IMHO the activation dilemma is the trickiest part of Bitcoin dealing with QCs.  On the one hand, you want a very long term plan, many years ahead of time, so that everyone has time to migrate and not get their coins stolen or destroyed.  But the further out a QC is, the less likely it seems it will ever occur, and thus the less reason there is to write software to deal with a theoretical, far off problem. (And that's not even getting into the fact that nobody's in charge of Bitcoin so there's no long term roadmap anyway.)

The ability to have a PQ fallback key with zero or very low on-chain cost helps a lot with this, whichever activation path ends up happening.  Picking something and committing to it in wallets today, before any kind of activation, is a bit scary since the PQ pubkey does become an exposed private key.  But I think there is a pretty good way to do it with a consensus level proof of quantum computer.

On Monday, December 16, 2024 at 7:35:47 AM UTC-5 Anthony Towns wrote:

This is true, but faced with a QC you're in trouble either way: either the coins are destroyed, or the first (non-nice) entity to get a QC steals them.  We can hope that if the QC ever does arrive there will be enough warning and coordination that there won't be *too* many of these utxos at that point.

But there are still a lot of lost coins where nobody knows the private keys anymore and in those cases, the lead time doesn't matter. The original owners who lost the keys would probably prefer those coins to be destroyed rather than stolen.  But of course there's no way for them to reliably express that preference since they can no longer sign.

An on-chain proof of quantum computer (PoQC I guess :) ) would be a way to reduce the damage of activation forks.  One way to build it: Create a NUMS point pubkey - something like described in BIP341.  Send some coins to that address, then watch if it gets spent.  Providing a preimage of the x-coordinate of a point, as well as a valid signature from that point means that either the hash function is broken or (what we're assuming here) the one-wayness of the EC base point multiplication has been broken.  Nodes can then have code which watches for such a proof and changes consensus rules based on it.

This can be useful for the activation, or persistence of a confiscatory restriction of key path spends.  For example:

Say people worry about an immanent QC.  They estimate it will be built in 5-8 years.  They write software which contains a temporary fork, which activates in 3 years and *de*activates in 8 years.  This fork disables almost all key path spends (as well as ECDSA signatures).  The only key path spends allowed are from the NUMS utxos, and if any NUMS utxo is spent, then the EC prohibition locks in to become permanent instead of reverting 3 years after initial enforcement.

In this case the soft fork is only (permanently) confiscatory if the QC provably exists and would have (presumably, sooner or later) confiscated all those coins anyway.  It also could also allow people to enable PQ signatures and disable EC signatures a bit sooner than they otherwise would have, since the cost of being wrong about a QC is lessened -- losing EC operations would be painful, but even more so if it turns out the nearly finished QC never quite gets there.

An opt-in, non-confiscatory fork could also use this mechanism.  A new P2TR output type (PQ2TR?) could be used which is explicitly not key-spendable post-PoQC, but the older P2TR, P2WPKH, etc output types are still EC spendable (better move em quick).

It can also work the other way: The new PQ output type can work just like P2TR, except that one opcode (the OP_PQCHECKSIG) becomes an OP_FAIL until the PoQC.  Given PoQC, it's OP_SUCCESS.  That way we don't have to have a consensus level definition the actual PQ signature algorithm yet; we've just put a placeholder PQ signature opcode in, and an activation method.  A later soft fork can then define the signature algo.  You'd want to define it pretty soon after, since wallets committing to PQ pubkeys for schemes that end up not getting implemented doesn't help.  But it does allow wallets to do something soon for people who are worried and want to be "quantum safe".

-Tadge