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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<Chris_Stewart_5>
el gamal commitments are orthogonal to what is written about in the bullet proof paper right? I.e. the optimizations dont apply to those
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<sipa>
indeed
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<Chris_Stewart_5>
damn
<sipa>
or rather, it would work, but you wouldn't get the soundness guarantee that el gamal commitments otherwise have
<Chris_Stewart_5>
sipa: Hmm, so it is severely diminished? Because isn't perfect binding way more important?
<Chris_Stewart_5>
like would it be trivial to unmask the amount?
<Chris_Stewart_5>
for a 3rd party to unmask the amount obviously
<sipa>
Chris_Stewart_5: el gamal commitments are perfectly binding but not perfectly hiding
<sipa>
pedersen commitments are perfectly hiding but not perfectly binding
<sipa>
our former rangeproof construction can be made to work with either
<sipa>
bulletproofs cannot be perfectly binding
<Chris_Stewart_5>
ah
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<waxwing>
sipa, "A hypothetical future CT proposal for Bitcoin could make the rangeproofs not affect the weight." <- how so? rangeproofs are witness data right, but how would it be possible to not affect the weight at all?
<aj>
waxwing: you'd have a separate witness for it with a different weighting?
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<waxwing>
aj, re: different weighting, sure i could understand that (depending on how expensive verification is i guess), but i didn't read the above quote in that way; perhaps that was the intent.
<sipa>
waxwing: yes, new witness type for CT
<sipa>
which is costed differently
<sipa>
possibly as 0
<waxwing>
ok. so .. unfairly private transactions? :)
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<sipa>
it was a hypothetical :)
<waxwing>
yeah it's unfortunate that there's a zero lower bound here :) negative weight may lead to some ... rather large witnesses being produced :)
<sipa>
well, if the cost for a rangeproof is 0, you'd still want it strictly limited i size
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<munchee>
do wingardia leviosum work on bitcoin price
<munchee>
perhaps cause of recent gains
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<grexeter>
if you think about it, how does scaling bitcoin by not scaling bitcoin at all (lightning) make sense? they need to use their own network and nodes, to scale bitcoin?
<grexeter>
that doesnt even seem like scaling bitcoin. that seems like diverting bitcoin to a 2nd network
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<Taek>
grexeter: wrong channel. For casual discussion, #bitcoin
<grexeter>
nah im good here, im a wizard
<grexeter>
why cant we talk amongst wizards about scaling bitcoin, by not scaling bitcoin at all?
<grexeter>
Taek: do you have anything meaningful to add to our convo, or are you just a door greeter good at redirecting people?
<andytoshi>
grexeter: please take this elsewhere
<grexeter>
if you dont like it, take yourself elsewhere and mind your own biz dicknoz
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grexeter was kicked from #bitcoin-wizards by andytoshi [or i can take you elsewhere]
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<nsh>
andytoshi, when are you coming to the UK?
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<surlyray>
;;sl "Andrew Poelstra bitcoin"
<gribble>
https://www.weusecoins.com/andrew-poelstra/ | Andrew Poelstra is a Mathematician at Blockstream. ... He became involved in Bitcoin in late 2011, and joined Blockstream cofounders Greg Maxwell and Pieter ...
<surlyray>
quit blocking non blockstreamers from speaking honestly
<andytoshi>
earlygrey: don't be daft, coming onto a research channel and insulting regulars is not "speaking honestly"
<surlyray>
its honest if its my feelings
<surlyray>
you can inslut me all day all you want
<wumpus>
feeeelings
<surlyray>
i dont get upset if you're honest and its how you feel
<andytoshi>
nsh: not sure, i've got a lot of travel in the new year, maybe i'll be able to fit it it
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* nsh
nods
<nsh>
let me know if you do :)
<andytoshi>
if you're able to travel to europe, i'll be in milan at some point in february. will do :)
<nsh>
unlikely, but many things are possible
<surlyray>
andytoshi: now that we've got the formalities out of the way, can we discuss our difference, or, you are just resolved to ban and pretend my opinion is fake?
<nsh>
surlyray, be civil and on-topic please
<surlyray>
nsh, im trying my best to be patient -- please realize that isnt one of the things i was blessed with in this world -- but, how is discussing scaling bitcoin not ON TOPIC when thereis a war going on about scaling?
