<CodeShark>
zkp does not require fully homomorphic crypto
<gmaxwell>
er right.
<gmaxwell>
I wasn't saying it couldn't be done, just that it may not be anywhere near as efficient as even the linear code based schemes.
<gmaxwell>
Anyways, perhaps email Craig Gentry; since he's worked on all of these things.
<CodeShark>
google search turns up a baseball player :p
<CodeShark>
ok, I think I found the right guy now
<CodeShark>
stanford?
<CodeShark>
oh, no...berkeley
<CodeShark>
will P != NP be proven in our lifetimes? and what the hell is wrong with our axioms?
<gmaxwell>
(in particular, the SNARK stuff is based on his work, as was the breakthrough of slightly feasble FHE based on LWE.)
<CodeShark>
computational complexity is at once one of the most useful mathematical theories AND one of the mathematical theories with the least ability to actually prove its main claims
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<CodeShark>
imagine archimedes sitting around and saying "we believe there's an infinite number of primes but we can't prove it" - I guess euclid's parallel postulate is a closer parallel
<CodeShark>
(pun intended)
<gmaxwell>
there are many unproven things which seem totally trivial.
<CodeShark>
in this case it must have something to do with our axioms
<CodeShark>
i.e. P != NP is independent of diagonalization methods
<bramc>
CodeShark, There are the relativization, naturalization, and algebrization barriers to showing P!=NP, which combined together exclude almost all classes of approaches to the problem, although there's been some (comically limited, but still extraordinarily impressive) work which has gotten around them. There's a plausible approach which requires merely proving a generalization of a generalization of a generalization of th
<bramc>
e riemann conjecture
<CodeShark>
hah
<CodeShark>
it all seems to come back to the riemann conjecture
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<gmaxwell>
there are zillions of things which imply P!=NP, e.g. existance of one way functions implies P!=NP.
<bramc>
the riemann conjecture is directly related to the general problem of pseudorandomness, because it's equivalent to a statement about the error term in the formula for the approximate number of primes less than a given value
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<gmaxwell>
proof of any of the zillions of proven NP-complete problems is not in P would also prove P!=NP.
<bramc>
CodeShark, Your guess that there's a deep issue along the lines of diagonalization not working is essentially correct. You can look up 'relativization computational complexity' and 'naturalization computational complexity' for more info
<bramc>
gmaxwell, That... doesn't help
<CodeShark>
so we're missing some basic axioms here...or perhaps the universe allows for a computational model where P = NP
<gmaxwell>
There actually has been a lot of interesting progress in complexity theory on bounding approximations (which is often more pratically interesting than P/NP in any case)
<bramc>
Adding axioms is unlikely to help, unless you add an axiom just saying P != NP, which is, uh, not useful.
<CodeShark>
well, the point is that perhaps like the parallel postulate, we can formulate a fully self-consistent theory where P = NP
<bramc>
CodeShark, Probably not, P vs. NP doesn't have the same kind of untouchable feel as the sorts of problems where those issues come up.
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<bramc>
Certainly not like the parallel postulate, p != np is either true or false in a much stricter sense than the parallel postulate.
<CodeShark>
well, sorta - I would argue that to ancient geometers, the parallel postulate also seemed to be pretty strictly true or false
<CodeShark>
of course, allowing it to be false forced us to change the definition of "straight"
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<bramc>
there's a deep philosophical distinction between 'independent' and 'true but unprovable'
<CodeShark>
perhaps near black holes or near the big bang, P = NP or something :p
<CodeShark>
our concepts of time and space fly out the window
<bramc>
There has been some interesting work done on computational complexity around the surface of a black hole, but it doesn't relate to whether P!=NP, because it's a different computational model
<bramc>
The more immediate and interesting question is the one of quantum complexity, which has a much more, ahem, complex relationship with classical complexity than popular writings indicate.
<CodeShark>
but even quantum complexity suggests P != NP...with problems strictly contained in NP and strictly containing P
<bramc>
In the meantime we have symmetric key primitives which are *probably* just fine, albeit rather inefficient compared with optimal constructions.
