light client today would have to download about 12MB of data in filters.  My
>> personal SPV wallet is using 31MB currently.  It's not clear this is a bandwidth
>> win, though it's definitely a win for computing load on full nodes.
>>
>>
>> [1] https://www.cs.cmu.edu/~dga/papers/cuckoo-conext2014.pdf
>>
>> --
>> Cheers, Bob McElrath
>>
>> "For every complex problem, there is a solution that is simple, neat, and wrong."
>>     -- H. L. Mencken 
>>
>>
>>
>> !DSPAM:5733934b206851108912031!
>
>
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> --
> Cheers, Bob McElrath
>
> "For every complex problem, there is a solution that is simple, neat, and wrong."
>     -- H. L. Mencken 
>
>
>
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