Re: [bitcoindev] Post-Quantum commit / reveal Fawkescoin variant as a soft fork

[Nagaev Boris <bnagaev@gmail.com>]

Hi Adam, hi list,

Thank you for clarifying the nuances of the scheme!

> that same system but with keypath spending invalidated, so it's QR because of the hash function, but also, the tapleaf contains a QR or PQC signing scheme in it

I assume that some future QR signing algorithm might be added in a new
segwit version, resembling the current Taproot structure but with
keypath spending disabled (or otherwise addressed, so it doesn't
present a way to steal funds in a post-quantum world), and a new
opcode added to tapscript to enable QR signing. Also, such an address
type would need to handle the EC opcodes if they remain enabled in
tapscript. I didn't go deep into the details of this hypothetical
address type, as it's a separate complex topic. For the purpose of
this discussion, I assume that some version of it will be deployed
before or alongside the proposed scheme.

> I believe the *real* point here is not "nobody knows you committed something" though that may be practically significant, it's instead "nobody knows the exact commitment value (hash) you used".

I think this is a good observation! We can clarify it further: *nobody
should be able to replicate your commitment*.

I've identified a potential attack that, if it were possible, would
undermine this property. Let's assume, for a second, that a new
address type is just a Merkle root of a Merkle tree. Then an attacker
could build their own Merkle tree on top of the original Merkle root.
The attacker's tree would include the legitimate Merkle tree as a
subtree. If they learn the EC pubkey and the full path in the original
Merkle tree from the pubkey to the root, they could reconstruct the
full path in their tree embedding the original. They could learn this
information when the output is spent, so they would have everything
needed to produce a malicious proof.

Fortunately, with the Taproot we have today, such an extension isn't
possible. There's a step (among others) involving a tagged hash
function (h_tapTweak) that hashes the internal pubkey and Merkle root
together before producing the final public key. This prevents
constructing a Taproot output embedding another tree as a subtree
based solely on the output address. We should ensure that any future
taproot-like address type retains this property to prevent the attack
described above.

The scheme must be carefully analyzed to ensure it satisfies this
crucial property: nobody should be able to replicate your commitment.

I'm curious if anyone sees further edge cases we should consider.

> In these analyses, I think it's common to overlook a potentially crucial point: the UTXO set is enumerable in practical time, so we must always remember that we can check our calculations against existing addresses, even if they are hash-covered keys.

I would propose hardening the requirement further: assume the attacker
already knows exactly which EC address is protected with which QR
output from the beginning. Even with this knowledge, the attacker
should not be able to succeed. If we prove the scheme secure under
these strong assumptions (which are very favorable for the attacker),
then it is also secure under weaker assumptions where the attacker has
less information.

> This commitment is *not* literally perfectly hiding as in a properly formed Pedersen commitment

I agree that the hiding property of a properly formed Pedersen
commitment is stronger than in the proposed scheme. A Pedersen
commitment is perfectly hiding: the committed value is statistically
independent of the commitment, and even an attacker with unbounded
computational power cannot learn anything about the value. In
contrast, the proposed scheme relies on a hash of the pubkey for
hiding, which is only computationally hiding: it depends on the
preimage resistance of the hash function and can be weakened if
quantum attacks on hash functions improve.

However, I believe we cannot use Pedersen commitments here, because
their binding property would be broken by a quantum computer. Pedersen
commitments rely on the hardness of the discrete logarithm problem
(DLP) in an elliptic curve group for binding, and Shor's algorithm can
efficiently solve DLP on a quantum computer. This would allow an
attacker, once the legitimate opening (v,r) is revealed, to compute an
alternative opening (v',r') for the same commitment C. As a result, if
Pedersen commitments were used in the scheme, they would be vulnerable
during the reveal phase under a quantum attack.