<bramc>
Yeah, quantum computation doesn't speed up all that many things all that much.
<CodeShark>
there's probably something fundamentally wrong with our notions of time and space as applied to complexity classes
<CodeShark>
we know that the universe doesn't quite work that way
<CodeShark>
turing machines and their kin use somewhat contrived notions of them
<CodeShark>
which our theories in physics suggest otherwise
<bramc>
turing machines and the like are a good representation of any 'reasonable' model of computation. Quantum mechanics is not a reasonable model of computation :-)
<CodeShark>
lol
<bramc>
We have no reason to think, for example, that the human brain pulls off any sort of quantum trickery to do its reasoning.
<CodeShark>
well, some people do
<CodeShark>
reminds me of conversations with Penrose :p
<CodeShark>
the superposition principle does seem to apply to our conscious perception in some subtle ways...like our ability to imagine something in many different states at once
<CodeShark>
our ability to hypothesize...to consider potential outcomes that haven't yet manifested
<bramc>
*sigh* superposition has nothing to do with consciousness, and penrose's theories of the brain are, sadly, strictly wackadoodle.
<bramc>
Considering potential outcomes doesn't require quantum anything. Chess programs do it quite well.
<CodeShark>
the ability to abstract...to remove the concrete...and replace it with variables that can take on entire ranges
<CodeShark>
the more advanced we get in math, the more we do this
<bramc>
Again, this is not even vaguely quantum stuff
<CodeShark>
we make statements that apply to entire infinite sets at once
<bramc>
If you're really interested in the computer scientist view of quantum mechanics, you can look through the 'quantum computing since democritus' stuff by scott aaronson.
<CodeShark>
all we need are negative probabilities and we're there :p
<bramc>
quantum mechanics is basically complex probabilities whose magnitude is less than 1
<CodeShark>
well, the interesting thing is how those probabilities interfere
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<CodeShark>
from continuous waves we get discrete events...
<CodeShark>
"complex probabilities whose magnitude is less than 1" is the kind of phrase you get when one's math formalisms are way far ahead of one's sensory intuition :p
<CodeShark>
in a sense, the development of the language behind complex numbers is a little unfortunate because opportunities were missed to make it a little more intuitive
<CodeShark>
i.e. the spinor/rotor language...or geometric algebra
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<CodeShark>
then you end up with things like pauli matrices - which are perfectly legit mathematical formalisms...but bear very little connection to our sensory experience
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<CodeShark>
It's worthwhile to read through Hestenes' reformulations to try to regain some geometric insight
<bramc>
This conversation has strayed far enough off topic
<the_last>
i wonder if lots of other people will short
<the_last>
because of the hype around this event
<the_last>
and cause the market to drop anyway
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<gmaxwell>
it's a little goofy though, esp in that this has nothing to do with blocksize. regardless of the blocksize anyone can generate transactions and fill up whatever and delay transactions that aren't paying more.
<the_last>
yeah, but the hivemind is easily persuaded and manipulated when it comes to things surrounding the block size
<phantomcircuit>
the_last, it appears to be much less the hive mind and much more a series of paid shills
<the_last>
paid by who?
<phantomcircuit>
an excellent question
<gmaxwell>
there has been some funded attack on bitcoin lately, e.g. that full page ad that had a thread on reddit recently.
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<the_last>
full page ad? I must have missed that
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<Xh1pher>
sweden... enough said, a land where u pay 80% taxes and woman stand above the law, sure they dont like btc
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<leakypat>
It was funny watching the 21inc dude presenting Bitcoin to Goldman Sachs
<leakypat>
He was like, "there's a patch being worked out there to scale it to billions of transactions"
<leakypat>
I mean, it's true...
<leakypat>
They way he said patch though made it sound like it was a one line code change
<leakypat>
Instead of a whole new network layer
<leakypat>
I need to learn to talk like that
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<nsh>
--
<nsh>
Mr. Burns: Smithers, I've designed a new plane! I call it the Spruce Moose, and it will carry 200 passengers from New York's Idlewild Airport to the Belgian Congo in 17 minutes!
