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| gmaxwell | kanzure: this is that approach that assumes hashpower (for the defenders and attackers) increases exponentially forever, and only obtains a non-negligible probablity in the limit and not over any remotely sane timeframe (like 1000 years)? | 12:19 |
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| kanzure | that's what i assumed when i saw it referenced, but i haven't confirmed | 12:21 |
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| gmaxwell | If so, it's something that I found intellectually very interesting, but it seemed to be of no pratical interest itself. | 12:28 |
| kanzure | agreed, i'm more surprised that someone has already bothered to work out the exact scenario or w/e | 12:31 |
| amiller | it's totally false that that attack has a negligible probability over a finite time frame | 12:35 |
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| amiller | (it's not even clear here what you would want "negligible" to mean here, because the attack does not involve hash collisions so there's no security parameter, and the strength of the attacker is denoted by a hashpower fraction p rather than some poly(k) function) | 12:40 |
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| amiller | "Her chances of succeeding are about ∆·p / (t−2015)" | 12:41 |
| amiller | p is the attacker's strength (as a fraction of the honest rest of the network) | 12:41 |
| gmaxwell | amiller: yes. this is attacker has 0.0001% of the hashpower forever, and the hashpower goes up exponentially forever (physically impossible). What I mean by negligible was that I ran numbers for some things assuming e.g. 1000 years and still ended up with success probablities under 1/2^128. | 12:41 |
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| amiller | okay the expression for the success probability in a finite time is for constant hashpower, no assumptoin about it going up | 12:43 |
| gmaxwell | it's quite surprising and curious that they go up over time, but didn't seem to be consequential in any real sense. (Since external processes will effortless reject a 1 year rewrite, much less a 1000 year one; so ... why bother trying?) | 12:43 |
| amiller | they only bring up increasing hashpower in the last paragraph, it's not required for the finite time probability | 12:43 |
| gmaxwell | Okay then this is a different argument than the one I'm aware of. | 12:43 |
| amiller | the paper presents the attack in sort of increasing complexity as it models more of the practical countermeasures bitcoin has for this | 12:44 |
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| amiller | to understand the basic attack, suppose the attacker can set choose an arbitrarily high difficulty for bocks he mines | 12:45 |
| amiller | also suppose he has 10% of the hashpower, that he wants to rewind history to a point 1 month ago (from the time that the attack starts), and he wants to succeed at this by 1 month from now. | 12:47 |
| amiller | on average it takes the adversary 20 months to build a chain with 2 months of work, regardless of the difficulty, right? | 12:47 |
| amiller | but to succeed at this attack he has to find a *single* 2 month block in only 1 month, which is in like 5% of the expected amount of time | 12:48 |
| amiller | he has roughly a 1/20 chance of attack success. | 12:49 |
| amiller | 1-poisson.cdf(0,0.05) = ~0.049 | 12:50 |
| amiller | (that's the probability of finding at least 1 block in 0.05 of the mean time to find a block) | 12:51 |
| gmaxwell | I follow that. Yep. So how does this bridge to Bitcoin? The paper I read before on the diff ramping attack still required exp hashrate growth because the fixed retargeting windows meant the network still made progress. | 12:51 |
| gmaxwell | (and so it needed the growth so the attacker could wipe out his past losses with constant probablity no matter how far behind he'd fallen) | 12:52 |
| amiller | yes they introduce that (goofy) assumption so they can claim a finite "mean time to success" | 12:52 |
| amiller | if that assumption isn't in place, the average amount of time to successfully revert to a fixed point in history is infinite... however the median time is finite | 12:53 |
| amiller | meaning there's a finite time where the attack succeeds with probaility 50% | 12:53 |
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| gmaxwell | (the paper I'm thinking actually uses it to prove p=1 in the limit, ... but its not useful :) ) | 12:55 |
| amiller | yeah we're talking about the same paper i think... http://arxiv.org/pdf/1312.7013.pdf | 12:56 |
| gmaxwell | yep. K. | 12:57 |
| kanzure | is there anything in the current bitcoind that rejects a 1 year rewrite, other than existing checkpoints? | 12:59 |
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| amiller | okay so because the difficulty by a factor of 4 each time, the attacker has to spend a lot more time just to increase the difficulty enough. But still the attacker has a probability of success in a finite time interval that's basically proportional to his hashpower, and the finite amount of time he's willing to try for | 13:01 |
| amiller | even with the network having constant hashpwoer. | 13:01 |
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| gmaxwell | (well not 'each time' he has to mine 2016 blocks at the current difficulty, this is part of how I can't see that it ever reaches 50% success probablity, since there is progress enforced by the difficulty changing) | 13:05 |
| amiller | if the 10% attacker starts today, he can create a fork with increased difficulty at the tip every 20 weeks (yes, admittedly that's already pretty impractical!)... let's say he spends a year and does this twice | 13:06 |
