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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<adlai>
Taek: colatz cycle post tag go
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<tromp>
isn't Definition 8 equivalent to: forall <s,u,w> in R: <P(s,u,w),V(s,u)> = 1 ?
<andytoshi>
tromp: good catch on definition 4. for definition 8 the answer is yes but it's awkward to write that
<andytoshi>
because (u, w) comes from the adversary
<andytoshi>
well, i guess just add a third line on the rhs with "(s, u, w) in R" and remove the first line from the lhs. but that seems equally hard to read
<tromp>
the point is that entire quantification over adversaries is redundant
<tromp>
if my condition above holds, then your condition holds trivially for all adversaries, whether poly time onr not
<tromp>
and if my condition above doesn't hold, then you can trivially make an adversary to fail your condition
<andytoshi>
ah, yeah, i think you're right
<andytoshi>
but using an adversary-less definition would require adding a bunch of lies to the proof of the forking lemma :P (which i guess is not in this paper..)
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<andytoshi>
actually no, it may be that there is a counterexample to your definition that no ppt adversary can find
<tromp>
ok, just wanna make sure i'm not missing something
<tromp>
oh really?
<tromp>
that doesnt make sense to me
<andytoshi>
yeah, like a hash preimage
<tromp>
since only a single counterexample suffices
<tromp>
which is by definition ppt
<tromp>
the adversary would be constant time, to output that single counterexample
<andytoshi>
no, there is a "single counterexample" of a collision on SHA2, which you can guarantee by counting
<andytoshi>
but you can't define a ppt adversary that outputs it
<tromp>
i can, just not constructively
<andytoshi>
because it wouldn't be uniform (itself generated by a ppt algo that takes as input the security parameter) (ok, and you need to generalize sha2 to have a security parameter)
<andytoshi>
right
<andytoshi>
so there is an additional requirement for an algorithm to be polytime (or any time) which is "uniformity", to prevent exactly these shenanigans
<tromp>
your qunatification over non-uniform adversaries includes all those outputting single counterexamples
<andytoshi>
oh derp
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<andytoshi>
the word "non-uniform" is right there :P
<andytoshi>
yeah you're right
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<tromp>
ok, there's another problem
<tromp>
your definitions doesn't quantify over lambda
<tromp>
is it supposed to say for all lambda?
<tromp>
my counterexample adversary can ignore lambda and output the fixed counterexample that invalidates one lambda
<tromp>
(i.e. ignore sigma too)
<andytoshi>
yeah, it is implicitly over all lambda
<andytoshi>
or maybe the definition is parameterized over lambda? like it can be "perfectly complete" for lambda=256 but not for others? that seems dumb, and nothing else in the paper restricts lambda, but it's one way to read the definition
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<tromp>
def 9 also looks odd to me. how can one A have both sigma and trace as input?
<andytoshi>
FYI def 8 is verbatim definition 6 from [1] (the bootle "zk arithmetic circuits from dl" paper which has passed peer review and also made quite a splash)
<andytoshi>
it may itself have come from something earlier but i haven't traced back that far
<andytoshi>
tromp: A is implicitly two algorithms here
<andytoshi>
in older papers it was common to have two adversaries, one which generated challenges and one which verified traces, but IMO this way of writing is clearer
<tromp>
peer review is not what it used to be:-(
<andytoshi>
yes, very true, i have a rant about CS crypto peer review somewhere..
<andytoshi>
so i am glad that you're dissecting this
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<tromp>
what your definition of ~ (squigly equality) ?
<andytoshi>
within a negilgible function
<andytoshi>
where does it appear?
<andytoshi>
negligible in lamda*
<tromp>
it compares the probabilities in Def 9
<andytoshi>
this also came from the bootle paper (def 7 there, except it's stastistical rather than computational). i agree that the squiggly line should be defined.
<tromp>
if you're gonna use ~ then it shld also be used in Def 3 and 4
<tromp>
def 3 can use ~ 1/2 and Def 4 can use ~ 0
<andytoshi>
yeah, agreed.
<andytoshi>
i'll forward these comments to benedikt (tho i think he can't update the paper at this point in the review process)
<tromp>
by negligible do you mean inverse superpolynomial?
<sipa>
andytoshi: where was the paper submitted to?
<andytoshi>
tromp: yeah
<andytoshi>
sipa: benedikt said "oakland" which i believe means http://www.ieee-security.org/TC/SP-Index.html ... which note is a security conference, not a crypto one, because the stanford folks were worried a pure crypto conf would think "rangeproofs with these asymptotics are solved"
<tromp>
if in MW you use one aggregate rangeproof per tx, then that conflicts with tx aggregation?
