Aligning privacy incentives in P2MR

[conduition]

Hi list. I'm following up on an idea I sketched in this thread debating P2MR vs P2TRv2. 

The premise is this: What if we modified this line of BIP360:

The last stack element is called the control block c, and must have length 1 + 32 * m, for a value of m that is an integer between 0 and 128, inclusive. Fail if it does not have such a length.

To this:

The last stack element is called the control block c, and must have length 1 + 32 * m, for a value of m that is an integer between 1 and 128, inclusive. Fail if it does not have such a length.

The key change is that the control block must now include at least one merkle authentication path. This effectively bans depth-zero script trees in P2MR, and requires every P2MR address to always pay the cost of having at least two spending conditions.

This seems like a reduction in P2MR's features and efficiency. Why would we want to ban depth-zero script trees? Well these seem to be the source of a perverse incentive, as pointed out by Matt Corallo and Antoine Poinsot in prior threads. Bitcoin script users are economically and practically incentivized by P2MR to use depth-zero script trees because their witnesses are smaller than if the same script were used in a taproot script spend.

Furthermore, depending on the exact scripts and the developers' resources, devs using P2MR for a multi-party scripting protocol may not be sufficiently incentivized to add a cooperative spending path, even if their protocol might allow it. Doing so would require a depth-1 tree, which increases the witness size of the non-cooperative script spend path by 32 bytes. For some short scripts, e.g <height> CLTV <pubkey> CHECKSIG​, the devs may actually have incentive not to add a cooperative spending path, because the cooperative path would actually be less-efficient than just using the non-cooperative path as the single leaf of a depth-zero tree. This leads to easy fingerprinting of scripting protocols, less privacy for everyone else, and undoes a key design goal of P2TR.

In Matt's words:

The value of taproot is that its design natively adds [a cooperative spending path] *for free* to every contracting protocol, and not only adds it for free but *forces* every contracting protocol to carry at least some of the cost if they decline to do this. This results in a massive net privacy win across the entire Bitcoin ecosystem...

a goal of taproot is *privacy* while offering efficiency for the common (all-sign) case. That is generally true across contracting protocols and makes things net-cheaper with a taproot-style system where you hit the common case often. This is another reason why P2MR is quite a loss

By eliminating depth-zero script trees, we'd force all P2MR users to pay for the cost of having at least two spending conditions. We'd eliminate the incentive for script devs to use P2MR over P2TR because both are equally efficient, and incentivize P2MR users to add a cooperative spending path using BIP340, since those users are already paying for the cost of having a depth-1 tree anyway.

This change to BIP360 wouldn't affect the recommended standard use-cases for single-signer and multisig P2MR: hybrid addresses with one Schnorr leaf and one PQ leaf. If anything, this change would encourage the proper use of PQ fallback scripts, because the incentive logic can be applied to someone who tries to use P2MR with only a single EC Schnorr leaf: This user must pay for the cost of a second leaf script anyway, so why not follow best-practices and add a PQ leaf?

AFAICT this change only affects use cases which would otherwise degrade the fungibility of the UTXO set according to BIP360 critics, and encourages those use-cases to adopt a cooperative spending path which (assuming all other factors equal) will be indistinguishable from a regular single-signer P2MR wallet with a PQ fallback leaf.

I've already chatted about this off-list with some BIP360 proponents and they seem receptive, but I'm really curious about the opinions of those who are leaning towards P2TRv2. Would this change to BIP360 address your concerns surrounding P2MR's privacy incentives? If not, why?

regards,

conduition

[Antoine Poinsot]

Hi conduition,

I think this would address the perverse incentive concern, but still fail in not disincentivizing mass migration.

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. And i think the additional costs of using P2MR compared to P2TRv2 is one of them. Most likely all "long-tail" users, who would be the least likely to seek migration, use single-key spending policies. In fact, most Bitcoin users do: in the past 90 days of blocks, 93.6% of all transaction inputs are for single-key spending policies. For a typical 2-input 2-output transaction for a "single-key wallet", P2MR is about 15% more expensive to use than P2TRv2 [^0].

I understand that P2MR does not introduce this additional cost just for kicks, but i think "long-range" protection is a red-herring and not worth hindering individual migration to the escape-hatch output type, which is critical to the systemic migration of Bitcoin away from relying on EC cryptography.

So your proposal does address one of my concerns with a P2MR + PQ opcode strategy. However, i still believe P2TRv2 to be a superior strategy for the reason outlined above.

Best,

Antoine

[^0]: Using 57.5*2 + 43*2 = 201 vbytes as the base size. P2MR adds an additional 32 witness bytes in the control block for the PQ spend path, and an additional 35 witness bytes for the EC leaf script reveal. That's 33.5 more vbytes per input, which is 116.66% the size of the same transaction with P2TRv2.