| amiller | er... that's still not good, he's a year behind, and the 16x difficulty only lets him clear less than a year with a single block. | 13:07 |
| amiller | how about he spends 60 weeks (a year and two months) but now he has a fork with 64x difficulty, which lets him clear 2 years in a single lucky block | 13:08 |
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| amiller | so, he spends an average of 1 year grinding on his fork to increase the difficulty to 64x, then he spends 1 year hoping to get a lucky block at that difficulty.... which again he can succeed at with probability 1/20 or so | 13:10 |
| gmaxwell | there are around 52k blocks in a year, so you need a diff of roughly 100k higher to clear two years in a single lucky block. | 13:10 |
| amiller | oh, crap yeah i messed up with 2 weeks instead of 10 minutes sheesh | 13:10 |
| gmaxwell | bbiaf | 13:11 |
| amiller | hmmm right i calculated that wrong anyway... | 13:18 |
| amiller | okay i think you're right here, so it takes an attacker with constant hashpower something like 4^k time (also with very low variance) to increase the difficulty by 4^k... ok i'd have to work that out more | 13:24 |
| amiller | maybe this is more fun with like a 49% attacker that doesn't fall that much behind. | 13:28 |
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| amiller | bbl | 13:29 |
| Taek | The attacker in the DRA needs to find 2016 blocks at a given difficulty to push the difficulty up 4x | 14:08 |
| Taek | Each time the attacker does this, it will take E(4x) longer than the last time | 14:08 |
| Taek | which means the dominant term is the current 2016 blocks | 14:08 |
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| Taek | So the attacker only needs to get lucky on one set of 2016 blocks to be able to make up for all of the lost time | 14:09 |
| Taek | Meaning the attacker can just keep driving the difficulty up and starting over | 14:09 |
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| Taek | In the meantime, the honest network is producing an exponential number of blocks with regards to the attackers re-rolls | 14:10 |
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| Taek | But getting lucky over the space of 2016 blocks seems very unlikely | 14:11 |
| Taek | and has the attacker investing an exponential amount of time per retry | 14:12 |
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| Taek | Assuming the attacker has 40% total hashing power, remaining network has 60% (attacker is 2/3 strength of remaining network) | 14:15 |
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| Taek | The attacker needs to create 1008 blocks to catch up with his work from the previous tries, and 1008/3 blocks to catch up from being 1/3 less powerful | 14:17 |
| Taek | So if the attacker can make 2016 blocks in the amount of time where you'd expect to see ~650, then the attacker succeeds in getting ahead | 14:19 |
| Taek | So at 40% strength, the attacker just needs to raise the difficulty until he can create 2016 blocks in the space where you'd expect to see 650 | 14:19 |
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| Taek | using a poisson distribution (perhaps incorrectly), I'm getting a 10^-400 chance of success per retry | 14:33 |
| Taek | needing to spend an approximate eternity, even at 40% hashing power | 14:33 |
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| amiller | i still think that's not the right way to look at it | 15:03 |
| amiller | suppose the attacker doesn't want to rewrite a particular point in history | 15:03 |
| amiller | but just wants to pull off a history revision attack that's X blocks long (from whatever the front of the main chain is when the attack succeeds) | 15:03 |
| amiller | the point is the attacker can put in exactly the expected amount of work to increase the difficulty, and then has to get lucky on only the blocks after that | 15:05 |
| Taek | Right how *how* lucky is important | 15:07 |
| Taek | the longer the attacker takes to increase the difficulty, the luckier they have to get | 15:07 |
| Taek | and each time they don't get lucky, they have that much more work to do catchup with | 15:07 |
| Taek | *but how lucky | 15:08 |
| Taek | so you have to keep driving up the difficulty as you fail to get lucky or you just fall behind from your unlucky attempts | 15:09 |
| amiller | if you want to rewind history to a fixed date, then it gets more and more unlikely because you fall behind yeah | 15:16 |
| amiller | but if you want to make *some* rewinding attack that rewinds T amount of history, then your probability of success each time you make a finite attempt is nonnegligible in T | 15:17 |
| Taek | ok that makes sense. But then each time you have to start over in pushing the difficulty up? | 15:20 |
| Taek | And all the mining from a failed attempt just goes to waste? (you can't get a reward?) | 15:20 |
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| amiller | Taek, yeah absolutely. | 15:32 |
| amiller | it's still a pretty crappy and unrealistic attack, but it's not "negligible" in one way you'd want it to be | 15:32 |
| amiller | i think the blck ramping cap is a pretty good defense. | 15:32 |
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| Taek | if we ended up colonizing Mars, would Bitcoin be forced to stay on Earth? | 17:40 |
| Taek | 10 minute block time would stop being sufficient I imagine | 17:41 |
| Taek | esp. if we got to the further planets, or some asteroids, etc. | 17:41 |
