# Element Finance Aztec Connect Contract

**Background**

Element is a fixed rate lending protocol. The protocol turns DeFi's variable interest rates that arise from Lending pools / vaults into a predictible fixed rate over a fixed term.

Element does this by depositing collateral to the underlying DeFi protocol (usually Yearn) and splitting the resultant yield bearing assets into two assets, a principal token and a yield token.

**Principal Token**
The principal token represents the collateral the lender put into the protocol.

**Yield Token**
The yield token represents the variable interest due to the lender from depositing the collateral.

In order to give fixed rates the principal token is minted at a discount. e.g 95DAI = 100pyDAI. 1 principal token equals 1 unit of collateral at maturity.

The discount on the principal token is set by Element's AMM, and fluctuates based on traders speculation on how the underlying variable rate will perform over a 90 day term.

# **Options for bridge contracts**

After discussing with Element, there are a few flows that would make useful for bridge contracts:

1. Buy principal tokens at a discount from the AMM, hold for term and redeem.
2. Batch redeem
3. Auto rollover of mints.

It was agreed that the simplest flow to support is purchasing tokens via the AMM and allowing tokens to be redeemed.

There are three potential ways for supporting this flow depending on the assets being deposited, and the granularity we want to support.

### Option 1: Direct Async Bridge Flow

This bridge expects the user to already have the source assets inside zk.money or be willing to pay the gas price to deposit them.

**Supports All Element Assets**

DAI
USDC (TBC if we can support)
WBTC

Complex assets

crv3crypto
steCRV
etc.

### User Flow

1. To use the bridge, the user sends a DeFi deposit transaction from their shielded balance in one of the supported assets.

2. The rollup provider will batch these transactions in groups of 10 with a 6 hour backstop.

2. When the bridge contract receives an aggregated transaction from the Aztec Rollup contract, it will do the following:

1. If there are multiple Element pools for the input asset, the DBC should use the value in the `auxData` to pick the correct pool expiry.
2. Will purchase `totalInputValue` principal tokens via the Element AMM with the given input asset ERC20 tokens.
3. Record the amount of purchased principal tokens against the interaction nonce for this interaction.
4. Record the maturity date against the interaction nonce so this async transaction can be finalised at a later date
5. Return `isAsync=true` to the rollup contract.

The bridge contract should have a public function on it to return a list of bridges that can be finalised.

`function checkBridgeInteractions() view returns uint256[]`

For each bridge `interactionNonce` returned, an Ethereum transaction can be created to `RollupContract.processAsyncDefiInteraction(uint256 interactionNonce)`, which will call finalise on the bridge contract.

The finalise function for the Element bridge should do the following:

1. Redeem the principal tokens for the underlying collateral
2. Pay a fee to `block.coinbase` or `msg.sender` for doing this work. This should be calculated as a gas multiplier and paid from the collateral. redemption.
3. Return the underlying collateral + interest to the rollup, and return the correct value of `outputAssetA`

**Gas cost analysis**

Assuming a user has the source assets in Aztec, gas costs for different batch sizes are as follows:

| Item | Gas | User Share |
| ---------------------- | ----- | ---------- |
| JoinSplit for chaining | 7,500 | 1 |
| DeFi Bridge Deposit | 7,500 | 1 |
| Element AMM Buy Interaction | 180,000 | 1/n |
| Element `withDrawPrincipal()` | 150-750,000 | 1/n |
| DeFi claim proof | 7,500 | 1 |

Totals below are for enter and exit.

Main-net: 330-000 - 930,000

Batch Size 10: gas = 55,500 - 111,500 ~6 - 10x
Batch Size 50: gas = 29,100 - 41,500 ~10 - 20x
Batch Size 100: gas = 25,800 - 31,800 ~12 - 40x

**Pros**

1. Very simple
2. Only requires 1 Aztec transaction and the gas cost of entry and Exit are amortized
3. User gets assets back on Aztec plus interest automatically.

