Weak Quantum Bounty Ceremony

[Erik Aronesty]

I have been thinking about a way to create publicly verifiable Bitcoin outputs whose recovery is intentionally tied to breaking a weaker cryptographic system.

The goal is to create a "quantum bounty." The output would be spendable by a valid secp256k1 private key, but the key would be generated in a public ceremony and intentionally limited to 160 bits of entropy. Recovery would additionally be facilitated by publishing an encryption of the same secret under a weaker elliptic curve system.

The basic idea is that a group of independent participants runs a distributed key generation ceremony. Each participant contributes a secret share. The shares are combined into a single 160-bit scalar x. At no point is x reconstructed on any machine or revealed to any participant.

From the same distributed shares, participants jointly derive:

1. A Bitcoin public key P = xG on secp256k1.

2. An encryption of x under a separate 160-bit elliptic curve system.

The transcript contains all commitments, public contributions, ciphertext contributions, and equality-of-discrete-log proofs needed to verify that both constructions are derived from the same hidden scalar.

The construction does not require SNARKs or any trusted setup. It appears sufficient to use Pedersen-style commitments, ElGamal-style encryption, and Chaum-Pedersen proofs showing consistency between participant contributions across the two groups.

After the transcript is finalized, participants destroy their secret shares and temporary randomness. Assuming at least one participant behaves honestly and destroys their material, the scalar x is no longer known to anyone.

The final artifact consists of:

* A Bitcoin public key P.

* A weak-curve ciphertext C.

* A complete public transcript proving that P and C were derived from the same hidden scalar.

Bitcoin can then be sent to the address corresponding to P.

Anyone who can recover x from the weak cryptosystem can spend the output. The effective security of the bounty is therefore determined by the weaker curve rather than by the full secp256k1 discrete logarithm problem.

The intended purpose is to create a publicly auditable cryptographic canary target.

One question I have not fully resolved is whether there are cleaner constructions for the recoverable encryption component than ElGamal-style encryption, while still preserving simple transcript verification and avoiding general-purpose zero-knowledge systems.

[Nikita Karetnikov]

Dear Erik,

The bounty idea has been discussed recently in “What if we let Quantum Hunters get Bitcoin rewards ?”
I’ve also seen it mentioned elsewhere.

Before going into the implementation, let’s discuss the concept.
I don’t understand what problem is being solved by the bounty.
To me it serves no purpose.

If the network is not updated to be post-quantum, the attackers can just go for the funds elsewhere.
The counterargument is that a discovery can be made by a lab that’s not interested in stealing.
What is the bounty for in that case?
The researchers are primarily motivated by producing novel results.
They already receive salary and the companies working on this have funding.
This also assumes that the lab would be allowed to publish this result publicly.
They would have other means to demonstrate their discovery as well.
Why would you optimize for this very specific use case?

And if the network is updated to be post-quantum, the PQ bounty has no purpose.

The bounty is already there, it’s the network itself, pre- or post-quantum.

Thanks,
Nikita

[Erik Aronesty]

>  If the network is not updated to be post-quantum, the attackers can just go for the funds elsewhere

.This assumes that quantum computing speedup for classical computing is feasible and finite-energy for classically interprable results, which has not been proven or demonstrated

> The counterargument is that a discovery can be made by a lab that’s not interested in stealing.

Yes, and this bounty would not be stealing, so labs can freely do this legally.

>  The bounty is already there, it’s the network itself, pre- or post-quantum.

This is a canary bounty with a weaker key, presumably it will be unlocked at least a few months in advance of any needed emergency upgrades, should they ever prove necessary.   

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[Garlo Nicon]

I think I saw a similar topic on Delving: https://delvingbitcoin.org/t/qcap-a-bitcoin-native-quantum-canary-alert/2498

> and intentionally limited to 160 bits of entropy

If you need 160-bit keys, then I think you can use secp160k1. As I said, there are four curves with similar properties: secp160k1, secp192k1, secp224k1, and secp256k1. Also, because the half of the generator in secp224k1 and secp256k1 is identical, it could make them easier to connect.

> After the transcript is finalized, participants destroy their secret shares and temporary randomness.

Well, we have some existing puzzle, where it was not done, but other than that, it looks exactly like you described. Also, the missing part here is proving, that private keys are in a given range: https://mempool.space/tx/08389f34c98c606322740c0be6a7125d9860bb8d5cb182c02f98461e5fa6cd15

I guess your puzzle would be similar to that, but would also contain some proofs, that private keys are really placed in a proper range.

> whether there are cleaner constructions

I wonder, if grinding some bits of x-value on secp256k1 has a similar difficulty, as finding the N-bit private key. Because in that case, it could be checked by OP_SIZE instead. And for that cases, we already have some puzzle: https://mempool.space/tx/aba3c2ae442aa20150996ee68f9aa4da83b57a4312891078be0c2e68c50b2801

Then, if OP_CHECKSIG would be completely broken, we would see 9-byte DER signatures. But if only secp256k1 would be, without breaking SHA-256, then we would have one-byte r-value, and then grinded s-value, which would mean 40-byte or smaller DER signatures.

