Hi Antoine, Conduition, Pieter, and list, I want to share my proposal for EC public key recovery in P2MR (BIP-360). It saves 35 bytes in the witness by removing the witness element that contains the script. https://delvingbitcoin.org/t/public-key-recovery-for-ec-leaves-in-p2mr-bip-360/2603
Best, Boris On Saturday, June 6, 2026 at 1:00:08 PM UTC-5 Pieter Wuille wrote: Hi Conduition, Some comments inline below. On Friday, June 5th, 2026 at 6:59 PM, 'conduition' via Bitcoin Development Mailing List <[email protected]> wrote: Hi Antoine, thanks for the feedback. Glad to hear you're receptive! It's important to consider that in any scenario where Bitcoin as we know it survives a CRQC, the vast majority of users would have had to migrate to an output type that includes an escape hatch long before we could have been reasonably certain that a CRQC would materialize. Therefore we should not assume that the vast majority of users strongly desire to migrate to an escape-hatch output type. (In fact, i think it would actually be reasonable to assume none have a strong desire to do so. This is because everyone has an incentive for everybody to migrate, but there is little incentive for each individual to migrate if nobody else does.) Therefore any additional barrier to encourage users to opt into an escape-hatch output type is working against CRQC risk mitigation. All else being equal, whether we use P2MR or P2TRv2 I believe we will end up with roughly the same (small) fraction of the UTXO set migrated by Q-day. I believe this because address format adoption is always slow even with good incentives. Even after 7 years and plenty of incentives to migrate, P2TR still secures only a small fraction of the UTXO-set compared to P2(W)PKH, and a tiny fraction (0.75%) of the supply. See this 2025 report from mempool.space <https://research.mempool.space/utxo-set-report/> and this 2025 report from Galaxy Digital <https://www.galaxy.com/insights/research/bitcoin-onchain-fees-utxo>. Incentivizing adoption doesn't always lead to adoption, so why expect it to do so with P2TRv2? It doesn't offer any incentive over P2TR beyond a shallow promise of *maybe-some-day-quantum-security*. I don't think that's necessarily the right conclusion. P2TR adoption is low, partially because wallets and especially commercial service providers generally don't ever upgrade their technology stacks unless there is a compelling reason; the ecosystem primarily updates through companies going out of business and being replaced by new ones, which are more likely to be built using modern technology. We obviously cannot ask for faster movement through business failure here, but as far as compelling reasons go, I think the quantum resistance debate is quite different from P2TR adoption. As Q-fear grows, I suspect there will be increasingly loud and hard-to-ignore voices (and possibly regulation...) to adopt post quantum cryptography technology stacks. At that point, wallets may start to offer users an "Upgrade to quantum-resistant addresses?" migration button. In the case of P2MR that will need to come with a "Warning: transactions will cost 15% more going forward" notice. In the case of P2TRv2, depending on what what used before it may have 0 impact on costs, or even be a discount going forward. If on-chain fees remain as low as they are now, this may not matter, but otherwise, I think the number may very well discourage a substantial amount of users who aren't convinced about CRQC threats. And I think those users do matter, unfortunately. Here's my timeline prediction, with the above precedent in mind. We deploy a PQ output type, some minority of UTXOs migrate to it. When the first confirmed ECDLP break is proven (e.g. if someone breaks a NUMS point) or suspected (someone stole Satoshi's coins), then we will deploy a rescue protocol which we hopefully prepared in advance to protect the majority procrastinator UTXOs. Maybe we disable EC spending at the same time (a valid option for either P2MR or P2TRv2). Then there will be a brief fork-war (hard or soft) revolving around the question of how to handle Satoshi's coins. After that IDK what happens, but I expect Bitcoin will survive if we prepare adequately today by deploying a quantum-safe address format and PQ signature scheme, and develop rescue protocols for later activation to move laggards over to PQ wallets. No offense, but this sounds like a fairly depressing scenario to me. If an ECDLP break happens before even a large majority of the "active" economy adopts Q-safe outputs, I don't think there is much of an interesting future for Bitcoin. Leaving many users' coins