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<andytoshi>
i have set the channel to +q ~a, which from https://freenode.net/kb/answer/registration should make all non-registered users +q. so fyi you have to auth to talk now
<kanzure>
we should prolly remove that at some point
<kanzure>
but not right now
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<waxwing>
i just saw someone link it earlier, no idea its status, but since it's the author, it's probably at least useful for investigation :)
* nsh
wonders if Bünz or Bootle might consider committing an hour or so to unbefuddling their innovations for the masses [that is a slightly larger group of non-masses nerds]
* nsh
nods
<nsh>
eeep, but for the grace of -wizards this whole thing would end up implemented in bouncycastle in java
<waxwing>
one venusian day perhaps nsh
<waxwing>
i mean, hour
<nsh>
:)
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<nsh>
i just want to grok the kernel of the advance, which seems to be this inner product argument of pederson multicommitments, but i may be missing sufficient understanding of sigma protocols
<waxwing>
nsh, yes i sort of had that idea, and worked through the inner product argument, understood it, but only mechanically. but then i read the range proof that comes after ... gulp ...
* nsh
nods, definitely the toggle is set to "MORE MAGIC" here :)
<waxwing>
the inner product 'improved' version in the new paper certainly seems easier to grok, more boiled down, than the version in the original bootle 16 paper. (see the diagonals thing)
<waxwing>
thx hadn't got round to looking that one up yet
<andytoshi>
i don't think it's necessary to understand groth to understand bulletproofs, though i'm sure it wouldn't hurt
<andytoshi>
i don't think there's a clean intuition for the rangeproof, it seems like there were a lot of forced moves regarding where to put blinding factors and hash challenges, and the result just wound up looking that way
<andytoshi>
but the inner product argument is pretty elegant, essentially observe that if you have commitments A, B to (a, b), take a challenge x = H(A, B), and commit to ax + bx^-1 in a verifiable way, you're unable to do this except in the honest fashion
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<andytoshi>
then if you have a dot product of vectors <a1, a2> and <b1, b2> consider the vectors of half size of hte form <a1x + a2x^-1> and <b1x + b2x^-1> .... the dot product of the first vectors is D = a1b1 + a2b2 .. the dot product of the second is D + a1b2 x^2 + a2b1 x^-2
<andytoshi>
so the dot product is preserved and offset by these ugly cross-terms
<waxwing>
yes i was just mulling over today the significance of the extra cross terms; it's not like they don't depend on a, b
<andytoshi>
so in the inner product argument, the size of the vectors is repeatedly halfed, the L and R commitments compensate for the cross-terms that appear, and the challenges x are hashes of the L's and R's, which prevents cheating
<waxwing>
that would be a nice "bullet point" if they didn't :)
<andytoshi>
yeah, the inner-product argument is not zero-knowledge at all, it's ok to have dependence on the input
<andytoshi>
i don't think this is really expanded, they assume you're familiar with the bootle 16 paper and think of the new argument as basically a tweak of that ... but the bootle16 paper is much more general and it's harder to see the forest for the trees there
<waxwing>
the ax + bx^-1 seems not to be arbitrary i guess, if you have only one challenge value x, you need the cancellation between the two vectors, so you need an inverse, so i guess nothing other than (x, x^-1) makes sense?
<andytoshi>
yeah, that's where i landed after spending a long time trying to make the scalar inverse go away
<waxwing>
heh
<waxwing>
i don't have the petty concerns of "how the hell am i going to code this so it doesn't take 5 hours to run"
<andytoshi>
lol
<andytoshi>
well, peterdettmann found a way to compute every necessary scalar with one multiplication per, plus a log-many multiplies and a single inversion
<andytoshi>
so in the end it's not a big deal to have the inverse, but i still spent a while exploring the design space
<waxwing>
cool
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<waxwing>
so hang on, if you like unrolled the recursion for the dot product itself, do you end up getting basically all the cross terms, sum( a_i * b_j) multiplied by (x^2 + x^-2) or something?
<andytoshi>
yup
<nsh>
hence it's one mega multiexponentiation in the curve, which is nice for parallelisability
<nsh>
iiuc
<andytoshi>
yep, during verification at least
* nsh
nods
<andytoshi>
during proving, the cross-terms depend on previous cross-terms so you have to do them in order
<waxwing>
ah but it's a bit weirder eh, because a_i * b_j at one level is actually a_i' * b_j' so not so simple i think
<andytoshi>
waxwing: yes, but that weirdness is hidden in the L's and R's, which are complicated for the prover to compute, but the verifier just takes them as opaque points
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<nsh>
'His construction relied on the PCP theorem though, and did not yield a practical scheme' # interesting phrasing... is the PCP theorem by itself non-constructive or something?
<nsh>
or just naively results in hugecrufts
<waxwing>
am i the only one who finds talk of 'multi-exponentiation' weird because only came to this via ECC stuff? (it really is scalar mults, isn't it?)
<andytoshi>
i haven't read it, but my understanding is that it's constructive but just huge
<andytoshi>
waxwing: yeah, sorry, it's because academics use "exponentiation" to mean scalar mults
<andytoshi>
it's just a notational difference, xG vs g^x, it comes from historically cryptosystems using multiplicative groups
<waxwing>
sure i get it. i guess there isn't a problem since it's not like it can mean anything else here.
