Subject: [bitcoin-dev] proposal: new opcode OP_ZKP to enable ZKP-based spending authorization

From: Weiji Guo <[email-masked]>
Date: Fri, 28 Apr 2023 16:29:10 +0800

Hey everyone,

I am writing this email to propose a new opcode to enable zero knowledge
based spending authorization for Bitcoin. This new opcode OP_ZKP will
enable the Bitcoin network to authorize spending based on off-chain
computation, provided acceptable proof is supplied. This will not only
equip the Bitcoin script with Turing completeness, but also enable the
building of payment channels more flexible, stablecoin, decentralized
exchange, DeFi, etc. directly over the Bitcoin network, or even a layer 2.
All these could be accomplished with a soft fork (and follow-up building).

Before any BIP could be requested, I’d like to discuss all the aspects in
more detail, to cover as many corners as possible, and hopefully to build
consensus among developers and the community.

*### 0. Overview*

Here are what I am currently considering, listed as starting points for
discussion. I hope that I have covered all major issues, but please do feel
free to add more.

   1. How it works: we add OP_ZKP and OP_ZKPVERIFY using some unused OP_NOP
   codes. OP_ZKP works similarly to OP_MULTISIG, with a number parameter to
   indicate how many public inputs are to be read;
   2. Security: to bind the spending conditions to certain UTXO set,
   amount, and recipients, the hash of all this information shall be used as
   public input to the proof;
   3. Dealing with system limitation: verification keys could be very long
   and exceed the MAX_SCRIPT_ELEMENT_SIZE (520 bytes). They could be put into
   configurations and only use their hash in the scriptPubKey. The
   configuration information such as new verification keys could be propagated
   through P2P messages (we might need a separate BIP for this);
   4. Scalability: arrangement for miners or computing power vendors to
   aggregate some proofs for scalability and fee reduction. Alternatively,
   this could be accomplished with recursive proof.
   5. ZKP scheme and curve choices.
   6. Potential uses are unlimited, although there is no apparent secret
   key (private key or seed) in play.
   7. Ecology implications. Impacts on wallets, etc.

Below, I will introduce/discuss the above-listed item one by one. Mostly I
have to keep the discussion minimal and brief. It is still a bit lengthy,
please bear with me.

*### 1. How it works*

Consider below script:

scriptPubKey: <hash of the verification key> <Groth16_BN254> OP_ZKP

scriptSig: <pubInput_1> <pubInput_2> … <pubInput_n> <n> <proof>

<Groth16_BN254> is only an example in place of an indicator for the ZKP
scheme and curve parameters. Other combinations are possible. Further
discussion is provided in section 5.

<hash of the verification key> - the node implementation should look up a
verification key that hashed to this value. Verification keys tend to be
long and exceed the limitation imposed by MAX_SCRIPT_ELEMENT_SIZE (520
bytes). And for various schemes/circuits, the size might be different. So a
hash is used here. Further discussion is covered in section 3.

<proof> refers to the proof data to be verified. Its size is also subject
to MAX_SCRIPT_ELEMENT_SIZE. This might limit our choices of the ZKP scheme,
although proof data could be split into several parts.

<n> refers to how many public inputs are to be read. It should depend on
the circuit in use. However, this is *not* the actual number. There is also
an implicit public input, which is the hash of the transaction, calculated
according to the script context.

The evaluation is pretty straightforward. The implementation of OP_ZKP
reads in (and removes) all its parameters from the stack, calculates the
implicit public input from the transaction (UTXO inputs, amount,
recipients, etc.), and then leave a true or false in the stack after ZKP
verification. The security reason behind this implicit public input design
is discussed in the next section.

OP_ZKPVERIFY works the same except for the last step, where it leaves
nothing or fails the verification.

*### 2. Security: replay protection*

Proof should not be replayed to authorize spending of another set of UTXO.
Therefore it is critical to bind the proof to the transaction. This is
similar to OP_CHECKSIG: the transaction hash is needed to verify the proof
for OP_ZKP. To calculate the hash, just follow what the context requires.
For a SegWit transaction, BIP 0143 seems natural. And most of the time this
will be the case. But if those opcodes are indeed used outside of SegWit,
then the hashing algorithm before SegWit should be fine.