<nsh>
Smithers: That's quite a nice model, sir.
<nsh>
Mr. Burns: Model?
<nsh>
--
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<leakypat>
nsh: lol
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<dgenr8>
;;seen Relos
<gribble>
Relos was last seen in #bitcoin-wizards 1 week, 0 days, 22 hours, 28 minutes, and 50 seconds ago: <Relos> I said enough, I just switched to the tab and saw your comment, I don't know if there was a real discussion ongoing and I wouldn't want to in anyway take up its space
<kanzure>
hahaha
<kanzure>
09:27 < Relos> and why have I been banned earlier today from #bitcoin-wizards.... I have never even said a word there
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<bramc>
An interesting wrinkle to the extension which allows a mutability fix: Once it's adopted there's a fairly trivial DOS of miners who don't support it
<bramc>
The extension here being one which allows a transaction to refer to an input by the transaction rather than its signature
<bramc>
You make a transaction of that type, then you connect to all miners directly and start giving them a double-spend of the old transaction every generation. Other miners will recognize it as a double-spend and treat their mining results as invalid
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<kanzure>
they would have treated other miners' results as invalid since the others did not accept the other blocks that were mined with the patch
<kanzure>
oh, you are probably talking about a different patch/idea, whoops
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<bramc>
kanzure, Not sure what patch you're talking about or which one you think I'm talking about
<bramc>
I'm referring to one where the malleability fix is opt-in. It unfortunately leads to a situation where older miners are mistaken about which utxos have and have not been spent
<bramc>
And you can't add that information in because the whole point is that it isn't there.
<bramc>
This isn't a reason not to add the extension - it's very important functionality - but it's something to keep in mind.
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<kanzure>
yes, i was definitely not talking about that; my bad.
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<zooko>
I refuse to read anything by Paul Krugman.
<akrmn>
Man no one gives me a clear answer on whether subchains can be used for scaling. Sipa didn't answer my last reply on bitcointalk. Jeff Garzik kinda said it can work in the far future (not clear). Peter Todd suggested that tree chains can work but no one still gave a solid proposal and UTXO commitments are already well established. Yes I read about UTXO commitments and P2Pool but I don't think either will help as much as subchains (P2P isn't helping rig
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<akrmn>
And now sipa is writing about hard forks on the mailing list and hiding out on #sidechain-dev (so I won't bother him). Why don't we consider all options first?
<kinlo>
akrmn: I think I can explain why subchains wont work for scaling
<akrmn>
For UTXO commitments, what gives incentive to nodes to relay the merkle trees branches? Miners have an incentive to relay blocks because that's how the fees they made are recognized, but no incentive for merkle trees of UTXOs.
<kinlo>
every client is now fully validating every block, in order to make sure nobody is cheating the system
<akrmn>
Well the point is that you can validate just the transactions you're interested in and the whole system is still sustainable
<kinlo>
you will need someone to validate all to ensure the next block is valid
<kinlo>
if you just look at a few chains, how do you produce new blocks?
<kinlo>
are you going to trust that the other chains are valid too when creating a new block?
<akrmn>
Its a tree of chains
<akrmn>
each of 1 MB
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<akrmn>
wallets can generate addresses so that they are constrained to one branch of that tree
<akrmn>
so you can monitor your wallet fully or someone else's (like your government representative)
<akrmn>
(be sure of the UTXOs and their coin value)
<kinlo>
ok but how do you validate the blockchain?
<kinlo>
you can just look at your chain, but then you can't mine, coz you don't know the entire tree
<akrmn>
there are multiple blockchains (synchronized)
<kinlo>
and those all need to be validated
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<kinlo>
the question is, if you mine a new block, do you require all chains to be valid inside that tree?