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[conduition]

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 and this 2025 report from Galaxy Digital. 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.

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.

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.

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.

regards,

conduition

[Pieter Wuille]

Hi Conduition,

Some comments inline below.

On Friday, June 5th, 2026 at 6:59 PM, 'conduition' via Bitcoin Development Mailing List <bitco...@googlegroups.com> 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 and this 2025 report from Galaxy Digital. 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

[Hayashi]

Dear Conduition, Antonie, and list,

A reasonable intersection of both opinions could be further witness discount of EC Schnorr of P2MR (Segwit v2). 
Further 2x witness discount (total 8x witness discount) makes P2MR EC-spend transaction cost almost at par with P2TRv2 key-spend path.

Anyway, we will have to discuss discount policy when we try to add PQ signature to Bitcoin. I think we could discount witness for those who use EC Schnorr leaf if larger transaction cost heavily discourages the migration.

Best Regards,
Hayashi

[conduition]

Hey Pieter, nice to hear from you too on this. 

Do you have any take on the OP idea about P2MR depth restrictions?

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.

I hope so too! It's totally possible that a significant majority of UTXOs migrate in time - say if you're right and there is a very public concerted push towards PQ, or if Q-day turns out to be 50+ years from now. But it's impossible to predict this. For now I hope for the best, but I also want to plan for the worst.

If PQ fear is indeed such a strong motivating factor as you hypothesize, wouldn't this be an argument against P2TRv2? P2TRv2 isn't quantum-resistant by default but P2MR is. Personally, if I thought a CRQC is imminent, I would rather sell my coins or stow them in a P2WSH address than migrate to an address format which requires a follow-up fork to be secure. 

To borrow a phrase, P2TRv2 bears a systemic risk (solving the fork timing problem), whereas P2MR has only local risk (address reuse, which btw would also be solved if we could solve fork-timing). Antoine drew this comparison on his post too but we apparently disagree on which is preferable.

Users and devs can control local risk with very simple software tweaks (to avoid address reuse) but they can't do anything about systemic risks. This is why I prefer P2MR. If the fork-timing problem can be solved conclusively then maybe P2TRv2 would be viable, but as you've alluded to, we have yet to hear any passable solution that doesn't require a cooperative CRQC.

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).

Agreed, it would suck, but would likely be viable.

I lack data, but I suspect that by Q-day most coins will have some knowledge-asymmetry with a CRQC (hash preimages, BIP32 parent keys, hidden P2TR script paths, etc) and so can be rescued with simple commit/reveal protocols - no heavy ZK machinery or hard-forks needed.

With that in mind, then it doesn't really matter how many recoverable coins migrate before Q-day, does it? If you can assume P2TRv2's PQ-security promise will be deployed on-time, then you can also assume any BIP32 wallet in-use today can be rescued. What we really must care about is migrating the unrecoverable fraction of coins (e.g. JBOK wallets with exposed pubkeys). These should already be rare and will only become rarer as more time passes.

So in order to argue your point that P2TRv2 makes confiscation/theft less likely, you'd need to show that P2TRv2 will result in a meaningfully higher number of unrecoverable coins migrating. And I don't see why that would be the case. Holders of ancient JBOK coins with exposed keys are probably either dead, or have lost their keys. If a holder does still have the keys, then why would they move to P2TRv2 but not P2MR?

On a more positive note, if we can someday say "Look, quantum computers appeared and screwed some people over, but most people can recover their coins as long as they fulfill any one of these common criteria," then that seems like Bitcoin's unique value and confiscation resistance is surprisingly intact to me. Certainly better than certain other altcoin migrations I've seen in the past, but I guess this is a subjective question, and everyone will have their own opinion.

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?

Sorry to string you along but I'm gonna hold off here as I don't want to take credit for the idea by jumping the gun and explaining it myself. I'll leave it open for the actual author to chime in on this thread if/when he's ready :)

A reasonable intersection of both opinions could be further witness discount of EC Schnorr of P2MR (Segwit v2).
Further 2x witness discount (total 8x witness discount) makes P2MR EC-spend transaction cost almost at par with P2TRv2 key-spend path.

I wouldn't rule out a discount in a future upgrade but for now i'm hesitant to bundle PQ addresses/signatures with anything that might disrupt the existing fee market, especially given the frustratingly controversial topic of inscriptions/spam. I can already picture the Knotsies decrying a witness-discounted PQ soft fork as "spam-support hidden behind quantum FUD". Never mind that we're already going to have to bump the stack element size limit...

regards,

conduition