Anonymous Zether

This is a private payment system, an anonymous extension of Bünz, Agrawal, Zamani and Boneh's Zether protocol.

The authors sketch an anonymous extension in their original manuscript. We develop an explicit proof protocol for this extension, described in the technical paper AnonZether.pdf. We also fully implement this anonymous protocol (including verification contracts and a client / front-end with its own proof generator).

High-level overview

Anonymous Zether is an private value-tracking system, in which an Ethereum smart contract maintains encrypted account balances. Each Zether Smart Contract (ZSC) must, upon deployment, "attach" to some already-deployed ERC-20 contract; once deployed, this contract establishes special "Zether" accounts into / out of which users may deposit or withdraw ERC-20 funds. Having credited funds to a Zether account, its owner may privately send these funds to other Zether accounts, confidentially (transferred amounts are private) and anonymously (identities of transactors are private). Only the owner of each account's secret key may spend its funds, and overdraws are impossible.

To enhance their privacy, users should conduct as much business as possible within the ZSC.

The (anonymous) Zether Smart Contract operates roughly as follows (see the original Zether paper for more details). Each account consists of an ElGamal ciphertext, which encrypts the account's balance under its own public key. To send funds, Alice publishes an ordered list of public keys—which contains herself and the recipient, among other arbitrarily chosen parties—together with a corresponding list of ElGamal ciphertexts, which respectively encrypt (under the appropriate public keys) the amounts by which Alice intends to adjust these various accounts' balances. The ZSC applies these adjustments using the homomomorphic property of ElGamal encryption (with "message in the exponent"). Alice finally publishes a zero-knowledge proof which asserts that she knows her own secret key, that she owns enough to cover her deduction, that she deducted funds only from herself, and credited them only to Bob (and by the same amount she debited, no less); she of course also demonstrates that she did not alter those balances other than her own and Bob's. These adjustment ciphertexts—opaque to any outside observer—conceal who sent funds to whom, and how much was sent.

Users need never interact directly with the ZSC; rather, our front-end client streamlines its use.

Our theoretical contribution is a zero-knowledge proof protocol for the anonymous transfer statement (8) of Bünz, et al., which moreover has appealing asymptotic performance characteristics; details on our techniques can be found in our paper. We also of course provide this implementation.

Anonymous Zether is feasible for mainnet use, as of EIP-1108. With that said, funding throwaway accounts (i.e., to pay for gas) represents a privacy challenge (as discussed in the original Zether paper). We don't yet endorse Anonymous Zether for use on the mainnet.

Quickstart

To deploy the ZSC (Zether Smart Contract) to a running Quorum cluster and make some anonymous transfers...

Install prerequisites

• Yarn, tested with version v1.19.2
• Node.js, tested with version v12.13.1
• Truffle, tested with version v5.1.1 (optional, required for Truffle tests only)

Setting things up

• Spin up a Quorum cluster (e.g., follow the steps of the 7nodes example).
  • For the Node.js example in this project to work, Quorum / geth needs to be run with Websockets enabled (i.e., use the flags --ws, --wsport 23000, --wsorigins=* on your first geth node).
  • The code as currently written only supports IBFT consensus (with --istanbul.blockperiod 1). The reason is that Raft reports block time differently (in nanoseconds, as opposed to milliseconds), an idiosyncrasy which interferes with epoch measurements. We don't plan on maintaining support for Raft at this time.
• In the main anonymous-zether directory, type yarn.

Run the Node.js demo

The Node.js example project in this repo will first deploy the necessary contracts: InnerProductVerifier.sol, ZetherVerifier.sol, BurnVerifier.sol, and finally ZCS.sol (which depends on these previous contracts).

Having done this, the Node.js application will fund an account, add a "friend", and make an anonymous transfer.

Simply navigate to the main directory and type node packages/example.

Detailed usage example

Let's assume that Client has been imported and that all contracts have been deployed, as in packages/example/index.js#L13-L23. In four separate node consoles, point web3 to four separate Quorum nodes (make sure to use WebSocket or IPC providers); for each one, execute

> var home
> web3.eth.getAccounts().then((accounts) => { home = accounts[accounts.length - 1]; })

to assign the address of an unlocked account to the variable home.

