sipa changed the topic of #bitcoin-wizards to: This channel is for discussing theoretical ideas with regard to cryptocurrencies, not about short-term Bitcoin development | http://bitcoin.ninja/ | This channel is logged. | For logs and more information, visit http://bitcoin.ninja
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<kanzure>
andytoshi: are you going to post a casual explanation of bulletproofs somewhere
<andytoshi>
kanzure: i'm still developing an intuition for it .. maybe with waxwing's help we could do something
<waxwing>
andytoshi, kanzure fwiw i am finding that it is ... not simple :) got a general feeling for the inner product argument, but the next step (the range proof) is completely leaving me in the dust so far :)
<waxwing>
i think maybe you really ought to read the precursor, the paper by Bootle et al?
<andytoshi>
waxwing: i have read that, i have a good feel for it, it's just hard to explain
<waxwing>
andytoshi, which thing? you mean the range proof as explained in 4.1 of bulletproofs?
<andytoshi>
yeah
<andytoshi>
the blog post you linked is new to me. very cool!
<waxwing>
yeah fun eh. love the idea that that was an elevator pitch. lol.
<andytoshi>
waxwing: so the inner product argument is basically that blog post (it could be a bit more technical for this crowd i guess). note that this is _not_ a zero-knowledge argument, it's just an argument which is way more efficient than just revealing the witness explicitly
<waxwing>
maybe like the elevator in that tall building in dubai whatever it's called :)
<andytoshi>
then the rangeproof uses this argument on two multivariate low-order polynomials, and when you take their inner product the 0 coefficient has (among other things) x(x - 1) for each `x` in your original vector. if `x` is 0 or 1 this term is zero and reveals no info about x
<andytoshi>
so the polynomials have some stuff that is supposed to be bits, plus some blinding so that they can be used in a non-zk proof, and as long as the "supposed to be bits" really are bits, the result is something that the verifier can compute itself using only public data
<waxwing>
right, i feel like i saw various older ideas about how to do range proofs based on bit decomposition then using x*(x-1). memory fails me on any further details.
<andytoshi>
if they're _not_ bits, the result will not be what the verifier expects so verification will fail, and as a side-effect some information about the non-bit things will be exposed
<andytoshi>
yeah, what's novel here is essentially this compress-by-half technique which comes from the bootle et al paper
<andytoshi>
tho bulletproofs improve even this by a constant factor of 3
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<nsh>
so bullet-proofs allow MW-type efficient aggregation of rangeproofs of ZK blocks with?
<nsh>
a new cryptocurrency might create a secondary economic reward for aggregation-shortening of the blockchain
<nsh>
then maybe it could be delegated from users to miners somehow without compromising confidentiality
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<waxwing>
well on the bright side, could be a huge coinjoin incentive, look at the table on p. 28, for 16 outputs you have 928 bytes so like 64 witness bytes per output or something, if you need interactivity anyway, you find you're actually saving tons of space by combining transactions.
<waxwing>
but it's already a huge saving without aggregation according to that table. hmm though i notice it says 64 bit amounts there.
<waxwing>
oh yeah that sounds about right i think it was originally 2.5kB for 32 bit amounts (and then there were some optimizations)
<waxwing>
"it" = CT
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<andytoshi>
yep. tho bear in mind that the verification time is still nearly linear in the bit-length, aggregation saves you some computation but not a ton
<andytoshi>
not linear, it's N/log(N) we believe. but we've gotta implement and benchmark to get a feel for perf.
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<instagibbs>
waxwing, from squinting at the equations, the proof size grows log with the number of bits, so the 64 bit comparison makes it more impressive(it is)
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<Riqz_>
Hi guys.
<Riqz_>
can someone help me out with a problem i'm having with sweeping BTG into my coinomi wallet?
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<andytoshi>
#bitcoin-forks
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