<akrmn>
Yes mining is decentralized because each chain requires a unique hashing problem to solve
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<kinlo>
in that case, you're dividing the entire hashing power into multiple chains
<kinlo>
and the idea is that the blockchain is unbreakable because there is nobody with more computer power then what is used for the blockchain
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<kinlo>
if we divide our hashingpower into 10, 2-3 chains can be stopped being mined to get the power to attack on another subchain
<akrmn>
Miners will have an incentive to validate the children chains of the chain theyre mining on, since they will commit the hashes of their headers into special transactions that give them outputs that are only valid on the children chains (but the deeper you go with the children the less important it gets)
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<kinlo>
so you are dividing themain blockchain into multiple seperatly mined chains?
<akrmn>
ok wait that may be one disadvantage that I have to think about
<kinlo>
it's basically the reason why all alt-coins are not safe, the hashing power is divided and people can quickly switch tree to perform an attack
<akrmn>
It needs to be done so that mining on a child chain helps the hash power of all parent chains...
<akrmn>
but not the other way around
<kinlo>
but that can only happen if you validate all chains
<kinlo>
which means you're not solving the problem, you're adding an extra layer and the combined blocksize - which needs to be validated - remains the same
<kinlo>
do you know how merged mining works?
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<akrmn>
Yes I know merged mining
<kinlo>
that partially solves that problem already
<kinlo>
however, the 2 chains are completly seperated
<akrmn>
but I dont want miners on the parent chain to be able to solve blocks on the child chains
<kinlo>
and the only way it would work is if every miner would be mining every chain at the same time
<akrmn>
that would result in decentralization
<akrmn>
centralization
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<kinlo>
akrmn: the whole bitcoin consensus model works on the fact that everyone works on one tree, making it "centralized" in a way
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<kinlo>
akrmn: did that answer your question ? :)
<akrmn>
Well the child chains are still part of the entire network, so putting hash power into them without putting it directly into the top chain isn't so bad
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<akrmn>
If too little hashpower exists on the main chain, then difficulty will drop and there will be incentive for more miners to mine on it to get the higher fees associated with the top chain
<akrmn>
so no I see everything still fine
<kinlo>
it's in the current situation already common for 3-4 pools to have 50+% of the chains
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<kinlo>
if you have 10 chains, you will still have 3-4 pools having 50% of each chain
<akrmn>
no because in the lower chains, there will be lower difficulty, so you don't need to be so powerful to mine on it
<akrmn>
the point of pools is to lower the variance
<kinlo>
I'm talkign about relative power
<kinlo>
let's say at this moment, the top pool has 25%
<akrmn>
and also there will be smaller pools and they will have to be different pools. It will be difficult for the miners on the top chain to also mine all the other chains
<kinlo>
and manages to keep 25% overall when we upgrade to 10 chains
<kinlo>
and lets say the difficulty of each subchain is equal, as you stated yourself, the network would balance out to that by itself
<kinlo>
then that particular pool would be able to pauze mining on 9 pools, and would have mining power equal to 10 times 25% of the subchain it is attacking
<kinlo>
so it would just blow away the competition on that chain and dominate it
<kinlo>
do you follow?
<akrmn>
kind of
<kinlo>
ehm, it would pauze mining on 9 subchains
<akrmn>
Attacks can always happen still so I don't see how doing it my way would be worse
<akrmn>
people using the subchains know that security is a little lower on the subchain
<kinlo>
ok but 10 times 1 mb is not enough for the future. let's say we go to 100 chains or 1000
<kinlo>
do the math then
<kinlo>
then the issues with your logic become more clear (altough theoretically they stay exactly the same)
<akrmn>
I'm not disregarding your criticisms (some are good points). But scaling is not a problem since you can just keep adding more child chains, and there is an incentive to keep the child chains safe, since miners are getting paid fees by the child chain miners to include their block header hashes in the block.
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<kinlo>
how do you validate the child chains?
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<akrmn>
Well miners can validate the direct children chains of the chain they are working on. They can do more if they want, but the deeper you go the less important. And the child chain miners will take care of validating the grandchildren anyway.
<kinlo>
I don't understand how a parent is validating their children?
<akrmn>
By downloading the blocks and making sure the transactions are following the rules
<kinlo>
but a child chain is only valid when all their child chains are valid, no?