Binding proof to the transaction, especially the UTXO entries, also
protects from proof malleability, since once spent, the UTXO entries will
be removed from the available UTXO set.

On the other hand, since proof could be calculated by anybody given the
witness, circuit developers must take this into account. The private inputs
should be kept confidential. In some other uses, there might not be any
private inputs but only an authoritative signature, then it is the
authority’s responsibility to only sign valid information, and circuit
developers’ responsibility to ensure proper protection. Further discussion
is deferred for now.

*### 3. Dealing with system limitations: verification key*

The size of proof data or verification key could exceed the limitation
imposed by MAX_SCRIPT_ELEMENT_SIZE, which is 520 (bytes). In this section,
we discuss its implications for the verification key.

The size of a verification key varies with different schemes and circuits.
However, the number of total different circuits will be rather limited, at
least at the Bitcoin network level. Therefore, using the hash of the
verification key instead of the key itself renders fixed-size data, and
flexibility without worrying if the verification key gets too long.

Further, it is not advisable to hard code the verification key in the code
base of nodes, as new verification keys arise every few days or months.
Rather, P2P messaging seems a suitable way to propagate new verification
keys. Once received, a node could save it to a configuration file, and also
forward it to other nodes. If an unknown hash is encountered, the node
could also request it from its connected peers. If the node cannot gather a
new verification key in time, then it has to fail the transaction
verification. If too many nodes cannot get the new verification key in
time, the new block containing the offending transaction will not be
accepted by the Bitcoin network. It is suggested that a separate BIP be
requested to address these issues.

*### 4. Scalability*

ZKP verification usually costs at least tens of milli-seconds, and might
also cost more data size. So, it should be fine to have a few dozen ZKP
transactions in a block. But a few thousand will cost too much time to
verify and too much block space. In this section, we discuss how this could
be mitigated.

There are two options: proof aggregation (batching), and recursive
verification.

Some ZKP proofs are known to be capable of aggregation, however, with
certain limitations. For example, aggregating Groth16 proofs seems to
require that all proofs are of the same circuit, so that the value of γ and
δ remain the same across different proofs, as both parameters are from
phase 2 setup, thus circuit specific. We can also aggregate KZG polynomial
commitment scheme-based proofs. Still, the aggregator needs to ensure that
the hash of each transaction has been verified as well.

On the other hand, recursive verification can handle these transaction hash
verification, along with verifying the correctness of each proof. It might
be very computationally intensive to generate a recursive proof for a few
thousand proofs but there are lots of room for further optimization.

It is also possible to develop a hybrid strategy, that some proofs are
aggregated, with additional verification being proved, then both the
aggregation and additional proof could be verified by a recursive proof.

We might need a new SegWit version so that transactions can refer to its
proper proof once aggregated or recursively verified.

Replay protection: once aggregated or proved via recursion to the network,
a transaction cannot be played to the Bitcoin network again, as the UTXO
entries have been spent.

*### 5. ZKP scheme and curve choice*

A major concern is the size of the script, proof, cost of verification, and
the feasibility to aggregate/batching many proofs.

Groth16 checks out here with short proof size, cheap verification, and
feasibility to aggregate. For example, the standard draft here ([1]) shows
an implementation that can aggregate 1024 proofs in 2s and verifies them in
23ms. Although it seems to require that all proofs belong to the same
circuit ( due to γ and δ, which are circuit-specific). Still, the short
proof size and cheap verification cost make Groth16 suitable to verify
other proofs recursively. And when the upper layer proving schemes (and
setup) is the same, so are the verification circuits, therefore those
proofs could be aggregated.

On the other hand, KZG commitment supports batching. So the zkSnarks based
on KZG should support as well. Further, this paper by Boneh, etc. ([2])
enhances KZG commitment to allow one or two group element opening for
multiple polynomials each evaluated at a different set of points.

This is not an exhaustive list, not even a list. Overall, if we can
aggregate/batch many proofs together, then proof size is of smaller
concern. In this case, Plonk might be a better scheme than Groth16, if we
can implement a batching technique to batch proofs from different circuits
together. But still, in the beginning, there might not be many proofs to be
batched/aggregated at all.

