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05:52 < andytoshi> tromp_: assuming equal difficulty, to dominate N-1 blocks (plus your own) requires hitting a target 1/Nth the size of the single-block target
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06:27 < tromp_> hi andytoshi
06:27 < tromp_> that assumes a different notion of dominating than what i understood
06:28 < tromp_> where the previous N-1 blocks did work exactly matching the target
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06:30 < tromp_> where the previous N-1 blocks did work exactly matching the target
06:30 < tromp_> the total target work proven by only following direct
06:30 < tromp_> predecessor links
06:31 < tromp_> i see now. that phrase says you ignore how much the predecessors improved on the target
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06:32 < tromp_> sorry for paste error
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06:33 < tromp_> note that this skipping is different from the one in your paper with "effective difficulty"
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11:15 < andytoshi> tromp_: yeah, i understand now
11:15 < andytoshi> the skipping is definitely different but i had thought the same proof would hold
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11:26 < tromp_> your paper also glosses over the possibility of infinite effective difficulty for hash==0 :(
11:27 < andytoshi> yes, it does, somebody gets a hash very close to zero it's a safe assumption the random oracle model has broken down for this hash anyway
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11:42 < tromp_>  i still like the idea of committing to a compact chain, althought its uses are not quite clear to me, beyond  informing the user like "branch ... claimed cumulative difficulty ... verified effective difficulty ... giving correlation ... "
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11:46 < tromp_> perhaps correlation is the wrong notion. one could compute the odds that the given the verified eff. diff. what are the oods of having at least the claimed cumulative difficulty
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11:58 < andytoshi> tromp_: the use is that you don't have consensus failures in the case that people drop blocks
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12:20 < tromp_> i don't know what you mean by dropping blocks
12:20 < andytoshi> tromp_: i mean in mimblewimble my design had been that blocks outside of the compact chain would be deleted by full nodes
12:21 < andytoshi> so if there wasn't a canonical chain, somebody could show up with blocks referencing old blocks that no longer existed, and this would cause trouble
12:22 < tromp_> i dont see full nodes  making use of compact chains
12:23 < andytoshi> in the mimblewimble paper this was the design
12:23 < andytoshi> because they had no need for any additional data
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12:24 < tromp_> full nodes need to be sure of highest work branch by checking all blocks pow
12:25 < andytoshi> if my lemma had been correct the compact chain would have been sufficient. as it is, i still think a factor of 2 somewhere in there will fix it
12:26 < andytoshi> they don't need to be sure of the highest work branch, they only need the statistical properties of the highest-work compact chain to be such that rewriting is as hard as writing
12:27 < andytoshi> same as a full blockchain
12:27 < tromp_> i don't hink that's fixable
12:27 < andytoshi> why doesn't defining a 1/2 into to the definition of effective difficulty fix it?
12:28 < tromp_> i will ponder that separately, but i mean full node needs more than statistical assurance
12:28 < andytoshi> they already have only statistical assurance in bitcoin
12:28 < andytoshi> you can get lucky and mine a million blocks in a million hashes, in principle
12:30 < tromp_> yes, but that will be an actual valid chain
12:30 < tromp_> while a lucky compact chain need not be part of an actual valid chain
12:30 < andytoshi> that's fine
12:31 < andytoshi> we can define a compact chain to be just as valid as a full chain, then as long as there's no work advantage to "mining" a compact chain directly, it's fine
12:32 < tromp_> surely a compact chain can only be valid if part of a prev-block chain?!
12:33 < andytoshi> no
12:33 < andytoshi> this is the point of all the sinking signature stuff
12:33 < andytoshi> you only need the compact chain to validate the whole history
12:34 < tromp_> i must admit i've been skipping the sinking signatures as being a little beyond me for now
12:34 < andytoshi> no worries, the paper has a ton of technical stuff that isn't super necessary .. but what is necessary is to know that it allows compressing blocks together
12:35 < andytoshi> but after doing this, you need your commitments and proven work to still be sensible
12:35 < andytoshi> so i did this compact chain thing, and said that each block can skip a ton of other blocks (and commit to the compressed aggregate of all the skipped blocks)
12:36 < andytoshi> which winds up being like log(n_skipped_blocks)^2 in size or something
12:37 < tromp_> so you're actually changing the longest chain rule. from most cumul diff to most effective diff on compact chain
12:37 < andytoshi> yeah
12:37 < andytoshi> section 3.3.2 talks about the consequences of this
12:37 < tromp_> and not requiring prev block hashing to be witnessable
12:38 < andytoshi> yep
12:38 < andytoshi> it is definitely a formal weakening of the security model
12:38 < andytoshi> but i argue that it's just as good, for all intents and purposes, in that section
12:40 < tromp_> btw, is there any more recent version of that paper than last october or so?