In the first window, Alice's let's say, execute

> var alice = new Client(web3, deployed, home)
> alice.register()
Promise { <pending> }
Registration submitted (txHash = "0xe4295b5116eb1fe6c40a40352f4bf609041f93e763b5b27bd28c866f3f4ce2b2").
Registration successful.

and in Bob's,

> var bob = new Client(web3, deployed, home)
> bob.register()

Do something similar for the other two.

The two functions deposit and withdraw take a single numerical parameter. For example, in Alice's window, type

> alice.deposit(100)
Initiating deposit.
Promise { <pending> }
Deposit submitted (txHash = "0xa6e4c2d415dda9402c6b20a6b1f374939f847c00d7c0f206200142597ff5be7e").
Deposit of 100 was successful. Balance now 100.

Now, type:

> alice.withdraw(10)
Initiating withdrawal.
Promise { <pending> }
Withdrawal submitted (txHash = "0xd7cd5de1680594da89823a18c0b74716b6953e23fe60056cc074df75e94c92c5").
Withdrawal of 10 was successful. Balance now 90.

In Bob's window, use

> bob.account.public()
[
  '0x17f5f0daab7218a462dea5f04d47c9db95497833381f502560486d4019aec495',
  '0x0957b7a0ec24a779f991ea645366b27fe3e93e996f3e7936bdcfb7b18d41a945'
]

to retrieve his public key and add Bob as a "friend" of Alice, i.e.

> alice.friends.add("Bob", ['0x17f5f0daab7218a462dea5f04d47c9db95497833381f502560486d4019aec495', '0x0957b7a0ec24a779f991ea645366b27fe3e93e996f3e7936bdcfb7b18d41a945'])
'Friend added.'

You can now do

> alice.transfer("Bob", 20)
Initiating transfer.
Promise { <pending> }
Transfer submitted (txHash = "0x4c0631483e6ea89d2068c90d5a2f9fa42ad12a102650ff80b887542e18e1d988").
Transfer of 20 was successful. Balance now 70.

In Bob's window, you should see:

Transfer of 20 received! Balance now 20.

You can also add Alice, Carol and Dave as friends of Bob. Now, you can try:

> bob.transfer("Alice", 10, ["Carol", "Dave"])
Initiating transfer.
Promise { <pending> }
Transfer submitted (txHash = "0x9b3f51f3511c6797789862ce745a81d5bdfb00304831a8f25cc8554ea7597860").
Transfer of 10 was successful. Balance now 10.

The meaning of this syntax is that Carol and Dave are being included, along with Bob and Alice, in Bob's transaction's anonymity set. As a consequence, no outside observer will be able to distinguish, among the four participants, who sent funds, who received funds, and how much was transferred. The account balances of all four participants are also private.

In fact, you can see for yourself the perspective of Eve—an eavesdropper, let's say. In a new window (if you want), execute:

> var inputs
> deployed._jsonInterface.forEach((element) => { if (element['name'] == "transfer") inputs = element['inputs']; })
> var parsed
> web3.eth.getTransaction('0x9b3f51f3511c6797789862ce745a81d5bdfb00304831a8f25cc8554ea7597860').then((transaction) => { parsed = web3.eth.abi.decodeParameters(inputs, "0x" + transaction.input.slice(10)); })

You will see a bunch of fields; in particular, parsed['y'] will contain the list of public keys, while parsed['C'], parsed['D'] and parsed['proof'] will contain further bytes which reveal nothing about the transaction.

Keep in mind that there are a few obvious situations where information can be determined. For example, if someone who has never deposited before appears in a transaction for the first time (this was the case of Bob earlier above), then it will be clear that this person was not the transaction's originator. Similarly, if a certain person has performed only deposits and withdrawals, then his account balance will obviously be visible.

More subtly, some information could be leaked if you choose your anonymity sets poorly. Thus, make sure you know how this works before using it.