19:43:36 kayabanerve: You asked "If I have 10% of the hash power and want to do a 10-block reorg, what period of time do I need to maintain 10% of the hash power before I successfully pull off such an unlikely event?" 19:43:38 This isn't a complete question because you don't specify a threshold probability for the second part of the question, i.e. do you mean "...what period of time do I need to maintain 10% of the hash power before I successfully pull off such an unlikely event _with 50% probability_?" 19:44:17 Yes 19:44:28 *am likely to successfully pull of 19:44:29 \*am likely to successfully pull off 19:44:58 (where 50% odds is the turning point from unlikely to likely) 19:45:03 As a draft, what I have now is a table where the rows are the N block lock, the columns are the number of blocks that the adversary possesses the 10% hashpower share (i.e. 30, 360, 720, 5040), and the cells are attack success probability 19:45:17 Ok I will change to making it a 50% threshold 19:46:42 So, the rows should be the N block lock, columns should be hashpower share, and the cells should be the duration, in number of blocks, that the adversary possesses the hashpower share. 19:47:02 ....to achieve the 50% probability of a successful attack 19:49:09 You would need <10% effort for 10 blocks in a row, and the rest of a network should have >100% average effort. It doesn't look like a high probability 19:50:20 It's not a high probability for a single attack. But kayabanerve wants to know the probability when you try again and again. 19:51:04 If I can pay 100k a year for a minority of hash power yet enough to cause disruptions which impact user privacy (even infrequently), I believe that's valuable to consider. 19:52:14 10^-10 probability or so, probably even less 19:53:41 What formula are you using? 19:54:10 <10% block effort = 10% probability, and you need it 10 times in a row 19:54:42 That's VERY approximate, but it's just a magnitude estimation 19:56:15 The magnitude is not correct. I get 7.859765e-04 using Theorem 1 of Grunspan & Perez-Marco (2018). "Double spend races." 19:58:28 That's the probability in percent: https://gist.github.com/Rucknium/da1e57b1864aca477dfa3b4e02e86e26 20:16:11 IMHO, it is a little unrealistic to assume that an adversary could have the resources to possess 10% of hashpower for a year, but not 50% of hashpower for a few hours. But I'll compute this scenario anyway. 20:20:33 There is an enormous difference in the attack success probabilities when an adversary has 10% of hashpower vs 30%. 20:21:05 For the record, current mining security budget is 157,680 XMR per year, so 100k XMR in a year would be almost two thirds of the security budget, which would be pretty impractical to guard against in any capacity 20:21:24 Oh you were probably talking about USD lol 20:21:27 *USD, jeffro256* 20:21:29 *USD* 20:22:00 fake money! 20:22:09 Yes, and that is very American-centric of me, but I promise I wasn't asking about spending 16m a year on DoSs. 20:22:38 🦅🦅🦅 20:22:56 *16m USD 20:25:09 My _very preliminary_ calculations say that the adversary has to possess 10% hashpower for about six years to have a 50% probability of maliciously re-orging a series of 10 blocks while constantly attacking. I'll double-check the numbers and present a table tomorrow at the meeting. 20:25:40 It would interesting to know what the "optimal" attack would be given a certain fixed budget, where the attacker gets to determine the timeline. Should one compress the attack into a few minutes and try to reorg as much as possible as quick as possible? Or should they try many many shallow reorgs over the period of a few weeks/months? Depends on the goals I guess 20:27:22 If they want to undermine confidence in the currency, a single very deep reorg at an opportune time might be the way to go 20:30:38 in reality surprisingly few people would actually care 20:31:18 This assumes (1) That the attacker halts the attack if the honest chain reaches 10 blocks, but the attacker has not yet reached 10 blocks (Theorem 1.2 of Grunspan & Perez-Marco (2021). "On Profitability of Nakamoto Double Spend.") and (2) After the attack halts, (1-q)/q blocks elapse on the honest chain before the attacker mines their next block and starts their attack again. I si mplified and took the average of the negative binomial distribution (Proposition 5.1 of Grunspan, C & Perez-Marco (2018). "Double spend races." 20:32:08 as long as they dont get personally affected by it 20:32:44 Also, this probability is for when _at least one_ attack succeeds. The attack would succeed multiple times in the time window, with lower probability. 20:35:12 monerobull: IMHO, it is "interesting" that very deep re-orgs on other chains had small effects on their exchange rates. e.g. Eth Classic and Firo. 20:35:36 And Firo's was 306 blocks deep lol 20:36:07 its because nobody actually uses these chains for anything real 20:36:08 I don't know if the reorger accompanied it with a double spend attack as well or it was just for the sake of disruption 20:36:19 Ppl trading on binance dont care what the chain does 20:36:47 Did my market maker bot stop? No? Then nothing happened 20:36:59 Okay apparently it was https://cointelegraph.com/news/privacy-focused-firo-cryptocurrency-suffers-51-attack 20:37:27 They might care if Binance loses money and halts trades on that chain 20:38:00 they would just let trades continue but block deposits 20:38:03 Right. "did my bot stop?" 20:38:19 Block withdrawals 😂 20:38:26 nah 20:38:47 Im poking fun at the fact that they do it all the time 20:38:54 "we sent the withdrawal, not our fault the chain you use is dogwater and erased a week of history" 20:38:58 jeffro256: "In [15], the authors introduce a profitability setup and look for the optimal number of blocks that an attacker should premine before launching a double-spend attack (we will answer this question in a future article)." Grunspan & Perez-Marco (2021). "On Profitability of Nakamoto Double Spend." 20:39:08 (Block dep/wd and ket ppl keep trading) 20:39:25 Maybe I should look around to see if they have posted the future article. We are in the future, after all. 20:39:42 Thanks Rucknium . I guess I should just suck it up and read that paper you keep referencing ;) 20:41:02 They are available on moneroresearch.info :) 23:01:16 jeffro256: IMHO Rosenfeld (2014) "Analysis of Hashrate-Based Double Spending" is easier to digest than the Grunspan & Perez-Marco papers: https://moneroresearch.info/index.php?action=resource_RESOURCEVIEW_CORE&id=191 23:05:39 Rosenfeld's equation 1, page 7 is equivalent to Theorem 1 of Grunspan & Perez-Marco (2018). Grunspan & Perez-Marco use the regularized incomplete beta function instead of Rosenfeld's summation of binomials. Grunspan & Perez-Marco are more rigorous and it looks like it is easier to prove that a majority hashrate attack has 100% success probability as time goes to infinity if you us e the version with the regularized incomplete beta function.