- N \log_2 \epsilon * 1.44

N = 41000 blocks
epsilon = 1/41000 (fp rate)

= 904689.8bits

~ 1 MB


On Thu, Jul 28, 2016 at 5:07 PM, Leo Wandersleb via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

> 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!
> >
> >
> >> _______________________________________________
> >> bitcoin-dev mailing list
> >> bitcoin-dev@lists.linuxfoundation.org
> >> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
> >>
> >>
> >> !DSPAM:5733934b206851108912031!
> > --
> > Cheers, Bob McElrath
> >
> > "For every complex problem, there is a solution that is simple, neat,
> and wrong."
> >     -- H. L. Mencken
> >
> >
> >
> > _______________________________________________
> > bitcoin-dev mailing list
> > bitcoin-dev@lists.linuxfoundation.org
> > https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
>
>
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