**Cons**

1. User can't trade and is locked in for term, they loose optionality.
2. Amortisation of `withDrawPrincipal` is limited to input batch size, not all users.
3. Coordination on batching entry is harder than batching exit, so likely batch size will be closer to 10, not 100, gas savings are only 3x - 9x.

### Option 2: Non-async Flow

This flow still requires the user to have the collateral already on Aztec, but breaks the flow into two parts.
#### Purchase Principal Tokens

Step 1 is to purchase the principal tokens on Element and return these to the user on Aztec.

1. The user sends a DeFi deposit transaction from their shielded balance in one of the supported assets.

2. The rollup provider will batch these transactions in groups of 10 with a 6 hour backstop.

2. When the bridge contract receives an aggregated transaction from the Aztec Rollup contract, it will do the following:

1. If there are multiple Element pools for the input asset, the DBC should use the value in the `auxData` to pick the correct pool expiry.
2. Will purchase `totalInputValue` principal tokens via the Element AMM with the given input asset ERC20 tokens.
5. Transfer the principal tokens to the rollup contract and return the amount transferred as `outputValueA`.

#### Redeem Principal Tokens

Now that a user has principal tokens inside Aztec, they can do a second DeFi bridge interaction which enables them to convert their principal tokens into the underlying collateral at maturity.

1. The user sends a DeFi deposit transaction from their shielded balance of the principal token.

2. The rollup provider will batch these transactions in groups of 10 with a 6 hour backstop.

2. When the bridge contract receives an aggregated transaction from the Aztec Rollup contract, it will do the following:

1. Redeem the principal tokens for the underlying collateral via `withDrawPrincipal()`
3. Transfer the resultant collateral tokens to the rollup contract and return the amount transferred as `outputValueA`.

This flow could optionally check the `auxData` to see if the user has set the redeem or rollover flag, if the rollover flag is set, the collateral would be re-invested by purchasing new principal tokens in the new tranche.

*Gas Analysis*

Entry

| Item | Gas | User Share |
| ---------------------- | ----- | ---------- |
| DeFi Bridge Deposit | 7,500 | 1 |
| Element AMM Buy Interaction | 180,000 | 1/n |
| DeFi claim proof | 7,500 | 1 | |

Main-net: 180-000

Batch Size 10: gas = 33,000 ~5x
Batch Size 50: gas = 18,600 ~10x
Batch Size 100: gas = 16,800 ~10x

Exit

The batch size is likely to be far higher here as all users can redeem together at maturity.

| Item | Gas | User Share |
| ---------------------------- | ----------------- | ---------- |
| Optional Deposit of Element PY tokens | 65,000 | 1? |
| DeFi Bridge Deposit | 7,500 | 1 |
| Element `withDrawCollateral` | 150,000 - 750,000 | 1/n |
| DeFi claim proof | 7,500 | 1 |

Main-net: 150-000 - 750,000

Batch Size 10: gas = 30,000 - 90,000 (5x - 8x)
Batch Size 50: gas = 18,000 - 30,000 (9x - 20x)
Batch Size 100: gas = 16,000 - 22,500 (9x - 30x)

With L1 Deposit For users that didn't enter on Aztec.

Batch Size 10: gas = 90,000 - 150,000 (1.5x - 5x)
Batch Size 50: gas = 78,000 - 90,000 (2x - 10x)
Batch Size 100: gas = 76,500 - 82,500 (2x - 10x)

**Pros**

1. All users should be able to redeem together with 30x gas savings.
2. Users who bought a fixed rate on L1 can use the bridge to redeem with ~2-10x gas savings.
3. Users can trade in and out of fixed rates - no lockin
4. Rollover support is possible

**Cons**

1. More complex to build
2. Redemptions are not automatic
3. Requires 2x Aztec transactions
4. How do we pay fees in element principal tokens.........
1. This is an issue, these tokens only have value if claimed on Element and this costs 150-750k gas.
2. The bridge can pay, but makes it hard to quote a fee to the user + falafel would have to assess based on the size of the defi tx how much it gets.

### Option 3:

This option is an add on for option 1 or 2. It does not require the user to have the source assets.

In this option, the user is only required to have zkETH.