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Date: Tue, 03 Jan 2017 12:24:35 -0800
From: bfd@cock.lu
To: Bob McElrath <bob_bitcoin@mcelrath.org>
In-Reply-To: <20160511202933.GR20063@mcelrath.org>
References: <71d822e413ac457a530e1c367811cc24@cock.lu>
	<20160511200648.GQ20063@mcelrath.org>
	<20160511202933.GR20063@mcelrath.org>
Message-ID: <019588aaf210830f55742bbc5db43ea3@cock.lu>
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Cc: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] Committed bloom filters for improved wallet
 performance and SPV security
Precedence: list

I believe the filter can be more compact than this, but even if not an
order of magnitude saving of disk space is still significant.


On 2016-05-11 13:29, Bob McElrath 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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>> 
>> 
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> 
> --
> Cheers, Bob McElrath
> 
> "For every complex problem, there is a solution that is simple, neat,
> and wrong."
>     -- H. L. Mencken