<sipa>
advantage of exponential notation is that it's clear what is a scalar and what is a point
<sipa>
disadvantage of exponential notation is that scalar formulas translated from scalar to point domain look vastly different, despite being ismorphic
<waxwing>
biggest disadvantage of exp notation: i can't read the paper without squinting :)
<sipa>
actually, the biggest advantage of exp notation is that the result look far more mathy
<waxwing>
yeah it's super-cool doing x^x^x^... in LaTex
<Alanius>
I'm sometimes tempted to switch to the triangle of power
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<sipa>
tetration?
<nsh>
.wik Tetration
<yoleaux>
"In mathematics, tetration (or hyper-4) is the next hyperoperation after exponentiation, and is defined as iterated exponentiation. The word was coined by Reuben Louis Goodstein, from tetra- (four) and iteration. Tetration is used for the notation of very large numbers." — https://en.wikipedia.org/wiki/Tetration
<waxwing>
log^a(b) and cos^(-k)(theta) are the ones that really get on my nerves
<sipa>
it's also ambiguous
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<Alanius>
how so?
<sipa>
f^{-1}(x) is sometimes used to indicate the inverse function of f (as in: f(f^{-1}(x)) == x)
<waxwing>
you mean what i said? yeah, that's why it gets on my nerves.
<waxwing>
yes cos is just a special case of that screw up
<nsh>
aye, functional inverse being notationally overloaded to reciprocal is one of the worst
<waxwing>
well, no, with f people don't confuse it, but for trig they do, and sometimes log.
<nsh>
someone will eventually restart mathematical notation from a higher categorical departure point and it will be beautiful and nobody will learn or use it
<waxwing>
yeah triangle of power, nice thought
<sipa>
waxwing: i don't think i understand the ambiguity you're talking about
<nsh>
log^x(b) is (log(b))^x where the logarithm base is notionally/conventially implicit, in my maths education anyway
<nsh>
but you get the same issue with -1
<waxwing>
cos^(-1)(theta) traditionally is used for the inverse function, while cos^(2)(theta) is universally the square, but that's inconsistent and confuses people. hmm OK maybe it really is the same for 'f', i forget now.
<waxwing>
nsh, yeah same for log. i'm not sure why but i have it in my head it's much worse with log and trig than just normal functions; probably because people only more rarely write f^2(x) (although they do, of course)
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* nsh
wonders why the sec parameter is given as 1^λ, which seems a lot like 1 for any value of λ
<nsh>
is it moral to say that a pederson NIZK scheme still has a CRS which is the ancillary group generator[s] and thus still has a trapdoor in theory but this is avoidable by picking the generator element[s] using a NUMS scheme?
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<waxwing>
'moral'? :) but that's what i've been assuming, too.
<nsh>
i mean fair, i guess. there's some mathematical use of "morally" that i'm failing to emulate :)
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<nsh>
in Bootle+'16 they also exp/mult the basic generator by a random value, which iirc isn't done in CT
<nsh>
' The commitment key is ck= (G,p,g,g1,...,gn) and acommitment is of the form c=g^r . n/i=1 g^m_i. '
<waxwing>
yes it's just a generalisation of the pedersen commitment to a vector; still only needs one blinding value (so r in the above)
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<kanzure>
nsh: i would prefer irc instead of hangouts for paper reading group. we could even call it #bitcoin-wizards.
<nsh>
there are many for whom line-based typing is not the most fluid and efficient real-time communications modality :)
<nsh>
i can speak at at least a tenth of the speed i think, for typing it's less than 1/100th
<nsh>
your mileage clearly varies :)
<waxwing>
lol
<waxwing>
but what if it's actually the same ratio for kanzure .. :mind_blown.gif:
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<kanzure>
no my bottleneck is input/output (both of them)
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<nsh>
unclear to me what form u [the statement to be proved] takes in the [improved] inner product argument
<nsh>
is it a vector (Z_p)^n?
<nsh>
cc andytoshi
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<andytoshi>
`u` in the inner product argument is a point
<andytoshi>
if you mean mu, that's a scalar blinding factor
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<nsh>
ah, ty
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<nsh>
'These polynomials are carefully constructed such that the zero-coefficient of <l(X),r(X)> ∈ Z_p[X] has a special form if and only if v is in the range.' # doesn't any inner product only have a zero-coefficient?
<andytoshi>
these "polynomials" have vector coefficients, they're basically vectors of polynomials. then their dot product is a polynomial whose coefficients are the dot products of the original polynomials' coefficients
<andytoshi>
so the inner product is itself a polynomial
<nsh>
oh right
<nsh>
thanks, was wondering about the vector-ness
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<nsh>
oh so you start with a single polynomial whose coefficients encode the value and then you blind by splitting it into a left and right polynomial whose blinding factors cancel out
<nsh>
nm
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