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