The argument that hashed public addresses provide meaningful quantum
resistance is flawed *when considered in the context*.of Bitcoin
itself.

This article by Andrew Chow is easy to read and makes a strong case
against the quantum utility of hashed public keys:
https://cryptowords.github.io/why-does-hashing-public-keys-not-actually-provide-any-quantum-resistance

And then, of course, one should be mindful of the case against quantum
computing itself - it is neither inevitable nor "just around the
corner".   Mikhail Dyakonov summarized the arguments well here:
https://t.co/cgrfrroTTT?amp=1.

My current stance (at my company at least) is that planning for
quantum computing should be limited to "a provable and written ability
to upgrade if it becomes clear that it's necessary."

Does anyone think it would it be useful to write up a more official,
and even partly functional plan for Bitcoin to use zero-knowledge
proofs to transition to quantum resistance?

- Erik Aronesty
  CTO, Atkama

On Mon, Mar 15, 2021 at 5:48 PM Luke Dashjr via bitcoin-dev
<bitcoin-dev@lists.linuxfoundation.org> 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.
>
> Mark Friedenbach explains on his blog:
>     https://freicoin.substack.com/p/why-im-against-taproot
>
> 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.
>
> 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!
>
> 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.
>
> 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.
>
> 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.)
>
> To conclude, I recommend anyone using Bitcoin to read Mark's article, my
> thoughts, and any other arguments on the topic; decide if this is a concern
> to you, and make your own post(s) accordingly. Mark has conceded the argument
> (AFAIK he doesn't have an interest in bitcoins anyway), and I do not consider
> it a showstopper - so if anyone else out there does, please make yourself
> known ASAP since Taproot has already moved on to the activation phase and it
> is likely software will be released within the next month or two as things
> stand.
>
> Luke
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