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
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