Subject: Re: [bitcoindev] Hashed keys are actually fully quantum secure

From: Agustin Cruz <[email-masked]>
Date: Sun, 16 Mar 2025 16:03:22 -0300

Hi Martin,

Your approach of using a committed QR signature to “anchor” the spending of
hashed keys is intriguing. If I understand correctly, the idea is:
- A user commits to a QR signature in a first transaction (Tx1), proving
ownership of the QR private key without exposing vulnerable data.
- Later, they spend both the old P2PKH output and the QR output together
(Tx2), revealing the QR signature, with rules ensuring the old output can’t
be spent independently.
- This forces an attacker to either forge a QR signature (infeasible with a
quantum-resistant scheme) or rewind the chain past Tx1’s confirmation
(infeasible with sufficient depth).

This seems to provide a solid defense against quantum theft, assuming the
QR scheme holds up and the blockchain remains secure. I also like how it
mitigates the “theft vs. freeze” dilemma. Temporary freezing is indeed less
catastrophic than permanent loss, and avoiding reputational damage is
crucial.

To better understand how this would work, I have two questions:

1. How would the QR signature commitment be encoded and verified in the
script?. Would this require new opcodes or script functionality to check
the commitment when spending?

2. How would you enforce that the old P2PKH output can only be spent with
the QR output? Would this need a soft fork, and if so, what consensus
changes would be required?

Regards,
Agustín

El dom, 16 de mar de 2025, 3:31 p. m., Martin Habovštiak <
[email-masked]> escribió:

> Hello list,
>
> this is somewhat related to Jameson's recent post but different enough to
> warrant a separate topic.
>
> As you have probably heard many times and even think yourself, "hashed
> keys are not actually secure, because a quantum attacker can just snatch
> them from mempool". However this is not strictly true.
>
> It is possible to implement fully secure recovery if we forbid spending of
> hashed keys unless done through the following scheme:
> 0. we assume we have *some* QR signing deployed, it can be done even after
> QC becomes viable (though not without economic cost)
> 1. the user obtains a small amount of bitcoin sufficient to pay for fees
> via external means, held on a QR script
> 2. the user creates a transaction that, aside from having a usual
> spendable output also commits to a signature of QR public key. This proves
> that the user knew the private key even though the public key wasn't
> revealed yet.
> 3. after sufficient number of blocks, the user spends both the old and QR
> output in a single transaction. Spending requires revealing the
> previously-committed sigature. Spending the old output alone is invalid.
>
> This way, the attacker would have to revert the chain to steal which is
> assumed impossible.
>
> The only weakness I see is that (x)pubs would effectively become private
> keys. However they already kinda are - one needs to protect xpubs for
> privacy and to avoid the risk of getting marked as "dirty" by some
> agencies, which can theoretically render them unspendable. And non-x-pubs
> generally do not leak alone (no reason to reveal them without spending).
>
> I think that the mere possibility of this scheme has two important
> implications:
> * the need to have "a QR scheme" ready now in case of a QC coming tomorrow
> is much smaller than previously thought. Yes, doing it too late has the
> effect of temporarily freezing coins which is costly and we don't want that
> but it's not nearly as bad as theft
> * freezing of *these* coins would be both immoral and extremely dangerous
> for reputation of Bitcoin (no comments on freezing coins with revealed
> pubkeys, I haven't made my mind yet)
>
> If the time comes I'd be happy to run a soft fork that implements this
> sanely.
>
> Cheers
>
> Martin
>
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