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[Nagaev Boris]

Hey Erik,

The scheme is interesting! I want to add my two cents.

Those not motivated by funds could publish a zero knowledge proof
instead of moving the funds. This means real funds are not even needed
in this case. Or the whole scheme can be deployed to testnet or signet
not to waste (or burn?) real coins.

Also I would like to propose some properties which the publishing
scheme should have to maximize the effect:

- anonymous for the publisher
- plausible deniable for the publisher
- uncensorable

For the plausible deniability thing, imagine a researcher who has
access to a particular signature made by quantum computer and can
prove it, but then it will be clear who leaked it, because the
signature has a unique nonce. This is where ZK can help. But how to do
ZK onchain to get censorship resistance? Maybe some BitVM construction
may help.

Using mainnet provides better censorship resistance than testnet or
signet - that is actually a good reason to use mainnet unless we come
up with a better approach.

Best,
Boris

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Best regards,
Boris Nagaev

[conduition]

Hey guys,

> Those not motivated by funds could publish a zero knowledge proof instead of moving the funds. This means real funds are not even needed in this case.

Why stop there? If the quantum adversary is willing to cooperate in convincing people of their capabilities, just ask them to find the discrete log of a NUMS point on some curve. Then we don't even need ZK machinery.

Informally: Given scalar k and preimage x, the verifier checks K = k*G = HashToCurve(x).

As stated this would permit a classical prover who finds a collision over all (x, k) pairs, which would be feasible for a 160-bit curve. To rule out collision attacks, we fix x as a constant as a part of the proof system.

This would all be off-chain, no BIPs or UTXOs needed.

If the quantum adversary demands payment to provide this proof, then one can use ZKCPs [1] [2]. But personally I think this would be an implausible scenario. A self-interested QC would bide their time and steal coins once they can factor secp256k1 keys.

regards,
conduition

[1]: https://en.bitcoin.it/wiki/Zero_Knowledge_Contingent_Payment
[2]: https://conduition.io/bitcoin/zkpreimage/

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>

[Saint Wenhao]

> Those not motivated by funds could publish a zero knowledge proof instead of moving the funds.

I think at least some financial incentive is needed. It could be something like 10k satoshis, or more, just to have a non-dust anchor for the puzzle, where other people could attach more coins. For example: if you have a puzzle, where the creator cannot move the coins, without solving the puzzle, then it is still possible to increase the reward later, as long as coins are signed with proper sighashes. See: https://mempool.space/tx/8349df0753e80cce322322f1b76789e1d0fd6693aed2f4de4e49576423081ae7

In this case, the puzzle from bc1qts0jh2d2nesmketmw3thedwrx939k2tqu04gy90x9hd4049g4uhs83ltjx uses SIGHASH_ANYONECANPAY, and is grinded by the solver. And bc1q9nw84cph4dn2pw78pnaec68c82h7pxvv55cla8 is someone, who bumped the reward, by signing it with SIGHASH_NONE, so the signature is valid only in the context of the puzzle.

> Or the whole scheme can be deployed to testnet or signet not to waste (or burn?) real coins.

We also did it:

mainnet: https://mempool.space/tx/aba3c2ae442aa20150996ee68f9aa4da83b57a4312891078be0c2e68c50b2801
testnet4: https://mempool.space/testnet4/tx/cc159432ffb7a166abeccc79800e9616a09ea9ac6937080c2ca37b38671970e5
signet: https://mempool.space/signet/tx/5aa27f3639c2218ee710fee9830924a129098dca94446661f37cae79c4e76712

However, if you think, that test coins are not traded, then you are wrong. For example: https://altquick.com/exchange/market/BitcoinSignet

I think, sooner or later, all test coins will be traded, and just handled like all other altcoins. To some extent, it can be prevented, by making next chains, and dropping previous ones, like it was between testnet3 and testnet4, but still: exchanges will list new coins faster, than Bitcoin Core will release a new version, where the support for some old test network will be dropped.

Which means, that creating the puzzle will always have a cost. Because even if initially some test chain will be worth exactly zero, then it will gain non-zero value over time. And because even signet uses Proof of Work, then creating any puzzle will always require at least some computing power, even if it will be negligible, and doable on CPUs.

> plausible deniable for the publisher

It can be done, by using SIGHASH_ANYONECANPAY, which we also did in our mainnet puzzle. In this way, an unconfirmed transaction with low fees can be made, and published anywhere, using any channel. And then, other people can add more inputs, or bump the fees, by solving some low hanging fruits, and claiming the easiest puzzles. In this way, the creator has to only prepare a single input, and all outputs, and then, it can be extended by the rest of the community, and pushed on-chain by the first solver (which would also set the challenge in stone, and prove, that at least some outputs are solvable, and people know, how to claim them).

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