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From: Anthony Towns <aj@erisian.com.au>
To: Karl-Johan Alm <karljohan-alm@garage.co.jp>,
	Bitcoin Protocol Discussion
	<bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] PSA: Taproot loss of quantum protections
Date: Tue, 16 Mar 2021 10:50:01 +1000	[thread overview]
Message-ID: <20210316005001.GA4304@erisian.com.au> (raw)
In-Reply-To: <CALJw2w4hBk1pZrV7E6FNDPDCWH=T_S6qAHGKvRC6JsT9iZevfg@mail.gmail.com>

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



  parent reply	other threads:[~2021-03-16  0:50 UTC|newest]

Thread overview: 29+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2021-03-15 21:48 [bitcoin-dev] PSA: Taproot loss of quantum protections Luke Dashjr
2021-03-15 22:05 ` Matt Corallo
2021-03-15 22:30   ` Robert Spigler
2021-03-15 22:40   ` Jeremy
2021-03-15 22:48     ` Matt Corallo
2021-03-15 23:01       ` Karl-Johan Alm
2021-03-15 23:19         ` Matt Corallo
2021-03-15 23:46         ` Lloyd Fournier
2021-03-16  0:50         ` Anthony Towns [this message]
2021-03-16  2:38           ` ZmnSCPxj
2021-03-16  3:44   ` Luke Dashjr
2021-03-16 13:28     ` Andrew Poelstra
2021-03-16 17:25     ` Matt Corallo
2021-03-17  1:23       ` Ryan Grant
2021-03-17 11:56         ` Eoin McQuinn
2021-03-15 23:12 ` Andrew Poelstra
2021-03-16 14:10   ` Andrea
2021-03-16 15:15     ` [bitcoin-dev] Provisions (was: PSA: Taproot loss of quantum protections) Andrew Poelstra
2021-03-17  4:24       ` ZmnSCPxj
2021-03-17  8:29         ` Andrea
2021-03-20 16:31           ` Andrea Barontini
2021-03-16  0:24 ` [bitcoin-dev] PSA: Taproot loss of quantum protections David A. Harding
2021-04-05  0:27   ` Lloyd Fournier
2021-04-16  3:47     ` ZmnSCPxj
2021-04-16  5:00       ` Lloyd Fournier
2021-03-22 14:24 ` Erik Aronesty
2021-03-23  9:36   ` Martin Schwarz
2021-03-23 10:50   ` Tim Ruffing
2021-08-12 22:08   ` Erik Aronesty

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