<andytoshi>
tromp: yes, i think for MW it doesn't make sense to use the aggregation
<andytoshi>
even without aggregation this beats the pants off of our previous construction
<tromp>
yes, i'm very happy with this work for that reason
<andytoshi>
ditto
<tromp>
gratz on your excellent results!
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<sipa>
andytoshi: oh yes, indeed
<andytoshi>
heh, my main contribution was being discouraging about whether these results would be possible :)
<andytoshi>
but i'll forward your congrats to benedikt who disagreed
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<tromp>
another concern: def 9 has order of quantification exists emulator forall adversaries, but informal statement at bottom of page has forall adversaries exists emulator ...
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<andytoshi>
i think def 9 says "forall adversaries exists emulator", which matches the text (and this is what's used in the forking lemma proof iirc)
<andytoshi>
ah, no
<andytoshi>
lemme check the proof in the bootle paper, the informal text might just be wrong..
<andytoshi>
yeah, the proof uses "there exists emulator forall adversaries", in the sense that it defines an emulator parameterized by the proof system which makes no reference whatsoever to the adversary itself
<andytoshi>
so the informal text is wrong but it's not important to the results
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<tromp>
ok, thx for checking
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<akrmn>
Thinking a bit about scaling, and I wondering whether all this talk about drivechains (miners voting for validity of sidechain transactions) is needed if we just implement a new scripting language (like Simplicity). For example, you want to send some btc to a sidechain (like rootstock)...Can't you just make a smart contract that puts a specification of what chain to send to and conditions for getting money back, and the amount
<akrmn>
You can specify the min amount of work on the sidechain, and put a hash of a block header of the sidechain for reference (into the smart contract specification)
<andytoshi>
that's the dream
<andytoshi>
in practice such a smart contract would be absurdly expensive to verify, even given known crypto techniques for compressing proofs
<sipa>
the problem is that the only condition for moving money back is "the sidechain's consensus rules - which hopefully mean no inflation - were satisfied in its entire history"
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<sipa>
or rather, the condition you want ideally
<sipa>
and verifying that condition, even if it can be written as a smart contract, involves redoing the entirety of validation work of the sidechain
<sipa>
SNARKs one day...
<akrmn>
thanks for the input. I feel like the verification can be done quite quickly with reasonable security, but I will think about it more
<sipa>
how do you prove no double spending happened in the sidechain?
<akrmn>
well ya basically I am thinking of a smart contract that trusts the hashpower (miners) of the sidechain
<sipa>
then drivechains is what you want
<akrmn>
which should correlate to the users validation...
<sipa>
but i don't think that's an interesting security model
<akrmn>
but I thought drivechains needs the miners of the bitcoin chain to decide
<sipa>
yes
<sipa>
inevitabl
<sipa>
at best, bitcoin's miners collectively have censorship rights
<sipa>
so they can always choose to not accept the proof of double spending or something
<akrmn>
well when you let the miners of the sidechain have the power, then at least you are not involving bitcoin miners in the process, and you let the user choose which miners to trust
<sipa>
how can you let the sidechain miners have power?
<sipa>
they not identifiable
<akrmn>
but ya these are just inital thoughts, would be good to read more about it if you have references
<sipa>
there is no way you can prevent bitcoin miners from stealing the sidechain's pegged funds
<andytoshi>
i think drivechains (and the writing about that) is exacly the security model you're pursuing, and IIRC paul has made the attack model pretty clear
<sipa>
unless you make validating the sidechain part of bitcoin's consensus rules
<sipa>
and even then the risk of reorganizations remains
<akrmn>
Well the requirement of the smart contract would be that you have a spendable output of some value on the sidechain that passed x amount of hashpower starting from block with hash h
<sipa>
the smart contract can't observe the sidechain
<sipa>
unless your bitcoin nodes are required to see it
<sipa>
which undoes all flexibility advantages your sidechain approach would have
<akrmn>
so there can be forks, but as long as you have a piece of the chain that passed the hashpower required. You just send the sequence of block headers or a short proof to show that the hashpower requirement was met
<kanzure>
akrmn: sounds like you would prefer sign-off directly by miners
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<akrmn>
ya I guess the problem is that each node would have to get block data from the sidechain...need a shorter way to prove it
* sipa
does the SNARK song
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<JackH>
what would be the consequences to have a difficulty adjustment to be more often? negative consequences I mean
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<bill___>
hey anybody here able to help with a question?
<bill___>
my bitchain is too large for my hard drive, if i delete and redownload the block chain wilthout deleting my wallet data will I be able to store the new file whilst retaining capital?
<sipa>
#bitcoin
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<mlz>
waxwing, yes there's a SNARK song, can't you hear sipa sing? :D
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