Why you can build a private Uniswap with weak secrecy in zkRollup

Intro

The previous post referred to the main idea of the private Uniswap or general private/secret smart contract execution.

This idea cannot be the denial of the post “Why you can’t build a private Uniswap with ZKPs,” but this can be the effective mitigation with some extension.

The previous post, titled “A zkRollup with no transaction history data,” was not appropriate to explain the effective secrecy since the scaling topic and the privacy topic were mixed and gave a vague explanation about the secrecy limitation.

Approach

1) First, you adopt the “Option 2” in zkRollup in this post.

Then you can make a batch of zkRollup without tx history data.
Tx history data will be part of the private input of a zkp circuit (like Groth16 or Plonk) and prove that final state diffs are the correct result of that hidden tx history data.

The remarkable thing is that the final state diffs are the result of many transactions.
Here you find the result is mixed, and hard to distinguish them IF THE USER BALANCES / STATES ARE HIDDEN.

2) Second, zkp and the “user state” model hide the user’s balance.

If you define the data model that every asset is described as a leaf of the small Merkle Tree for each user, each user can prove her assets and these relevant transitions with zkp without revealing their balance/assets themselves.

The Merkle proof of the inclusion of the assets bind to the last Merkle root, and the Merkle proof of the inclusion of the changed balance/assets bind to the next Merkle root, can be in the private input of the zkp circuit, and the relevant change of global states can be the public input.

Here you find that the user balances/states are hidden if you combine the first step (result mixing) and this second step.

This is what zkp can do as was researched in the works by Barry Whitehat.

However, as he said, zkp cannot hide the changes of global states that reveal users’ activities.

If you are the operator, you can know each content of trades in the batch you aggregate. (The important thing here is that other operators cannot know that from the batch.)
In this situation, only the operator and a transactor know what the transactor is doing since all tx histories banish into the private input, and the result is mixed.
So, at the same time, the operators themselves have the “mixing-level” privacy for their transactions because only the operator and a transactor know the activity.

3) Third, combining transactions makes “weak secrecy.”

If the operator is the last person who has secrets of the others, let’s make all transactors operators.

The final operator (is the usual operator) combines all batches all small operators (just the users) make.

The transactor has or generates several dummy accounts and integrates the dummy transactions (or cheap transactions from those) to the main transaction as a batch like at the first step. Then the final operator( the usual operator) only knows that one of the addresses with dummies sent a Uniswap trade transaction.

Such a batch, which is actually a transaction, can be combined with others by applying recursive zkp repeatedly. The proof can be the private input to the next proof.

Finally, the usual operator finds a Uniswap transaction mixed with many activities among many addresses.

1 Like

So the idea is basically

  1. Maintain an access list of accounts that are updated
  2. The coordinator knows the balances of everyone but this allows the coordinator to hide their own transactions in a block of other users transactions.
  3. Make everyone the coordinator os everyone can have private transaction.

Is this a good summary of the idea ?

My worry is that with step 3 you need to share the state with the new coordinator so they can make zkps then you lose privacy.

If the coordinator is the operator,

The coordinator (operator) does not know the balance.

With zkSNARKs, the user can prove the rightness of the relationship of these 3

  1. the previous merkle root of all his assets
  2. the new merkle root of all his assets after a transaction
  3. the change of the storage which is commonly shared in a Ethereum type contract

The coordinator can verify only the root, not the balance itself.

And the coordinator could know the activity of user by the change of the storage, then this hole is patched by combined transaction and dummy address with zkSNARKs described above.

Right so its like zcash and the mixing is used to make it difficult to see which user updates which state variable ?

Yes.

In ZCash, the assets are utxo, then I’m not sure it’s available to have the merkle root of all assets one has. But it can be difficult to see which user updates and which state variable in the user state from any node in zkRollup as described.