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| kanzure | colonization is not necessary to ask that sort of question (imagine distant non-colonization-reated equipment) | 17:47 |
| amiller | sometimes mars is within 10 minutes away | 17:50 |
| amiller | other times not | 17:50 |
| kanzure | instead of having different currencies for ever-expanding light-spheres it would be nice to have some sort of matrioshka shell thing that was built for the concept of a larger sphere of payments that take (extremely) longer to confirm | 17:52 |
| kanzure | oh right, that doesn't work for the same reasons it didn't work last week and the week before that. | 17:54 |
| Taek | It's interesting to think of how that could be applied on Earth today | 17:55 |
| Taek | Have different spheres for each continent, country, town | 17:56 |
| Taek | each with a substantially quicker block time than the last | 17:56 |
| kanzure | wont work because you can double spend in another "town" level at the same time | 17:56 |
| Taek | "Chicago experiencing a 51% attack all week" | 17:56 |
| Taek | kanzure you'd probably need coins that are only useful in a particular sphere | 17:57 |
| Taek | eg if you are able to spend coins in chicago, then NYC won't recognize them as in a NYC wallet | 17:57 |
| Taek | other problems aside, ofc | 17:58 |
| amiller | i think there's a kind of proof of work you can do if you are within a tiny lightsphere | 18:02 |
| amiller | rather than far apart | 18:02 |
| amiller | if there's a group of parties that has a really large hashpower among them, but the distribution of that hashpower is sufficiently distributed that like there's some 30% of it that's a minimum light distance away from some other 30% | 18:03 |
| amiller | then they can't build sequential proofs of work bigger than that | 18:04 |
| amiller | so if you had optimal fiber optic peering or something you could build a region local proof of work that couldn't be attacked even by a more powerful miner as long as the more powerful miner is far away | 18:04 |
| gmaxwell | amiller: the lightsphere limited one doesn't work for offline parties. So peopel can't easily come and leave from the system. | 18:05 |
| amiller | i think it does | 18:07 |
| amiller | it's like the difference between a sequentially-hard proof of work and one like bitcoin. | 18:07 |
| kanzure | is there an equivalent localized version of the problem of speed of light constraints? like, nodes aready don't get information instantly anyway, as they would due to light delay.. | 18:08 |
| amiller | you can do an offline-checkable proof of "concentrated work" | 18:08 |
| gmaxwell | amiller: it doesn't. say there are a bunch of parties mining in your lightsphere but you're not paying attention. Then later people from mars do ton of mining and send a time delayed alternative history. Then an evil group of local martians continue that one. Now you join the scene, how can you distinguish these two histories? one which was forged far away? | 18:08 |
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| kanzure | *related (not reated) | 18:11 |
| amiller | hrm. maybe you can interact *now* with the local chain and quickly figure out that's one's more current than the other | 18:13 |
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| gmaxwell | amiller: sure but they're both being run locally now "local martians". But the far away one has lots more work (martian computers) before you joined. | 18:13 |
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| amiller | hmm | 18:14 |
| gmaxwell | So it looks to you like the real chain is the imposter: less work, and both are local. | 18:14 |
| amiller | so the martians did a lot of work when they were on mars, but now they've landed and they're your neighbors and you can'ttell which one was there the whole time | 18:14 |
| amiller | that's a neat problem good point | 18:14 |
| kanzure | 18:14 < fenn> it would take a long time to agree on a price for anything | 18:16 |
| gmaxwell | I think it's related to some of the POS simulation problems. | 18:16 |
| kanzure | 18:16 < fenn> no shipping, this is an information-only product | 18:16 |
| kanzure | so trade might be off limits, but maybe there would be some proof system for "locking" funds in one region, but making them available in another? | 18:17 |
| kanzure | some of this has to be constrained by the nature of interstellar existence anyway, trade isn't one-to-one with current concepts i imagine | 18:18 |
| kanzure | if you pay someone a year away to give you data (if you could), it would take a year (at minimum) for an alert of the payment to reach them, and then some amount of time for data to get back to you (unless it was local and encrypted already?) | 18:19 |
| kanzure | 18:19 < fenn> you could send it to a local escrow agent who tell his partner on alpha centauri to forward alphacoins to your seller | 18:21 |
| kanzure | 18:20 < fenn> problem is alpha escrow services gets screwed when the exchange rate changes | 18:21 |
| kanzure | what does orion's arm have to say about this | 18:24 |
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| kanzure | :( they took the lazy path http://www.orionsarm.com/eg-article/537285c1964e8 | 18:27 |
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| Eliel | synereo seems like an interesting idea. That is, combining a social network with a monetary system. They appear to intend to use a miner based system, however, I started wondering if it might be usable to piggyback timestamping to people's status updates. The system naturally has social (trust) network links included. | 20:12 |
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