12:40 < andytoshi> no, sorry
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12:41 < andytoshi> i've moved away from the sinking signatures (and therefore compact chains) because they break my payment channel/scriptless script stuff
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12:42 < tromp_> why do compact chains require different kind of signatures?
12:42 < andytoshi> because only sinking signatures can be aggregated across blocks the way that i needed
12:43 < tromp_> does the paper explain why that fails with the regular sigs?
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12:44 < andytoshi> not directly .. defn 4 says that a sinking sig is one that can be aggregated with sigs from previous blocks but not from future ones
12:44 < andytoshi> which is the reason
12:45 < andytoshi> basically aggregation usually gets you negation, which in mimblewimble is sufficient to reverse transactions (swap inputs and outputs and negate the kernel signature)
12:46 < andytoshi> ECDSA sigs can't be aggregated, schnorr sigs only get you a 50% space reduction, BLS sigs on same message can be aggregated in constant space but allow negation
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12:47 < andytoshi> so, you can get aggregation within a block by having BLS sigs that sign the current blockheight, this lets you compress every kernel into a single point and every sig into a single sig, which is cool
12:48 < andytoshi> sinking sigs are BLS sigs that separately sign the current blockheight and a bunch of previous blockheights
12:48 < andytoshi> so by dropping the higher blockheights you can "migrate" them to earlier blocks, where they can be aggregated, but not to later ones
12:49 < tromp_> is BLS the type based on pairings?
12:49 < andytoshi> yep
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12:52 < tromp_> do schnorr signatures allow reversal of tx?
12:52 < andytoshi> no
12:52 < tromp_> is that equivalent to ECDLP?
12:53 < andytoshi> they also don't allow much aggregation (you can reduce a bunch of 64-byte sigs to a bunch of 32-byte ones plus one extra point)
12:53 < andytoshi> yes
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12:53 < andytoshi> BLS sigs i believe reduce to CDH (or something analogous when the paired groups are different)
12:54 < tromp_> i'm suspicious of pairing crypto. even though i'm no cryptographer by any means:(
12:54 < andytoshi> if it helps, so is adam :)
12:54 < tromp_> just don't feel comfortable with something that is  MUCH less stress tested than EC
12:55 < andytoshi> that is another motivation for me to explore other directions .. the pairing dependency is annoying
12:56 < tromp_> is it possible that ppl will find new ways to aggragate shnorr sigs, giving much more than 50% ?
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12:57 < andytoshi> pretty sure not (without interaction) because their security depends on a random hash messing up the linear algebra
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12:57 < tromp_> i mean, the ring sigs play some pretty neat trick with those hashes as well...
12:58 < andytoshi> very true
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12:58 < tromp_> but i agree aggregation starts from seemingly completely independet things
12:58 < tromp_> that leave much less room for tricks
12:59 < andytoshi> yeah. and it's been a more popular area of study for the last 20 years than have ringsigs or rangeproofs
13:00 < tromp_> btw, aggregation across blocks may be more beneficial for dropping rangeproofs than for copmacting sigs
13:01 < andytoshi> well, the rangeproofs can already be dropped when they're redundant
13:01 < andytoshi> err, when they are attached to spent outputs
13:01 < tromp_> not for new clients though
13:01 < andytoshi> and cannot be when they are attached to unspent outputs, regardless of the rest of the chain
13:01 < andytoshi> yes they can
13:02 < tromp_> oh, new clients only verify utxo...
13:02 < andytoshi> yes, all the non-utxo stuff is verified by checking the kernel sigs (which are sinking sigs in the paper)
13:10 < tromp_> to verify a coimpact chain, dont you need all the dropped blocks to check that effectively difficulty is computed correctly?
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13:13 < andytoshi> no, this is the point of the difficulty sumtree
13:13 < andytoshi> oh, you mean that the diffchanges are handled right?