We shall designate a parameter to OP_ZKP and OP_ZKPVERIFY to indicate which
scheme (and curve) to use.

For curve, BN254 is a natural choice as it has been adopted by many
blockchain projects. However, this is largely an open issue.

All being said, as a proposal, it is my opinion that we should support
Groth16-BN254 at the beginning. Based on that we could build recursive
verification circuits for other scheme, which does not require a soft fork.
Other schemes and curves, if much desired by the community, could be
included as well. Maybe we can designate a separate BIP for each
scheme-curve pair for direct support (instead of recursive verification).

*### 6. Potential uses*

The potential uses are unlimited: payment aggregation for a fee reduction
or anonymity, stablecoin, DeFi, decentralized exchange, DAO, NFT, etc.,
just to name a few. But still, we could take as an example some uses to
check if any issues arise and discuss how to address them.

A. ZKP-based smart contract. We could reasonably assume ZKP-based smart
contracts to be rather different from consensus-based smart contracts
(although OP_ZKP is part of a script). A notable difference is that with
Bitcoin’s UTXO model instead of account-model, account-balance type of
contracts are hard to build without involving external storage or state
management. And even with external storage involved to manage the states,
the security of the external storage is also a concern. Data might be lost
or corrupted. Bitcoin’s security does not extend to those contracts
automatically. It takes innovations to address these issues.

On the other hand, there could be smart contracts without a need for
explicit state management. This could be gaming or decentralized identity,
that a ZKP proof is used to prove ”something happens or exists according to
designated algorithm or criteria“.

B. Payment aggregation, or Bitcoin Layer 2. Every address can participate
in such a protocol by sending certain Bitcoin to the designated address
(the fund-holding address). Once signed up, participants can send Bitcoin
to each other with very little fee or pays a higher fee to send to Layer 1.
Bookkeeping each participant’s “balance” is a challenge, but might be
achievable via some complex circuits proving the ownership of certain UTXO
entries. Once proven, the fund-holding address can send Bitcoins to the
address as requested by the participant. It is another challenge to
maintain those UTXO entries off the Bitcoin network with high security. We
might also need to segregate those UXTOs from the Bitcoin network so that
no transaction can be replayed to the Bitcoin network or another Layer 2
protocol.

*### 7. Ecology implications*

Proof generation, computing power services/vendors. Some proof might be
very computationally intensive to generate, for example, recursive
verification of thousands of OP_ZKP transactions. In that case, computation
power services or vendors can work with miners to speed up the generation,
or simply propose a bundle of transactions to be included in a block. By
paying a higher fee miners are motivated to include the bundle, while the
service or vendor can still profit a lot. The immediate reward could
incentivize lots of efforts to further optimize the implementation,
engineering, algorithms, or even ZKP schemes.

Contract composability. We need to figure out a systematic way for one
smart contract to call another, either on-chain or assisted-off-chain. For
ZKP-based smart contracts, proof will have to be generated off-chain and
then used later to call the target contract. Off-chain vendors could
monitor closely related signals, generate the proof, and submit it to the
Bitcoin network. There should be incentives to ensure the proper running of
the system. It is still an open issue about how to define a cross-contract
API, how to signal the call, and how to incentivize computation power
vendors.

Impact on wallet applications. Generating proof to authorize spending seems
a heavy-duty computation task, and does not seem to fit into mobile
applications or hardware wallets, especially those with SoC and powered by
a small battery. However, we argue that this is not the case. If no secret
(private key or seed) is involved, there is no need to involve a wallet
that is tasked with safekeeping secrets. In such cases, the ZKP proof could
be proof that something has indeed happened or exists (including a
signature issued from a wallet), which makes up spending conditions.

That's it for now. I hope you are interested in this idea. I look forward
to your comments.

Thanks,

Weiji

[1] -
https://docs.zkproof.org/pages/standards/accepted-workshop4/proposal-aggregation.pdf

[2] - https://eprint.iacr.org/2020/081.pdf