Subject: Re: [bitcoindev] Trivial QC signatures with clean upgrade path

From: Tadge Dryja <[email-masked]>
Date: Mon, 16 Dec 2024 14:20:04 -0800 (PST)

Hi everyone
 (disclosure: I'm highly skeptical QCs will break secp256k1 in my lifetime, 
but who knows)

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:

- Disabling key path taproot spends via soft-fork is extremely 
confiscatory -- for the consensus cleanup, we worry about even the 
possibility of destroying funds due to transaction patterns never 
seen on the network; here, shutting down key path spends would be 
knowingly destroying an enormous range of utxos. 

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

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