vulnerable to theft will undermine short-term trust in the currency, possibly fatally so. The alternative, burning significant amounts of users' coins will be seen as confiscation that undermines the long-term stability value proposition bitcoin has, as it would be indistinguishable from a PQC altcoin that imports some fairly arbitrary subset of Bitcoin's UTXO set (see also https://antoinep.com/posts/quantum_risk_mitigation/, where Antoine makes that point in more detail). I cannot confidently state that your scenario is unlikely of course, but I think there is little we can do today that affects the outcome in this case. People can think about emergency recovery scenarios to scavenge what's left to save (BIP32 ZKPs and all that), and the result may well survive, but I don't think it'll be very interesting, and not something we as protocol designers should optimize for at this stage. The interesting scenarios to me are ones where either a CRQC doesn't happen, or where we get a large majority of users to adopt Q-safe outputs before that happens. Maximizing the probability that that will happen should be our priority. Whether we pick P2MR or P2TRv2 today, neither choice will affect the early stages of this plot-line very much, so we might as well optimize for the long-term future, and P2MR wins out there. The ideal long-term future is one where we get feature-rich cryptographic schemes that can replace most of the properties Bitcoin relies on today (homomorphic derivation, efficient multisigs, ...) with low costs (through discounts, smaller signatures/keys, efficient verification, ...). At that point, they can be introduced in PQC-only outputs even (say, P2MR without any EC opcodes ever), everyone can adopt them over time, and then when a CRQC appears or not won't really matter. That technology does not exist today, I think, so the best we can aim for today is something where most users can migrate to with minimal downsides before Q-day, even if it comes with some downsides afterwards, which will inevitably be chaotic but maybe not an existential threat. I don't think it matters much that P2TR(v2) is slightly less efficient than P2MR in this hopefully-avoidable chaos; we'll have much bigger fish to fry. I believe P2MR is effectively optimizing for the time after/if a CRQC appears (possibly only temporarily so if another migration to a more fully-features PQC scheme is needed anyway then) while P2TRv2 is optimizing for the time before a CRQC happens and minimizing barriers for adopting Q-safe coins. All of this is under the assumption that P2MR comes with a reasonable expectation of a narrow P2MR-only EC opcode disabling softfork when CRQCs happen (like P2TRv2); without it, I believe it is much worse, as P2MR would be entirely inadvisable to adopt by anyone whose workflow relies on sharing public keys with others (hardware wallets with descriptor-based watchonly software, wallets with indexing servers, multisig, Lightning, escrows, fee bumping, ...). So, I prefer P2TRv2 here, though under the assumption that the narrow EC opcode disabling softfork can be relied upon. I am not confident that that is possible, though I have more thoughts on the matter. That's for another post, though. any additional barrier to encourage users to opt into an escape-hatch output type is working against CRQC risk mitigation. And i think the additional costs of using P2MR compared to P2TRv2 is one of them. I have good news for you: there is an optimization to BIP360 which would make single-signer Schnorr spending significantly (32 bytes) cheaper. It's not my idea so I don't want to jump the gun in explaining the details, but expect another mailing list post soon with more info. It's possible to allow a Merkle tree whose leaves are either EC keys or scripts, and then allow spending from the key-leaves by revealing the path and a signature, but recover the expected public key from the signature. That needs a variation of BIP340 that doesn't commit to the public keys (which may break some of the proofs of higher-level schemes, but as long as there is no ANYPREVOUT like functionality, the message implicitly commits to the output so that may be fine). But even with that, efficiency is 32 bytes worse than P2TR, because in a Q-safe setting with at least one additional PQC branch, you have at least 32 bytes of Merkle path. Is this what you have in mind? -- Pieter -- You received this message because you are subscribed to the Google Groups "Bitcoin Development Mailing List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/bitcoindev/26684d8a-cdb3-43dd-a5b4-fc607ed95e8bn%40googlegroups.com.
