I think Luke is pointing out that with the Signature and the Message you
should be able to recover the key.

if your address is H(P) and the message is H(H(P) || txn), then the you can
use the public H(P) and the signature to recover the PK and verify that
H(P) == P (I think you then don't even have to check the signature after
doing that).

Therefore there is no storage benefit.

For the script path case, you might have to pay a little bit extra though
as you'd have to reveal P I think? But perhaps that can be avoided another
way...
--
@JeremyRubin <https://twitter.com/JeremyRubin>
<https://twitter.com/JeremyRubin>


On Mon, Mar 15, 2021 at 3:06 PM Matt Corallo via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

> There have been many threads on this before, I'm not sure anything new has
> been brought up here.
>
> Matt
>
> On 3/15/21 17:48, Luke Dashjr via bitcoin-dev wrote:
> > I do not personally see this as a reason to NACK Taproot, but it has
> become
> > clear to me over the past week or so that many others are unaware of this
> > tradeoff, so I am sharing it here to ensure the wider community is aware
> of
> > it and can make their own judgements.
>
> Note that this is most definitely *not* news to this list, eg, Anthony
> brought it up in "Schnorr and taproot (etc)
> upgrade" and there was a whole thread on it in "Taproot: Privacy
> preserving switchable scripting". This issue has been
> beaten to death, I'm not sure why we need to keep hitting the poor horse
> corpse.
>
> >
> > In short, Taproot loses an important safety protection against quantum.
> > Note that in all circumstances, Bitcoin is endangered when QC becomes a
> > reality, but pre-Taproot, it is possible for the network to "pause"
> while a
> > full quantum-safe fix is developed, and then resume transacting. With
> Taproot
> > as-is, it could very well become an unrecoverable situation if QC go
> online
> > prior to having a full quantum-safe solution.
>
> This has been discussed ad nauseam, and it all seems to fall apart once
> its noted just how much Bitcoin could be stolen
> by any QC-wielding attacker due to address reuse. Ultimately, no "pause"
> can solve this issue, and, if we learned about
> a QC attacker overnight (instead of slowly over time), there isn't
> anything that a non-Taproot Bitcoin could do that a
> Taproot Bitcoin couldn't.
>
> > Also, what I didn't know myself until today, is that we do not actually
> gain
> > anything from this: the features proposed to make use of the raw keys
> being
> > public prior to spending can be implemented with hashed keys as well.
> > It would use significantly more CPU time and bandwidth (between private
> > parties, not on-chain), but there should be no shortage of that for
> anyone
> > running a full node (indeed, CPU time is freed up by Taproot!); at
> worst, it
> > would create an incentive for more people to use their own full node,
> which
> > is a good thing!
>
> This is untrue. The storage space required for Taproot transactions is
> materially reduced by avoiding the hash indirection.
>
> > Despite this, I still don't think it's a reason to NACK Taproot: it
> should be
> > fairly trivial to add a hash on top in an additional softfork and fix
> this.
>
> For the reason stated above, i think such a fork is unlikely.
>
> > In addition to the points made by Mark, I also want to add two more, in
> > response to Pieter's "you can't claim much security if 37% of the supply
> is
> > at risk" argument. This argument is based in part on the fact that many
> > people reuse Bitcoin invoice addresses.
> >
> > First, so long as we have hash-based addresses as a best practice, we can
> > continue to shrink the percentage of bitcoins affected through social
> efforts
> > discouraging address use. If the standard loses the hash, the situation
> > cannot be improved, and will indeed only get worse.
>
> I truly wish this were the case, but we've been beating that drum for at
> least nine years and still haven't solved it.
> Worse, there's a lot of old coins that are unlikely to move any time soon
> that are exposed whether we like it or not.
>
> > Second, when/if quantum does compromise these coins, so long as they are
> > neglected or abandoned/lost coins (inherent in the current model), it
> can be
> > seen as equivalent to Bitcoin mining. At the end of the day, 37% of
> supply
> > minable by QCs is really no different than 37% minable by ASICs. (We've
> seen
> > far higher %s available for mining obviously.)
>
> Except its not? One entity would be able to steal that entire block of
> supply rather quickly (presumably over the course
> of a few days, at maximum), instead of a slow process with significant
> upfront real-world cost in the form of electricity.
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