Best,
Boris

On Mon, Jun 2, 2025 at 3:41 PM waxwing/ AdamISZ <ekaggata@gmail.com> wrote:
>
> Hi Boris, list,
>
> > In my scheme, a user creates a QR output that
> commits to a hash of a pubkey inside a Taproot leaf. This commitment
> is hidden until revealed at spend time. Later, when the user wants to
> spend a legacy EC output, they must spend this QR output in the same
> transaction, and it must be at least X blocks old.
>
> There's some nuances here that seem quite interesting. If an output commits (in a quantum-resistant way, i.e. hashing let's say) only to a pubkey, and not a pubkey plus spending-transaction, then, in the general case, that has the weakness that the commitment can be replicated, in another commitment tx, at the time of insertion of commitment into the blockchain; so that if the tiebreaker is "first commitment in the block(chain)" an attacker can mess with you. In your case you refer to "a QR output that commits to the hash of a pubkey inside a taproot leaf" but I'm finding it a tiny bit unclear what you mean there. Taproot itself isn't quantum resistant (QR), so Q = P + H(P,S)G is not QR even if P is NUMS. Whereas you might mean: that same system but with keypath spending invalidated, so it's QR because of the hash function, but also, the tapleaf contains a QR or PQC signing scheme in it (I guess this is what you actually mean). Or, you might mean something that is structurally the same as taproot but not using secp/BIP340, but instead a PQC scheme with a homomorphism so that that same design can be reused; call that "taproot2" .. though I don't think I've heard people talking about that.
>
> Then there's what I think you focus on: the commitment is hidden. To other readers, in case of confusion: I believe the *real* point here is not "nobody knows you committed something" though that may be practically significant, it's instead "nobody knows the exact commitment value (hash) you used".
>
> So, I believe that's a correct/valid point that actually *doesn't* depend on which "version" of taproot as per above. Focusing on current-taproot-but-script-path-only-with-QR-in-tapleaf:  we have a protection that the quantum attacker cannot find the S in the (P,S) tuple (indeed, they cannot even know the H in P + H(P,S)G). This commitment is *not* literally perfectly hiding as in a properly formed Pedersen commitment ([1]) but I do think you have the normal preimage resistance against revelation as expected even in post-quantum. So that prevents the "copy the commitment" problem I started out by mentioning. [2]
>
> If "taproot2" instead then we have something for which even the keypath isn't crackable so I guess it's obvious.
>
> > Since the commitment doesn't include a txid, the user can precommit to
> the pubkey hash far in advance, before knowing the details of the
> eventual transaction.
>
> Again, I believe you're right here, but we should try to unpack what's different; because the "reveal" step of commit-reveal is accompanied by the QR signing event of the pre-existing QR output, we have a sane security model, so there's no need to commit to the transaction in the preliminary step, as far as I can tell.
>
> > More efficient use of block space
>
> Makes sense.
>
> I think the only downside I see here is that the initial commitment step requires the PQC scheme to actually exist. That may not seem like a big deal, but I have a suspicion it actually will be. I think a protocol in which we just rely on existing hash primitives and put off the PQC scheme choosing event may be necessary .. though I could be for sure wrong, in more than one way, in saying that.
>
> Apart from that point I think this scheme seems good (as you mention, it has the virtue of not requiring new databases etc which is pretty huge).
>
> Cheers,
> AdamISZ/waxwing
>
> [1]  In these analyses, I think it's common to overlook a potentially crucial point: the utxo set is enumerable in practical time, so we must always remember that we can check our calculations against existing addresses, even if they are hash-covered keys.
>
> [2] The only caveat is if you're considering the possibility of the attacker knowing the key in advance of even the commitment step; generally, that's "game over", but i know that there is some attempt to analyze that case in some places, too. Not here.
>
> On Wednesday, May 28, 2025 at 6:54:21 PM UTC-3 Nagaev Boris wrote:
>>
>> Hi Tadge,
>>
>> Thanks for writing this up! The proposal is very thoughtful, and it's
>> great to see concrete work on post-quantum commit/reveal schemes.
>>
>> I've been exploring a related approach based on a similar