13:13 < tromp_> i mean accumulation of dropped difficulties must be verified
13:14 < andytoshi> you don't need to know that past diffchanges were done correctly except for anti-DoS
13:14 < andytoshi> accumulation is handled by the sumtree
13:14 < tromp_> but your sumtree is only on compact blocks
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13:14 < andytoshi> yes, that's fine
13:14 < tromp_> whose leaves have effetive difficulty up to twice their actual difficulty
13:15 < andytoshi> because of your problem with my lemma?
13:15 < tromp_> just using your definition of effective difficulty
13:15 < andytoshi> then we weight effective difficulty by 1/2 vs actual difficulty
13:16 < andytoshi> i'm confused, what do you mean by "actual difficulty"
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13:16 < tromp_> let's assume constant target T
13:17 < tromp_> and consider luck levels log_2 (T/hash)
13:17 < tromp_> you would reduce a chain 0 0 0 0 0 0 0 3 to just 3
13:18 < tromp_> actually lets forget the log_2
13:18 < tromp_> and reduce 1 1 1 1 1 1 1 8 to just 8
13:18 < tromp_> sorry to just 15
13:19 < tromp_> because the 8 dominates the 7 1s
13:19 < andytoshi> yep
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13:20 < tromp_> now the compact chain needs to distinguish between real chains 8 8 and 8 1 1 1 1 1 1 8
13:20 < tromp_> but both could claim to have compact chain 8 15
13:21 < tromp_> with the first unable to witness the dropping of 7
13:22 < tromp_> or maybe you no longer wish to distinguish these?
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13:25 < tromp_> i think they need to be distinguished or else a 7-deep reorg is too easy to pull off
13:25 < andytoshi> this is covered in section 3.3.2
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13:25 < tromp_> ok, lemme study that
13:26 < andytoshi> it's not too bad, it just says yes, you can pull off that reorg with nontrivial probability but the expectation is the same, so if you have a tail of explicit blocks you can tamp down the probability to negligible
13:26 < andytoshi> or rather, require luck followed by a ton of work
13:27 < tromp_> i guess this is why in the popow paper they also use the latest k blocks in addition to the compact chain
13:28 < andytoshi> yeah, it's sorta inherent, there is some theorem amiller pointed me to that pretty-much implies this is necessary
13:28 < andytoshi> https://en.wikipedia.org/wiki/Chernoff_bound
13:28 < tromp_> i agree that for k beyond a few dozen, that gives you pretty close to the full security
13:29 < andytoshi> :)
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13:31 < tromp_> but i'm still not sure whether your notion of effective difficulty can be made verifiable
13:33 < andytoshi> right
13:33 < tromp_> the popow paper just chains blocks of same luck-level
13:34 < tromp_> which obviously avoids the complication of effective diff
13:36 < tromp_> what if we siimply require decreasing luck?
13:36 < tromp_> in the compact chain
13:37 < tromp_> i guess that will make it too long
13:37 < tromp_> perhaps each next block on compact chain has to be 1-eps less lucky
13:37 < andytoshi> yes, everything i tried along these lines made the "compact chain" only linear
13:38 < andytoshi> or failed to accomplish whatever security improvement i wanted
13:40 < tromp_> so if eps = 0.1 then if you find a block with hash T/a, you then replace all blocks on compact chain with hash <= T/(a*0.9)
13:41 < tromp_> hmm, that's not gonna work:(
13:43 < tromp_> the thing is, you want bigger gaps near start of compact chain, but smaller gaps near end
13:44 < tromp_> in order to keep the length healthy
13:47 < tromp_> we want to find some auto-sizing single-chain version of KLS16+ that remains verifiable
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13:52 < andytoshi> yup
13:52 < andytoshi> as i recall from when i was thinking about this, the auto-sizing property really broke the "only one compact chain" property
13:52 < andytoshi> but i don't recall the details of why this would happen, basically the idea was that adding blocks could sometimes make blocks return
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14:12 < tromp_> if you require increasing hashes on the compact chain, and pick them greedily, then the compact chain starts with the lowest hash ever, followed by the lowest hash in the later blocks, etc., but it's possible that a non-greedily picked chain has higher cumulative difficulty
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19:01 < tromp> anfytoshi, in your MW atgomic swap proposal, how does igno obtain sconv = k - k' + ex - e'x' ? he only knows k, x, e, e', R' = k' G, and P' = x' G
19:01 < tromp> make that andytoshi :)
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--- Log closed Wed Feb 22 00:00:40 2017