Date: Tue, 16 Mar 2021 02:38:55 +0000
To: Anthony Towns <aj@erisian.com.au>,
 Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
From: ZmnSCPxj <ZmnSCPxj@protonmail.com>
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Subject: Re: [bitcoin-dev] PSA: Taproot loss of quantum protections
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Good morning aj,

> 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 pe=
r
> 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.

What you describe seems to match mining in its behavior: probabilistic, and=
 scalable by pushing more electricity into more devices.

From this point-of-view, it seems to me that the amount of energy to mount =
a "fast" attack may eventually approach the energy required by mining, in w=
hich case someone who possesses the ability to mount such an attack may ver=
y well find it easier to just 51% the network (since that can be done today=
 without having to pour R&D satoshis into developing practical quantum comp=
uters).

Regards,
ZmnSCPxj