<akrmn>
Yes, but in case of conflict, the parent decides
<akrmn>
is the rule I put
<kinlo>
so the parent needs to evaluate all child and granchildren etc
<akrmn>
so there can be mistakes, but it becomes less important the deeper you go
<kinlo>
so you basically end up with one big chain, let's just keep the bitcoin model then
<akrmn>
just the child is enough since the child will validate the grandchildren
<kinlo>
how does the child validate the grandchildren?
<akrmn>
just like the parent validates the children
<kinlo>
by deciding which block is the tip on that granchild?
<akrmn>
if the bitcoin model means centralization, I don't want that. I want to try to make things more decentralized that's all.
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<kinlo>
ok but how does a child validates their grandchildren/
<akrmn>
just by getting the blocks of the (direct grandchildren)
<akrmn>
chain of level n validates chains of level n+1
<akrmn>
and more if it wants
<kinlo>
how does it technically work?
<kinlo>
a block of a child has a list of the blockhashes of the grandchild?
<akrmn>
Ya block of a child has 10 special transactions, each with the hash of the header of a grandchild
<kinlo>
ok and how do I calculate that hash?
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<akrmn>
You just need the header and hash it (for whatever hash)
<kinlo>
where do I get that?
<akrmn>
from the miners/nodes responsible
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<kinlo>
so I blindly trust those miners?
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<kinlo>
bitcoin is about not trusting anyone else, you're saying I should pick some miners and trust them with whatever hash they come up with?
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<akrmn>
The child chain will have to follow what the parent chains commit to with their hashes. The parent may need to trust some miners deep down the tree, but even if they are wrong it doesn't matter because those miners will have to trust the parents hash, and those people using the deep chains already know the risks involved.
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<akrmn>
I am just allowing for a more choice instead of a one size fits all policy
<akrmn>
You can still have full nodes watching all chains and it's the same as having big blocks
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<kinlo>
so if I understand it correctly, a parent chain picks out a child chain, trusts it blindly, and then all other miners will trust that hash that ends up in the tree because the parent hash takes precedence?
<kinlo>
imagine that there isn't even foul play, say a bug creates an invalid block in a grandchildchain miner
<kinlo>
the parent of that chain accepts it because it trusts it, and might even validate it using the same buggy software, and then it submits that block into his own chain
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<akrmn>
o ok I see your point
<akrmn>
but I have to think
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<kinlo>
I'll let you think, I kinda like poking holes in ppl's theories :)
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<akrmn>
Well, after the next few blocks, the problem (in the grandchildren chain) may be discovered by the child chain miners and so they will fix it (equivalent to using a different fork in their chain) and the parents will in turn fix it, because the parents need to follow the chain the strongest child chain.
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<akrmn>
I think that's the main idea to resolve the problem
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<kinlo>
given enough mining power, I can reverse all transactions made today on the bitcoin blockchain
<akrmn>
yes true
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<kinlo>
the amount of mining power required is enormeous, I will never be able to do so
<kinlo>
if you have subchains, and subsubchains etc
<kinlo>
I will
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<akrmn>
there's also the issue of validating transactions coming in from a sibling chain you don't track but that's easy because you just need an SPV proof for that. Also at most 2 sibling chains can be involved in a transaction (to avoid many duplicates). But you can read that on my write up. Im too busy to get too involved in this but I will try my best to understand the current Bitcoin code and maybe do some development related to this.
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<akrmn>
If anyone knows much about UTXO commitments and whether they can work, let me know
<petertod1>
akrmn: define "work"
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<akrmn>
petertod1: What gives incentive to nodes to give out the merkle trees to peers who ask?
<akrmn>
Cause you need that tree of UTXOs to prove validity of a UTXO
<akrmn>
My idea is of subchains for scaling
<akrmn>
but with UTXO commitments it can possibly solve one problem that I want to solve
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<akrmn>
Well you just need the branches of the UTXO tree corresponding to your "outputs of interest". But if no nodes give you the branches that you need, then it can be a problem.
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