rich1.0Anthony Towns [ARCHIVE] (npub17r…x9l2h)https://yabu.me/npub17rld56k4365lfphyd8u8kwuejey5xcazdxptserx03wc4jc9g24stx9l2hnjumphttps://yabu.me📅 Original date posted:2021-03-15 📝 Original message:On Tue, Mar 16, 2021 at 08:01:47AM +0900, Karl-Johan Alm via bitcoin-dev wrote: > It may initially take months to break a single key. >From what I understand, the constraint on using quantum techniques to break an ECC key is on the number of bits you can entangle and how long you can keep them coherent -- but those are both essentially thresholds: you can't use two quantum computers that support a lower number of bits when you need a higher number, and you can't reuse the state you reached after you collapsed halfway through to make the next run shorter. I think that means having a break take a longer time means maintaining the quantum state for longer, which is *harder* than having it happen quicker... So I think the only way you get it taking substantial amounts of time to break a key is if your quantum attack works quickly but very unreliably: maybe it takes a minute to reset, and every attempt only has probability p of succeeding (ie, random probability of managing to maintain the quantum state until completion of the dlog algorithm), so over t minutes you end up with probability 1-(1-p)^t of success. For 50% odds after 1 month with 1 minute per attempt, you'd need a 0.0016% chance per attempt, for 50% odds after 1 day, you'd need 0.048% chance per attempt. But those odds assume you've only got one QC making the attempts -- if you've got 30, you can make a month's worth of attempts in a day; if you scale up to 720, you can make a month's worth of attempts in an hour, ie once you've got one, it's a fairly straightforward engineering challenge at that point. So a "slow" attack simply doesn't seem likely to me. YMMV, obviously. Cheers, aj