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 
> 
> 
> 
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--
Cheers, Bob McElrath

"For every complex problem, there is a solution that is simple, neat, and wrong."
    -- H. L. Mencken