>> commit/reveal idea. In my scheme, a user creates a QR output that
>> commits to a hash of a pubkey inside a Taproot leaf. This commitment
>> is hidden until revealed at spend time. Later, when the user wants to
>> spend a legacy EC output, they must spend this QR output in the same
>> transaction, and it must be at least X blocks old.
>>
>> https://groups.google.com/g/bitcoindev/c/jr1QO95k6Uc/m/lsRHgIq_AAAJ
>>
>> This approach has a few potential advantages:
>>
>> 1. No need for nodes to track a new commitment store
>>
>> Because the commitment remains hidden in a Tapleaf until the spend,
>> observers (including attackers) don't see it, and nodes don't need to
>> store or validate any external commitment set. The only requirement is
>> that the QR output must be old enough, and Bitcoin Core already tracks
>> coin age, which is needed to validate existing consensus rules.
>>
>> 2. Commitment can be made before the transaction is known
>>
>> Since the commitment doesn't include a txid, the user can precommit to
>> the pubkey hash far in advance, before knowing the details of the
>> eventual transaction. This allows greater flexibility: you can delay
>> choosing outputs, fee rates, etc., until spend time. Only knowledge of
>> the EC pubkey needs to be proven when creating the QR output.
>>
>> 3. More efficient use of block space
>>
>> Multiple EC coins can be spent together with a single QR output,
>> holding EC pubkey commitments in Taproot leaves. If EC coins share the
>> same EC pubkey (e.g., come from the same address), they can reuse the
>> same commitment.
>>
>> Would love to hear your thoughts on this variant. I think this one
>> might be a simpler, lower-overhead option for protecting EC outputs
>> post-QC.
>>
>> Best,
>> Boris
>>
>> On Wed, May 28, 2025 at 2:28 PM Tadge Dryja <r...@awsomnet.org> wrote:
>> >
>> > One of the tricky things about securing Bitcoin against quantum computers is: do you even need to? Maybe quantum computers that can break secp256k1 keys will never exist, in which case we shouldn't waste our time. Or maybe they will exist, in not too many years, and we should spend the effort to secure the system against QCs.
>> >
>> > Since people disagree on how likely QCs are to arrive, and what the timing would be if they do, it's hard to get consensus on changes to bitcoin that disrupt the properties we use today. For example, a soft fork introducing a post-quantum (PQ) signature scheme and at the same time disallowing new secp256k1 based outputs would be great for strengthening Bitcoin against an oncoming QC. But it would be awful if a QC never appears, or takes decades to do so, since secp256k1 is really nice.
>> >
>> > So it would be nice to have a way to not deal with this issue until *after* the QC shows up. With commit / reveal schemes Bitcoin can keep working after a QC shows up, even if we haven't defined a PQ signature scheme and everyone's still got P2WPKH outputs.
>> >
>> > Most of this is similar to Tim Ruffing's proposal from a few years ago here:
>> > https://gnusha.org/pi/bitcoindev/1518710367.3...@mmci.uni-saarland.de/
>> >
>> > The main difference is that this scheme doesn't use encryption, but a smaller hash-based commitment, and describes activation as a soft fork. I'll define the two types of attacks, a commitment scheme, and then say how it can be implemented in bitcoin nodes as a soft fork.
>> >
>> > This scheme only works for keys that are pubkey hashes (or script hashes) with pubkeys that are unknown to the network. It works with taproot as well, but there must be some script-path in the taproot key, as keypath spends would no longer be secure.
>> >
>> > What to do with all the keys that are known is another issue and independent of the scheme in this post (it's compatible with both burning them and leaving them to be stolen)
>> >
>> > For these schemes, we assume there is an attacker with a QC that can compute a quickly compute a private key from any secp256k1 public key. We also assume the attacker has some mining power or influence over miners for their attacks; maybe not reliably, but they can sometimes get a few blocks in a row with the transactions they want.
>> >
>> > "Pubkey" can also be substituted with "script" for P2SH and P2WSH output types and should work about the same way (with caveats about multisig). The equivalent for taproot outputs would be an inner key proving a script path.
>> >
>> > ## A simple scheme to show an attack
>> >
>> > The simplest commit/reveal scheme would be one where after activation, for any transaction with an EC signature in it, that transaction's txid must appear in a earlier transaction's OP_RETURN output.
>> >
