# [bitcoin-dev] Committed bloom filters for improved wallet performance and SPV security

Bob McElrath bob_bitcoin at mcelrath.org
Wed May 11 20:06:48 UTC 2016

I like this idea, but let's run some numbers...

bfd--- via bitcoin-dev [bitcoin-dev at 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.

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
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

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