>> > When a user wants to spend their coins, they first sign a transaction as they would normally, compute the txid, get that txid into an OP_RETURN output somehow (paying a miner out of band, etc), then after waiting a while, broadcast the transaction. Nodes would check that the txid matches a previously seen commitment, and allow the transaction.
>> >
>> > One problem with this scheme is that upon seeing the full transaction, the attacker can compute the user's private key, and create a new commitment with a different txid for a transaction where the attacker gets all the coins. If the attacker can get their commitment and spending transaction in before the user's transaction, they can steal the coins.
>> >
>> > In order to mitigate this problem, a minimum delay can be enforced by consensus. A minimum delay of 100 blocks would mean that the attacker would have to prevent the user's transaction from being confirmed for 100 blocks after it showed up in the attacker's mempool. The tradeoff is that longer periods give better safety at the cost of more delay in spending.
>> >
>> > This scheme, while problematic, is better than nothing! But it's possible to remove this timing tradeoff.
>> >
>> >
>> > ## A slightly more complex scheme with (worse) problems
>> >
>> > If instead of just the txid, the commitment were both the outpoint being spent, and the txid that was going to spend it, we could add a "first seen" consensus rule. Only the first commitment pointing to an outpoint works.
>> >
>> > So if nodes see two OP_RETURN commitments in their sequence of confirmed transactions:
>> >
>> > C1 = outpoint1, txid1
>> > C2 = outpoint1, txid2
>> >
>> > They can ignore C2; C1 has already laid claim to outpoint1, and the transaction identified by txid1 is the only transaction that can spend outpoint1.
>> >
>> > If the user manages to get C1 confirmed first, this is great, and eliminates the timing problem in the txid only scheme. But this introduces a different problem, where an attacker -- in this case any attacker, even one without a QC -- who can observe C1 before it is confirmed can flip some bits in the txid field, freezing the outpoint forever.
>> >
>> > We want to retain the "first seen" rule, but we want to also be able to discard invalid commitments. In a bit flipping attack, we could say an invalid commitment is one where there is no transaction described by the txid. A more general way to classify a commitment as invalid is a commitment made without knowledge of the (secret) pubkey. Knowledge of the pubkey is what security of coins is now hinging on.
>> >
>> >
>> > The actual commitment scheme
>> >
>> >
>> > We define some hash function h(). We'll use SHA256 for the hashing, but it needs to be keyed with some tag, for example "Alas poor Koblitz curve, we knew it well".
>> >
>> > Thus h(pubkey) is not equal to the pubkey hash already used in the bitcoin output script, which instead is RIPEMD160(SHA256(pubkey)), or in bitcoin terms, HASH160(pubkey). Due to the hash functions being different, A = HASH160(pubkey) and B = h(pubkey) will be completely different, and nobody should be able to determine if A and B are hashes of the same pubkey without knowing pubkey itself.
>> >
>> > An efficient commitment is:
>> >
>> > C = h(pubkey), h(pubkey, txid), txid
>> > (to label things: C = AID, SDP, CTXID)
>> >
>> > This commitment includes 3 elements: a different hash of the pubkey which will be signed for, a proof of knowledge of the pubkey which commits to a transaction, and an the txid of the spending transaction. We'll call these "address ID" (AID), sequence dependent proof (SDP), and the commitment txid (CTXID).
>> >
>> > For those familiar with the proposal by Ruffing, the SDP has a similar function to the authenticated encryption part of the encrypted commitment. Instead of using authenticated encryption, we can instead just use an HMAC-style authentication alone, since the other data, the CTXID, is provided.
>> >
>> > When the user's wallet creates a transaction, they can feed that transaction into a commitment generator function which takes in a transaction, extracts the pubkey from the tx, computes the 3 hashes, and returns the 3-hash commitment. Once this commitment is confirmed, the user broadcasts the transaction.
>> >
>> > Nodes verify the commitment by using the same commitment generator function and checking if it matches the first valid commitment for that AID, in which case the tx is confirmed.
>> >
>> > If a node sees multiple commitments all claiming the same AID, it must store all of them. Once the AID's pubkey is known, the node can distinguish which commitments are valid, which are invalid, and which is the first seen valid commitment. Given the pubkey, nodes can determine commitments to be invalid by checking if SDP = h(pubkey, CTXID).
>> >
>> > As an example, consider a sequence of 3 commitments:
>> >
>> > C1 = h(pubkey), h(pubkey', txid1), txid1
>> > C2 = h(pubkey), h(pubkey, txid2), txid2
>> > C3 = h(pubkey), h(pubkey, txid3), txid3
>> >
>> > The user first creates tx2 and tries to commit C2. But an attacker creates C1, committing to a different txid where they control the outputs, and confirms it first. This attacker may know the outpoint being spent, and may be able to create a transaction and txid that could work. But they don't know the pubkey, so while they can copy the AID hash, they have to make something up for the SDP.
>> >
>> > The user gets C2 confirmed after C1. They then reveal tx2 in the mempool, but before it can be confirmed, the attacker gets C3 confirmed. C3 is a valid commitment made with knowledge of the pubkey.
>> >
>> > Nodes can reject transactions tx1 and tx3. For tx1, they will see that the SDP doesn't match the data in the transaction, so it's an invalid commitment. For tx3, they will see that it is valid, but by seeing tx3 they will also be able to determine that C2 is a valid commitment (since pubkey is revealed in tx3) which came prior to C3, making C2 the only valid commitment for that AID.
>> >
>> >
>> > ## Implementation
>> >
>> > Nodes would keep a new key/value store, similar to the existing UTXO set. The indexing key would be the AID, and the value would be the set of all (SDP, CTXID) pairs seen alongside that AID. Every time an commitment is seen in an OP_RETURN, nodes store the commitment.
>> >
>> > When a transaction is seen, nodes observe the pubkey used in the transaction, and look up if it matches an AID they have stored. If not, the transaction is dropped. If the AID does match, the node can now "clean out" an AID entry, eliminating all but the first valid commitment, and marking that AID as final. If the txid seen matches the remaining commitment, the transaction is valid; if not, the transaction is dropped.
>> >
>> > After the transaction is confirmed the AID entry can be deleted. Deleting the entries frees up space, and would allow another round to happen with the same pubkey, which would lead to theft. Retaining the entries takes up more space on nodes that can't be pruned, and causes pubkey reuse to destroy coins rather than allow them to be stolen. That's a tradeoff, and I personally guess it's probably not worth retaining that data but don't have a strong opinion either way.
>> >
>> > Short commitments:
>> >
>> > Since we're not trying to defend against collision attacks, I think all 3 hashes can be truncated to 16 bytes. The whole commitment could be 48 bytes long. Without truncation the commitments would be 96 bytes.
>> >
>> >
>> > ## Activation
>> >
>> > The activation for the commit/reveal requirement can be triggered by a proof of quantum computer (PoQC).
>> >
>> > A transaction which successfully spends an output using tapscript:
>> >
>> > OP_SHA256 OP_CHECKSIG
>> >
>> > is a PoQC in the form of a valid bitcoin transaction. In order to satisfy this script, the spending transaction needs to provide 2 data elements: a signature, and some data that when hashed results in a pubkey for which that signature is valid. If such a pair of data elements exists, it means that either SHA256 preimage resistance is broken (which we're assuming isn't the case) or someone can create valid signatures for arbitrary elliptic curve points, ie a cryptographically relevant quantum computer (or any other process which breaks the security of secp256k1 signatures)
>> >
>> > Once such a PoQC has been observed in a confirmed transaction, the requirements for the 3-hash commitment scheme can be enforced. This is a soft fork since the transactions themselves look the same, the only requirement is that some OP_RETURN outputs show up earlier. Nodes which are not aware of the commitment requirement will still accept all transactions with the new rules.
>> >
>> > Wallets not aware of the new rules, however, are very dangerous, as they may try to broadcast signed transactions without any commitment. Nodes that see such a transaction should drop the tx, and if possible tell the wallet that they are doing something which is now very dangerous! On the open p2p network this is not really enforceable, but people submitting transactions to their own node (eg via RPC) can at least get a scary error message.
>> >
>> >
>> > ## Issues
>> >
>> > My hope is that this scheme would give some peace of mind to people holding bitcoin, that in the face of a sudden QC, even with minimal preparation their coins can be safe at rest and safely moved. It also suggests some best practices for users and wallets to adopt, before any software changes: Don't reuse addresses, and if you have taproot outputs, include some kind of script path in the outer key.
>> >
>> > There are still a number of problems, though!
>> >
>> > - Reorgs can steal coins. An attacker that observes a pubkey and can reorg back to before the commitment can compute the private key, sign a new transaction and get their commitment in first on the new chain. This seems unavoidable with commit/reveal schemes, and it's up to the user how long they wait between confirming the commitment and revealing the transaction.
>> >
>> > - How to get op_returns in
>> > If there are no PQ signature schemes activated in bitcoin when this activates, there's only one type of transaction that can reliably get the OP_RETURN outputs confirmed: coinbase transactions. Getting commitments to the miners and paying them out of band is not great, but is possible and we see this kind of activity today. Users wouldn't need to directly contact miners: anyone could aggregate commitments, create a large transaction with many OP_RETURN outputs, and then get a miner to commit to that parent transaction. Users don't need to worry about committing twice as identical commitments would be a no op.
>> >
>> > - Spam
>> > Anyone can make lots of OP_RETURN commitments which are just random numbers, forcing nodes to store these commitments in a database. That's not great, but isn't much different from how bitcoin works today. If it's really a problem, nodes could requiring the commitment outputs to have a non-0 amount of bitcoin, imposing a higher cost for the commitments than other OP_RETURN outputs.
>> >
>> > - Multiple inputs
>> > If users have received more than one UTXO to the same address, they will need to spend all the UTXOs at once. The commitment scheme can deal with only the first pubkey seen in the serialized transaction.
>> >
>> > - Multisig and Lightning Network
>> > If your multisig counterparties have a QC, multisig outputs become 1 of N. Possibly a more complex commit / reveal scheme could deal with multiple keys, but the keys would all have to be hashed with counterparties not knowing each others' unhashed pubkeys. This isn't how existing multisig outputs work, and in fact the current trend is the opposite with things like Musig2, FROST and ROAST. If we're going to need to make new signing software and new output types it might make more sense to go for a PQ signature scheme.
>> >
>> > - Making more p2wpkhs
>> > You don't have to send to a PQ address type with these transactions -- you can send to p2wpkh and do the whole commit/reveal process again when you want to spend. This could be helpful if PQ signature schemes are still being worked on, or if the PQ schemes are more costly to verify and have high fees in comparison to the old p2wpkh output types. It's possible that in such a scenario a few high-cost PQ transactions commit to many smaller EC transactions. If this actually gets adoption though, we might as well drop the EC signatures and just make output scripts into raw hash / preimage pairs. It could make sense to cover some non-EC script types with the same 3-hash commitment requirement to enable this.
>> >
>> > ## Conclusion
>> >
>> > This PQ commit / reveal scheme has similar properties to Tim Ruffing's, with a smaller commitment that can be done as a soft fork. I hope something like this could be soft forked with a PoQC activation trigger, so that if a QC never shows up, none of this code gets executed. And people who take a couple easy steps like not reusing addresses (which they should anyway for privacy reasons) don't have to worry about their coins.
>> >
>> > Some of these ideas may have been posted before; I know of the Fawkscoin paper (https://jbonneau.com/doc/BM14-SPW-fawkescoin.pdf) and the recent discussion which linked to Ruffing's proposal. Here I've tried to show how it could be done in a soft fork which doesn't look too bad to implement.
>> >
>> > I've also heard of some more complex schemes involving zero knowledge proofs, proving things like BIP32 derivations, but I think this gives some pretty good properties without needing anything other than good old SHA256.
>> >
>> > Hope this is useful & wonder if people think something like this would be a good idea.
>> >
>> > -Tadge
>> >
>> > --
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>>
>>
>>
>> --
>> Best regards,
>> Boris Nagaev
>
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